text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
package org.zalando.logbook.json;
import lombok.AllArgsConstructor;
import lombok.extern.slf4j.Slf4j;
import org.apiguardian.api.API;
import org.zalando.logbook.BodyFilter;
import javax.annotation.Nullable;
import java.io.IOException;
import static org.apiguardian.api.API.Status.MAINTAINED;
/**
* @see FastCompactingJsonBodyFilter
*/
@API(status = MAINTAINED)
@Slf4j
@AllArgsConstructor
public final class CompactingJsonBodyFilter implements BodyFilter {
private final JsonCompactor compactor;
public CompactingJsonBodyFilter() {
this(new ParsingJsonCompactor());
}
@Override
public String filter(@Nullable final String contentType, final String body) {
if (!JsonMediaType.JSON.test(contentType)) {
return body;
}
try {
return compactor.compact(body);
} catch (final IOException e) {
log.trace("Unable to compact body, is it a JSON?. Keep it as-is: `{}`", e.getMessage());
return body;
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 637 |
WorkPlace Systems plc, supplier of workforce management solutions in the cloud, has announced that Coral, part of Gala Coral Group, have rolled out WorkPlace OnLine Workforce Management (WFM) across 1700 licensed betting shops for 10,000 colleagues. The solution will help it improve service levels, increase staff productivity, reduce costs and reduce administration time.
Coral is one of the largest retail bookmaking businesses in the UK and critical to its ongoing success in a competitive market is the effective management of its employees so that an excellent service level is provided to its customers. Coral have implemented WorkPlace OnLine Cloud Schedule and Attendance Management with USB biometric registration devices. The solution will enable the company to deploy the right people in the right place at the right time to meet customer demand and provide visibility of labor across all shops.
"It is easy to use for staff, reliable and gives us excellent visibility and control of our workforce. It's a real example of how cloud has efficiently delivered a reliable, scalable solution of strategic importance to the company." Andy Hicks, Central Operations Director, Coral.
A speedy deployment was enabled by a number of key factors including the WorkPlace Rapid Implementation Approach, WorkPlace OnLine cloud based WFM, USB biometric registration, effective training and Coral management's commitment and focus.
WorkPlace OnLine reduces administration; shop managers can now quickly and easily create schedules for their shop. The intuitive interface means that shop managers can be trained in its use in just a few hours.
"This is one of the fastest large scale workforce management deployments in the UK," said Barney Quinn, CEO of WorkPlace Systems. "Without question managing your workforce efficiently is strategically important, cloud services are making this possible." | {
"redpajama_set_name": "RedPajamaC4"
} | 4,472 |
package serviceaccess_test
import (
. "github.com/vmwarepivotallabs/cf-mgmt/serviceaccess"
. "github.com/onsi/ginkgo"
. "github.com/onsi/gomega"
)
var _ = Describe("Service", func() {
Context("GetPlan", func() {
It("Should find service plan", func() {
service := &Service{
Name: "p-mysql",
}
service.AddPlan(&ServicePlanInfo{Name: "small"})
service.AddPlan(&ServicePlanInfo{Name: "large"})
plans, err := service.GetPlans([]string{"small"})
Expect(err).To(Not(HaveOccurred()))
Expect(len(plans)).To(Equal(1))
Expect(plans[0].Name).To(Equal("small"))
})
})
It("Should return all service plans", func() {
service := &Service{
Name: "p-mysql",
}
service.AddPlan(&ServicePlanInfo{Name: "small"})
service.AddPlan(&ServicePlanInfo{Name: "large"})
plans, err := service.GetPlans([]string{"*"})
Expect(err).To(Not(HaveOccurred()))
Expect(len(plans)).To(Equal(2))
})
It("Should return no service plans", func() {
service := &Service{
Name: "p-mysql",
}
service.AddPlan(&ServicePlanInfo{Name: "small"})
service.AddPlan(&ServicePlanInfo{Name: "large"})
plans, err := service.GetPlans([]string{""})
Expect(err).To(HaveOccurred())
Expect(len(plans)).To(Equal(0))
})
It("Should error when plan doesn't exist", func() {
service := &Service{
Name: "p-mysql",
}
service.AddPlan(&ServicePlanInfo{Name: "small"})
service.AddPlan(&ServicePlanInfo{Name: "large"})
_, err := service.GetPlans([]string{"blah"})
Expect(err).To(HaveOccurred())
Expect(err.Error()).Should(ContainSubstring("No plans for for service p-mysql"))
})
})
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,888 |
\section*{Introduction}
The emergence of cooperation in human populations has been an object of study in many different disciplines ranging from social sciences \cite{rand_human_2013, nowak_five_2006, gracia-lazaro_human_2012}, physics and complex systems \cite{santos_social_2008, perc_statistical_2017, perc_heterogeneous_2010} to biology \cite{ashlock_exploration_2006, dugatkin_guppies_1988, lombardo_mutual_1985} and computer science \cite{de_melo_social_2018, fernandez-domingos_delegation_2021}, among many others. While cooperation is widespread in human societies, its origins remain unclear, although many mechanisms have been proposed to explain its evolutionary advantage \cite{nowak_five_2006}. In fact, many social situations pose a dilemma, in which, while being cooperative towards society is beneficial for the population as a whole, free-riding on the efforts of others may generate substantial individual gains \cite{dawes_social_1980, lange_social_2014}. While many studies have explored which individual behaviors can promote cooperation in these social dilemmas \cite{fernandez-domingos_delegation_2021, han_emergence_2013, rand_direct_2009} or aimed to find how much human decision-making aligns with those cooperative strategies \cite{rand_human_2013,baek_comparing_2016}, not so much is known about which strategies effectively can be extracted from experimental game-theoretical data, which often do not end in full cooperation. Identifying the actual decision-making schemes is essential, especially if one wants to understand why cooperation is not achieving anticipated levels, to grasp the incentives needed to promote beneficial outcomes or how artificial systems may need to be designed so that they align with human pro-social behavior.
Using a data science approach we aim to provide an answer to such questions here, focusing on a new cohort of game theoretical experiments within the well-known framework of the pairwise Iterated Prisoner's Dilemma (IPD)\cite{axelrod_evolution_1987}. In the IPD, when both players cooperate (C) in a round, they both get a reward (represented by $R$), while if one of them defects (D), and the other cooperates they get a payoff $T$ and $S$ respectively. If both defect, they both get a payoff $P$. The dilemma emerges when $T>R>P>S$, with $2R>T+S$. The payoff is accumulated by the interacting players at each round until the game ends. In this iterated version of the one-shot PD there are a plethora of possible equilibrium outcomes \cite{garcia_no_2018}, including cooperative ones \cite{fudenberg_folk_1986}.
The literature has reported on many strategies that can induce cooperation in the IPD with fixed partners. These results were produced mainly through models and simulations. In the famous first Axelrod tournament \cite{axelrod_evolution_1981}, for instance, Tit-for-Tat (TFT) emerged as the most successful strategy. TFT starts by signaling the intention to cooperate and afterwards mimics the previous action of the opponent, and it has been argued to be a good representation of reciprocal behavior in human societies. Reciprocity has been thoroughly researched as one of the most important mechanisms to favour cooperation \cite{trivers_evolution_1971, nowak_five_2006, rand_human_2013}. More generally, conditionally cooperative strategies appear to generate the right set of opportunities for cooperative behavior to spread in large populations \cite{nowak_stochastic_1990, reuben_revisiting_2012, fernandez-domingos_timing_2020}, highlighting the importance of context and past experiences in the effectiveness of cooperative strategies. Reciprocity thus justifies, from an evolutionary perspective, the existence of altruistic and pro-social behaviors \cite{gurven_collective_2008}.
However successful TFT was to explain aspects such as direct reciprocity and conditional cooperation, this strategy is known to dissolve into mutual defection in the presence of execution errors, i.e. when participants fail to keep the implicit cooperative agreement at a given round \cite{wu_how_1995}, especially in heterogeneous populations \cite{nowak_tit_1992}. Attempts to repair this flaw lead to the introduction of Generous-Tit-for-Tat (GTFT) \cite{wedekind_human_1996} which cooperates if the opponent cooperates, but if the opponent defects it sometimes "forgives" and continues to cooperate. This strategy is also a reactive strategy, but unlike TFT, it is stochastic, because the player's next action is now given with some probability. Yet, GTFT has its own problems leading to the introduction of the Win-Stay-Lose-Shift (WSLS) \cite{kraines_learning_1993} strategy that repeats the action from the previous round if the player is happy with the obtained payoff ($T$ and $R$), otherwise changes to the opposite action (when the payoff is $P$ or $S$). More strategies have been proposed and analyzed since then (see Martinez-Vaquero et al \cite{martinez-vaquero_generosity_2012} for a comprehensive study).
From an experimental angle, only a few works have examined how participant actions in the IPD may be translated into relevant strategies used by humans, while also studying what factors may affect the observed behavior. Some experiments with animals showed that guppies \cite{dugatkin_guppies_1988}, sticklebacks \cite{milinski_tit_1987} and tree swallows \cite{lombardo_mutual_1985}, exhibit a TFT-like behavior. In human behavioral economic experiments, both the theoretical GTFT and WSLS appear to align with the decision-process of the subjects \cite{milinski_working_1998}. Dal Bó et al \cite{dal_bo_strategy_2013} showed in another IPD experiment that, when given the choice among theoretical strategies, subjects preferred strategies like Always Defect (AllD), TFT, and Grim Trigger (starts cooperating, cooperates as long as both players have cooperated in the last round, and defects otherwise) and did not use WSLS, which was shown to have more "desirable" properties, such as not defecting forever after a deviation.
While matching theoretical strategies to experiments or asking people to select their preferred strategy provides insight into how they relate to human preferences, it does not immediately reveal how humans actually decide to act in the IPD while playing freely, since their strategies can change with time and respond to different factors, such as their opponents' actions or simply by learning the game and reach their own equilibrium. Alternatively, their strategy may be directly inferred from the data itself, using algorithmic models \cite{breiman_statistical_2001}. This approach was taken to determine the strategies in an Ultimatum game experiment, where binary decision trees were used to model the strategies \cite{engle-warnick_inferring_2003} or symbolic regression \cite{duffy_using_2002}. A similar approach was taken to infer the behavior of participants in Trust games \cite{engle-warnick_inferring_2006, engle-warnick_evolution_2004} or in a market simulation, where strategies were inferred using using Bayesian inference \cite{engle-warnick_strategies_2002, kleiman-weiner_non-parametric_2018}. Yet so far, no inference of strategic models has been performed on IPD, a caveat this work is overcoming.
We present thus, on the one hand, the results of a behavioral economics experiment that investigates how subjects act in the IPD and, on the other hand, the strategies that can be extracted from the data. The experiment consists of two treatments: i) one where the subjects play the IPD with a fixed partner over a large, unspecified number of rounds, which will be called the \emph{fixed partners} or \emph{FP} treatment; and ii) a second long IPD treatment where the opponent changes each round, which we call \emph{shuffled partners} or \emph{SP} treatment. The objective of collecting the data over a large number of rounds was to understand what the effect is of a long experiment on the level of cooperation in the IPD and to study how the inferred behavior differs over time and between a setting where partnerships can be established or one where one is repeatedly confronted by strangers\cite{grujic_consistent_2012, andreoni_partners_2001, gachter_conditional_2007}.
It is not clear from the literature how many rounds of the IPD are needed to observe a stabilization in the human decision-making process, meaning that the learning phase has passed and people are acting according to a clearly defined strategy. Some works have studied the strategies subjects play for ten rounds \cite{heuer_cooperation_2019}, another one that studied the evolution of cooperation in the IPD lasted on average 1.96 and 4.42 rounds, for their two treatments \cite{dal_bo_evolution_2011}, another work studied strategies in the IPD with noise lasted on average 8 rounds, where they noticed a considerable strategic diversity, suggesting the subjects did not learn the game completely \cite{fudenberg_slow_2012}, others, a range of 10 to 35 rounds \cite{fleis_once_2014}, 15 rounds \cite{majolo_human_2006} and 100 rounds\cite{liu_learning_2014}, to cite a few. Yet, the latter focuses on an interaction with a fixed theoretically defined agent. To study the evolution in the decision-making process, we need to know how long the subjects need to learn the game among themselves in different points in time. Given this insight, one can then use the algorithmic modeling approach to infer the actual behaviors, comparing them over time and over different treatment settings, as is the case here.
As experience determines the behavior of each participant, which we will call context, we will use unsupervised clustering techniques to identify the contexts that are found in both IPD treatment data and then determine which strategic algorithmic models may be inferred from the data in each of the contexts (with the context being defined by their own actions and their opponents' in the previous round). Our hypothesis is that different behaviors will be inferred from the differing context experiences. Iterating the game for a sufficient time, as specified earlier, will thus allow to clearly discern their short and long-term behavior. We designed the experiment to last $100$ rounds, without explicitly informing this hard limit to the participants, which is much longer than previous experiments \cite{dal_bo_evolution_2011, fudenberg_slow_2012, fleis_once_2014} to cite a few, and investigated how many rounds are actually needed before the learning process ends and the participant behavior appears to become consistent. In other long experiments, this stabilization seemed to appear after 10-20 rounds\cite{grujic_three_2012}, which will be examined in more in a detailed analysis here.
The participant behavior is modeled using Hidden Markov Models (HMM) \cite{rabiner_tutorial_1989}, and its parameters are trained using hmmlearn\cite{weiss_hmmlearn_2016} on the treatment data separated in behavioral clusters, while simultaneously trying to find the preferred minimal HMM structure (number of states and transition structure) to achieve this. The resulting HMM models are both simple and transparent, containing enough modeling power to represent subjects' strategies in the IPD while also being generative. The latter is of interest as the inferred strategies could be directly be used within the context of theoretical simulations assessing their performance, which is left for future work.
\section*{Methods}
\subsection*{Experimental data collection}
As explained in the Introduction, data was collected for two treatments wherein participants played long IPD in two different pairwise configurations, i.e. fixed partners (FP) and shuffled partners (SP). The data from these experiments were collected in Brussels, Belgium, at the Brussels Experimental Economics Laboratory (BEEL), part of the Vrije Universiteit Brussel (VUB). Twelve sessions were held, in total 188 participants were recruited. The group of participants consisted of 48\% female and 52\% male. The average age in all sessions was 22$\pm$8 years old (see the Supplementary Information for the detailed data about the participants). All experiments followed the relevant guidelines and regulations of data protection and experiments with human participants and were approved by the Ethical Commission for Human Sciences at the VUB (ECHW2015\_3). Moreover, all participants gave consent to the experiment by signing a consent form after the instructions of the experiment were read and all questions the participants had were answered and addressed. The participants played the IPD on individual isolated laptops, designated to avoid any type of communication or arrangements by the participants, who remained anonymous throughout the experiment. At the end of the experiments, subjects were asked optional questions about their age, gender, and information about the game they just played (see the Supplementary Information for the detailed questions and answers).
The FP treatment consisted of 6 sessions where 92 participants played pairwise IPD with the same opponent. The SP treatment consisted of 6 sessions where participants played the same IPD as FP but with a different opponent each round, hence the "shuffled" name. In the IPD one normally has a probability that the game is continued given by a parameter $\omega$, producing an average of $(1-\omega)^{-1}$ rounds. Also, in our design, participants were not told exactly when the IPD would end, and we designed them in such a way (see the descriptions in the Supplementary Information) that there were $100$ rounds. Table \ref{table:payoff} shows the payoff matrix containing the per round rewards used in the two treatments. For both treatments, participants could observe the actions of their partner in the previous round, even when this partner changed from the previous to the current round.
\begin{table}[!ht]
\centering
\begin{tabular}{|c|l|l|}
\hline
\textbf{} & \textbf{C} & \textbf{D} \\\hline
\textbf{C} & 3,3 & 0,4 \\\hline
\textbf{D} & 4,0 & 1,1 \\\hline
\end{tabular}
\caption{Payoff matrix for both IPD treatments.}
\label{table:payoff}
\end{table}
At the beginning of the experiment, every participant read a detailed instruction document with a small test at the end to make sure they understood the game dynamics (see Supplementary Information). At the end of the experiment, participants were given their gains (mean = 7.85 euros, SD = 1.67 in the SP treatment and mean = 10.61, SD = 3.87 in the FP treatment) and a show-up fee of 2.5 euros. Most players spent a total of one hour from the moment they entered the computer room to the moment they were paid for their participation.
For each participant in both treatments we collected their choices, as is visualized by panel A in Supplementary Figure \ref*{fig:hmm_example}. The combination of two actions, i.e. $CC$, $CD$, $DC$ or $DD$ (action format: player-opponent, e.g. $CD$ means the focal player cooperated and their opponent defected in the previous round), provides a context for the next round, as participants will get this information when making their decision. Each context can now be combined with the action of a participant after observing that context and this combination, as shown in panel B of Supplementary Figure \ref*{fig:hmm_example}, can now be translated into one of eight values. The entire sequence of actions of a participant and the associated contexts can thus be transformed into a new sequence of numbers that represent the \emph{conditional actions} of each participant. This new sequence will be used to train an HMM, representing in its emission probabilities in every state the conditional response, i.e. cooperate or defect, based on the context they experienced. We also collect for each context, the probability of observing a conditionally cooperative action, as visualized in Figures \ref{fig:prob_coop_fix} and \ref{fig:prob_coop_rand} in the Results section.
\subsection*{Clustering contexts and context-dependent behaviors}
People act according to their preferences, which includes how they think others should behave. In order to understand the strategies that are being used one needs to explicitly consider the context wherein they happen. Thus, to find the strategies in the FP and SP treatments, we first separate participants according to their experiences. Once this is complete one can question whether each participant displays the same response for the contexts they experience. This allows one to correctly grasp how humans act in the IPD. To identify the context groups and the behaviors within those groups, a cluster analysis was performed here: we first clustered the subjects based on the number of times of $(CC)$, $(CD)$, $(DC)$ and $(DD)$ happened, providing a \emph{contextual clustering}. Subsequently, another clustering was performed on the number of cooperative actions in the sequence for each of the previous action combinations, i.e. $(CC)C$, $(CD)C$, $(DC)C$ and $(DD)C$, providing thus a \emph{behavioral clustering per context}. These variables are used to generate the t-distributed stochastic neighbor embedding (t-SNE)\cite{maaten_visualizing_2008} plot in Figure \ref{fig:context_cluster_chart} and Supplementary Figure \ref*{fig:tsne}.
Different clustering approaches were considered (e.g. K-means, Hierarchical Clustering, and Network Modularity analysis, as can be observed in Supplementary Information, see section \ref*{methods:mod_net} for more information on the Modularity Network clustering) but in the end, K-means is sufficient as the other approaches generated similar results (see for Supplementary Figure \ref*{fig:curves_cluster_context}, Figure \ref*{fig:tsne} top row, for a comparison with Hierarchical Clustering and Figure \ref{fig:modnet} for Modularity Network Clustering). The implementations were done in Scikit learn \cite{pedregosa_scikit-learn_2011}. To determine the optimal number of clusters, we used the "elbow" method by Santopaa et al \cite{satopaa_finding_2011} which plots a curve with the sum of squared distances of samples to their closest cluster center and chooses the minimum best number of clusters that minimize the inertia. See Supplementary Figures \ref*{fig:curves_cluster_context} and \ref*{fig:curves_sub_cluster} for the results produced but the "elbow" method.
To evaluate the quality of the results generated by clustering algorithms, we use the silhouette measure\cite{rousseeuw_silhouettes_1987}, which measures the mean intra-cluster Euclidean distance and the mean nearest-cluster Euclidean distance for each observation, with 1 is being the best score and values near zero indicate that some clusters might be overlapping, while negative values indicate observations assigned to a wrong cluster.
\subsection*{Inferring Hidden Markov Models}
Given the context clusters and the context-dependent behavioral sub-clusters, a HMM, using the conditional action sequences (see Figure \ref*{fig:hmm_example}), is produced for each sub-cluster. As shown in the figure, a HMM is composed of a number of states ($s_1$ and $s_2$ in the figure) which are connected by transitions (yellow arrows). The HMM is a probabilistic Markov Model in which each observation of a sequence is produced by a hidden (non-observable) state \cite{rabiner_tutorial_1989}. We used a multinomial model for HMM with a sequential structure, this means that the model has states connected from left to right, where a transition to another state can only be made in that direction. Returns to a previous hidden state are thus not possible. As also shown in the figure, the transformed sequence of conditional actions is used to train the HMM.
The procedure to determine the optimal number of hidden states is specified in Algorithm \ref{alg:hmm}. Up to 4 hidden states were tested, and the selected number of states $h$ corresponded to the number of different hidden states predicted by the model itself, a low number of hidden states is preferred, both to avoid overfitting and to facilitate interpretation. One last reason to pick fewer hidden states is that some of these states and their transition probabilities are small, which between runs can tend to zero, and it will end up leaving the hidden state disconnected. To ensure connectedness, no model was accepted with a probability of transition less or equal to 0.01. These models were fitted over one million trials and picked the one that resulted with the highest log-likelihood to fit the sequences.
\begin{algorithm} \caption{Hidden Markov Model per sub-cluster}\label{alg:hmm}
\begin{algorithmic}[1]
\ForEach {sub-cluster $s \in $ cluster $c$ }
\State $X_{train}$, $X_{test}$ = data[sub-cluster == s]
\State ll\_max = 0, best\_model = null
\ForEach {$h \in $ [4,3,2,1] \Comment{Number of Hidden States} }
\State model = MultinomialHMM(h)
\State trans\_matrix, emission\_matrix, initial\_probs = model.fit($X_{train}$)
\State ll = log\_likelihood(model.predict($X_{test}$))
\State if ll $>$ ll\_max AND $p \in $ trans\_matrix $>= 0.01$: best\_model = model
\EndFor
\EndFor
\end{algorithmic}
\end{algorithm}
To train the HMM, the hmmlearn library\cite{weiss_hmmlearn_2016} was used. To visualize the resulting models the GraphViz package for Python\cite{bank_graphviz_2021} was used. We expect the participant choices to be stochastic since subjects were not instructed to use any strategy in particular, but the action they considered was best according to their expectations. For this reason, we expect the inferred strategies to be noisy. For visualization, we mapped the number sequences back to human-readable triplets, and all the emission probabilities in the HMM less than $0.05$ were discarded, as shown in Figure \ref*{fig:hmm_example}.
\subsection*{Evolution of the strategies}
To analyze how the players changed and adapted their strategy over all the $100$ rounds, the same procedure of the two-fold clustering and HMM modeling was performed on four different round windows, i.e. from round 1-25, 26-50, 51-75, and finally rounds 76-100). The objective is to assess whether the strategy stabilizes over time and to examine how the treatment, i.e. fixed or shuffled partners, affects the results.
\section*{Results}
\subsection*{Specific contextual subgroups with associated behavioral responses emerge in each treatment}
Before identifying the different clusters in the data provided by both treatments (see Methods and Supplementary Information for details), we first examine the distribution of contexts experienced by participants during the experiment. Figure~\ref{fig:context_chart} shows this distribution while also revealing the fraction of times each context led to a cooperative response by a participant. In the case of the FP treatment, mutual cooperation ($CC$) or mutual defection ($DD$) is observed most often and was matched with the expected response (i.e. either $(CC) \rightarrow C$ or $(DD)\rightarrow D$, which we write as $(CC)C$ and $(DD)D$ respectively). In the SP treatment, mutual defection $DD$ and the anticipated response $D$ was most prevalent. Although a similar cooperation probability was shared by the two treatments (see Supplementary Table~\ref*{table:context}) in the case of $DC$ and $CD$, there was a higher probability of cooperation in FP than in SP in the $DC$ context, i.e. responding positively to an act of cooperation of the co-player. Overall, the figure shows that by shuffling partners cooperation is reduced, as anticipated by prior experiments \cite{grujic_consistent_2012}. Also, it already hints at different clusters that could be inferred from both data sets.
\begin{figure}[ht!]
\centering
\includegraphics[width=0.7\linewidth]{context_coop_bars.png}
\caption{Probability of each context and the cooperation rate per treatment. In the x-axis, the context of each decision is shown, i.e. the actions of the previous round. The green bar in each chart shows the fraction of subsequent cooperative actions when experiencing the particular context. This way, in FP (panel A), there are many rounds with context CC (mutual cooperation) and DD(mutual defection). In SP (panel B) DD occurs clearly more often.}
\label{fig:context_chart}
\end{figure}
Clustering the treatments on the contextual information that each participant experiences (the frequency of contexts $CC$, $CD$, $DC$ and $DD$) with K-means (see Methods) singled out 3 groups in both FP and also 3 in SP. As reported in Methods and visualized in Supplementary Figure \ref*{fig:curves_cluster_context}, different algorithms (network modularity and hierarchical clustering) were tested, revealing that a similar number of clusters was obtained in each case. Cluster quality is assessed using silhouette scores, which are $0.5445$ and $0.4201$ respectively for the FP and SP treatment. These results indicated that a relatively good separation is found between the different contextual clusters.
\begin{figure}[!ht]
\centering
\includegraphics[width=\linewidth]{context_bars.png}
\caption{Probability of cooperation given each context per cluster (using K-Means). \textbf{A)} Top row shows the context composition of each cluster in the FP treatment, the bottom row does the same for each SP cluster. In the FP treatment, clusters A and B are composed of opposing experiences, either $CC$ for A or $DD$ for B. Cluster C is a mix with a bias towards mutually cooperative encounters. In the SP treatment, bottom row, the experiences tend to be more of the $DD$ kind, as shown in clusters D and E. Cluster F in SP showed a mixed experience, yet with a different context composition as C. \textbf{B)} tSNE visualization of the different clusters A-F. As can be seen, cluster A and B lie at the two extremes of this embedding. The clusters D and E have more in common with the defective behaviors in B than the cooperative ones, i.e. A and C. C differentiates itself from the defective clusters as $CC$ is more likely to occur, yet part of C overlaps with the behaviors observed in F.}
\label{fig:context_cluster_chart}
\end{figure}
Panel A in Figure \ref{fig:context_cluster_chart} shows the composition of each cluster in terms of its context. In the FP treatment (A, top row), three different groups are identified: Cluster A containing the players who experience mutual cooperation $CC$ most often, cluster B where they experience mutual defection $DD$ most, and then cluster C where experiences are mixed. These results were anticipated, given the differences shown in Figure \ref{fig:context_chart}. In SP (bottom row Figure \ref{fig:context_cluster_chart}A) mutual defection is favored over mutual cooperation in two of the clusters, i.e. clusters D and E. Nonetheless, there are sufficient differences between them which are captured by our clustering approach.
The tSNE plot (see Methods) in panel B of Figure \ref{fig:context_cluster_chart} allows for the exploration of these differences and compares the clusters identified in both treatments. This plot reveals that clusters A and C, which are more cooperative in experienced contexts and responses, clearly differentiate themselves from the rest, and one can find them at completely the other side of experiences and responses to those belonging to cluster B of the FP treatment. There seems nonetheless to be an overlap between some members cluster C and those in F in the SP treatment, yet most C members form a group on themselves. The experiences and behaviors of members of the E cluster, on the other hand, are close to those in B, which one can also observe when comparing the two bar charts. Finally, cluster D consists of participants that have experiences and responses that lie in between all others, separating the more defective and cooperative spectrum.
Given these observations, in the following sections, we show how we can infer the behaviors adopted by participants in each contextual cluster. It is important to note that not considering explicitly the experiences of the participants and focusing directly on the conditional behavior may result in grouping together participants that have encountered a different distribution of contexts. It is therefore essential to first partition the participants in function of their contexts distribution and then determine how they differ in their choices given these experiences.
\begin{table}[!ht]
\centering
\begin{tabular}{|c|c|c|c|c|}
\hline
\textbf{Treatment} & \textbf{Context } & \textbf{No. behavioral} & \textbf{Silhouette}\\
& \textbf{Cluster} & \textbf{sub-clusters} & \textbf{ score}\\
\hline
FP & A ($n=30$) & 2 & 0.6868 \\
FP & B ($n=30$) & 3 & 0.3848 \\
FP & C ($n=32$) & 3 & 0.4627 \\
\hline
SP & D ($n=38$) & 4 & 0.2993 \\
SP & E ($n=38$) & 4 & 0.4417 \\
SP & F ($n=20$) & 3 & 0.4176 \\
\hline
\hline
\end{tabular}
\caption{Summary of the clustering results using K-Means . The contextual clustering results in 3 clusters of similar sizes. The behavioral clustering per context yielded 8 behavioral sub-clusters in FP and 11 behavioral sub-clusters in SP. The scikit-learn \cite{pedregosa_scikit-learn_2011} silhouette analysis was used to determine the quality of the clusters generated with the "elbow" method (see Methods).}
\label{table:sub-clustering}
\end{table}
\subsection*{Fixed partners promotes behavioral self-selection to cooperative or defecting behaviors}
\begin{figure}[!ht]
\centering
\includegraphics[width=\linewidth]{prob_cluster_fix.png}
\label{fig:prob_coop}
\caption{Probability of cooperation given each context per cluster for the FP treatment. In each plot, the conditional probability of cooperating for each context is given. The bars represent the binomial error. Each contextual cluster is divided into sub-clusters that were identified using the frequency of cooperation given a context. It can be seen that in cluster A (left) that the differences between the sub-clusters are due to the difference in cooperation for the context $DD$. In cluster B (center), they all have a similar response to the $DD$ context, which explains the distribution seen in Figure \ref{fig:context_cluster_chart}. Cluster C (right) shows a mixed experience among the sub-clusters, with cluster C.0 showing significantly stronger cooperative response in case of the context $CD$.}
\label{fig:prob_coop_fix}
\end{figure}
\begin{figure}[!ht]
\centering
\includegraphics[width=\linewidth]{strategies_FP.png}
\caption{Hidden Markov Models for the FP treatment. Here, the eight sub-clusters found in FP have a HMM that describes each sub-cluster's strategy for the data over all rounds. Bold rectangles represent the initial state, while the others represent subsequent hidden states. Symbols with a probability lower than 0.05 are not shown, as well as the transition probability between states lower or equal to 0.01. For example, in sub-cluster A.0, the subjects play $D$ in the context $CD$ with a very small probability to continue, but a big one to pass to the other hidden state in the sequence, where they mutually cooperated ($(CC)C$). On the other hand, sub-cluster A.1 has some probability to defect given mutual defection $(DD)D$, which A.0 does not show. Overall, it appears a model with only one state is preferred by the training method (see Methods).}
\label{fig:strat_FP}
\end{figure}
Table~\ref{table:sub-clustering} reports the number of behavioral sub-clusters for each contextual cluster (see Methods): in total, 8 subgroups were inferred from the raw data of the FP treatment, i.e., 2 in cluster A, 3 in cluster B and 3 in cluster C. Supplementary Figure~\ref*{fig:tsne} shows a tSNE visualization of how the treatment data is divided into clusters and sub-clusters for FP. As before, the best settings for $K$ in K-means clustering was produced using the "elbow" method \cite{satopaa_finding_2011} (see Methods and Supplementary Figure \ref{fig:curves_sub_cluster}).
The behaviors in each contextual cluster are captured each time by two plots: i) a first plot that shows the likelihood of cooperation when experiencing a given context in a contextual cluster, and ii) a second plot that provides the inferred HMM in the behavioral sub-cluster (see Methods). Figures \ref{fig:prob_coop_fix} and \ref{fig:strat_FP} provide both plots for all the sub-clusters in each contextual cluster for the FP treatment.
For cluster A, one can observe the difference in response when it comes to a $DD$ situation, when comparing both sub-clusters (results in red): Individuals in cluster A.0 are more likely to cooperate again, than those in A.1 (see Figure~\ref{fig:prob_coop_fix}). Moreover, the resulting HMM for cluster A.0 shows how an initial strategy of reciprocating defection ($(CD)D$), leads to mutual cooperation ($(CC)C$). In addition, an increase in forgiving defective behavior ($(CD)C$) can be observed in Cluster A.1 (see HMM for A.1 in Figure~\ref{fig:strat_FP}), which is present less often in cluster A.0. Note that for this and following HMM, more elaborate models (with more states and transitions) could be constructed. As explained in Methods, we identify the optimal number of states for the model so as to avoid overfitting and to keep the HMM easy to understand.
Although cluster B is divided into three sub-clusters, there are actually two essential ones in terms of the number of participants they represent (see both Figure~\ref{fig:prob_coop_fix} and the green HMM in Figure~\ref{fig:strat_FP}). This next FP cluster mainly experienced mutual defection, and it is situated at the opposite of the behaviors present in the other two FP clusters (see Figure \ref{fig:context_cluster_chart}B). Looking at B.1 and B.2 in both figures, participants in sub-cluster B.1 appear to respond more often with cooperation than those in sub-cluster B.2 (see Figure \ref{fig:prob_coop_fix}, center panel), given that the triplets $(CD)C$ and $(DD)C$ occur at a higher frequency and that unconditional defection $(DC)D$ occurs with a high frequency in sub-cluster B.2. The two participants within cluster B.0 appear to be outliers with respect to the other members of the cluster as they were able to establish mutual cooperation more often than the participants in both other sub-clusters in cluster B.
Finally, in cluster C of the FP treatment, participants experienced a mixture of contexts, with a preference for mutually cooperative interactions. Clustering this group and inferring the corresponding HMM still revealed some differences (see again Figure~\ref{fig:prob_coop_fix}, Cluster C and Figure~\ref{fig:strat_FP}, blue group). Sub-cluster C.0 presents different behavior, members of this sub-cluster unconditionally cooperated despite their opponent's defection ($(CD)C$). Sub-cluster C.1 had a mixed strategy of reciprocating their opponent's previous action, but their rate of exploitation ($(CC)D$ = 0.33 and $(DC)D$ = 0.07) is higher than other sub-clusters. Lastly, the sub-cluster C.2 was mainly matching their opponent's previous action.
So clusters A and B in the FP treatment consist mostly of (forgiving as well as strict) cooperators and defectors respectively. It appears to indicate that a behavioral self-selection occurred among the participants in FP. In complex systems and evolutionary game theory, a self-selection mechanism (also called self-organization) occurs when parts of the system appear to reach a stable state \cite{yackinous_chapter_2015}. In this case, self-organization brings them to either of the extreme cases, i.e. mostly cooperation or mostly defection. This phenomenon could be happening because of the possibility for imitation of the choices by their neighbors in FP, as argued by Mahmoodi et al. \cite{mahmoodi_self-organizing_2017}. Members of the third cluster are in some sense still in between, either switching between matching choices or trying to outsmart the co-player.
\subsection*{While stranger interactions induce defection, cooperative aspirations remain}
\begin{figure}[!ht]
\centering
\includegraphics[width=\linewidth]{prob_cluster_rand.png}
\caption{Probability of cooperation given each context for the Shuffled Partners treatment. In the x-axis, it is shown the probability of cooperating given that in the previous round there was a certain context. The bars represent the binomial error. Each cluster is divided into sub-cluster that were divided using the frequency of cooperation given a context. As in FP (Figure \ref{fig:prob_coop_fix}), the sub-clusters present differences even when in their clusters a certain context dominates. For example, in p($C|CC$), it is shown how sub-cluster E.2 has a very low probability to cooperate given cooperation in the previous round, while the other sub-clusters are situated between 0.4 and 0.6. }
\label{fig:prob_coop_rand}
\end{figure}
\begin{figure}[!ht]
\centering
\includegraphics[width=\linewidth]{strategies_SP.png}
\caption{Hidden Markov Models for the Shuffled Partners treatment. Here, the eleven sub-clusters found in SP have a HMM that describes each sub-cluster's strategy. Symbols with a probability less than 0.05 were not shown, as well as the transition between states less or equal to 0.01. Then, for example in cluster E.1, it is shown how the subjects here played unconditionally defect with a probability of $0.919$, the other symbols' probabilities ($(CC)C$, $(CC)D$, etc.) are not shown.}
\label{fig:strat_SP}
\end{figure}
In the SP treatment, a larger variety of behaviors can be observed, i.e. 11 in total spread again over 3 contextual clusters. Figures \ref{fig:prob_coop_rand} and \ref{fig:strat_SP} immediately reveal some interesting information about the participants' behavior in the three clusters found for the SP treatment. Over all three clusters, i.e, D, E and F, we can observe, through their associated HMM models, that they have different degrees of mutual defection ($DD$), with E containing the most (as also was clear from Figure \ref{fig:context_cluster_chart}, bottom row, panel A). Moreover, the HMM models for E reveal a high tendency to defect even when the co-player acts cooperatively, even more than the defecting cluster B in FP. The opposite seems to occur in cluster F, where mutual cooperation is the highest and players are more likely to ignore a unilateral defection of the co-player. These two SP clusters thus represent opposing behavior given by their differences in context, as can also be seen in the tSNE plot in Figure \ref{fig:context_cluster_chart}B: clusters E and F are most distant in the SP treatment data in the tSNE embedding (More details can be observed in Supplementary Figure~\ref*{fig:tsne}). Based on Figure~\ref{fig:context_cluster_chart}B we also saw that F has a strong overlap with a subset of cluster C of the FP treatment, i.e. the group with a mixed contextual distribution, biased towards mutual cooperation. Considering the HMM, this mapping appears to be the closest to the sub-cluster C.0 between and F.0. This overlap is most likely to the high likelihood of continuing cooperation even when the co-player defected, i.e. $(CD)C$. For the rest, there appears to be little overlap between the behaviors in both treatments, demonstrating that human responses in both treatments are apparently different.
Cluster D on the other hand, appears to represent intermediate behavior with players still more mutually defecting but the frequency of some other response patterns has increased, which is also visible in Figure \ref{fig:context_cluster_chart}B. Sub-cluster D.1 shows to be more conditionally cooperative ($(CC)C$ and $(DC)C$) than the other sub-clusters in D, i.e. with probability 0.3 (see Figure \ref{fig:strat_SP}, cluster D). Players in sub-cluster D.3 and E.2 appear to try to signal their co-players to cooperate given the high frequency of $(DD)C$ in that subgroup to establish cooperation. The cluster D.0 is very similar to the sub-cluster D.2, where the difference is how forgiving and relentless they appear to be in relation to their co-player (see frequency of $(CD)C$ and $(DC)D$ in D.0 versus D.2). These variations between the HMM models are highly interesting as they reveal that although some general rules may be inferred on the behaviors, there are some important variations in the responses that push the overall outcome of the interactions towards cooperation or defection.
\subsection*{Decision-making simplifies over time and outcomes are decided early}
Although the HMM models in Figures \ref{fig:strat_FP} and \ref{fig:strat_SP} provide detailed insights into the behaviors observed over a complete (long) IPD experiment, we need to understand whether these behaviors are consistent over time, or whether early decision-making differs from downstream decision-making, which would indicate a learning effect in the experiment. To achieve this goal, the treatment data for each participant is divided into four parts, each consisting of 25 rounds. For each window of 25 rounds, a separate HMM is trained, collectively visualized in the Supplementary Figure \ref*{fig:strategies_FP_rounds} for the FP treatment and Supplementary Figure \ref*{fig:strategies_SP_rounds} for the FP treatment.
For FP one can observe that each strategy seems to converge with time to a dominating decision-making pattern. For example, the differences we observed between sub-clusters A.0 and A.1 are determined by how they act in the first 25 rounds, where it seems participants were still exploring their options. For example, participants in sub-cluster A.1, show a mix of unconditional cooperation ($(CD)C$ = 0.292), unconditional defection ($(DC)D$ = 0.083) and conditional behaviors ($(CD)D$ = 0.125, $(DD)D$ = 0.208, $(CC)C$ = 0.167). After 25 rounds, they coordinated on mutual cooperation for the remainder of the game. Cluster A.0 appears to have led to cooperation thanks to an initial reciprocal behavior ($(CD)D = 0.922$) that was followed by being resolving mistakes if they occur ($(DC)C = 0.922$). Something similar, but then for defection, happens in SP (see Supplementary Figure \ref*{fig:strategies_SP_rounds} ), where sub-clusters E.0 and E.1 differs essentially in how they react to contexts in the first 25 rounds, yet converge to the same behavioral pattern in the end.
The evolution of sub-cluster B.0 underlines the importance to have long enough experiments: as can be observed, these two participants started out exploring actions in the first 25 rounds, then mutually defected in the next 50 rounds, and finally found a way to cooperate in the last 25. The other two sub-clusters, B.1 and B.2 increase their probability to reciprocate defection $(DD)D$, but participants in sub-cluster B.1 showed from rounds 26-75 a willingness to establish cooperation ($(CD)C = 0.24$ and $0.12$ respectively) and ended up acting conditionally in the last quarter of the game.
Additionally, although cluster C in FP appeared to have less well-defined behaviors associated with it, one can see that C.0 and C.2 are in fact also very specific in their HMM description. Only for C.1 do we see many different contexts and responses in the emission probabilities of the HMM, yet this abundance of responses remains consistent over all rounds. A very similar situation happens in SP (see Supplementary Figure \ref*{fig:strategies_SP_rounds}), where even though in some clusters the strategies became more concise by having less diversity of contexts (see for instance cluster D.0). Yet, the majority of behaviors appear to remain rather stable over time, which is especially clear for cluster E. Overall, the HMM models in the figure reveal explicitly how having new partners at each round induces noise in the decision-process and hinders participants to converge to a clear strategy, relevant for the experiences they have.
\subsection*{FP Participants organize according to their behavioral clusters}
In FP we can clearly observe that the participants either ended up in full cooperation or defection. A form of self-organization or behavioral self-selection appears to be happening (see also earlier), which was unable to establish itself in the SP treatment. To confirm this hypothesis, the inter- and intra-cluster interactions between participants are analyzed, as visualized in Supplementary Figure \ref*{fig:nets}. In panel A of that figure, the results are shown for the FP treatment: The members of each behavior cluster are always interacting in the same contextual cluster. Moreover, some behavioral clusters are completely isolated (e.g. see clusters A.0 and A.1) or interact strongly with a specific other sub-cluster in the same contextual cluster (e.g. C.0 and C.1).
This analysis for the SP treatment shows a completely different picture: the members of one behavioral cluster interact often with members of another behavioral cluster. Even more, members of cluster E and F are more likely to interact with members of another contextual cluster than those inside their own. One can conclude here that stranger matching disrupts the self-selection process observed for FP, generating strategies that try to deal in a different manner with the situations they encounter.
The behavioral self-selection in FP is clearly a consequence of the fixed relationships in that treatment. In that case, previous actions play a more significant role than in the case of the SP treatment. This hypothesis is confirmed by the information obtained in the short questionnaire at the end of the experiment: Each participant was asked if her decision was influenced by what the other player did in the previous round (see Supplementary Information for more details). In the SP treatment, 50 players responded that they were influenced ($52.08\%$) by the other's actions. Yet, in the FP treatment, 74 participants responded "yes" to the same question ($80.43\%$). This means that FP participant actions were shaped strongly by actions in the last round, while in SP this shaping did not take place as almost half of the participants did not care about what their opponents did, leaving them with a different approach to decide between cooperating or defect.
Yet, notwithstanding this complexity, Supplementary Figure \ref*{fig:nets} also reveals that there is some structure in the network of possible interactions between all behavioral sub-clusters found in the SP treatment. Within the same contextual cluster, E.1 - E.2 and D.0 - D.1 represent strong interaction pairs while between contextual clusters the combinations E.0 - F.0, E.1 - F.2, D.0 - E.3 and D.3 - F.1 are accentuated. These associations are stronger than the within behavior cluster associations (i.e. the loops) and many of the other possible associations. This result indicates that the clustering is finding specific, non-random, behaviors that were used by the different participants, reminiscent of some kind of strategy.
Repeated interactions with the same partner thus lead to behavioral self-selection of participants into behavioral clusters . Similar results were previously observed in a Surplus Allocation game \cite{di_guida_repeated_2021}, wherein participants could themselves decide to continue with the same group, leading to a behavioral self-selection of groups of short and long duration, where the latter corresponded to cooperative ones.
\subsection*{Conditional strategies like TFT and WSLS are observed but not consistently used}
How do the strategies inferred from the treatment data relate to those proposed in the literature for the origins of cooperative behavior? To answer this question, the HMM results in Supplementary Figures \ref*{fig:strategies_FP_rounds} need to be considered as the theoretical strategies have been analyzed mostly in fixed partners interactions. Focusing on cluster A in FP first, one can derive that both sub-clusters in A may be associated with TFT-like or a WSLS-like behavior. Considering A.0, one can observe from round 1-25 that this cluster is associated with a reciprocal strategy: It starts out by defecting when the co-player defects (i.e. $(CD)D$) but still cooperating when she does ($(DC)C$), leading quickly to mutual cooperation ($(CC)C$) for the remainder of the FP treatment. Given the strong presence of $(CD)D$, this behavior is almost like a form of TFT.
Behaviors in A.1 also end up in mutual cooperation but achieve this in a different, yet less clear, manner: one could say the participants in A.1 also use a form of reciprocation when the co-player defects but cooperation appears to have been promoted while being generous ($(CD)C$ in combination with $(CD)D$) and signaling to go back to cooperation when both defect ($(DD)C$). This behavior is very much associated with the idea of WSLS (Win-Stay, Lose-Shift) or Pavlov as explained by Kraines and Kraines \cite{kraines_learning_1993}: When winning ($(DC)$ and $(CC)$ contexts) continue with the same action, when loosing ($(CD)$ and $(DD)$) switch. This makes sense in the way that this strategy was designed to promote cooperation in defective environments, and to mimic the stochasticity of biological and social interactions \cite{kraines_learning_1993}. Although non-WSLS responses are still present, it appears that together they were sufficient to induce cooperation.
This positive outcome did not occur for members of the behavioral cluster C.2, which contains a subset of participants that have similar cooperative ambitions as those in A.1 (visualized in Figure \ref{fig:context_cluster_chart}B through the proximity of a subset of C.2 participants with the A cluster), nor for members of C.1 and C0. While the behavior of C.2 in the first 25 rounds is very noisy, it too turns into something reminiscent of WSLS in the following window (rounds 26-50). Although C.2 participants played mostly among themselves (see Figure \ref{fig:nets}A), cooperation was not achieved given that mutual defection did not lead to cooperation ($(DD)C$). Similarly, for C.1, the frequency of $(DD)D$ is much higher than $(DD)C$, the exploitative action $(DC)D$ is dominating, which may explain again why cooperation is not achieved (note that C.0 players that interacted with C.1 players did not follow WSLS, stimulating the exploitation by C.1 members). In SP (see Supplementary Figure \ref*{fig:strategies_SP_rounds}), approximations of WSLS can also be observed, see for instance D.3, E.1. and E.2. Yet in all those cases $(CC)C$ is missing, again not leading to cooperation, with the stranger interaction possibly being the reason for the failure of observing that part of WSLS.
So in the case of fixed partnership interaction, we see successful cases of TFT- and WSLS-like behavior but more often the "implementations" of these strategies did not lead to cooperation, most likely because they were not rigorously applied, as opposed to the case when working with theoretical models. We also see cases of non-conditional behavior, for example in sub-cluster E.0 and E.1 in rounds 26 to 100 where the participants in these clusters defect unconditionally $(DC)D$ and $(DD)D$, which resembles the theoretical strategy AllD. The contrary also holds, where for example, sub-cluster F.0 unconditionally cooperates $(CD)C$ and $(CC)C$ during the whole game.
\section*{Discussion}
As seen in the Introduction, many approaches can be taken to study the strategies in the IPD. In this work, we clustered participants based on the context they experience. This is an important difference from other works since it allows us to see the nuances between people reacting to the same situation. We choose this approach because the act of either cooperating or defecting can mean different things depending on the context of the action. It is not the same to defect to exploit your opponent than to defect to reciprocate your opponents' actions. Moreover, it is not the same to cooperate with a fixed opponent as to cooperate with a stranger, that has been interacting with strangers as well. We used unsupervised methods which make no prior assumptions about what strategies players could use, for this, we tested several methods with the same goal to group participants with similar experiences, and we confirmed there is a significant overlap between different approaches.
A second level clustering (behavioral clustering), on how often they cooperated is necessary to analyze the individual differences given their opponents' actions, and how they signal their intentions in each situation. In fact, in the sub-clusters we found, we could identify players that faced the same context but behaved differently. There are plenty of examples, one of them is how participants in cluster E in SP faced defection, but when presented with mutual cooperation ($CC$), players in E.2 had 20 opportunities to respond with cooperation, which only one of them did so, once in the whole game, while the participants in the same cluster and context cooperated more, while having fewer opportunities to do so. This means that to understand the strategies people use in the IPD, it is necessary to see what was happening around them in the past and observe how they play in such situations.
Another factor that has an effect on people's strategies in the IPD is their opponent structure. Since we had two treatments, one with fixed co-players and one with shuffled ones, we could see how they act and what strategies they use given each context. Not only players in FP achieved more cooperation, but their strategies looked similar to their co-players. In other words, they were better at self-organizing and the intra-cluster behavior was very similar, as opposed to players of the SP treatment, who had to interact with members of other sub-clusters, who at the same time, had different strategies in mind.
One last hypothesis that we were able to prove here was the learning effect on people's strategies in the IPD. By dividing the analysis into windows of 25 rounds, we could see that the initial quarter was used by the players to explore and try different options, we could even see this effect in a chaotic environment such as SP, where establishing an action plan can be difficult due to its opponent structure.
Using Hidden Markov Models proved to be a handful tool to visualize the strategies and approximate how these underlying factors (in this case, represented as hidden states) shape participants' behavior. Taking a probabilistic approach, rather than a rigid, deterministic one accounts for the stochastic nature of our interactions.
Our findings have implications on how strategies in the IPD are studied: first, performing long experiments allowed us to observe that the participants may not have one but many strategies throughout the game before reaching an equilibrium. This means that when we talk about "how do we really act" we need to account for an exploration stage and a stabilization point. Second, we found that the opponent structure has an effect on people's behavior, and therefore, their strategies. Whether they are more adaptive to their opponents' actions or persistent based on their initial expectations and preferences, this depends on how the game is designed, different strategies might arise. For this reason, we believe that a logical step towards developing these results further is to analyze these strategies in other scenarios, such as N-player IPD, as opposed to the pairwise setting we presented in this paper. Previous work has stated that cooperation could be hindered \cite{grujic_three_2012}, but it is uncertain whether they will still be able to reach an equilibrium in their strategies as fast as the pairwise game, and from the strategic point of view, their rationale of what constitutes exploitation or reciprocation changes in this case.
Although we could observe some identifiable strategies thanks to the theoretical work behind the IPD, it is still challenging to determine and predict human behavior in these games, and this was represented by the big diversity of options on each HMM. And while taking a probabilistic approach to model decision-making might help us to understand our heuristics, this will continue to be an open issue in research on human cooperation, since all models have their limitations and there are many other scenarios to take into account. Another factor that is well known is the noise that not only our actions produce, but also our perception of what others are doing and their expectations, which they may also have about us. This is a caveat of human interaction to overcome and we are still trying to understand through these experiments.
\bibliographystyle{ieeetr}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,304 |
\section{Introduction}
Alain Connes introduced the notion of a spectral triple
which consists of a separable, infinite dimensional
complex Hilbert space $\mathcal{H}$, a $*$-algebra
of bounded linear operators on $\mathcal{H}$, $A$,
and a self-adjoint unbounded operator $D$ such that
$( 1 + D^{2})^{-1}$ is a compact operator.
The key relation is that for all
$a$ in $A$, $[D, a] = D a - a D$ is densely defined
and extends to a bounded operator~\cite{Co89}.
The motivating example is where $A$ consists
of the smooth functions on a compact
manifold and $D$ is some type of elliptic
differential operator.
In spite of its geometric origins, there has been
considerable interest in finding examples where
the algebra $A$ is the continuous functions
on a compact, totally disconnected metric space with
no isolated points. We refer to such a space as a Cantor set.
The first example was given by Connes~\cite{Co85, Co89, Con94}
but many other authors have also contributed:
Sharp~\cite{Sha12}, Pearson--Bellissard~\cite{PB09},
Christensen--Ivan~\cite{CI06}, etc.
Many of these results concern not just a Cantor set,
but also some type of dynamical system on a Cantor set.
Many such systems are closely related to
aperiodic tilings and are important as mathematical models
for quasicrystals.
We continue these investigations here by studying
subshifts. Let $\mathcal{A}$ be a finite set
(called the alphabet). Consider $\mathcal{A}^{\mathbb{Z}}$
with the product topology and the homeomorphism $\sigma$
which is the left shift: $\sigma(x)_{n} = x_{n+1},
n \in \mathbb{Z}$, for
all $x$ in $\mathcal{A}^{\mathbb{Z}}$.
A subshift $X$ is any non-empty, closed and shift-invariant subset
of $\mathcal{A}^{\mathbb{Z}}$.
Is is regarded as a dynamical system for the map $\sigma|_{X}$.
Our aim here is to construct and study examples
of spectral triples for the algebra of locally
constant functions on $X$, which we denote
$C_{\infty}(X)$. Besides, we let $C(X)$ denote the $C^{*}$-algebra
of continuous functions on $X$ and $C(X) \times \mathbb{Z}$ be the
crossed product $C^*$-algebra generated by $C(X)$ and a canonical unitary $u$.
We will also consider the $*$-subalgebra of the crossed product
generated by $C_{\infty}(X)$ and $u$ and study how our spectral triples extend to this algebra.
Our construction is just a special case of
that given by Christensen and Ivan for
AF-algebras \cite{CI06}. Given an increasing
sequence of finite-dimensional
$C^{*}$-algebras
\[
A_{1} \subseteq A_{2} \subseteq A_{3} \subseteq \cdots
\]
one considers their union and a representation
constructed by the GNS method. The same sequence
of sets provides an increasing sequence of finite-dimensional
subspaces for the associated Hilbert spaces which is used
the construct the eigenspaces for the operator $D$.
The one other piece of data needed for our construction
is a $\sigma$-invariant measure with support $X$,
which we denote $\mu$.
Our case of the subshift has some special features. The
first is that the sequence of finite-dimensional
subalgebras we construct is canonical, arising
from the structure as a subshift. Secondly, the
choice of eigenvalues for the operator $D$ is
constrained by the dynamics (see Theorem 3.2)
in such a way that we find a canonical choice for $D$,
which we denote by $D_{X}$.
One similarity with the situation of Christensen and Ivan
is that our operator $D_{X}$ is positive, meaning that,
at least to this point, it has no interesting index data,
but is rather regarded as a noncommutative metric structure
as in Rieffel's work~\cite{Rie99, Rie04}.
We mention one other result by Bellissard, Marcolli and
Reihani~\cite{BMR10} which is relevant and
motivated our work. They begin with a spectral triple
$( \mathcal{H}, A, D)$ and an action $\alpha$
of the integers on $A$ by automorphisms. Under the
assumption that the action is quasi-isometric
(that is, there is a constant $C \geq 1$ such that
\[
C^{-1} \Vert [D, a] \Vert \leq \Vert
[D, \alpha^{n}(a)] \Vert \leq C \Vert
[D, a] \Vert,
\]
for all $a$ in $A$ and $n $ in $\mathbb{Z}$, they construct
a spectral triple for $A \times \mathbb{Z}$
satisfying certain conditions. Moreover, they show that
every spectral triple on $A \times \mathbb{Z}$ satisfying
these conditions arises this way. While this is
a very good result, it is somewhat disappointing
since the hypothesis of quasi-isometric is very strong
and quite atypical in dynamical systems of interest.
In fact, subshifts are expansive. That is, if
$d$ is any metric on the shift space,
there is a constant $\epsilon_{0} > 0$ such that for
every $x \neq y$, there is an
integer $n$ with $d(\sigma^{n}(x), \sigma^{n}(y)) \geq \epsilon_{0}$. In some sense, this is the opposite
of quasi-isometric. Of course, our spectral triples do not satisfy
the conditions given in~\cite{BMR10}. The key point
is that the representation of $A \times \mathbb{Z}$ used
in~\cite{BMR10} is the left regular one on
$\mathcal{H} \otimes \ell^{2}(\mathbb{Z})$. Our representations
are on the Hilbert space $L^{2}(X, \mu)$, which
may be regarded as more natural from a dynamical perspective.
We also mention previous constructions of spectral triples for
subshifts or tiling spaces (see also the review article~\cite{JKS15}).
Kellendonk, Lenz and Savinien~\cite{KSav12, KLS13} built spectral
triples for the commutative algebra of one-dimensional subshifts.
Their construction is similar to ours in the sense that it is based
on the ``tree of words'' (which is related to our increasing family
of subalgebras).
In their papers, however, the algebra is represented on a Hilbert space
of the form $\ell^2(E)$, where $E$ is a countable set built from a discrete
approximation of the subshift. It is
unclear how the shift action reflects on this set, and there doesn't seem
to be an obvious extension to the noncommutative algebra.
They can still relate combinatorial properties of the subshift (namely
the property of being repulsive) to properties of the spectral triples.
Their construction also seems to be topologically quite rich, as the $K$-homology
class of their triple is in general not trivial.
In a recent paper, Savinien extended some results to higher-dimensional tilings~\cite{Sav15}.
Previously, Whittaker~\cite{Whi13} had proposed a spectral triple construction
for some hyperbolic dynamical systems (Smale spaces), a family which contains
self-similar tiling spaces.
In Whittaker's construction, the triple is defined on a noncommutative algebra
which corresponds to $C(X) \times \mathbb{Z}$ in our case. His representation
is however quite specific to the Smale space structure, and it is unclear
how our construction compares to his.
This paper is organized as follows. In the next section,
we discuss the basics of subshifts. This includes an
introduction to three important classes which
will be our main examples. The third section gives the construction of the spectral triples and
some of their basic properties. In the fourth section,
we establish results on the summability of the
spectral triples. Leaving the precise statements
until later, various aspects of summability are closely
linked with the entropy of the subshift and also
its complexity. In the fifth section, we discuss
the Connes metric. At this point all of our results
here deal with the algebra $C_{\infty}(X)$. We hope
to extend these to $C_{\infty}(X) \times \mathbb{Z}$
in future work. Again leaving the precise statements
until later, it turns out that the behaviour
of the Connes metric depends on very subtle
properties of the dynamics and varies quite wildly between
our three classes of examples.
\subsection*{Summary of the main results}
Given a subshift $X$ with an invariant measure $\mu$, we represent $C(X) \times \mathbb{Z}$ on $L^2(X,\mu)$. Let $C_\infty(X)$ be the algebra of locally constant functions on $X$.
For any increasing sequence going to infinity $(\alpha_n)_{n \geq 0}$, we define a Dirac operator with these eigenvalues, so that $(C_\infty(X),L^2(X,\mu),D)$ is a spectral triple (Theorem~\ref{thm:spectral-triple}).
It extends to a spectral triple on $C_\infty(X) \times \mathbb{Z}$ if and only if $(\alpha_n - \alpha_{n-1})$ is bounded. This leads to the definition of a canonical operator $D_X$ (with $\alpha_n = n$), which is studied in the rest of the paper (Definition~\ref{def:DX}).
The summability depends on the complexity of the subshift. The complexity counts the number of factors of length $n$ appearing in the subshift. If the subshift has positive entropy $h(X)$ (which corresponds to the complexity function growing exponentially), the summability of $e^{sD_X}$ depends on whether $s < h(X)$ or $s > h(X)$ (Theorem~\ref{thm:theta-summable}). In the case of zero entropy, the complexity may grow asymptotically like $n^d$ for some number $d$. Whether $D_X$ is $s$-summable then depends whether $s < d$ or $s > d$ (Theorem~\ref{thm:finite-summable}).
In the last section, we investigate the Connes metric for various subshifts. In this section, we focus on the spectral triple restricted to the commutative algebra $C_\infty (X)$.
For (aperiodic, irreducible) shifts of finite type, the Connes metric is infinite (Theorem~\ref{thm:connes-SFT}).
For linearly recurrent subshifts, the Connes metric is finite and induces the weak-$*$ topology (Theorem~\ref{thm:LR}). This result is
positive in the sense that it includes many examples
of interest related to one-dimensional quasicrystals, including
primitive substitution subshifts.
For Sturmian subshifts,
the results depend rather subtly (but probably not surprisingly)
on the continued fraction
expansion of the irrational number which parameterizes the
subshift.
We show that there is a large class of
numbers $\theta \in (0,1)$ such that the subshift with parameter $\theta$ has finite Connes metric and induces the
weak-$*$ topology (Theorem~\ref{thm:sturm-bounded-ae}).
In particular, this is the case
for almost all $\theta \in (0,1)$ (for the Lebesgue measure). However, we also exhibit Sturmian subshifts having
infinite Connes metric (Theorem~\ref{thm:sturm-unbounded}).
\subsubsection*{Acknowledgments}
Substantial part of this work was done while A.~Julien was working at the University of Victoria, funded in part by the Pacific Institute for the Mathematical Sciences (PIMS). We also thank the referee for a
thorough reading of the paper and many helpful
suggestions.
\section{The Connes metric}
\label{sec:connes}
In this section, we develop some tools to analyze the Connes metric and apply them to our specific cases of interest.
These results are very technical so it may be of some value to indicate, at least vaguely, what is going on.
It seems that a number of factors influence the behaviour of the Connes metric for a subshift $X$.
The two most important ones are:
\begin{enumerate}
\item For a given $x$ in $X$, the sequence $\{ n \in \mathbb{N} \mid \pi_{n}(x) \in X_{n}^{+} \}$.
That is, in looking at the sequence of words $\pi_{n}(x)$, how often do we have strict
containment $U(\pi_{n}(x)) \supsetneq U(\pi_{n+1}(x))$? Generally speaking, large gaps
between such values of $n$ will tend to help keep the Connes metric finite. For example, in
linearly recurrent (in particular substitutive) subshifts, this sequence tends to grow exponentially (see
the discussion after Lemma~\ref{lem:LR-bound-Rw}).
\item For the various $w$, the ratio ${\mu(\pi(w))}/{\mu(w)}$. These ratios remaining bounded
seem to help keep the Connes metric finite.
\end{enumerate}
Our main interest is in the operator $D_{X}$ whose eigenvalues are the natural numbers. However, we will treat
the more general case of $D$ for most of our estimates, partly so that we can see the exact
r\^{o}le of the eigenvalues $\alpha_{n}$. We will assume that this sequence is increasing and unbounded.
\subsection{Technical preliminaries}
\label{ssec:connes-technical}
For $w$ in $X^{+}_{n}$, we introduce a space of functions
\[
F_{w} = \Span \big\{ \xi(w') \mid \pi(w') = w \big\} \cap C_{n}^{\perp}.
\]
In fact, we could also make the same definition for any $w$ in $X_{n}$,
but $F_{w}$ is non-zero if and only if $w$ is in $X_{n}^{+}$.
This is a finite-dimensional space and it will be convenient to have an estimate
comparing the supremum norm with the $L^{2}$-norm for its elements.
\begin{lemma}
\label{lemma:L2-Linfinity}
For $w$ in $X^{+}_{n}$ and $f$ in $F_{w}$, we have
\[
\Vert f \Vert_{2} \leq \mu(w)^{\frac{1}{2}} \Vert f \Vert_{\infty} \leq R(w)^{\frac{1}{2}} \Vert f \Vert_{2}.
\]
\end{lemma}
\begin{proof}
The first inequality is trivial. For the second, since $f$ is in $F_{w}$, $f= \sum_{\pi(w')=w} a_{w'} \xi(w')$
and so $ \Vert f \Vert_{\infty} = | a_{w'} |$, for some $w'$ with $\pi(w') = w$. Then we have
\[
\Vert f \Vert_{2}^{2} = \int_{U(w)} f^{2} d\mu \geq |a_{w'}|^{2} \mu(w') = \mu(w') \Vert f \Vert_{\infty}^{2}
\geq \mu(w) R(w)^{-1} \Vert f \Vert_{\infty}^{2}.
\]
Multiplying by $R(w)$ and taking square roots yields the result.
\end{proof}
We are next going to introduce a special collection of functions. At the simplest level they provide
spanning sets for our subspaces $F_{w}$. More importantly and subtly, their interactions with the operator $D$
are quite simple.
Suppose that $\pi(w)$ is in $X^{+}_{n}$, let
\[
\eta(w) = \frac{\mu(\pi(w))}{ \mu(w)} \xi(w) - \xi(\pi(w) ).
\]
Notice that we could make the same definition for any $w$, but if $\pi(w)$ is not in
$X^{+}_{n}$, for some $n$, then $\eta(w)=0$. Also, if $w$ is in $X^{+}_{n}$, the
vectors $\{ \eta(w') \mid \pi(w')=w \}$ span $F_{w}$, but are linearly dependent since their
sum is zero.
Also observe that for any $w$ in $X_{n}$, the sequence of vectors $\eta(\pi_{m+1}(w))$, for those $m < n$ with
$\pi_{m}(w)$ in $X_{m}^{+}$ are an orthogonal set.
We summarize some properties of $\eta(w)$.
\begin{lemma}
\label{lemma:eta}
Suppose that $\pi(w)$ is in $X^{+}_{n}$.
\begin{enumerate}
\item $\eta(w)$ is in $C_{n+1}$.
\item $\eta(w)$ is in $C_{n}^{\perp}$.
\item $\eta(w)^{2} = \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 2 \right)\eta(w)
+ \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 1 \right) \xi(\pi(w)) $.
\item $\Vert \eta(w) \Vert_{2}^{2} = \mu(\pi(w)) \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 1 \right)$.
\item If we consider $\eta(w)$ in $C(X)$ and $\eta(w) + \mathbb{C}$ in the quotient space $C(X)/ \mathbb{C}$, then
$\Vert \eta(w) + \mathbb{C} \Vert_{\infty} = \frac{\mu(\pi(w)) }{2 \mu(w)}$.
\end{enumerate}
\end{lemma}
\begin{proof}
The first part is clear. For the second, $\eta(w)$ is clearly supported on $\xi(\pi(w))$ so it
is perpendicular to $\xi(w')$, for all $w' \neq \pi(w)$ in $X_{n}$. In addition, we compute
\[
\langle \eta(w), \xi(\pi(w)) \rangle = \frac{\mu(\pi(w)) }{ \mu(w)} \mu(w) - \mu(\pi(w)) = 0.
\]
For the third part, use the fact that $\xi(w)$ and $\xi(\pi(w))$ are idempotents and their
product is the former, so that
\[\begin{split}
\eta(w)^{2} & = \left( \frac{\mu(\pi(w))^{2}}{\mu(w)^{2}} - 2 \frac{\mu(\pi(w))}{\mu(w)} \right) \xi(w) + \xi(\pi(w)) \\
& = \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 2 \right) \frac{\mu(\pi(w))}{\mu(w)} \xi(w) + \xi(\pi(w)) \\
& = \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 2 \right) (\eta(w) + \xi(\pi(w))) + \xi(\pi(w)) \\
& = \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 2 \right) \eta(w) + \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 1 \right) \xi(\pi(w)).
\end{split}\]
For the fourth part, we know already that $ \frac{\mu(\pi(w)) }{ \mu(w)} \xi(w) = \eta(w) + \xi(\pi(w))$.
Moreover, the two terms on the right are orthogonal, so we have
\[
\left( \frac{\mu(\pi(w)) }{ \mu(w)}\right)^{2} \mu(w) = \Vert \eta(w) \Vert^{2}_{2} + \mu(\pi(w)),
\]
and the conclusion follows.
For the last part, the function $\eta(w)$ takes on three values: $0$,
$a = \frac{\mu(\pi(w)) }{ \mu(w)} - 1 > 0$ (on $U(w)$) and
$b = -1 < 0$.
For any such function, the minimum norm on $\eta(w) + \mathbb{C}$ is obtained
at $\eta(w) - \frac{a+b}{2}$ and equals $a - \frac{a+b}{2} = \frac{a -b}{2}$. The rest is a
simple computation.
\end{proof}
We next want to summarize some of the properties of the functions $\eta(w)$ as operators. In
particular, their commutators with $D$ are of a simple form.
\begin{lemma}
\label{lemma:zeta}
Suppose that $w$ is in $X_{n+1}$ with $\pi(w) $ in $X^{+}_{n}$. Considering $\eta(w)$ as an element of $C(X)$, we have
the following.
\begin{enumerate}
\item $\eta(w) C_{n} \subset \mathbb{C} \eta(w) \subset C_{n+1} \cap C_{n}^{\perp}$.
\item $[\eta(w), D] = \eta(w) \otimes \zeta(w)^{*} - \zeta(w) \otimes \eta(w)^{*}$,
where \newline $\zeta(w) = \mu(\pi(w))^{-1}(D - \alpha_{n+1})\xi(\pi(w))$.
\item $\Vert [ \eta(w), D ] \Vert = \Vert \eta(w) \Vert_{2} \Vert \zeta(w) \Vert_{2}$.
\item $\zeta(w)$ is in $C_{n}$ and is non-zero.
\item $\Vert [ \eta(w), D ] \Vert \leq \left( \frac{\mu(\pi(w)) }{ \mu(w)} \right)^{1/2} \alpha_{n+1} $.
\end{enumerate}
\end{lemma}
\begin{proof}
For the first point, the support of $\eta(w)$ is contained in $U(\pi(w))$.
So for any $w'$ in $X_{n}$, $\eta(w) \xi(w') = 0$ unless $w' = \pi(w)$,
in which case $\eta(w) \xi(w') = \eta(w) \in C_{n+1} \cap C_n^\perp$.
For the second point, we know that $D C_{n} \subset C_{n}$ and $D(C_{n+1} \cap C_{n}^{\perp})$ is a subspace of $(C_{n+1} \cap C_{n}^{\perp})$.
Combining this with the first part above, we see that
$D \eta(w)$ and $\eta(w)D$ both map $C_{n}$ into $(C_{n+1} \cap C_{n}^{\perp})$.
We also know that $\restr{[\eta(w), D]}{C_{n+1}^{\perp}} = 0$. In other words, $[\eta(w),D](I-P_{n+1})=0$.
From above, we have $P_{n}[\eta(w), D]P_{n} = 0$. In addition, we compute
\begin{align*}
( & P_{n+1} - P_{n}) [\eta(w), D] ( P_{n+1} - P_{n}) \\
& \qquad = ( P_{n+1} - P_{n}) (\eta(w) D - D \eta(w)) ( P_{n+1} - P_{n}) \\
& \qquad = ( P_{n+1} - P_{n}) \eta(w) D ( P_{n+1} - P_{n}) - ( P_{n+1} - P_{n}) D \eta(w) ( P_{n+1} - P_{n}) \\
& \qquad = ( P_{n+1} - P_{n}) \eta(w) \alpha_{n+1} ( P_{n+1} - P_{n}) \\*
& \qquad \quad - ( P_{n+1} - P_{n}) \alpha_{n+1} \eta(w) ( P_{n+1} - P_{n}) =0
\end{align*}
From all this---writing $I=P_n + (P_{n+1}-P_n) + (I-P_{n+1})$---, we have
\[
[\eta(w), D] = (P_{n+1}-P_{n}) [\eta(w), D] P_{n} + P_{n} [\eta(w), D] (P_{n+1}-P_{n})
\]
Since $[\eta(w), D]$ is skew adjoint, the second term is the opposite of the first. From part 1, the
first is a rank one operator of the form $\eta(w) \otimes \zeta(w)^{*}$, for some
$\zeta(w)$ in $C_{n}$.
To find $\zeta(w)$, the simplest thing is to apply $[\eta(w), D]$ to $\eta(w)$ so that
\begin{align*}
&\Vert \eta(w)\Vert_{2}^{2} \zeta(w)
= - [\eta(w), D](\eta(w)) \\
& \qquad = - \eta(w) D(\eta(w)) - D(\eta(w)^{2}) \\
& \qquad = - \alpha_{n+1} \eta(w)^{2} - D(\eta(w)^{2}) \\
& \qquad = - (\alpha_{n+1} - D) (\eta(w)^{2}) \\
& \qquad = - (\alpha_{n+1} - D)
\left[ \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 2 \right)\eta(w)
+ \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 1 \right) \xi(\pi(w)) \right] \\
& \qquad = 0 + \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 1 \right) (D - \alpha_{n+1}) \xi(\pi(w)).
\end{align*}
Now using the fact that $\Vert \eta(w)\Vert_{2}^{2} = \left( \frac{\mu(\pi(w)) }{ \mu(w)} - 1 \right) \mu(\pi(w))$, we have
\[\begin{split}
\zeta(w) & = \Vert \eta(w)\Vert_2^{-2} \left( \frac{\mu(\pi(w))}{\mu(w)} - 1 \right) (D - \alpha_{n+1}) \xi(\pi(w)) \\
& = \mu(\pi(w))^{-1} (D - \alpha_{n+1}) \xi(\pi(w)).
\end{split}\]
For the third part, having
expressed $[\eta(w), D] = \eta(w) \otimes \zeta(w)^{*} - \zeta(w) \otimes \eta(w)^{*}$,
we note that the first term maps $C_{n}$ to $C_{n}^{\perp}$ and the second maps
$C_{n}^{\perp}$ to $C_{n}$. Hence the norm is equal to the supremum of the norms of
the two terms which is simply $\Vert \eta(w) \Vert_{2} \Vert \zeta(w) \Vert_{2}$.
The first statement of the fourth part follows from the fact that $\xi(\pi(w))$ is in $C_{n}$, which is invariant under $D$,
and the formula for $\zeta(w)$. The second part follows because $D- \alpha_{n+1}$ is invertible on $C_{n}$ as
$\alpha_{n+1} > \alpha_{1}, \alpha_{2}, \ldots, \alpha_{n}$.
For the last part, we have
\begin{align*}
& \Vert [\eta(w), D] \Vert = \Vert \eta(w) \Vert_2 \Vert \zeta(w) \Vert_2 \\
& \quad = \left( \frac{\mu(\pi(w))}{\mu(w)} - 1 \right)^{1/2} \mu(\pi(w))^{1/2}
\mu(\pi(w))^{-1} \Vert (D- \alpha_{n+1}) \xi(\pi(w)) \Vert_{2} \\
& \quad \leq \left( \frac{\mu(\pi(w))}{\mu(w)}\right)^{1/2}
\mu(\pi(w))^{-1/2} \Vert (D - \alpha_{n+1}) \xi(\pi(w)) \Vert_{2}.
\end{align*}
It remains only to note that $\mu(\pi(w))^{1/2} = \Vert \xi(\pi(w)) \Vert$ and that $\xi(\pi(w))$ is a vector in
$C_{n}$, with $ 0 \leq D|_{C_{n}} \leq \alpha_{n+1}$ so that $\Vert D - \alpha_{n+1} \Vert \leq \alpha_{n+1}$.
\end{proof}
A nice simple consequence of this result is that the only functions in $C_{\infty}$ commuting with $D$ are the scalars.
We introduce now the notation $Q_{w}$ for the orthogonal projection of $L^{2}(X, \mu)$ onto $F_{w}$.
It will be convenient to break a function $f \in L^2(X, \mu)$ into its components $Q_w(f)$.
Since the commutator of $D$ with the functions $\eta(w')$ has a fairly simple form and $Q_w$ is the projection onto the span of the
of $\eta(w') $ for $\pi(w') = w$, we can hope that the quantities $[D,Q_w(f)]$ are accessible to computations.
Note that $Q_{w}(f) = \xi(w)(P_{n+1}(f) - P_{n}(f))$, for any $f$ in
$L^{2}(X, \mu)$.
\begin{thm}
\label{thm:commutator-of-D}
Let $X$ be a subshift and assume the sequence $\alpha_{n}$ is strictly increasing.
If $f$ is in $C_{\infty}(X)$ and $[f, D] = 0$, then $f$ is in $C_{0} = \mathbb{C} 1$.
\end{thm}
\begin{proof}
Begin by adding a scalar to $f$ so that $f $ is in $C_{0}^{\perp}$ which clearly alters neither hypothesis nor
conclusion. Suppose that $f$ is in $C_{n}$. We will prove by induction on $n$ that $f=0$. The case
$n=0$ is straightforward, since $f$ lies in both $C_{0}$ and $C_{0}^{\perp}$.
Now assume $n \geq 1$.
We may write
\[
f = \sum_{0 \leq m < n} \sum_{ \pi(w) \in X_{m}^{+}} \beta(w) \eta(w),
\]
where the $\beta(w)$ are scalars.
Fix $w_{0}$ in $X_{n-1}^{+}$ and let $w_{1} $ be in $X_{n}$ with $\pi(w_{1}) = w_{0}$.
We will compute $[f, D] \eta(w_{1})$,
which is zero by hypothesis. This will be done term by term in the sum above for $f$, using
part~2 of Lemma~\ref{lemma:zeta}.
First, suppose that $w$ is in $X_{m}$ with $m < n$. In this case, both $\eta(w)$ and $\zeta(w)$ lie in $C_{n-1}$
and hence their inner products with $\eta(w_{1})$ are zero so this term contributes nothing.
Secondly, if $w$ is in $X_{n}$ with $\pi(w) \neq w_{0}$, then $\eta(w)$ is
supported on $U(\pi(w))$ while $\eta(w_{0})$ is supported on $U(w_{0})$. As these sets are
disjoint, the vectors are orthogonal. Since $\zeta(w)$ is in $C_{n-1}$, it is also orthogonal
to $\eta(w_{0})$.
This leaves us to consider $w$ with $\pi(w) = w_{0}$. For each such $w$, $\zeta(w)$ is again in
$C_{n-1}$ and is orthogonal to $\eta(w_{1})$. We conclude that
\[
[f, D] \eta(w_{1}) = \sum_{\pi(w) = w_{0}} \beta(w) \langle \eta(w_{1}), \eta(w) \rangle \zeta(w).
\]
Observe from the formula in part 2 that $\zeta(w)$ depends only on $\pi(w)=w_{0}$ and is non-zero. We conclude that
\[
\sum_{\pi(w) = w_{0}} \beta(w) \langle \eta(w_{1}), \eta(w) \rangle = 0.
\]
Since $\eta(w)$ and $\eta(w_{1})$ are real-valued, we also have
\begin{align*}
0 & = \sum_{\pi(w) = w_{0}} \beta(w) \langle \eta(w), \eta(w_{1}) \rangle
= \Big\langle \sum_{\pi(w) = w_{0}} \beta(w) \eta(w), \eta(w_{1}) \Big\rangle \\
& = \langle Q_{w_{0}}(f) , \eta(w_{1}) \rangle.
\end{align*}
If we now vary $w_{1}$ over $\pi^{-1}\{ w_{0} \}$, this forms a spanning set for
$F_{w_{0}}$. We conclude that $Q_{w_{0}}(f) = 0$. As this holds for every $w_{0}$ in
$X_{n}^{+}$, we conclude that $f$ actually lies in $C_{n-1}$. By induction hypothesis
$f=0$.
\end{proof}
It is a good time to observe the following fairly simple consequence of these estimates. We will use this
later to give examples of Sturmian systems where the Connes metric is infinite.
\begin{thm}
\label{thm:sufficient-for-unbounded}
Let $X$ be a subshift and let $\mu$ be a
$\sigma$-invariant probability measure with support $X$. If the set
\(
\left\{ (n+1)^{-2} {\mu(\pi(w))}/{\mu(w)} \mid n \geq 1, \pi(w) \in X_{n}^{+} \right\}
\)
is unbounded, the Connes metric associated with $(C_{\infty}(X), L^{2}(X, \mu), D_{X})$ is infinite.
\end{thm}
\begin{proof}
It follows from the last part of Lemma~\ref{lemma:zeta} that the functions
\[
f_{w} = (n+1)^{-1} \left( \frac{\mu(\pi(w))}{\mu(w)} \right)^{-1/2} \eta(w)
\]
all satisfy $\Vert [f_{w}, D] \Vert \leq 1$. On the other hand, from
part 5 of Lemma \ref{lemma:eta}, we have
\[
\Vert f_{w} + \mathbb{C} \Vert_{\infty} = (2(n+1))^{-1} \left( \frac{\mu(\pi(w))}{\mu(w)} \right)^{1/2},
\]
which, by hypothesis, is unbounded.
\end{proof}
The next results will be used as tools in showing the the Connes metric is finite
and induces the weak-$*$ topology for some subshifts. The point is really to get estimates
on how a function may move vectors in
$C_{n} \cap C_{n-1}^{\perp}$ to $C_{m} \cap C_{m-1}^{\perp}$, for values $n > m$.
The second is the important estimate; we include the first because it seems
convenient to divide it into two steps.
\begin{lemma}
\label{lem:control-Qw}
Let $f$ be in $\cup_{n} C_{n}$. Let $w$ be in $X^{+}_{n}$ and $m<n$ with $\pi_{m}(w)$ in $X^{+}_{m}$.
We have
\[
\big\langle [D, f] \eta\big(\pi_{m+1}(w)\big), Q_{w}(f) \big\rangle = (\alpha_{n+1} - \alpha_{m+1}) \Vert Q_{w}(f) \Vert _{2}^{2}
\left( \frac{\mu(\pi_{m}(w))}{\mu(\pi_{m+1}(w)} -1 \right).
\]
\end{lemma}
\begin{proof}
For convenience let $w' = \pi_{m+1}(w)$.
Observe that the function $Q_{w}(f)$ is in $C_{n+1}\cap C_{n}^{\perp}$ while $\eta(w')$ is in $C_{m+1}\cap C_{m}^{\perp}$ .
Therefore, we have
\begin{align*}
\langle [D, f] \eta(w'), Q_{w}(f) \rangle
& = \langle Df \eta(w'), Q_{w}(f) \rangle - \langle fD \eta(w'), Q_{w}(f) \rangle \\
& = \langle f \eta(w'), D Q_{w}(f) \rangle - \langle \alpha_{m+1}f\eta(w'), Q_{w}(f) \rangle \\
& = \langle f \eta(w'), \alpha_{n+1} Q_{w}(f) \rangle - \langle \alpha_{m+1}f\eta(w'), Q_{w}(f) \rangle \\
& = (\alpha_{n+1} - \alpha_{m+1}) \langle f \eta(w'), Q_{w}(f) \rangle.
\end{align*}
Now we observe that $Q_{w}(f)$ is supported on $U(w) \subset U(w')$ (since $w' = \pi_{m+1}(w)$)
and $\eta(w')$ is identically $ \left( \frac{\mu(\pi(w'))}{\mu(w')} -1 \right) $ on the latter. Therefore, we have
\begin{align*}
\langle [D, f] \eta(w'), Q_{w}(f)) \rangle
& = (\alpha_{n+1} - \alpha_{m+1}) \langle f \eta(w'), Q_{w}(f) \rangle \\
& = (\alpha_{n+1} - \alpha_{m+1}) \left( \frac{\mu(\pi(w'))}{\mu(w')} -1 \right) \langle f, Q_{w}(f) \rangle \\
& = (\alpha_{n+1} - \alpha_{m+1}) \left( \frac{\mu(\pi(w'))}{\mu(w')} -1 \right) \langle Q_{w}(f), Q_{w}(f) \rangle.
\end{align*}
\end{proof}
\begin{prop}
\label{prop:control-Qw}
Let $f$ be in $\cup_{n} C_{n}$. Let $w$ be in $X^{+}_{n}$ and $m<n$ with $\pi_{m}(w)$ in $X^{+}_{m}$.
If $\Vert [D, f] \Vert \leq 1$, then
\[
\Vert Q_{w}(f) \Vert_{\infty} \leq R(w)^{1/2} R(\pi_{m}(w) )^{1/2}
(\alpha_{n+1} - \alpha_{m+1})^{-1} \mu(w)^{-1/2} \mu(\pi_{m+1}(w))^{1/2} .
\]
\end{prop}
\begin{proof}
Let $w' = \pi_{m+1}(w)$.
From the hypothesis and the last Lemma, we have
\begin{align*}
\Vert \eta(w') \Vert_{2} \Vert Q_{w}(f) \Vert_{2}
& \geq \abs{ \big\langle [D, f] \eta(w'), Q_{w}(f) \big\rangle } \\
& = (\alpha_{n+1} - \alpha_{m+1}) \Vert Q_{w}(f) \Vert_{2}^{2} \left( \frac{\mu(\pi(w'))}{\mu(w')} -1 \right),
\end{align*}
and hence
\(
\Vert \eta(w') \Vert_{2} \geq (\alpha_{n+1} - \alpha_{m+1}) \Vert Q_{w}(f) \Vert_{2}
\left( \frac{\mu(\pi(w'))}{\mu(w')} -1 \right)
\).
Now we invoke our estimate for $\Vert \eta(w') \Vert_{2} $ from Lemma~\ref{lemma:eta} and
recall from Lemma~\ref{lemma:Rw} that
\(
\left( \frac{\mu(\pi(w'))}{\mu(w')} -1 \right)^{-1} \leq R(\pi(w')) = R(\pi_{m}(w))
\),
so we have
\begin{align*}
\Vert Q_{w}(f) \Vert_{\infty}
& \leq \mu(w)^{-1/2} R(w)^{1/2} \Vert Q_{w}(f) \Vert_{2} \\
& \leq \mu(w)^{-1/2} R(w)^{1/2} \Vert \eta(w') \Vert_{2}
(\alpha_{n+1} - \alpha_{m+1})^{-1} \left( \frac{\mu(\pi(w'))}{\mu(w')} -1 \right)^{-1} \\
& = \mu(w)^{-1/2} R(w)^{1/2} \mu(w')^{1/2} \left( \frac{\mu(\pi(w')}{\mu(w')} -1 \right)^{1/2} \\*
& \qquad \qquad \qquad \qquad (\alpha_{n+1} - \alpha_{m+1})^{-1} \left( \frac{\mu(\pi(w'))}{\mu(w')} -1 \right)^{-1} \\
& \leq \mu(w)^{-1/2} R(w)^{1/2} \mu(w')^{1/2}
(\alpha_{n+1} - \alpha_{m+1})^{-1} \left( \frac{\mu(\pi(w'))}{\mu(w')} -1 \right)^{-1/2} \\
& = \mu(w)^{-1/2} R(w)^{1/2} \mu(\pi_{m+1}(w))^{1/2}
(\alpha_{n+1} - \alpha_{m+1})^{-1} R(\pi_{m}(w))^{-1/2}.
\end{align*}
The conclusion follows.
\end{proof}
\subsection{Shifts of finite type}
\label{ssec:connes-SFT}
\begin{thm}
\label{thm:connes-SFT}
Let $G$ be an aperiodic, irreducible graph, $X^{G}$ be its associated shift of finite type and $\mu$ be the Parry measure.
The Connes metric from $(C_{\infty}(X^{G}), L^{2}(X^{G}, \mu), D_{X^{G}})$ is infinite.
\end{thm}
The proof will involve some technical lemmas. Let us first lay down some basic tools.
Recall that we write our vertex set $G^{0} = \{ 1, 2, \ldots, I \}$. Also recall that $u_{G}, v_{G}$
are the left and right
Perron eigenvectors for the incidence matrix $A$ with Perron eigenvalue $\lambda_{G}$,
appropriately normalised.
For convenience, we shorten these to $u, v$ and $\lambda$ respectively.
The invariant measure is defined by Equation~\eqref{eq:SFT-measure}.
Since $G$ is aperiodic there exists a vertex $j$ with
$\# t^{-1}\{ j \} > 1$.
Let us assume that $j=1$. It follows then
that for any word $w= e_{1}e_{2} \cdots e_{n}$ of even length with $i(e_{1}) = 1$, $w$ is in
$X^{+}_{n}$.
From the fact that $G$ is irreducible, we may find a word $w= e_{1}e_{2} \cdots e_{p}$ with
$i(e_{1}) = 1 = t(e_{p})$.
For each $k \geq 1$, we define $w_{k} = e_{p}w^{2k}$. Note that $w_{k}$ is in
$X_{2kp + 1}$ and $\pi(w_{k}) = w^{2k}$, which is in $X^{+}_{2kp}$.
We note that $\mu(w_{k}) = \Vert \xi(w_{k}) \Vert_{2} ^{2} = v_{i(e_{p})}u_{1} \lambda^{-2kp}$ and
that $\mu(\pi(w_{k})) = \Vert \xi(\pi(w_{k})) \Vert_{2} ^{2} = v_{1}u_{1} \lambda^{-2kp+1}$.
It follows that
\begin{equation}\label{eq:a}
1 < \frac{\mu(\pi(w_{k}))}{\mu(w_{k}) } = v_{1}v_{i(e_{p})}^{-1} \lambda.
\end{equation}
This is constant in $k$ and we denote its value by $a$ for convenience.
For $K \geq 1$, consider the function $f_{K} = \sum_{k=1}^{K} k^{-1} \eta(w_{k})$.
Notice this function
is in $C_{0}^{\perp}$, so it takes on both positive and
negative values. Secondly, from the definition, we see that
\[
f_{K} | U(w_{k}) = \sum_{k=1}^{K} k^{-1} \left( \frac{\mu(\pi(w_{k}))}{ \mu(w_{k})} - 1 \right)
= ( a - 1 ) \sum_{k=1}^{K} k^{-1}.
\]
Since $f_{K}$ takes on negative values, we conclude that in the quotient $C(X)/\mathbb{C}$, we have
$\Vert f_{K} + \mathbb{C} \Vert_{\infty} \geq \frac{a-1}{2} \sum_{k=1}^{K} k^{-1}$. The obvious
conclusion being that these norms go to infinity as $K$ does. We will now show that
$\Vert [ f_{K}, D] \Vert$ is bounded and the conclusion follows from \cite[Theorem 2.1]{Rie04}.
It follows from part~3 of Lemma~\ref{lemma:zeta} that
\[ \begin{split}
[f_{K}, D] & = \sum_{k=1}^{K} k^{-1} \big( \eta(w_{k}) \otimes \zeta(w_{k})^{*} - \zeta(w_{k}) \otimes \eta(w_{k}) ^{*} \big) \\
& = \left( \sum_{k=1}^{K} k^{-1} \zeta(w_{k}) \otimes \eta(w_{k})^{*} \right)^{*} - \sum_{k=1}^{K} k^{-1} \zeta(w_{k}) \otimes \eta(w_{k})^{*}.
\end{split} \]
Let $T_{K} = \sum_{k=1}^{K} k^{-1} \zeta(w_{k}) \otimes \eta(w_{k})^{*}$. It suffices
to prove that $\Vert T_{K} \Vert$ is bounded, independent of $K$.
First notice that $T_{K}$ is zero on the orthogonal complement of the
span of the $\eta(w_{k}), 1 \leq k \leq K$. Secondly, this set
is orthonormal.
Therefore, in order to control $\nr{T_K}$, it suffices to evaluate the norm of products $\nr{T_K \eta}$ for vectors $\eta$ of the form
\[
\eta = \sum_{k=1}^{K} \beta_{k} \mu(\pi(w_{k}))^{-1/2} (a-1)^{-1/2} \eta(w_{k}).
\]
It follows from Lemma~\ref{lemma:eta} and~Equation~\eqref{eq:a} that $\Vert \eta \Vert_{2}^{2} = \sum_{k=1}^{K} \vert \beta_{k} \vert^{2}$.
We also have
\begin{align*}
T_{K} \eta & = \left[ \sum_{k=1}^{K} k^{-1} \zeta(w_{k}) \otimes \eta(w_{k})^{*} \right]
\sum_{k'=1}^{K} \beta_{k'} \mu(\pi(w_{k'}))^{-1/2} (a-1)^{-1/2} \eta(w_{k'}) \\
& = \sum_{k=1}^{K} \sum_{k'=1}^{K} k^{-1} \beta_{k'} \mu(\pi(w_{k'}))^{-1/2} (a-1)^{-1/2} \langle \eta(w_{k'}) , \eta(w_{k}) \rangle \zeta(w_{k}) \\
& = \sum_{k=1}^{K} k^{-1} \beta_{k} \mu(\pi(w_{k}))^{-1/2} (a-1)^{-1/2} \mu(\pi(w_{k})) (a-1)\zeta(w_{k}) \\
& = \sum_{k=1}^{K} k^{-1} \beta_{k} \mu(\pi(w_{k}))^{1/2} (a-1)^{1/2} \zeta(w_{k}).
\end{align*}
\begin{lemma}\label{lemma:technical-SFT}
For all $k \geq 1$, we have
\begin{enumerate}
\item $P_{2p(k-1) } \xi(\pi(w_{k})) = \lambda^{-2p} \xi(\pi(w_{k-1}))$,
\item $\xi(\pi(w_{k})) - \lambda^{-2p} \xi(\pi(w_{k-1}))$ is in $C_{2pk} \cap C_{2p(k-1)}^{\perp}$,
\item $\Vert \xi(\pi(w_{k})) - \lambda^{-2p} \xi(\pi(w_{k-1})) \Vert^{2}_{2} = u_{1} v_{1} (\lambda - \lambda^{1-2p}) \lambda^{-2pk}$.
\item
\(\displaystyle
\xi(\pi(w_{k})) = \sum_{j=1}^{k} \lambda^{-2p(k-j)} \left[ \xi(\pi(w_{j})) - \lambda^{-2p} \xi(\pi(w_{j-1})) \right] + \lambda^{-2pk}
\).
\end{enumerate}
\end{lemma}
\begin{proof}
The vectors $\xi(w), w \in X_{2p(k-1)}$ form an orthonormal set in $C_{2p(k-1)}$.
The only one of these with a non-zero inner product with $\xi(\pi(w_{k}))$ is
$\xi(\pi(w_{k-1}))$. Hence we have
\begin{align*}
P_{2p(k-1)} \xi(\pi(w_{k})) & =
\frac{ \langle \xi(\pi(w_{k})), \pi(\xi(w_{k-1})) \rangle}{ \langle \xi(\pi(w_{k-1})), \pi(\xi(w_{k-1})) \rangle} \xi(\pi(w_{k-1})) \\
& = \frac{\mu(\xi(\pi(w_{k})))}{\mu( \xi(\pi(w_{k-1})))} \xi(\pi(w_{k-1}))
= \lambda^{-2p} \xi(\pi(w_{k-1})).
\end{align*}
The second part follows immediately from the first. The third follows from the orthogonality of $\lambda^{-2p} \xi(\pi(w_{k-1}))$
and $\xi(\pi(w_{k})) - \lambda^{-2p} \xi(\pi(w_{k-1}))$, so we have
\begin{align*}
\Vert \xi(\pi(w_{k})) - \lambda^{-2p} \xi(\pi(w_{k-1})) \Vert^{2}_{2}
& = \Vert \xi(\pi(w_{k})) \Vert^{2}_{2} - \Vert \lambda^{-2p} \xi(\pi(w_{k-1})) \Vert^{2}_{2} \\
& = u_{1}v_{1}\lambda^{-2kp+1} - \lambda^{-4p}u_{1}v_{1}\lambda^{-2(k-1)p+1} \\
& = u_{1}v_{1} (\lambda - \lambda^{1-2p}) \lambda^{-2kp}.
\end{align*}
The last also follows from the first and an easy induction argument, which we omit.
\end{proof}
In the following computation, we denote
$\xi \big( \pi(w_{j}) ) - \lambda^{-2p} \xi(\pi(w_{j-1}) \big)$ by
$\xi_{j}$, for $ 1 \leq j \leq K$.
We compute
\begin{align*}
T_{K} \eta
& = \sum_{k=1}^{K} k^{-1} \beta_{k} \mu(\pi(w_{k}))^{1/2} (a-1)^{1/2} \zeta(w_{k}) \\
& = \sum_{k=1}^{K} k^{-1} \beta_{k} \mu(\pi(w_{k}))^{-1/2} (a-1)^{1/2} (2pk+1 - D) \xi(\pi(w_{k})) \\
& = \sum_{k=1}^{K} k^{-1} \beta_{k} (u_{1}v_{1} \lambda^{-2pk+1})^{-1/2} (a-1)^{1/2} (2pk+1 - D) \xi(\pi(w_{k})) \\
& = \left( \frac{a-1}{u_{1}v_{1} \lambda} \right)^{1/2} \sum_{k=1}^{K} k^{-1} \beta_{k}\lambda^{pk} (2pk+1 - D) \\*
& \qquad \left[ \sum_{j=1}^{k} \lambda^{-2p(k-j)} ( \xi(\pi(w_{j})) - \lambda^{-2p} \xi(\pi(w_{j-1}))) + \lambda^{-2pk} \right] \\
& = \left( \frac{a-1}{u_{1}v_{1} \lambda} \right)^{1/2} \sum_{k=1}^{K} \sum_{j=1}^{k} k^{-1} \beta_{k} \lambda^{-pk}\lambda^{2pj} (2pk+1 - D) \xi_{j} \\*
& \qquad + \left( \frac{a-1}{u_{1}v_{1} \lambda} \right)^{1/2}\sum_{k=1}^{K} k^{-1} \beta_{k} \lambda^{pk}(2pk+1 - D)\lambda^{-2pk}. \\
\end{align*}
Let us begin by considering the second term on the right which is simply a constant function considered
as a vector in $L^{2}(X, \mu)$. Ignoring the constants in front of the sum, the norm of this vector is bounded by
\begin{align*}
\sum_{k=1}^{K} \vert \beta_{k} \vert k^{-1} (2pk+1 )\lambda^{-pk}
& \leq \sum_{k=1}^{K} \vert \beta_{k} \vert (2p+1) \lambda^{-pk} \\
& \leq (2p+1) \left( \sum_{k=1}^{K} \vert \beta_{k} \vert^{2} \right)^{1/2} \left( \sum_{k=1}^{K} \lambda^{-2pk} \right)^{1/2} \\
& \leq (2p+1) \left( \frac{\lambda^{-2p}}{1 - \lambda^{-2p}} \right)^{1/2} \Vert \eta \Vert_{2}.
\end{align*}
Now we turn to the first term.
For any given $j$, the vector $\xi_{j}$ is in $C_{2pj} \cap C_{2p(j-1)}^{\perp}$
and on this space $1 + 2p(j-1) \leq D \leq 2pj$.
For values of $k \geq j$, we have $0 \leq 2pk +1 -D \leq 2p(k-j+1)$
and, in particular, $\Vert 2pk +1 -D \Vert \leq 2p(k-j+1)$.
Fixing $k$ for the moment, the norm of the vector $\sum_{j=1}^{k} \lambda^{-pk}\lambda^{2pj} (2pk+1 - D) \xi_{j}$ is bounded by:
\begin{multline*}
\sum_{j=1}^k \lambda^{2pj} \lambda^{-pk}(k-j+1)\bigl( u_1 v_1 (\lambda - \lambda^{1-2p}) \lambda^{-2pk} \bigr)^{1/2} \\
\leq C \sum_{j=1}^k \lambda^{-2p(k-j)} (k-j+1)
= C \sum_{j=1}^k j \lambda^{-2p(j-1)}
\end{multline*}
where $C$ gathers the constants and the equality is a change of variable.
Now, by deriving the power series $\sum x^n$ and letting $x=\lambda^{-2p}$ we get
\[
\sum_{j=1}^k j\lambda^{-2p(j-1)} \leq \frac{1}{(1-\lambda^{-2p})^2}.
\]
If we now sum over $k$ and apply the Cauchy--Schwarz inequality, we get
\begin{align*}
\biggl\Vert \sum_{k=1}^{K} \sum_{j=1}^{k} k^{-1} \beta_{k} \lambda^{-pk}\lambda^{2pj} (2pk+1 - D) \xi_{j} \biggr\Vert
& \leq C' \sum_{k=1}^K \abs{\beta_{k}} k^{-1} \\
& \leq C' \nr{\beta}_2 \Bigl({\sum_{k \geq 1} k^{-2}}\Bigr)^{1/2} \leq C'' \nr{\beta}_2.
\end{align*}
Putting all of this together we have shown that $\Vert T_{K} \eta \Vert_{2} $ is bounded above by a constant, independent of $K$, times $\Vert \eta \Vert_{2} $.
This complete the proof of Theorem~\ref{thm:connes-SFT}.
\subsection{Linearly recurrent subshifts}
\begin{thm}
\label{thm:LR}
Let $X$ be a linearly recurrent subshift and
let $\mu$ be its unique invariant measure.
Then the spectral triple
\[
(C_{\infty}(X), L^{2}(X, \mu), D_{X})
\]
has finite Connes distance and the topology induced on the state space of $C(X)$ is the weak-$*$ topology.
\end{thm}
The proof will occupy the remainder of the subsection, and use Proposition~\ref{prop:control-Qw} in a crucial way.
The general idea of the proof goes along these lines:
starting from a function $f \in C_\infty (X)$ with $\nr{ [f,D]} \leq 1$,
Proposition~\ref{prop:control-Qw} allows to control $\nr{Q_w(f)}_\infty$ where $w \in X_n^+$, in terms of~$n$.
Since any such function can be written up to a constant term as
$f=\sum_{w \in X^+} Q_w(f)$, this allows to control the norm of~$f$ in the algebra $C(X) / \mathbb C$.
Eventually, Rieffel's criterion~\cite{Rie99,Rie04} is applied.
First, this lemma is an immediate consequence of Proposition~\ref{prop:LR-measure-clopen}.
\begin{lemma}\label{lem:LR-bound-Rw}
Let $X$ be a linearly recurrent subshift.
There are $C_1, C_2 > 0$ such that for all $n$ and all $w \in X_n$, $C_1 \leq R(w) \leq C_2$.
\end{lemma}
Let us consider now $w \in X_n^+$. Any such $w$ is the prefix of a word of the form $rw$ where $r$ is a return word to~$w$.
Therefore, all sufficiently long right-extensions of $w$ start by a word of the form $rw$, with $r$ some return-word to be picked in a finite set. Besides, the length of $rw$ is always at least $(1+1/K) n$.
Therefore, $w$ has at most $K(K+1)^2$ right-extensions of length $(1+1/K)n$.
As a conclusion, there are at most $K(K+1)^2$ indices $n < k \leq (1+1/K)n$ for which the right-extension of length $k$ of $w$ (say $w'$) is a special word.
A similar result holds for left-extensions.
The conclusion is then that for any $w \in X_n$, the number of indices $n < k \leq n(1+1/K)$ for which there is a $w' \in \pi_n^{-1}(\{w\}) \cap X_k^+$ is bounded above, and this bound is uniform in $n$ (it only depends on $K$).
Consider now a sequence $f_i \in C_\infty$, such that $\nr{[D,f_i]} \leq 1$ for all $i$.
The goal is to extract a converging subsequence from the image of the sequence $(f_i)_i$ in the quotient algebra $C(X)/\mathbb C$.
If we assume that all the $f_i$ belong to $C_0^\perp$ (which is possible up to adding a suitable scalar multiple of the identity), it is then sufficient to prove that the sequence $(f_i)_i$ has a convergent subsequence in $C(X)$.
Since $f_i \in C_0^\perp$, we can write
\[
f_i = \sum_{w \in X^+} Q_w (f_i).
\]
For a fixed $w$ in $X_{n}^{+}$, $ n \geq 1$, we may apply Proposition~\ref{prop:control-Qw} with $m=0$
to conclude that
\begin{equation}\label{eq:Qw-LR}
\begin{split}
\nr{Q_{w}(f_{i})}_{\infty} & \leq R(w)^{1/2} R(\varepsilon)^{1/2} (n+1)^{-1} \mu(w)^{-1/2} \\
& \leq C_0 (n+1)^{-1} \mu(w)^{-1/2},
\end{split}
\end{equation}
where $C_0$ is a constant which does not depend on $w$.
In particular, this is bounded independent of $i$. Since the vector space $F_{w}$
is finite-dimensional, any bounded sequence must have a convergent subsequence.
Enumerate $X^{+} = \{ w_{1}, w_{2}, w_{3}, \ldots \}$.
Let $(f^{1}_{n})_{n \geq 1}$ be a subsequence of $(f_{n})_{n \geq 1}$ such that $Q_{w_{1}}(f^{1}_{n})$ converges.
Inductively define a sequence $(f^{k}_{n})_{n \geq 1}$ as a subsequence
of $(f^{k-1}_{n})_{n \geq 1}$ such that $(Q_{w_{k}}(f^{k}_{n}))_n$ converges.
We now prove that the sequence $(f^n_n)_{n \geq 1}$ converges in $C(X)$.
It is enough to show that it is Cauchy.
The goal is to show that $\nr{f_n^n(x)-f_m^m(x)}_\infty$ goes to zero uniformly in $x$ when $n,m$ tend to infinity.
To prepare this, consider a function $f$ and evaluate
\(
\sum_{w \in X^+} Q_w(f) (x)
\)
for $x \in X$. For a given $x$, infinitely many terms of the sum are zero.
It is possible to rewrite it: if $f \in C_0^\perp$ and $\nr{[D,f]} \leq 1$,
\[
\abs{f(x)} = \Bigl\vert \sum_{n \in \mathbb N} \mathbf{1}_{ \{\pi_n(x) \in X_n^+\}} (n) Q_{\pi_n(x)}(f)(x) \Bigr\vert.
\]
In particular,
\begin{equation}\label{conv-fx}
\Bigl\vert f(x) - \sum_{n=1}^N \sum_{w \in X_n^+} Q_w(f) (x) \Bigr\vert \leq \sum_{n > N} \mathbf{1}_{\{\pi_n(x) \in X_n^+\}} (n) \nr{Q_{\pi_n(x)}(f)}_\infty.
\end{equation}
By the argument above, the cardinality of the set
\[
\bigl\{ n \in [(1+1/K)^k, (1+1/K)^{k+1}) \mid \pi_n(x) \in X_n^+ \bigr\}
\]
is bounded above by $K(K+1)^2$, independently of $k$ and $x$. Call $I_k$ the interval $[(1+1/K)^k, (1+1/K)^{k+1})$. One has
\begin{multline}\label{conv-fx-bis}
\Bigl\vert f(x) - \sum_{n=1}^N \sum_{w \in X_n^+} Q_w(f) (x) \Bigr\vert
\leq \sum_{k \geq k_0} K(K+1)^2 \max \big\{ \nr{Q_{\pi_n(x)}(f)}_\infty \ : \\ \ n \in I_k \text{ such that } \pi_n(x) \in X_n^+ \big\}.
\end{multline}
Now, it turns out that if $n \in I_k$, then $\mu(w)^{-1/2} \leq K^{1/2} (1+1/K)^{(k+1)/2}$, and $1/n \leq (1+1/K)^{-k}$, so using the bound of Equation~\eqref{eq:Qw-LR} with $w = \pi_n(x)$ together with Lemma~\ref{lem:R-LR}, we get
\[
\nr{Q_{\pi_n(x)}(f)}_\infty \leq C \alpha^k, \quad \text{for } \alpha = \Big( 1+\frac{1}{K}\Big)^{-1/2} < 1.
\]
It is crucial to notice that both constants $C$ and $\alpha$ are completely independent of $f$ and $x$ (as long as $\nr{[D,f]} \leq 1$).
In conclusion, the convergence in~\eqref{conv-fx-bis} is geometric, and
\(
\sum_{w \in X^+} Q_w(f)
\)
converges uniformly to $f$ on $X$. In particular, its norm converges.
Back to the sequence $(f^n_n)_{n \geq 1}$. Let $\varepsilon > 0$. First, choose $M$ such that $\nr{\sum_{n \geq M}\sum_{w \in X_n^+} Q_w(f)}_\infty$ is smaller than $\varepsilon/4$ (independent of $f$).
Next, number the elements of $\bigcup_{i < M} X_i^+ := \{ w_1, \ldots, w_L \}$. For each $1 \leq l \leq L$, pick a number $I_l$ such that for all $n,m \geq I_l$,
\[
\nr{Q_{w_l}(f_n^l) - Q_{w_l} (f_m^l)}_\infty \leq \frac{\varepsilon}{2L}.
\]
Pick $I = \max \{I_l \mid 1 \leq l \leq L\}$.
Then, for all $n,m \geq I$, we can compute
\begin{align*}
& \bigl\Vert{f_n^n - f_m^m}\bigr\Vert_\infty = \Bigl\Vert{ \sum_{w \in X^+} Q_{w}(f_n^n - f_m^m) }\Bigr\Vert_\infty \\
& \quad \leq \Bigl\Vert{ \sum_{l=1}^L Q_{w_l} (f_n^n - f_m^m) }\Bigr\Vert_\infty
+ \Bigl\Vert{\sum_{\substack{n \geq M \\ w \in X_n^+}} Q_{w}(f_n^n)}\Bigr\Vert_\infty
+ \Bigl\Vert{\sum_{\substack{n \geq M \\ w \in X_n^+}} Q_{w}(f_m^m)}\Bigr\Vert_\infty \\
& \quad \leq \sum_{l=1}^L \Bigl\Vert{ Q_{w_l} (f_n^n) - Q_{w_l} (f_m^m) }\Bigr\Vert_\infty
+ \Bigl\Vert{\sum_{\substack{n \geq M \\ w \in X_n^+}} Q_{w}(f_n^n)}\Bigr\Vert_\infty
+ \Bigl\Vert{\sum_{\substack{n \geq M \\ w \in X_n^+}} Q_{w}(f_m^m)}\Bigr\Vert_\infty \\
& \quad \leq L \frac{\varepsilon}{2L} + \frac{\varepsilon}{4} + \frac{\varepsilon}{4} = \varepsilon.
\end{align*}
Therefore, the sequence is Cauchy, so it converges in $C(X)$.
\subsection{Sturmian systems}
In this section, it is understood that the subshift in question is $X=X^\theta$.
The following result is a consequence of Theorem~\ref{thm:freq-sturm}.
\begin{lemma}\label{lem:sturm}
Let $X^\theta$ be a Sturmian subshift with $0 < \theta < 1$ irrational.
Let $\theta=[0;a_1, a_2, \ldots]$ be the continued fraction expansion of $\theta$.
Then:
\begin{enumerate}
\item Assume $q_n + q_{n-1} - 1 \leq m < q_{n+1} + q_n - 1$. Then for all $w \in X_m^+$, $R(w) \leq a_{n+1}+1$.
\item For any $n$, there exist $q_n + q_{n-1} \leq m < q_{n+1} + q_{n}$ and $w$ in $X_{m}$ such that ${\mu(\pi(w))}/{\mu(w)} \geq a_{n+1}$.
\item Let $x \in X$. Then, for all $n$,
\[
\# \big\{ m \in \mathbb{N} \cap [q_n + q_{n-1} , q_{n+1} + q_n) \mid \pi_m (x) \in X_m^+ \big\} \leq a_{n+1} + 2
\]
\item $q_n \geq 2^{(n-1)/2}$.
\end{enumerate}
\end{lemma}
\begin{proof}
Point 1 is obtained by direct inspection of the formulas in Theorem~\ref{thm:freq-sturm}.
If $w \in X_m^+$ with $q_n + q_{n-1} \leq m < q_{n+1} + q_n - 1$, then the biggest quotient of the form $\mu (w) / \mu(w')$ for $\pi(w')=w$ is of the form
\[
\frac{\lambda_n - k' \lambda_{n+1}}{\lambda_{n+1}} \leq \frac{\lambda_n}{\lambda_{n+1}} < a_{n+1}+1
\]
for some $0 \leq k' \leq a_{n+1}$.
If $m= q_{n} + q_{n-1} - 1 = (a_n + 1)q_{n-1}+q_{n-2}$, such a quotient is of the form
\(
{\lambda_{n}}/{\lambda_{n+1}} \leq a_{n+1}+1
\).
Similarly for point 2, observe that the frequencies associated with words of length $q_n+q_{n-1}-1$ are $\lambda_{n+1}$ and $\lambda_n$, while the frequencies associated with words of length $q_n + q_{n-1}$ are $\lambda_n$, $\lambda_{n+1}$ and $\lambda_n - \lambda_{n+1}$.
Since $\# X_m^+ = 1$ for all $m$, let $w'$ be the unique word in $X^+_{q_n+q_{n-1}-1}$.
By inspection, $\mu(w') = \lambda_n$ and it has two extensions of frequencies $\lambda_{n+1}$ and $\lambda_n - \lambda_{n+1}$. Let $w$ be its extension of frequency $\lambda_{n+1}$. Then $\mu(w')/ \mu(w) = \theta_{n+1}^{-1} \geq a_{n+1}$.
Point 3 can also be deduced from Theorem~\ref{thm:freq-sturm}: $w \in X_m^+$ if and only if $\mu(w) \neq \mu(w')$ for $w' \in \pi^{-1}(\{w\})$.
Now, $\mu(w)$ can only take $a_{n+1} + 2$ values if $w \in X_m$ and $q_n + q_{n-1} \leq m < q_{n+1} + q_n$.
This proves the result.
Point 4 is classic (see~\cite[Theorem~12]{Khi97}).
\end{proof}
Let us begin with the less positive result, simply because it is easier to prove.
\begin{thm}
\label{thm:sturm-unbounded}
There exists $0 < \theta < 1 $ irrational such that the spectral triple
$(C_{\infty}(X^{\theta}), L^{2}(X^{\theta}, \mu), D_{X^{\theta}})$
has infinite Connes metric.
\end{thm}
\begin{proof}
Choose $a_{1}= 1$. Define $a_{n}$ inductively by
$a_{n+1} = n (q_{n} + q_{n-1})^{2}$. Letting $m$ and $w$ be as in part 2 of Lemma~\ref{lem:sturm},
we have
\[
(m+1)^{-2} \frac{\mu(\pi(w))}{\mu(w)} \geq
(m+1)^{-2} a_{n+1} \geq (q_{n+1} + q_{n})^{-2} a_{n+1} = n.
\]
The conclusion follows from Theorem~\ref{thm:sufficient-for-unbounded}.
\end{proof}
On the more encouraging side, we prove the following.
\begin{thm}
\label{thm:sturm-bounded-ae}
Let $0 < \theta < 1 $ be irrational with $\theta = [0;a_{1}, a_{2}, \ldots ]$. If there exist
constants $C \geq 1$, $s \geq 1$ such that $a_{j} \leq C j^{s}$, then
the spectral triple
$(C_{\infty}(X^{\theta}), L^{2}(X^{\theta}, \mu), D_{X^{\theta}})$
has finite Connes metric and the topology induced on the state space
of $C(X^{\theta})$ is the weak-$*$ topology.
\end{thm}
This result has an immediate consequence.
\begin{cor}
For almost all $\theta \in (0,1)$ (for the Lebesgue measure), the spectral triple $(C_{\infty}(X^{\theta}), L^{2}(X^{\theta}, \mu), D_{X^{\theta}})$
has finite Connes metric and the topology induced on the state space of $C(X^{\theta})$ is the weak-$*$ topology.
\end{cor}
\begin{proof}
By a result of Khinchin~\cite[Theorem 30]{Khi97},
if $\phi$ is a positive function defined on the natural numbers, then the estimate $a_n = O(\phi(n))$ holds for almost all $\theta \in (0,1)$ if and only if $\sum_{n \geq 1}(\phi(n))^{-1}$ converges.
In this case, we consider the function $\phi(n) = n^s$ for $s > 1$.
It follows that for almost all $\theta \in (0,1)$, the numbers $a_n$ satisfy $a_n \leq C n^s$.
In particular, almost all $\theta \in (0,1)$ satisfy the hypotheses of Theorem~\ref{thm:sturm-bounded-ae}.
\end{proof}
We now turn to the proof of Theorem~\ref{thm:sturm-bounded-ae}.
It is actually quite similar to that of Theorem \ref{thm:LR} for linearly recurrent subshifts.
As for linearly recurrent subshift, if $f \in C_0^\perp$, we estimate
\begin{equation}\label{eq:unif-conv}
\Bigl\vert{f(x) - \sum_{n=1}^N \sum_{w \in X_n^+} Q_w(f) (x)}\Bigr\vert \leq \sum_{n > N} \mathbf{1}_{\{\pi_n(x) \in X_n^+\}} (n) \nr{Q_{\pi_n(x)}(f)}_\infty.
\end{equation}
Now, we partition the positive integers into intervals $[q_k + q_{k-1} - 1, q_{k+1} + q_{k} - 1)$.
For $w \in X_n^+$ with $n$ in this interval, we can use Proposition~\ref{prop:control-Qw} together with points 1 and 2 of Lemma~\ref{lem:sturm} to get the following estimate.
This estimate holds for any $m$ in $[q_{k-2} + q_{k-3}-1, q_{k-1} + q_{k-2} - 1)$ such that $\pi_m(w) \in X_m^+$.
\[
\begin{split}
\nr{Q_w (f)}_\infty & \leq R(w)^{1/2} R(\pi_m(w))^{1/2} (n-m)^{-1} \mu(w)^{-1/2} \mu(\pi_{m+1}(w))^{1/2} \\
& \leq (a_{k+1} a_k)^{1/2} (n-m)^{-1} \mu(w)^{-1/2} \mu(\pi_{m+1}(w))^{1/2}.
\end{split}
\]
Now, given the intervals chosen,
\[
(n-m)^{-1} \leq (q_k - q_{k-2})^{-1} = (a_k q_{k-1})^{-1} \leq 2^{-(k/2-1)} \leq \alpha^k
\]
for some $\alpha < 1$.
Furthermore, it results directly from Theorem~\ref{thm:freq-sturm} that $\mu(w)^{-1/2} \leq \lambda_{k+1}^{-1/2}$, and $\mu(\pi_{m+1}(w))^{1/2} \leq \lambda_{k-2}^{1/2}$.
Therefore, we have
\[
\nr{Q_w (f)}_\infty \leq (a_{k+1} a_k)^{1/2} \alpha^k (\theta_{k-1} \theta_k \theta_{k+1})^{-1/2}.
\]
It is straightforward from the definition that $\theta_k^{-1} \leq a_k + 1$. So using the assumption that $a_k = O(k^s)$, we can write
\[
\nr{Q_w (f)}_\infty = O\big( k^{5s/2} \alpha^k \big).
\]
In other words, this is bounded above by a geometric series in $k$.
The rest is similar to the proof for linearly recurrent subshifts: using point 3 of Lemma~\ref{lem:sturm}, we prove that the expressions in Equation~\eqref{eq:unif-conv} are dominated by
\[
\sum_{k \geq k_0} k^s (k^{5s/2} \alpha^k),
\]
for some $k_0 = k_0(N)$. It is essentially the remainder of a geometric series, which does not depend on $x$. Therefore the convergence of $\sum_w Q_w(f)$ to $f$ is uniform.
The rest of the proof is identical as before.
\section{Spectral triples}
\label{sec:ST}
From this point on, we assume that a subshift $(X,\sigma)$ is given. In time, we will assume that it is a shift of finite type, a linearly recurrent subshift, or a Sturmian subshift.
We consider the crossed product $C^{*}$-algebra $C(X) \times \mathbb{Z}$, which is generated by $f \in C(X)$ and a unitary $u$
satisfying $u f = f \circ \sigma^{-1} u$, for all $f$ in $C(X)$. This is represented on $L^{2}(X, \mu)$ by
\begin{align*}
(f \xi) (x) & = f(x) \xi(x), &
(u \xi) (x) & = \xi(\sigma^{-1}(x)),
\end{align*}
for $\xi$ in $L^{2}(X, \mu)$, $f$ in $C(X)$ and $x$ in $X$.
Let $C_{0} = \mathbb{C} 1 $ be the constant functions and,
recalling that $\xi(w)$ denotes the characteristic function
of the set $U(w)$, $w \in X_{n}, n \geq 1$, let
$C_{n} = \Span \{ \xi(w) \mid w \in X_{n} \}$, for
$ n \geq 1$. Notice that $C_{0} \subset C_{1} \subset C_{2} \cdots$, each $C_{n}$ is a finite-dimensional
subspace of $L^{2}(X, \mu)$ and a finite-dimensional $*$-subalgebra of $C(X)$. Moreover, the union of the
$C_{n}$ is dense in both, with the appropriate norms. For convenience, let $C_{-1} = \{ 0 \}$.
Let $P_{n}$ denote the orthogonal projection of $L^{2}(X, \mu)$ on $C_{n}$, for each non-negative $n$.
We let $C_{\infty}(X) = \cup_{n = 1}^{\infty} C_{n}$. We will denote by
$C_{\infty}(X) \times \mathbb{Z}$ the $*$-algebra of operators on $L^{2}(X, \mu)$ generated by $C_{\infty}(X)$ and $u$.
As we indicated above, our main interest is in the crossed product $C(X) \times \mathbb{Z}$. We have here a specific
representation of this $C^{*}$-algebra, but it is a reasonable question to ask if it is faithful.
First, the representation of $C(X)$ on $L^{2}(X, \mu)$ is faithful since we assume our measure $\mu$ has support equal to $X$.
Secondly, we use the fact that, if our system is topologically free, that is, for every $n$ in $\mathbb{Z}$, the set
$\{ x \in X \mid \sigma^{n}(x) = x \}$ has empty interior in $X$, then every non-trivial, closed, two-sided ideal
in $C(X) \times \mathbb{Z}$ has a non-trivial intersection with $C(X)$. (See \cite{EH67} for a precise statement.)
In our case, since the representation of $C(X)$ is faithful, so is that of $C(X) \times \mathbb{Z}$, provided our
system is topologically free. We make this assumption implicitly from now on and remark that it holds
in all of our examples.
We define an operator $D$ as follows. First, we choose a strictly increasing sequence of
positive real numbers, $\alpha_{n}, n \geq 0$, and define
the domain of our operator
\[
\mathcal{D} = \Bigl\{ \sum_{n \geq 0} \xi_{n} \mid \xi_{n} \in C_{n} \cap C_{n-1}^{\perp}, \ \sum_{n} (\alpha_{n} \Vert \xi_{n} \Vert)^{2} < \infty \Bigr\}.
\]
We define
\[
D \xi = \alpha_{n} \xi, \ \xi \in C_{n} \cap C_{n-1}^{\perp}.
\]
\begin{lemma}
\label{lemma:Cn}
Let $n \geq 0$. For all $f$ in $C_{n}$, we have
\begin{enumerate}
\item $f C_{m} \subset C_{m}$, for all $m \geq n$,
\item $f \mathcal{D} \subset \mathcal{D}$,
\item $[D, f] | C_{n}^{\perp} = 0$.
\end{enumerate}
\end{lemma}
\begin{proof}
For the first item, we know that $C_{n} \subset C_{m}$ whenever $m \geq n$ and that $C_{m}$ is a unital subalgebra so that
$f C_{m} \in C_{n} C_{m} \subset C_{m} C_{m} = C_{m}$. For the second, suppose that
$\xi$ is in $C_{m} \cap C_{m-1}^{\perp}$, for some $m > n$. $C_{m}$ and $C_{m-1}$
are invariant under $C_{n}$. Hence so is $C_{m-1}^{\perp}$ and $C_{m} \cap C_{m-1}^{\perp}$.
The second part follows from this.
On the space $C_{m} \cap C_{m-1}^{\perp}$, $D$ is a scalar and hence commutes with $f$.
Taking direct sums over all $m > n$ yields the result.
\end{proof}
\begin{thm}
\label{thm:spectral-triple}
Let $X$ be a subshift.
\begin{enumerate}
\item $(C_{\infty}(X) , L^{2}(X, \mu), D)$ is a spectral triple if and only if the sequence $\alpha_{n}, n \geq 0$ tends to
to infinity.
\item $[D, u]$ extends to a bounded linear operator on $L^{2}(X, \mu)$ if and only if $\alpha_{n} - \alpha_{n-1}, n \geq 1$ is bounded.
\item $(C_{\infty}(X) \times \mathbb{Z} , L^{2}(X, \mu), D)$ is a spectral triple if and only if the sequence $\alpha_{n}, n \geq 0$ tends to
to infinity and $\alpha_{n} - \alpha_{n-1}, n \geq 1$ is bounded.
\end{enumerate}
\end{thm}
We use here Connes' definition of a spectral triple (or $K$-cycle)~\cite[Chapter IV-2]{Con94} (see also~\cite[Def.~9.16]{G-BVF01}).
There is a variety of conditions that may be required on a spectral triple depending on the context.
For example, in the context of quantum spaces, Rieffel~\cite{Rie99,Rie04} requires that a certain metric induced by $D$
on the state space of the algebra coincides with the weak-* topology.
We make no such assumption at this stage, however we shall investigate this Connes metric in Section~\ref{sec:connes}.
We remark also that $D$ is defined
to be a positive operator. It follows that the associated
Fredholm module has a trivial class in $K$-homology and carries no index data.
\begin{proof}
We see from the third part of Lemma~\ref{lemma:Cn}, that for any $f$ in $C_{\infty}(X)$,
$f$ maps the domain of $D$ to itself and from the final part, $[D,f]$ obviously
extends to a bounded linear operator on $L^{2}(X, \mu)$. The final condition is that
$(1+D^{2})^{-1}$ is compact is evidently equivalent to its eigenvalues
converging to zero, and also to the sequence $\alpha_{n}, n \geq 0$ tending to
infinity.
Fix a positive integer $n$ and let $\mathcal{P}_{n}$ be the partition of $X$
given by the cylinder sets:
$\{ U(w) \mid w \in X_{n} \}$. It is can easily be seen that the partition
\[
\sigma(\mathcal{P}_{n}) = \{ \sigma(U(w)) \mid w \in X_{n} \}
\]
is clearly finer than $\mathcal{P}_{n-2}$ while it is coarser than $\mathcal{P}_{n+2}$.
(It is probably easiest to check the cases of $n$ even and odd separately.)
From this it follows that $C_{n-2} \subset uC_{n} \subset C_{n+2}$. Hence, we also have
$C_{n-2}^{\perp} \supset uC_{n}^{\perp} \supset C_{n+2}^{\perp}$ as well.
Let $\xi$ be any vector in $C_{n} \cap C_{n-1}^{\perp}$. We know that
$u \xi$ is in $C_{n+2} \cap C_{n-3}^{\perp}$ and on this space, which is invariant under $D$,
we have $\alpha_{n-2} \leq D \leq \alpha_{n+2}$.
Now, we compute
\[
[D, u] \xi = D u \xi - u D \xi = Du\xi - \alpha_{n} u \xi = (D - \alpha_{n}) u \xi,
\]
and the conclusion follows.
\end{proof}
In particular cases, we will consider the following spectral triple.
\begin{defn}\label{def:DX}
Let $X$ be a subshift and let $\mu$ be a $\sigma$ invariant probability measure with support $X$. The spectral triple $(C_\infty(X), L^2(X,\mu), D_X)$ is defined as above, associated with the sequence $\alpha_n=n$.
\end{defn}
\begin{thm}
Let $X \subseteq \mathcal{A}^{\mathbb{Z}}$ and
$X' \subseteq \mathcal{A}'^{\mathbb{Z}}$ be subshifts with
invariant probability measures $\mu$ and $\mu'$, respectively.
If there exists a homeomorphism
$h : X \rightarrow X'$ such that
$h \circ \sigma|_{X} = \sigma|_{X'} \circ h$ and
$h^{*}(\mu') = \mu$, then $v \xi = \xi \circ h$
is a unitary operator from $L^{2}(X', \mu')$ to
$L^{2}(X, \mu)$ such that
\begin{enumerate}
\item $v C_{\infty}(X') v^{*} = C_{\infty}(X)$,
\item $ v u_{X'} v^{*} = u_{X}$,
\item $v$ maps the domain of
$D_{X'}$ onto the domain of $D_{X}$ and $vD_{X'}v^{*} - D_{X}$ is bounded.
\end{enumerate}
\end{thm}
\begin{proof}
That $v$ is unitary and the first two parts of the conclusion
all follow trivially from the hypotheses. For the last
part, we use the result of Curtis--Lyndon--Hedlund~\cite[Theorem 6.2.9]{LM95} that
$h$ arises from a sliding block code. That is, there
exist positive integers $M,N$ and function
$h_{0}: X_{N+M+1} \rightarrow \mathcal{A}'$ such that
\[
h(x)_{n} = h_{0}(x_{n-M} \ldots x_{n+N}),
\]
for all $x$ in $X$. We lose
no generality in assuming that $M=N$.
It then easily follows that for any $w$ in
$X_{n}, n > N$, $h(U(w))$ is contained in
$U'(w')$, where $w'$ is in $X_{n-2N}$ and is given by
$w'_{i} = h_{0}(w_{i-N} \ldots w_{i+N})$, for all
appropriate $i$. It follows that
\[
v C'_{n-2N} v^{*} \subseteq C_{n}.
\]
A similar result
also holds for $h^{-1}$ and we may assume without loss
of generality, it uses the same $N$. This means that
\[
v C'_{n} v^{*} \supseteq C_{n-2N},
\]
as well. From these two facts, it is easy to see that
$\Vert vD_{X'}v^{*} - D_{X} \Vert \leq 2N$.
\end{proof}
\section{Subshifts}
\label{sec:subshifts}
Let $\mathcal{A}$ be a finite set. We let
$\sigma: \mathcal{A}^{\mathbb{Z}} \rightarrow \mathcal{A}^{\mathbb{Z}} $ denote the left shift
map. That is, $\sigma(x)_{n} = x_{n+1}$, for $x$ in $\mathcal{A}^{\mathbb{Z}} $ and $n$ in $\mathbb{Z}$.
Let $X \subset \mathcal{A}^{\mathbb{Z}}$ be a subshift; that is, it is a closed subset with $\sigma(X) = X$.
Let $\mu$ be a $\sigma$-invariant probability measure on $X$ with support equal to $X$. The system $(X, \sigma)$ always admits
invariant measures, but the hypothesis that it has full support
is non-trivial. It
is satisfied in most cases of interest.
For $n \geq 1$, we let $X_{n}$ denote the words in $X$ of length $n$. That is,
we have
\[
X_{n} = \{ (x_{1}, x_{2}, \ldots, x_{n}) \mid x \in X \}.
\]
We say that such finite words are \emph{admissible}.
For convenience, we let $X_{0}$ be the set consisting of the empty word, which we denote
$\varepsilon$.
For $w$ in $X_{n}$, we define the associated cylinder set
\begin{align*}
U(w) & = \{ x \in X \mid (x_{-m}, \ldots, x_{m}) = w \}, n = 2m+1, \\
U(w) & = \{ x \in X \mid (x_{1-m}, \ldots, x_{m}) = w \}, n = 2m.
\end{align*}
We let $\xi(w)$ be the characteristic function of $U(w)$. The set $U(w)$ is clopen and
$\xi(w)$ lies in both $C(X)$ and $L^{2}(X, \mu)$. We let $\mu(w) = \mu(U(w))$, for
convenience. The fact that we assume the support of $\mu$ is $X$ means that $\mu(w) \neq 0$, for
any word $w$.
We define $\pi : X_{n} \rightarrow X_{n-1}$, for $n > 1$, by
\begin{align*}
\pi(w_{-m}, \ldots, w_{m}) & = (w_{1-m}, \ldots, w_{m}) & & \text{if } n = 2m+1, \\
\pi(w_{1-m}, \ldots, w_{m}) & = (w_{1-m}, \ldots, w_{m-1}) & & \text{if } n = 2m.
\end{align*}
We extend this to $n=1$ by defining $\pi(a)$ to be the empty word, for all $a$ in $X_{1}$.
We also define $U(\varepsilon)$ to be $X$.
Notice with this indexing, we have $U(\pi(w)) \supset U(w)$, for all $w$ in $X_{n}$, $n > 1$.
Of course, the function $\pi$ may be iterated and for all positive integers $k$,
$\pi^{k} : X_{n} \rightarrow X_{n-k}$. This leads to the unfortunate notation
$\pi^{n-m} : X_{n} \rightarrow X_{m}$, when $n > m$. For convenience,
we let $\pi_{m}$ be the map defined on the union of all $X_{n}, n > m$, which
is $\pi^{n-m}$ on $X_{n}$. Thus $\pi_{m}: \cup_{n > m} X_{n} \rightarrow X_{m}$.
We also extend this function to be defined on $X$ by
\begin{align*}
\pi_{2m+1}(x) & = (x_{-m}, \ldots, x_{m}), &
\pi_{2m}(x) & = (x_{1-m}, \ldots, x_{m}).
\end{align*}
Observe that if $w$ is in $X_{n}$ then $\# \pi^{-1}\{ w \} > 1$ if and only if, for any
$w'$ with $\pi(w') = w$, we have $U(w) \supsetneq U(w')$. For
$n \geq 1$, we denote by $X^{+}_{n}$ the $w$ in $X_{n}$ satisfying either condition.
Such words are called (left-\ or right-) \emph{special words}.
Of basic importance in the dynamics of subshifts is the \emph{complexity} of the shift
$X$, which is simply $\# X_{n}, n \geq 1$, regarded as a function on the natural numbers.
Notice first that if $X = \mathcal{A}^{\mathbb{Z}}$ is the full shift, then the number of words
of length $n$ is simply $(\# \mathcal{A})^{n}$, for $n \geq 1$. More generally, if $X$ is a somewhat large subset
of $ \mathcal{A}^{\mathbb{Z}}$, then we reasonably expect the growth of the complexity to
be exponential. To capture the base of the exponent, the \emph{entropy} of
$X$, denoted $h(X)$, is defined to be
\begin{equation}\label{eq:entropy}
h(X) = \lim_{n \rightarrow \infty} \frac{\log ( \# X_{n})}{n}
= \inf \left\{ \frac{\log ( \# X_{n})}{n} \ ; \ n \geq 1 \right\}.
\end{equation}
Of course, it is a non-trivial matter to see the limit exists, and equals the infimum.
This ``configuration entropy'' or ``patch-counting entropy'' agrees with the topological entropy for the dynamical system. See~\cite{LP03,BLR07}.
Secondly, there is some variation in the literature on dynamical systems as to the base with which the logarithm should be taken.
We will use $\log$ to mean natural logarithm throughout.
We also define $R(w)$ for any $w$ in $\cup_{n \geq 1} X_{n}$
\[
R(w) = \sup \Bigl\{ \frac{\mu(w)}{\mu(w')} \mid \pi(w') = w \Bigr\}.
\]
Notice that $R(w) \geq 1$, with strict inequality if and only
if $w$ is in $\cup_{n} X^{+}_{n}$.
\begin{lemma}
\label{lemma:Rw}
For any $w$ in $X^{+}_{n}, n \geq 1$ and $w'$ with $\pi(w') = w$, we have
\[
\left( \frac{\mu(w)}{\mu(w')} - 1 \right)^{-1} \leq R(w).
\]
\end{lemma}
\begin{proof}
Let $\pi^{-1}\{ w \} = \{ w_{1}, \ldots, w_{I} \}$, arranged so that \newline
$ \mu(w_{1}) \leq \mu(w_{2}) \leq \ldots \leq \mu(w_{I})$. Since $w$ is in $X^{+}_{n}$,
we know that $I \geq 2$. Since $U(w)$ is the disjoint union of the sets $U(w_{i}), 1 \leq i \leq I$,
we have $\mu(w_{1}) + \mu(w_{2}) + \ldots + \mu(w_{I}) = \mu(w)$.
It follows that for any $ 1 \leq i \leq I$, we have
\[
\left( \frac{\mu(w)}{\mu(w_{i})} - 1 \right)^{-1} = \frac{\mu(w_{i})}{\mu(w) - \mu(w_{i})} \leq
\frac{\mu(w)}{ \mu(w_{1})} = R(w).
\]
\end{proof}
\subsection{Shifts of finite type}
\label{ssec:sft}
Let $G = (G^{0}, G^{1}, i, t)$ be a finite directed graph. That is, $G^{0}, G^{1}$ are finite sets
(representing the vertices and edges, respectively) and
$i,t$ (meaning 'initial' and 'terminal') are maps from $G^{1}$ to $G^{0}$.
The set of edges in the graph is our symbols, $\mathcal{A} = G^{1}$, and $X^{G}$ consists of all
doubly infinite paths in the graph, \emph{i.e.}
\[
X^{G} = \{ ( x_{n})_{n \in \mathbb{Z}} \mid x_{n} \in G^{1}, t(x_{n}) = i(x_{n+1}), \text{ for all } n \in \mathbb{Z} \}.
\]
This set $X^G$ is a subshift of the set $\bigl(G^1 \bigr)^\mathbb{Z}$ and is called a (nearest-neighbour)
\emph{subshift of finite type}, or simply \emph{shift of finite type}, or SFT.
Associated to the graph $G$ is an incidence matrix $A$. It is simplest to describe if we
set $G^{0} = \{ 1, 2, \ldots, I\}$, for some positive integer $I$. In tis case, $A$ is
an $I \times I$ matrix and
\[
A_{i,j} = \# \{ e \in G^{1} \mid i(e)=i, t(e) = j \}, \ 1 \leq i, j \leq I.
\]
For any $n \geq 1$, $1 \leq i, j \leq I$, $A^{n}_{i,j}$ equals the number of paths of length $n$
from $i $ to $j$.
We say that $G$ is \emph{irreducible} if for each $i,j$, there exists $n$ with $A^{n}_{i,j} > 0$.
We say that $G$ is aperiodic if $X^{G}$ is infinite. For an irreducible, aperiodic
shift of finite type, the matrix $A$ has a unique
positive eigenvalue of maximum absolute value called the Perron eigenvalue, which we denote
by $\lambda_{G}$.
We denote $u_G$ and $v_G$ (or simply $u$ and $v$) respectively the left and right eigenvectors
associated with $\lambda_G$, normalised such that $\sum_k v_k = 1$ and $\sum_k u_k v_k = 1$. The subshift has a unique invariant measure of maximal entropy (see for example~\cite{CP74}) which we refer to as the Parry measure.
It is defined by
\begin{equation}\label{eq:SFT-measure}
\mu (w_1, \ldots, w_n) = u_{i(w_1)} v_{t(w_n)} \lambda^{-(n-1)}.
\end{equation}
We remark that if $G$ is an irreducible graph, then the entropy of the associated
shift of finite type is $h(X^{G}) = \log( \lambda_{G})$.
\subsection{Linearly recurrent subshifts}
\label{ssec:LR}
Linear recurrence (or linear repetitivity) is a very strong regularity condition for a subshift.
The name refers to estimates on the size of the biggest gap between successive repetitions of patterns of a given size.
Equivalently, it refers to the biggest return times in small neighbourhoods of a given size in the dynamical
system $(X,\mathbb Z)$.
\begin{defn}
If $w$ is a finite admissible word of a subshift $X$, a \emph{right return word} to $w$ of $X$ is any word $r$ such that: --~$rw$ is admissible; --~$w$ is a prefix of $rw$; --~there are exactly two occurrences (possibly overlapping) of $w$ in $rw$.
\end{defn}
\begin{defn}
A minimal subshift $X$ is \emph{linearly recurrent} if (or LR) there exists a constant $K$ such that for all $n \in \mathbb{N}$, any word $w \in X_{n}$ and any right return word $r$ to $w$, we have
\[
\abs{r} \leq K \abs{w}.
\]
\end{defn}
It is a bound on the return time in the cylinders $U(w)$ for $w \in X_n$: for any $x \in U(w)$, there is $0 < k \leq K \abs{w}$ such that $\sigma^k(x) \in U(w)$.
Here are a few important consequences of linear recurrence.
\begin{prop}[Durand \cite{Dur00, Dur03}]
Let $X$ be a linearly recurrent subshift. Then $(X,\sigma)$ is uniquely ergodic.
\end{prop}
\begin{prop}[Durand \cite{Dur00, Dur03}]\label{prop:LR-measure-clopen}
Let $X$ be a linearly recurrent subshift with constant $K$, and $\mu$ be its unique invariant measure. Then for all $n \in \mathbb{N}$ and all $w \in X_n$,
\begin{equation}\label{LR-frequencies}
\frac{1}{K} \leq n \mu(w) \leq K.
\end{equation}
\end{prop}
This presentation is actually somewhat backwards. In~\cite{Dur00}, Durand proves that equation~\eqref{LR-frequencies} holds for any invariant measure, and uses it in conjunction with a result of Boshernitzan~\cite{Bos92} to prove unique ergodicity.
\begin{prop}[Durand \cite{Dur00, Dur03}]
Let $(X,\sigma)$ be a linearly recurrent subshift with constant $K$. Then
\begin{itemize}
\item Any right return word $r$ to $w \in X_n$ has length at least $\abs{r} > \abs{w}/K$;
\item For any fixed $w \in X_n$, there are at most $K(K+1)^2$ return words to~$w$.
\end{itemize}
\end{prop}
Also proved in~\cite{Dur00}, is the fact that any linearly recurrent subshift has sub-linear complexity in the sense that $\# X_n \leq C n$ for some constant $C$.
Proposition~\ref{prop:LR-measure-clopen} has an immediate consequence.
\begin{lemma}\label{lem:R-LR}
Let $X$ be a linearly recurrent subshift. Then there exists a constant $C > 1$ such that for all $w \in X_n^+$,
\[
C^{-1} \leq R(w) \leq C.
\]
\end{lemma}
Note that the class of linearly recurrent subshifts contains the class of primitive substitution subshifts.
Many well-known examples, such as the Fibonacci or the Thue--Morse subshifts are given by primitive substitutions, hence are linearly recurrent, and are therefore covered by our results (see~\cite{Fog02}, for example for a survey on substitutions).
\subsection{Sturmian systems}
\label{ssec:sturmian}
There are many different equivalent ways to define a Sturmian sequence (see~\cite{Arn02}, for example).
We give here the definition as the coding of an irrational rotation of angle $\theta$ on a circle.
A crucial ingredient to identify properties satisfied by a Sturmian sequence is the continued fraction expansion of the number $\theta$. We remind the reader of a few of its properties.
The results on continuous fraction, which are stated here without proof, can be found in the classic book by Khinchin\footnote{Also transcribed ``Khinchine'' in the French-language publications.}~\cite{Khi97}.
To fix notations, $\lfloor \theta \rfloor$ (integer part of $\theta$) refers to the unique integer satisfying $\theta-1 < \lfloor \theta \rfloor \leq \theta$, and $\{\theta\} := \theta - \lfloor \theta \rfloor \in [0,1)$ refers to the fractional part of $\theta$.
Let $\theta$ be a real number, which we assume irrational. Let $\theta_0 = \theta$ and $\theta_1 = \{\theta\}$, so that $\theta = a_0 + \theta_1$, with $a_0 \in \mathbb{Z}$ and $\{\theta \} \in [0,1)$.
Then there are a unique $a_1 \in \mathbb{N}$ and $0 < \theta_2 < 1$ such that
\[
\theta = a_0 + \frac{1}{a_1+\theta_2},
\]
namely $a_1 = \lfloor 1/\theta_1 \rfloor$ and $\theta_2 = \{1/\theta_1\}$.
By iteration, there is a sequence $a_2, a_3, \ldots$ of positive integers such that for all $n$,
\[
\theta = a_0 + \cfrac{1}{a_1 +
\cfrac{1}{\ddots
\cfrac{1}{a_n+\theta_{n+1}}}}.
\]
The number $\theta$ is entirely determined by its sequence of \emph{partial quotients} $(a_n)_{n \geq 0}$, and we write $\theta = [a_0; a_1, a_2, \ldots]$.
The finite continued fraction (truncating after the term $a_n$)
is called the $n$-th convergent and is denoted $[a_0; a_1, \ldots, a_n]$. It is a rational number, which has a unique representation as an irreducible fraction $p_n/q_n$.
It is a standard result that $p_n$ and $q_n$ satisfy the recurrence relations
\[
\left\{ \begin{aligned}
p_{n} & = a_n p_{n-1} + p_{n-2} \\
q_{n} & = a_n q_{n-1} + q_{n-2}
\end{aligned}\right.
\quad
\text{with the convention }
\left\{ \begin{aligned}
p_{-2} = 0, & \ \ p_{-1} = 1 \\
q_{-2} = 1, & \ \ q_{-1} = 0 \, .
\end{aligned}\right.
\]
\begin{lemma}\label{lem:cont-frac}
Let $0 < \theta < 1$ be irrational, so that $\theta = [0;a_1, a_2, \ldots]$. Let $(\theta_n)_{n\geq 0}$ be defined as above.
We define $\lambda_n (\theta)$ (or just $\lambda_n$) by
\(
\lambda_n = \prod_{i=1}^n \theta_i
\),
for $n \geq 1$ (with the convention $\lambda_0 = 1$).
Let $p_n/q_n$ be the $n$-th convergent.
Then the following holds.
\begin{enumerate}
\item For all $n$,
\(
\theta = ({\theta_n^{-1} p_{n-1} + p_{n-2}})\big/({\theta_n^{-1} q_{n-1} + q_{n-2}}).
\)
\item For all $n$, $q_n p_{n-1} - p_n q_{n-1} = (-1)^n$.
\item For all $n$, $\theta_n^{-1} q_{n-1} + q_{n-2} = \lambda_n^{-1}$.
\item For all $n$, $\lambda_{n+1} =(-1)^n (\theta q_n - p_n)$.
\end{enumerate}
\end{lemma}
\begin{proof}
The first two points are classic (see for example Theorem~2 and the proof of Theorem~7 in~\cite{Khi97}).
The third point is proved by induction. For $n=1$, this is the equality $\theta_1^{-1} = \lambda_1^{-1}$.
Assume it holds for fixed $n$.
Then
\[ \begin{split}
\theta_{n+1}^{-1} q_{n} + q_{n-1} & = \theta_{n+1}^{-1}\big( (a_n+ \theta_{n+1}) q_{n-1} + q_{n-2} \big) \\
& = \theta_{n+1}^{-1}\big( \theta_n^{-1} q_{n-1} + q_{n-2} \big) \\
& = \theta_{n+1}^{-1} \lambda_n^{-1} = \lambda_{n+1}^{-1}.
\end{split}
\]
For the fourth point, we start apply points 1, 2 and 3 in succession:
\[
\begin{split}
(-1)^n(\theta q_n - p_n) & = (-1)^n \frac{q_n(\theta_{n+1}^{-1} p_n + p_{n-1}) - p_n(\theta_{n+1}^{-1} q_n + q_{n-1})}{\theta_{n+1}^{-1} q_n + q_{n-1}} \\
& = (-1)^n \frac{q_n p_{n-1} - p_n q_{n-1}}{\theta_{n+1}^{-1} q_n + q_{n-1}}
= (-1)^{2n} \lambda_{n+1} = \lambda_{n+1}.
\end{split}
\]
\end{proof}
\begin{defn}
Sturmian sequences of irrational parameter $0 < \theta < 1$ are defined as the sequences $w \in \{0,1\}^{\mathbb{Z}}$ such that
\[
w_n = \begin{cases}
0 & \text{if } \{n \theta - x\} \in I, \\
1 & \text{otherwise},
\end{cases}
\]
where $x$ is a real number, $\{y\} = y- \lfloor y \rfloor$ is the fractional part of the real number $y$, and $I$ is either $[0,1-\theta)$ or $(0,1-\theta]$
Let $X^\theta$ be the set of all Sturmian sequences of parameter $\theta$.
\end{defn}
It is well known that $X^\theta$ is a closed shift-invariant subspace of the full shift.
By irrationality of $\theta$, it is aperiodic and minimal.
\begin{prop}
If $X^\theta$ is a Sturmian subshift with irrational $\theta$, then $\# X^\theta_n = n+1$. It implies that $\# (X_n^\theta)^+ = 1$ for all~$n$.
\end{prop}
It is well known that the subshifts $X^\theta$ are uniquely ergodic, and the frequency of the letter $1$ is equal to the length of the interval $I$, \emph{i.e.}\ $\theta$ (the frequency of the letter $1$ is defined as the measure of the cylinder set associated with the word $1 \in X^\theta_1$ for the unique invariant measure).
The measure of the cylinder sets for a Sturmian subshift is very well controlled in terms of the partial quotients.
This fact can be seen as a consequence of the three-distances theorem.
We use the three distance theorem the way it is presented in~\cite{AB98} (noting that our $\lambda_{n+1}$ is their $\eta_n$, by point~4 of Lemma~\ref{lem:cont-frac}). The relationship between this theorem and the frequencies of Sturmian sequences is established in~\cite{Ber96}.
\begin{thm}[\cite{AB98,Ber96}]\label{thm:freq-sturm}
Let $X^\theta$ be a Sturmian subshift of parameter $0 < \theta < 1$ irrational.
If $kq_n + q_{n-1} \leq m < (k+1)q_n +q_{n-1}$ for some $n \geq 1$ and $0 < k \leq a_{n+1}$, then the frequencies $\mu(w)$ ($w \in X^\theta_m$) are in the set:
\[
\bigg\{ \big(\lambda_n - k \lambda_{n+1} \big),\ \lambda_{n+1} ,\ \big( \lambda_n - (k-1) \lambda_{n+1} \big) \bigg\}.
\]
If $m= (k+1) q_n + q_{n-1} -1 $, the third frequency does not occur.
\end{thm}
Remark in particular that if $m= q_n + q_{n-1} -1 = (a_n+1) q_{n-1} + q_{n-2} -1$, then the $\mu(w)$ is either $\lambda_{n}$ or $\lambda_{n-1} - a_n \lambda_n = \lambda_{n+1}$ for $w \in X_m^\theta$.
\section{Summability}
The goal of this section is to study the summability of the operator $D_{X}$ as introduced in Definition~\ref{def:DX}, for a shift space $X$.
For $p \geq 1$, the
spectral triple $D_X$ is said to be
\emph{$p$-summable} if $(1+D_X^2)^{-p/2}$ is trace class; and \emph{$\theta$-summable} if for all $t>0$, $e^{-tD_X^2}$ is trace class.
Recall the definitions from Section~\ref{sec:subshifts}, in particular Equation~\eqref{eq:entropy}.
Also note that in our construction earlier, $\dim (C_{n}) = \# X_{n}$, for all $n \geq 1$, while
$\dim(C_{n} \cap C_{n-1}^{\perp}) = \# X_{n} - \# X_{n-1}$, for all $n \geq 0$.
\begin{thm}
\label{thm:theta-summable}
Let $X \subset \mathcal{A}^{\mathbb{Z}}$ be a subshift and $D_{X}$ be defined as in Definition~\ref{def:DX}.
\begin{enumerate}
\item If $s > h(X)$, then $e^{-s D_{X} } $ is trace class.
\item If $s > 0$ is such that $e^{-s D_{X} }$ is trace class, then $s \geq h(X)$.
\end{enumerate}
\end{thm}
\begin{proof}
For the first part, choose $s > s' > h(X)$. There exists $n_{0} \geq 1$ such that
$\frac{1}{n} \log(\# X_{n}) < s'$, for all $n \geq n_{0}$. Hence, we have
$\# X_{n} \leq e^{ns'}$ and $e^{-sn} \# X_{n} \leq e^{n(s'-s)}$, for $n \geq n_{0}$. Since $s' < s$ the series
$e^{n(s'-s)}$ is a summable geometric series. It follows that $e^{-sn} \# X_{n} $ is also summable.
Also, we have
\[
\Tr(e^{-sD_{X}}) = \sum_{n =0}^{\infty} e^{-sn} \dim(C_{n} \cap C_{n-1}^{\perp})
\leq \sum_{n =0}^{\infty} e^{-sn} \dim(C_{n}).
\]
Since $\dim (C_n) = \# X_n$, this completes the proof of the first part.
Conversely, suppose that $e^{-s D_{X} } $ is trace class. This operator is positive and its trace is
\[
\Tr(e^{-s D_{X}} ) = \sum_{n=0}^{\infty} e^{-sn}( \dim(C_{n}) - \dim(C_{n-1})).
\]
An Abel transform (summation by part) on the partial sum gives:
\[
\sum_{n=0}^{N} e^{-sn}( \dim(C_{n}) - \dim(C_{n-1}))
\geq \sum_{n=0}^{N-1} (1 - e^{-s} ) e^{-sn} \dim(C_{n}).
\]
Since the left-hand side converges, the series
$\sum e^{-sn} \dim(C_{n})$ is convergent and
hence the terms go to zero. Thus, we have
\[
0 = \lim_{n \rightarrow \infty} e^{-sn} \dim(C_{n})
= \lim_{n \rightarrow \infty} e^{-sn + \log(\dim(C_{n}))}
= \lim_{n \rightarrow \infty} \bigl( e^{-s + \frac{1}{n} \log(\# X_{n})} \bigr)^{n}
\]
We conclude that for $n$ sufficiently large, $e^{-s + \frac{1}{n} \log(\# X_{n})}$
is less than $1$. On the other hand we know that
$\frac{1}{n}\log(\# X_{n} )$ tends to $h(X)$. The conclusion follows.
\end{proof}
\begin{thm}
\label{thm:finite-summable}
Let $X \subset \mathcal{A}^{\mathbb{Z}}$ be a subshift and $D_{X}$ be defined as in Definition~\ref{def:DX}.
\begin{enumerate}
\item If, for some constants $C, s_{0} \geq 1$,
$\# X_{n} \leq C n^{s_{0}}$, for all $n \geq 1$, then $D_{X}$ is
$s$-summable for all $s > s_{0} $.
\item If $D_{X}$ is
$s$-summable for some $s > 0$, then there exists $C \geq 1$ such that
$\# X_{n} \leq C n^{s}$, for $n \geq 1$.
\end{enumerate}
\end{thm}
\begin{proof}
For the first part, let $s > s_0$ and compute
\begin{multline*}
\Tr\bigl( (1+ D_{X}^{2})^{-s/2} \bigr) = \lim_{N \rightarrow \infty}
\sum_{n=0}^{N} (1 + n^{2})^{-s/2} \big( \dim(C_{n}) - \dim(C_{n-1}) \big) \\
= \lim_{N \rightarrow \infty} \bigg[ \sum_{n=1}^{N} \Big( \big(1 + n^{2} \big)^{-s/2} - \big(1 + (n+1)^{2} \big)^{-s/2} \Big) \dim(C_{n}) \\
+ \big(1 + N^{2}\big)^{-s/2} \dim(C_{N}) \bigg]
\end{multline*}
The second term $(1 + N^{2})^{-s/2} \dim(C_{N})$ tends to zero
from the hypothesis. For the first term, we denote
\[
S_N := \sum_{n=1}^{N} \bigl( (1 + n^{2})^{-s/2} - (1 + (n+1)^{2})^{-s/2} \bigr) \dim(C_{n})
\]
for convenience.
Consider the function $f(x) = -(1 + x^{2})^{-s/2} $.
Its derivative is $f'(x) = s x(1 + x^{2})^{-s/2 - 1}$ which is positive and decreasing for $x \geq 1$.
By an application of the mean value theorem to this function on the interval $[n, n+1]$, we obtain
\[
\big(1 + n^{2}\big)^{-s/2} - \big(1 + (n+1)^{2} \big)^{-s/2} \leq s n ( 1 + n^{2})^{-s/2 -1} \leq sn^{-s-1}.
\]
We multiply by $\dim(C_{n})$ and sum. Since $s > s_0$, we obtain
\[
S_{N} \leq s \sum_{n=1}^{N} n^{-s-1} \dim(C_{n})
\leq s \sum_{n=1}^{N} C n^{s_0-s-1}
< \infty.
\]
For the second statement, assume $D_X$ is $s$-summable for a fixed $s$, and
let $\beta_{n}, n \geq 0$ be any $\ell^{1}$ sequence.
We denote $r_n := \sum_{m \geq n} \abs{\beta_m}$.
Define a bounded operator $B$ on
$L^{2}(X, \mu)$ by setting it equal to $r_n$ on the space
$C_{n} \cap C_{n-1}^{\perp}$, for all $n \geq 0$. Notice that $B$ is positive and commutes with $D_{X}$.
The operator $(1+D_X^{2})^{-s/2}B$ is then a positive, trace class operator so, for every $N \geq 1$,
we have (line 2 to line 3 is a summation by parts):
\begin{align*}
\infty & > \Tr \Big( (1+D_{X}^{2})^{-s/2}B \Big) \\
& \geq \sum_{n=0}^{N} (1 + n^{2})^{-s/2}
r_n \big( \dim(C_{n}) - \dim(C_{n-1}) \big) \\
& \geq \sum_{n=0}^{N-1} \dim(C_{n})
\bigl[ r_n (1 + n^{2})^{-s/2} - r_{n+1} (1 + (n+1)^{2})^{-s/2} \bigr] \\
& \geq \sum_{n=0}^{N-1} \dim(C_{n})
\bigr[ (r_n -r_{n+1}) (1 + n^{2})^{-s/2} \bigl]
= \sum_{n=0}^{N-1} \dim(C_{n})
\bigr[ \vert \beta_{n} \vert (1 + n^{2})^{-s/2} \bigl].
\end{align*}
We have shown that for any $(\beta_{n})_{n \geq 0} \in \ell^1$, the sequence
$(\beta_{n} \dim(C_{n}) (1 + n^{2})^{-s/2})_{n \geq 0}$ is also in $\ell^{1}$. It follows that
$(\dim(C_{n}) (1 + n^{2})^{-s/2})_{n \geq 0}$ is bounded.
The conclusion follows after noting that $(1 + n^{2})^{s/2} \leq C n^{s}$, for some constant $C$ and all $n \geq 1$.
\end{proof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,856 |
\section{Introduction}
A \emph{Bloom Filter} is a very basic data structure which, given a set of n elements, allows us to quickly decide whether a given element is in the set or not. The main advantage of Bloom Filters is that they are very memory efficient --- a Bloom Filter only requires space linear in the number of elements in the set, while other data structures use memory linear in the size of the represented elements in the set. When the elements stored in the set do not have a succinct representation, this is a very significant advantage. For example, consider strings, with average size of 800 bits. A hashtable for storing 100,000,000 such strings would require at least 800*100,000,000 bits, so a hard disk must be used for the table, and lookups would be rather slow. A basic Bloom Filter based structure would only require 145,000,000 bits, which can easily be stored in the main memory. On the other hand, the Bloom Filter achieves this at a certain cost. A Bloom Filter has a certain probability of returning a wrong answer. The error is one sided: if the key is in the set, the Bloom Filter will always return the correct answer, but if the key is not in the set, it might return a wrong answer. However, for many applications, it is possible to overcome this problem, and still gain from the low space requirements of the Bloom Filter.
The main use of the Bloom Filter is to reduce the memory that the data structure uses. The basic Bloom Filter~\cite{bloom} (invented in 1970) used $n\log e$ memory bits and returned the answer using a single probe to memory, with error probability of $\frac{1}{2}$ (for a false positive). One way to reduce the error probability is to run the basic Bloom Filter $k$ times, therefore it would require $nk\log e$ memory bits and $k$ memory probes in order to answer a query.
During the past few years, several papers have been published on Bloom Filter~\cite{BM99,Mitzenmacher02,CM03,CKRT04,pagh05}. Most of which provided methods for reducing the memory and the number of probes required, but only considered the case where $k$ is big enough. One more disadvantage of these newer methods is that they do not allow ``insertion'' operations, which were possible to perform using the original Bloom Filter technique. Yet another disadvantage of these newer methods is that they require universal hash functions. Such functions are computationally inefficient, or have large memory requirements.
In this paper we provide a new data structure that can replace Bloom Filters, and has lower space requirements. Our data structure requires $nk+o(n)$ memory bits (which is optimal up to $o(n)$), and each query takes $O(1)$ memory probes. However, like most of the other Bloom Filter replacements, our data structure is static and does not support insertions. Building our data structure requires $O(n)$ preprocessing time and $O(n)$ memory. This data structure is based on solving equations, and uses hash functions. We only require hash functions that are \emph{pairwise} independent.
In addition, we suggest a similar data structure that requires only $nk$ memory bits, $O(\log n)$ query time, and $O(n^2)$ preprocessing time. However, this data structure requires uniform hash functions.
\subsection{Applications of Bloom Filters}
Bloom Filters, as well as Bloom Filter replacements such as the one we suggest, have many applications. A good survey of Bloom Filter uses can be found in~\cite{broder02network}. A few examples are given below.
\emph{Dictionaries:}
Early versions of UNIX's spell checker used a Bloom Filter of the dictionary instead of the dictionary itself. This Bloom Filter left several words misspelled, but the memory in these days was valuable resource and the memory it save was worth it~\cite{McIlroy82, MM90}.
The Bloom Filter was proposed as a method to succinctly store a dictionary of unsuitable passwords for security purposes by Spafford~\cite{Spafford92}. Manber and Wu describe a simple way to extend the technique so that passwords that are within edit distance 1 of the dictionary word are also not allowed~\cite{MW94}. In this setting, a false positive could force a user to avoid a password even if it is not really in the set of unsuitable passwords.
\emph{Databases:}
Bloom Filters can also be used for differential files~\cite{Gremillion82, Mullin83}.
Suppose that all the changes to a database that occur during the day are stored in a differential file and are updated back to the database only at the end of a day. During that day, every read from the database should first be checked in that differential file to be sure that the record read is the most recent. This file might be large, so reading through it can be slow, as opposed to querying a database, but still obligated. A possible solution to this problem is keeping a Bloom Filter of the records that have changed. Here, a false positive forces a read of the differential file even when a record has not been changed.
\emph{Internet Cache Protocol:}
Fan, Cao, Almeida, and Broder describe Summary Cache, which uses Bloom Filters for Web cache sharing~\cite{FCAB00}. In this setup, proxies cooperate in the following way: on a cache miss, a proxy attempts to determine if another proxy cache holds the desired Web page; if so, a request is made to that proxy rather than trying to obtain that page from the Web. For such a scheme to be effective, proxies must know the contents of other proxy caches. In Summary Cache, to reduce message traffic, proxies do not transfer URL lists corresponding to the exact contents of their caches, but instead periodically broadcast Bloom Filters that represent the contents of their cache. If a proxy wishes to determine if another proxy has a page in its cache, it checks the appropriate Bloom Filter. In the case of a false positive, a proxy may request a page from another proxy, only to find that that proxy does not actually have that page cached. In that case, some additional delay has been incurred. But the load on the proxy servers was reduced therefore making them work faster.
\emph{Caching for Google's BigTables:}
BigTable is a distributed storage system for managing structured data that is designed to scale to a very large size: petabytes of data across thousands of commodity servers. Many projects at Google store data in BigTables, including web indexing, Google Earth, and Google Finance. These applications place very different demands on the BigTable, both in terms of data size (from URLs to web pages to satellite imagery) and latency requirements (from back end bulk processing to real-time data serving). Despite these varied demands, BigTable has successfully provided a flexible, high-performance solution for all of the above Google products. In some of the BigTable applications most of the queries aren't in the table. In BigTables Bloom Filter is used to determine whether a query is in the BigTable in first place, thus reducing disk accesses. A Bloom Filter can be also used in the client side as well to reduce the communication and latency.
\section{Outline}
The structure of this paper is as follows: In section~\ref{l_dictionary} we define the dictionary data structure and give a high-level view of our method, as well as a basic result. In section~\ref{l_improved_dictionary} we show how to improve the data structure to support queries in $O(1)$ time, and how to do the preprocessing in $O(n)$ time. In section~\ref{l_practicale_improvements} we show several methods to reduce constants hidden in these space complexity, which may be important in practice. In section~\ref{l_simple_hash_functions} we explain why and how simple pairwise independents hash function are enough. In section~\ref{l_membership_query} we show how to use the dictionary data structure in order to get a good Bloom Filter replacement.
\section{Dictionary Based on Matrix Solving}
\label{l_dictionary}
Dictionaries are data structures that hold key-value pairs. This section describes a method for concise representation of dictionaries with one sided errors, in the spirit of Bloom Filters.
\begin{definition}
{A one sided error dictionary (U,k,n)} is a data structure that holds values for keys. It is a mapping from $x_1,x_2,\ldots,x_n\in U$ to $d_1,d_2,\ldots,d_n\in \{0,1,\ldots ,2^k-1\}$. Given a key $x_i$, a dictionary allows retrieving $d_i$. However, given a key $x$ which is not one of the $x_i$'s it may return any value.
\end{definition}
We now show how to build a dictionary which requires a storage space of $nk+o(n)$ bits. The high level concept behind our method is solving equations. Assume we have a fully random hash function $h$ from $U$ to $n$ variable equation in $GF(2^k)$ (we later show how to remove the fully random assumption later), i.e. $h:U\rightarrow GF(2^k)^{n}$. We go over all the $x_i$'s and we write the equation $h(x_i)\cdot \vec{b}=d_i$. We get $n$ equations with $n$ variables. If these equations are \emph{independent} we can solve them in $O(n^3)$ time. This can be done in a one time preprocessing, after which we can store the hash function $h$ and the vector $\vec{b}$ as our data structure. The vector $\vec{b}$ requires $nk$ bits space. To answer a query $x$ we apply $h$ on $x$ and compute $h(x)\cdot\vec{b}$ and return the answer. If $x$ is one of the $x_i$'s we get the correct $d_i$. If $x$ is not one of the $x_i$'s we might return an erroneous answer. The overall query time is $O(n)$.
However, this process only works when we get an \emph{independent} set of equations. We now examine the probability of obtaining such an independent equation set.
\begin{thm}
The probability that our method generates an \emph{independent} set of $n$ equations on $n+c$ variables in the field $GF(2^k)$ is at least $1-\frac{1}{2^{kc}(2^k-1)}$
\end{thm}
\begin{proof}
We order the generated equations according to the order in which they are constructed. The set of the equations is dependent when there exist $i$ such that equations $1,2,\ldots,i-1$ and equation $i$ are dependent. The probability that equation $i$ and equations $1,2,\ldots,i-1$ are dependent is at most $\frac{(2^k)^i}{(2^k)^{n+c}}$ (the probability is even lower when there are dependent equations before that index).
We apply the union bound and get that the probability that there exists an $i$ such that the equation $i$ and the equations before it are dependent is at most $\sum^{n}_{i=0} \frac{(2^k)^i}{(2^k)^{n+c}}<\frac{1}{2^{kc}(2^k-1)}$
\end{proof}
\begin{cor}
Even for $c=0$ we get an independent set of equations with constant probability. Therefore we need to run the preprocessing algorithm $O(1)$ time, each time with a different hash function, in order to get an independent set of equations.
\end{cor}
The main disadvantage of this data structure is that it requires $O(n)$ time in order to answer a query. One possible improvement can be achieved by using {$t$-sparse equations}.
\begin{definition} {$t$-sparse equations} are equations of the form $\sum^{n}_{i=1} a_i$, where $|\{a_i|a_i\ne 0\}|\le t$.
\end{definition}
Using $t$-sparse equations the query time shrinks to $t$ memory probes, $O(t)$ time.
However we need at least $m=n(1+e^{-t-\epsilon})$ variables in our equations set in order to have a full independent equations set.
\begin{thm}
If we have $n$ $t$-sparse random equations in less than $m=n(1+e^{-t-\epsilon})$ variables, the equations will be dependent with high probability.
\end{thm}
\begin{proof}
When we have $n$ $t$-sparse random equations on $m=n(1+e^{-t-\epsilon})$ there are some variables that we do not use. Because we can look on it as throwing $t\times n$ balls to $m$ cells. The expected number of empty cells is $m(1-\frac{1}{m})^{tn}\approx me^{-\frac{tn}{m}}$. Therefore the expected number of variables we use in our equations is $m(1-e^{-\frac{tn}{m}})$. If $m(1-e^{-\frac{tn}{m}})<n$, we get $n$ equations on less then $n$ variables and therefore they will not be independent.
\end{proof}
Actually if we take $n(1+e^{-t})$ we will have a good probability to get independent set of equations.
Note that the preprocessing of the ``sparse'' data structure is $O(tn^2)$, using the Wiedemann algorithm~\cite{Wiedemann86} for solving sparse linear equations.
\section{Improved Dictionary}
\label{l_improved_dictionary}
We now show how to reduce the query time to $O(1)$ memory probes. We also reduce the preprocessing time to $O(n)$. The high level idea behind the method suggested in this section is to divide $x_1,x_2,\ldots,x_n$ randomly to small buckets, and to run the same algorithm on each of the buckets.
We can randomly hash the keys to $\frac{n}{s}$ buckets using hash function $h_1:U\rightarrow \{1,2,\ldots,\frac{n}{s}\}$. The expected number of keys in each bucket would be $s$, and if $s$ is big enough, with high probability there will not be a bucket with more then $2s$ keys (if there such a bucket we can choose another hash function $h_1$ and so on). Querying for $x$ is done by simply applying $h_1(x)$ and going to the $h_1(x)$'th data structure. In that data structure we query for $x$ as done in section~\ref{l_dictionary}. The $h_1(x)$ data structure does not contain more then $2s$ keys, so it would take $O(s)$ time to answer the query. The preprocessing is now performed by choosing $h_1$ and checking if there is no bucket with more than $2s$ keys. If there is such a bucket, we choose another hash function $h_1$. This is done $O(1)$ times. We then divide the keys $x_1,x_2,\ldots,x_n$ to the buckets and run the same preprocessing method described in section~\ref{l_dictionary} on each bucket.
Overall it would take $O(\frac{n}{s}s^3)=O(ns^2)$. The memory that this data structure consumes is $nk+O(\frac{n}{s}\log n)$ memory bits. The $O(\frac{n}{s}\log n)$ is required in order to maintain pointers to each of the data structures. Naturally, our method works best when $s$ is small. However, if we reduce $s$ too much we we lose the fact that with high probability there is no bucket which is bigger then $2s$, and the $O(\frac{n}{s}\log n)$ becomes significant.
We solve this problem by using a two-level hashing. We first explain the preprocessing and then show how to run a query. Given $x_1,x_2,\ldots,x_n$ we hash them using $h_1:U\rightarrow \{1,2,\ldots,\frac{n}{\log^2 n}\}$, which we now only require to be pairwise independent, to $\frac{n}{\log^2 n}$ buckets. It might be the case that there are some buckets which more then $2\log^4 n$ keys. We call such big buckets \emph{bad buckets}. We choose another $h_1$ hash function only if we will get more then $\frac{n}{\log^2n}$ keys hashed to bad buckets.
\begin{thm}
The probability that there are more then $\frac{n}{\log^2n}$ keys hashed to bad buckets is at most $\frac{1}{2}$
\end{thm}
\begin{proof}
We denote by $B_i$ the number of keys hashed to bucket $i$. Using Markov's inequality we get:
$$Pr\left[Bucket\ i\ is \ bad \right]=Pr\left[B_i>2\log^4 n\right]=Pr\left[B_i>2\log^2 E(B_i)\right]<\frac{1}{2\log^2 n}$$
Denote by $X_i$ the event that $x_i$ is hashed to a bad bucket, and by $X=\sum^{n}_{i=1} X_i$ the number of keys hashed to a bad bucket. $Pr\left[ X_i=1 \right]<\frac{1}{2\log^2 n}$ therefore $E(X)<\frac{n}{2\log^2 n}$. $Pr\left[ X > \frac{n}{\log^2 n} \right]<Pr\left[ X > 2E(X) \right]<\frac{1}{2}$ by markov inequality.
\end{proof}
\begin{cor}
It takes $O(n)$ time to find a hash function $h_1$ that we can use for the rest of the procedure.
\end{cor}
After we find a good hash function $h_1$, we deal with all the keys that are hashed to a bad bucket using a regular dictionary data structure. It takes at most $O(\frac{n}{\log n})=o(n)$ bits (we can easily modify it to take $O(\frac{n}{\log^c n})$ bits for any constant $c$).
Denote by $B_i$ the number of keys hashed by $h_1$ to bucket $i$. Each good bucket $i$ (such that $B_i<2\log^4 n$) is splitted again to sub-buckets using $h_{2,i}:U\rightarrow \{1,2,\ldots,\frac{B_i}{\frac{1}{2}\sqrt{\frac{\log n}{k}}}\}$ (we now assume that $h_{2,i}$ is fully random, in section~\ref{l_simple_hash_functions} we show how to relax this assumption). If we get a sub-bucket which is bigger then $\sqrt{\frac{\log n}{2k}}$ we choose another $h_{2,i}$.
\begin{thm}
When we split a bucket to a sub-buckets the probability that there exist sub-bucket which more then $\sqrt{\frac{\log n}{2k}}$ keys hashed to it is at most $\frac{1}{2}$
\end{thm}
\begin{proof}
The expected number of keys hashed to a sub-bucket is $\frac{1}{2}\sqrt{\frac{\log n}{k}}$.
Using Chernoff's inequality we get that the probability for each sub-bucket to have more then $\sqrt{\frac{\log n}{2k}}$ is much smaller then $\frac{1}{\log^4 n}$. Using the union bound we get that the probability that there exist a sub-bucket with more then $\sqrt{\frac{\log n}{2k}}$ is smaller then $\frac{1}{2}$, since we have less then $\frac{\log^4 n}{2}$ sub-buckets.
\end{proof}
\begin{cor}
It takes $O(B_i)$ time to find such an $h_{2,i}$. Overall, finding a hash function $h_{2,i}$ for all $i$'s requires $O(n)$ time.
\end{cor}
We now have many smaller dictionary sub-problems. Each one of them has a size of less then $\sqrt{\frac{\log n}{2k}}$. We solve each one of them using the method mentioned in section~\ref{l_dictionary}. For each sub problem we get a random matrix of size bounded by $\sqrt{\frac{\log n}{2k}}\times\sqrt{\frac{\log n}{2k}}$ over $GF(2^k)$. The number of different such matrices is at most $2^{k(\sqrt{\frac{\log n}{2k}})^2}=\sqrt{n}$. Thus we can list all the different matrices and solve them in advance in time $O(\sqrt{n}\log^{1.5} n)$, and the list would require $O(\sqrt{n}\log n)$ memory bits.
Thus the preprocessing takes $O(n)$ time, since we can solve each sub-problem by simply looking in the list.
We store the data structure as follows. We store all the keys which map to bad buckets using a regular dictionary, with $o(n)$ memory bits. We store a big array of less then $n$ words, each consisting of $k$ bits which are the concatenation of all the sub-buckets in all the buckets. We also store a select data structure which gives us the ability to jump in $O(1)$ memory probes to each of the buckets and sub-buckets. It requires $o(n)$ memory bits as well. Finally, we store all the hash functions. In section~\ref{l_simple_hash_functions} we show how they can be stored. Overall we use $nk+o(n)$ memory bits.
To answer a query we simply use $h_1$ in order to see to which of the bucket we need to go. If it is a bad bucket, we look for the query in the regular dictionary data structure. Otherwise we use $h_{2,i}$ in order to find in which sub-bucket the query falls. All the operation up to this point take $O(1)$ time, and we use one probe to the memory to retrieve $h_{2,i}$. We use the dictionary data structure of the sub-bucket in order to answer the query. It takes $O(1)$ probes to the memory (we retrieve $\sqrt{\frac{\log n k}{2}}$ bits in these probes, and in the last probe we take a word), but it takes $O(\sqrt{\frac{\log n }{2k}})$ time to retrieve the answer. In order to reduce that time to $O(1)$ we have two options: we can either use sparse equations or we can construct a table holding all the answers to all of the possible equations on all of the possibles assignments, and answer the query in $O(1)$ time by probing a table for getting the answer\footnote{We can play a little more with the size of each sub-bucket in order to do this in $o(n)$ space}.
\section{Practical Improvements}
\label{l_practicale_improvements}
We now examine a few practical improvements for our method.
\emph{Sparse equations: } Whenever we use the solution of section~\ref{l_dictionary} (even inside the sub-buckets) we can use $\ln n $ sparse equations set (in the sub-bucket case it is $\ln \log n$). This still works fine even when we use only $n$ variables, therefore it requires $nk+o(n)$ memory bits. Note that this will not work if we take only even number of variables per equation.
Another sparse equations improvement is to create equations which will be more or less local i.e. the $\{i |a_i\ne 0 \}$ will be close to each other. This way need less memory probes, because in each memory probe we can get $O(\log n)$ continues bits.
\emph{Another counting argument: } If we make each sub-bucket bigger, we can gain in the $o(n)$ overhead. Denote by $s$ the maximum number of keys hashed to a sub-bucket. For each such sub-bucket (from section~\ref{l_improved_dictionary}). In section~\ref{l_improved_dictionary} we had a certain preprocessing analysis. We now give an alternative one. In each sub-bucket we hash keys to $\{1,2,\ldots,s^2\}$. With probability of at least $\frac{1}{2}$ there will not be any collision in this hash. If we do have a collision we choose another hash function. On average, $2$ bits are required to store which hash function we use in each sub-bucket. We now have a list of at most $s$ keys from the universe $\{1,2,\ldots,s^2\}$, where each key gets a value in $GF(2^k)$. Note that if we have the same set of keys in two different sub-buckets, we can use the same set of equations even if they do not get the same values --- being a full rank equations set does not depand on the values (the free vector).
Thus, the number of different sets of equations we use is $s^2 \choose s$. For $s<\frac{\log n}{2\log\log n}$ we get $o(\sqrt{n})$ different equations sets.
For each of the equations sets we compute the inverse and store it in a hashtable. The naive way to perform the preprocessing using this technique takes $\sum^{\#sub-bucket}_{i=1}O(sub-bucket-size^2)=O(n\frac{\log n}{\log\log n})$ time, because we need to multiply the inverse matrix by the data for each sub-bucket. However we can collect $O(\log n)$ sub-buckets that map to the same matrix (inverse matrix) and multiply the same matrix by $O(\log n)$ different values vectors. We get $O(\log n)$ speed up in time using word operations. Therefore the preprocessing running time shrinks back to $O(n)$. Making the equations $O(\ln \log n)$ sparse and local we get $O(1)$ query time as well\footnote{using tables as well}.
\emph{A real $nk$ solution: } We can get rid of the extra $o(n)$, by solving $n$ equations in $n$ variables. Each equation will be $\ln n$ sparse equation. The preprocessing time takes $O(n^2)$ using the block Wiedemann algorithm~\cite{villard-study}, and the query takes $O(\log n)$ time. Note that we need to use a uniform hash function for this result.
\section{Using simple hash functions}
\label{l_simple_hash_functions}
We only assume a truly random hash function inside the buckets. Each bucket consist of at most $\log^4 n$ keys. Therefore we can construct hash function by simply using array $R$ of $\log^8 n$ random numbers and a pairwise independent hash function $h:U\rightarrow \{0,1,\ldots,\log^8 n\}$. The result for the new hash function is $R[h(x)]$. Given that we hash at most $\log^4 n$ keys. The probability that there exist two keys that use the same random number is less then $\frac{1}{2}$. Therefore we got a random enough hash function with probability $\frac{1}{2}$. If we store $2\log $ hash functions like this, with probability bigger then $1-\frac{1}{n}$ each bucket will have at least one hash function which will satisfied it. The only extra space required is $O(\log^9 n)$ memory bits.
\section{Membership Queries}
\label{l_membership_query}
We first define a membership data structure.
\begin{definition}
{A Membership data structure(n,k) for $x_1,x_,\ldots,x_n\in U$} is a data structure that allows answering membership queries. Given a query $x$ where $x$ is one of the $x_i$'s, the data structure always returns $1$, and given a query $x$ where $x$ is not one of the $x_i$ it returns 0 with probability of at least $2^{-k}$.
\end{definition}
We can easily build a membership data structure given a dictionary data structure. We simply choose random pairwise independent hash function $h:U\rightarrow \{0,1,\ldots,2^k-1\}$ and we store a dictionary that map $x_i$ to $h(x_i)$.
In order to check if $x$ is in the data structure we simply query $x$ from the dictionary data structure and check if it's value equal to $h(x)$. If $x$ is in the data structure it will always return $1$.
\begin{thm}
If $x$ isn't in the data structure we will return $1$ with probability $2^-k$.
\end{thm}
\begin{proof}
We choose the hash function independent from the dictionary data structure. Therefore the answer of the query $x$ from the dictionary data structure, if $x$ isn't a member is a $k$-bit string which is independent to $h(x)$. Then the probability that they are equal is $2^{-k}$ because $h(x)$ is random.
\end{proof}
\section{Conclusions and Open problems}
We have suggested a new data structure that can replace Bloom Filters. This data structure allows maintaining a dictionary mapping keys to values, and allows retrieving the value for a key with a one sided error. Our method has significant advantages over Bloom Filter and other previously know Bloom Filter replacements. It uses only $nk+o(n)$ memory bits (which is optimal up to $o(n)$), and each query takes $O(1)$ memory probes. Also, we only require pairwise independent hash function.
We have also suggested a similar data structure, that has an even lower space requirement, of only $nk$ memory bits. However, it has a $O(\log n)$ query time and requires $O(n^2)$ preprocessing time. Also, this data structure requires uniform hash functions.
Despite its advantages, the method we suggest, like several other Bloom Filter replacements, does not allow ``insertion'' operations, which the original Bloom Filter technique does support.
We believe the preprocessing phase of our algorithm can be distributed easily. In fact, we believe it should be distributed in most applications, due to the memory it consumes.
There are several directions open for future research. First, it will be interesting to see if it is possible to design a data structure which only requires one pass on the input elements and with small additional memory. Also, it may be possible to develope a fully \emph{dynamic} data structure, with space requirements lower than those of the traditional Bloom Filter.
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,205 |
Q: Disconnection issues with azure service bus relay We are running some long-running test apps with Azure Service Bus relay over http, hosted in a windows service and most of the time, these run fine for 2-3 days. However every so often an internal network glich may occur (e.g. firewall reboots) that kills the internet connection.
At this point, the relay is dropped in Azure and our web app can no longer communicate with the on-premise service.
I would have thought that the Azure relay client was fault-tolerant - in that if it realises that it's lost connection with Azure then it will re-establish the connection andf if it can't keep trying until it can.. but it appears that this is not the case. This seems pretty fundamental...?
Only once have I ever seen a "System.ServiceModel.CommunicationException" where the service can't communicate on the internet, and that was when the client was starting up and trying to establish the connection in the first place.
Is there any advice or feedback on handling transient disconnections through the relay service (as it's a cloud --> on-prem direction then the client can't AFAIK ping the server).
A: If you are still experiencing issues, you may want to contact Azure support to understand why it is disconnecting. The Relay client should reconnect if something happens to the existing connection.
You may want to add ConnectionStatusBehavior to your ChannelFactory to have it output when the status for the connection changes. It will contain the error that caused it to change status.
var connectionStatusBehavior = new ConnectionStatusBehavior();
connectionStatusBehavior.Online += ConnectionStatusOnlineMethod;
connectionStatusBehavior.Offline += ConnectionStatusOfflineMethod;
channelFactory.Endpoint.Behaviors.Add(connectionStatusBehavior);
A: This issue is solved by Microsoft in version 2.6.5 of Microsoft Azure Service Bus dll. After 1 month of testing it seems to work.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,886 |
\section{Introduction}\label{secIntro}
The soft X-ray excess is a contribution to the 0.2-2 keV flux
in some Type I AGN beyond that predicted by
extrapolating the hard X-ray power-law. It
was first reported by \citet{arna85}, who suggested that it was caused by
thermal emission from the hot inner portion of the AGN accretion disk.
Early observational work by \citet{turn89} using EXOSAT and subsequently
by Walter \& Fink (1993; WF93) using ROSAT further explored the properties
of the soft excess in an attempt to conclusively determine its origin.
\citet{turn89} found their results to be consistent with the
soft excess arising from the high-energy tail of
the thermal accretion disk emission for AGN, but WF93 found
that their measurements using a combination of X-ray
measurements from ROSAT and Ginga and
UV fluxes from the International Ultraviolet Explorer (IUE)
were inconsistent with simple thick or thin accretion disk models.
They also discovered that the ROSAT spectral indices ($\alpha_{\rm x}$)
of AGN with soft excesses were strongly correlated with the
strength of the excess.
The results of WF93 were later verified by \citet{walt94} using
simultaneous IUE and ROSAT observations.
Several alternative theories for the origin of the soft excess have
since been proposed. The current models tend to favor
either reprocessing of thermal disk emission via Compton scattering in
thermal plasmas (e.g. \citealt{kawa01}, \citealt{nied06}) or
relativistically broadened absorption (e.g. \citealt{schu07}).
Models invoking atomic processes
to generate the soft excess were originally proposed by \citet{gier04}, who
noted that the soft excess shows very consistent ``temperature''
across AGN with a wide variety of black hole masses.
\citet{schu06} recently proposed an alternative picture
to the usual wind model for atomic origins. Their ``failed''
wind model does not require the massive outflow from the accretion
disk usually required to make an atomic origin viable.
Several additional theories have also been proposed, including Compton
reflection of hard X-ray photons by the dense, low-ionization gas
in the accretion disk, resulting in an emergent spectrum that
is very steep in the soft X-ray regime (\citealt{ross93}; \citealt{sobo07};
\citealt{done07}).
Alternatively, hard X-ray photons could be absorbed by the
disk instead of being reflected, and the absorbed energy
would be re-emitted as soft
X-ray photons with spectral indices that depend on the properties
of the disk \citep{roza02}.
Another popular class of model is
the slim disk model, originally proposed by \citet{much82}, in which
super-Eddington accretion causes changes in the properties of the standard
thin disk, causing it to become geometrically thick and optically
thin in its inner region and emit high-energy photons \citep{chen04}.
For more recent theoretical treatments of slim disks, see e.g.
\citet{hein06} and \citet{hein07}.
After WF93, much of the observational work on the
soft excess focused on the X-ray
properties at the expense of the UV. The seminal
paper from \citet{boll96}, which first reported the different distributions
of $\Gamma_{\rm x}$ seen in Narrow-Line Seyfert 1 galaxies (NLS1s)
and normal Seyfert 1 galaxies (BLS1s) is one example. However, it is
often difficult to distinguish between the various competing models
based only on goodness of fit to X-ray spectra (e.g. \citealt{sobo07};
\citealt{piro97}),
and each of the competing models has its drawbacks. Comptonization
models require nearly constant temperatures, and absorption models tend
to produce sharper absorption lines than desirable, for example.
In Grupe et al. (1998, 2004; G98, G04), large samples of Seyfert 1 galaxies
with strong soft excesses were drawn from the full set
of optically-identified ROSAT All-Sky Survey (RASS) sources.
Some of their conclusions were similar to those of
WF93, but in neither paper did the authors examine the
UV fluxes of their sample. Since the publication of WF93, a number
of papers have examined
the UV properties of a handful of soft excess AGN (\citealt{puch95a};
\citealt{puch95b}) and NLS1 galaxies (\citealt{kura00}; \citealt{leig04}).
Other work has focused on large samples of AGN with data from
multiple wavelength regimes (e.g. \citealt{stra05}, \citealt{main07}
\citealt{kell08}),
but there have been no attempts to study the UV properties of a
moderately large, uniformly-selected sample of soft excess AGN.
The samples of G98 and G04 were selected to show unusually soft
ROSAT spectra, so these AGN all show significant soft
excesses. The samples were also selected uniformly in their X-ray
properties, and they contain reasonably large numbers of objects.
We use Galaxy Evolution Explorer (GALEX) fluxes to study
the UV properties of these objects, determining the shape and
relative strength of the Big Blue Bump (BBB). By measuring the
BBB directly and relating its properties to the soft excess, we
can provide additional constraints on the physical mechanism responsible
for generating the soft X-ray excess. In \S\ref{secObservations} we
discuss the observations we collected and the extraction of the necessary
parameters. In \S\ref{secAnalysis} we discuss the analysis
we perform on the extracted parameters, and in \S\ref{secModels}
we compare our results with the predictions of theories for the
origin of the soft excess.
Luminosities in this paper are calculated using $H_{0}=72\ {\rm km s^{-1}}$,
$\Omega_{m}=0.27$ and $\Omega_{\Lambda}=0.73$.
\section{AGN Sample}\label{secObservations}
Grupe et al. (1998, 2004) selected samples of soft,
X-ray bright AGN at high Galactic latitude from the RASS.
They required that their objects all have ROSAT hardness ratios (HR)
less than zero, yielding a sample of AGN with relatively strong
soft excesses.
We acquired GALEX Release 3 (GR3)\footnote{http://galex.stsci.edu/GR3}
images of the G98 and G04 AGN wherever possible. Measuring
the Near-UV ($NUV$, $\lambda_{eff}=2271$\AA) and Far-UV
($FUV$, $\lambda_{eff}=1528$\AA) fluxes from the GR3 images,
we constructed a sample of 54 AGN with measurements of both the
UV and soft X-ray fluxes. These AGN are listed in Table \ref{tabGalaxies}.
We extracted X-ray count rates and spectral indices for the
AGN in our sample from Grupe et al. (2001, 2004) wherever possible,
and from Grupe et al.
(1998, 1999) otherwise. Following the convention in these papers,
we list X-ray spectral indices in energy units, i.e.
$F_{\nu} \propto \nu^{-\alpha_{\rm x}}$, where $\alpha_{\rm x}$ is measured
in the ROSAT band (0.2-2.0 keV). This differs from the
convention of WF93, who list photon indices ($\Gamma_{\rm x}=\alpha_{\rm x}+1$,
where $N_{\nu}\propto\nu^{-\Gamma_{\rm x}}$). We have accounted
for this difference
when comparing with their results.
The spectral indices for galaxies in the Grupe et al.
catalogs are higher than for the average AGN, as expected for a sample
of soft excess AGNs, but our $\langle\alpha_{\rm x}\rangle$ is
even higher than the average of the WF93 sample (2.1 compared to 1.5 in
WF93). This shift
in $\langle\alpha_{\rm x}\rangle$ is due
primarily to the inclusion of a large Narrow-Line
Seyfert 1 (NLS1) subsample, as NLS1s are known to exhibit softer
X-ray continua (larger $\alpha_{\rm x}$; \citealt{boll96}).
Our AGN sample has only three objects (NGC 4593, Mrk 142 \& 478) in common with
the WF93 sample, despite covering roughly the same ranges in
redshift and X-ray flux. This is due to selection effects,
as WF93 required that their objects have UV (International
Ultraviolet Explorer; IUE), 5 GHz radio continuum and hard X-ray (Ginga)
flux measurements in addition to their ROSAT fluxes.
We supplemented the information in the Grupe et al. catalogs with
IRAS 25$\mu m$ fluxes from the NASA Extragalactic Database
(NED\footnote{http://nedwww.ipac.caltech.edu},
various authors). We found 25$\mu m$ fluxes for only 17 of the 54
objects in our sample, so we use the IRAS fluxes only to verify that our
primary strength indicator for the BBB is unbiased with
respect to the strengths reported by WF93 (see Section \ref{secObservables}).
The majority of the GALEX images available for
our sample come from the GALEX All-Sky Imaging Survey (AIS), which
have $\sim$100 s exposure per field. Two objects
(Mrk 1048 and PG 1244+026) also had deeper Medium Imaging Survey
exposures, and Markarian 1048 had another, still deeper, exposure from
the Guest Investigator program. QSO 0056-36 also had a second AIS exposure.
The GALEX exposure times associated with each object are listed in Table
\ref{tabGalaxies}, along with several other important parameters
including UV fluxes, X-ray count rates and
H$\beta$ line widths.
We required that all objects in our sample have detections in both the
$NUV$ and $FUV$, but this restriction did not result in excluding any objects
from our sample.
We divided our AGN into Narrow-Line Seyfert 1 (NLS1) and normal
Seyfert 1 (BLS1) classes based on the width of the
${\rm H}\beta$ emission line. All objects with
${\rm FWHM(H}\beta)<2000\ {\rm km\ s^{-1}}$ were classified as NLS1s.
We used the line widths listed in \citet{grup04a} wherever
possible and widths from \citet{grup99} otherwise, classifying
29 of our 54 AGN as NLS1s.
Markarian 734, which is listed only in the \citet{grup99} catalog,
has FWHM(H$\beta$) and $\alpha_{\rm x}$ similar to four NLS1s that would
be classified as BLS1s based on their \citet{grup99} line widths
(see Table \ref{tabReclassified}).
This suggests that the classification of Mrk 734 as a BLS1 may be
erroneous. Removing it from the sample has no significant effect on our
conclusions.
\subsection{Flux Extraction}
We measured GALEX $FUV$ and $NUV$ count rates within $18''$ photometric
apertures for each AGN in our sample. We converted the measured count rates
to magnitudes using the GALEX photometric zero-points of \citet{morr05},
\begin{equation}
m_{FUV}=-2.5\log(C_{FUV})+18.82
\end{equation}
\begin{equation}
m_{NUV}=-2.5\log(C_{NUV})+20.08
\end{equation}
where $C_{x}$ is the count rate in bandpass $x$. To compute
the Galactic extinction corrections, we averaged the
reddening law of \citet{card89} across the $FUV$ and $NUV$ effective
area curves,
\begin{equation}\label{eqExtinction}
R_{\rm X} = \frac{\int^{\lambda_{2}}_{\lambda_{1}} R(\lambda)T(\lambda)d\lambda}
{\int^{\lambda_{2}}_{\lambda_{1}} T(\lambda)d\lambda},
\end{equation}
where $R(\lambda)$ is the \citet{card89} R-value at wavelength $\lambda$,
and $T(\lambda)$ is the filter bandpass. We found ${\rm R}_{FUV}=8.24$
and ${\rm R}_{NUV}=8.10$. The R-values and
${\rm E}\left(B-V\right)$ color excesses for each line of sight \citep{schl98}
were used to compute total extinction and correct the measured
fluxes for each object. We used the AB-magnitude relation to convert
the dereddened magnitudes to UV flux densities, and we
used PIMMS to solve for $F_{\nu}({\rm 2\ keV})$
for our AGN using the X-ray count rates and spectral indices
recorded in the Grupe catalogs. Grupe et al. fixed column
densities at the Galactic
value unless $N_{H,fit}>N_{H,gal}+2\times10^{20}\ {\rm cm^{-2}}$,
in which case the fitted value was used.
Determining $F_{\nu}$ in this way assumes that $\alpha_{\rm x}$
provides a good description
of the X-ray spectrum across the entire ROSAT energy range.
This assumption is not perfect and is likely to do worse in objects
with steeper spectra, so some results may be biased.
However, the number of objects with extremely steep spectra is limited
(4 objects with $\alpha_{\rm x}>3$), and the uncertainties on these
indices are relatively large, so any biases in the measurements are
covered by the error budget.
\subsection{Black Hole Masses}\label{secBlackHole}
We use black hole masses and Eddington ratios ($L/L_{\rm edd}$)
from \citet{grup04c}, which include 30 of our 54 AGNs. These black hole
masses were determined using the \citet{kasp00} relations, which
was calibrated empirically using reverberation
mapped AGNs. The calibration sample included several AGN
with luminosities similar to the AGN in our sample, so
the Kaspi relation
should yield reasonably robust black hole masses.
\citet{bent06} reported a different scaling relation
with a power law index of $0.52\pm0.04$, which is in agreement with the value
expected from theory. If we use the Bentz relation instead of the
Kaspi relation, we find significantly larger black hole masses
than computed by \citet{grup04c}, but this is not unexpected since
the stellar continuum has not been subtracted from $L_{5100\ \AA}$
for our AGN sample, resulting in an over-estimate of the radius of
the Broad Line Region (BLR).
The alternative masses have a significant impact on some
of the measured correlations, which can be seen by comparing the
correlation coefficients in Tables \ref{tabBentz} and
\ref{tabPhysicalCorrelation}. Unsurprisingly, using the alternative
$L_{\lambda}(5100\ {\rm \AA})$--$R_{\rm BLR}$ relation has the largest impact
on correlations with $L_{\lambda}(5100\ {\rm \AA})$; the other changes are
rarely significant. Because we
have no information on the host galaxies of our AGN,
we have elected to use the empirically calibrated Kaspi
relation. This will add scatter to our inferred black hole
masses, but based on the few qualitative differences between
Tables \ref{tabBentz} and \ref{tabPhysicalCorrelation} we
infer that the potential to introduce
or hide correlations is limited.
We might also consider the impact of radiation pressure
on the derived black hole masses, as described by \citet{marc08}.
Qualitatively, the impact of radiation pressure should result in higher
masses for systems radiating closer to their Eddington rate, and
\citet{marc08} found that, after applying this correction, the Eddington
ratios of NLS1 systems are less extreme than result from applying the
Bentz and Kaspi relations. Computing black hole masses using the Marconi
relation rather than the Kaspi relation yields masses that are, on average,
0.2 dex larger. The new masses are correlated with the old masses
with $r_{s}=0.69$.
However, Marconi et al. failed to account for
the lower Eddington ratios and reduced radiation pressure implied by
the adjusted black hole masses. As a result, their results overestimate
black hole masses in systems where the corrections for radiation pressure
are significant, and the difference between the ``true'' black hole masses
and the results calculated using the Kaspi relation will be less than
the 0.2 dex implied by applying the Marconi relation.
\citet{netz09} found that black hole masses determined using the Marconi
relation are distributed differently from black hole masses in type 2 AGNs,
suggesting that radiation pressure is not important in nearby AGNs. However,
\citet{marc09} in turn suggested that the differences found by \citet{netz09}
can be attributed to scatter in the underlying scaling relations rather than
a lack of radiation pressure support in the BLR. Nevertheless,
\citet{marc09} and \citet{netz09} agree that the \citet{marc08}
relation is unable to successfully reproduce the ``true,'' underlying
mass distribution, indicating that more work is needed.
For the rest of this paper,
we consider masses resulting from the Kaspi relation with the caveat
that the systematic uncertainties associated with the alternative methods
for calculating black hole mass must also be considered.
The masses resulting from applying the Kaspi relation are more properly
called virial products, which differ from the true black hole
mass by a geometric factor $f$. There is significant debate in the
literature on the proper value of this constant.
Using the dispersion of the H$\beta$\ emission line to
measure the virial products, \citet{onke04} found that a statistical
correction of $f=5.5$ was required to bring their virial masses
into agreement with black hole masses predicted by the
${\rm M_{BH}}-\sigma_{*}$ relation.
By contrast, \citet{wats07} found a correction of $f=2.2$ for
AGN in the \citet{grup04a} sample using the line dispersion or $f=0.55$
using FWHM. The latter value disagrees with the results of \citet{kasp00},
who found $f=0.75$. \citet{wats07} also
found that there is a systematic difference between the geometric corrections
required to bring the BLS1 and NLS1 samples into agreement with the
$M_{BH}-\sigma_{*}$ relation. Given this disagreement,
we choose not to apply a geometric
factor and simply use the virial products.
As a result, the absolute masses and Eddington ratios
we use are incorrect, but there will be
little effect on the measured correlations as long as $f$
is a constant. If the geometric corrections required by NLS1s and
BLS1s do indeed differ, the impact of using virial products instead
of actual black hole masses might be significant.
\section{Correlation Analysis}\label{secAnalysis}
In this section,
we examine the differences in several measurable parameters between
NLS1s and BLS1s. We also study the relationships between
the parameters themselves. We examine several
observables, including flux ratios and $\alpha_{\rm x}$, as well as the
physical characteristics ($M_{BH}$, $L/L_{\rm edd}$ and $L$)
that determine the properties of each AGN.
\citet{walt93} found that the strength of the soft X-ray excess,
measured using hard X-ray fluxes from Ginga and soft X-ray fluxes
from ROSAT, correlates well with the ROSAT spectral index
(WF93, Fig 7). Based on this result, they used $\Gamma_{\rm x}$ as a
proxy for the strength of the soft excess. We take a similar approach,
using $\alpha_{\rm x}$ instead of $\Gamma_{\rm x}$, to examine the
relationships between the soft X-ray excess and the UV
properties of the AGN in our sample. However, it is important to note
that when we discuss the ``soft X-ray excess'' below, we actually mean
the shape of the soft X-ray continuum.
\subsection{Observables}\label{secObservables}
In Figure \ref{figSlope}, we compare an indicator for the
strength of the BBB with respect to the hard X-ray continuum
$\biggl(\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV}) \biggr)$ with
$\alpha_{\rm x}$ to verify that the correlation between the strength
of the BBB and the soft excess, as reported by WF93, also appears in
our sample.
We find a significant correlation in both the NLS1 and
BLS1 samples as well as in the merged
sample, as indicated in Table \ref{tabFluxCorrelation}.
It is apparent that the majority of the BLS1s lie on or near the
WF93 relation, but the NLS1s are located
systematically above the WF93 best-fit power law.
Computing the best-fit relation to our data points in the figure yields
\begin{equation}\label{eqAlphaFit}
\alpha_{\rm x}=(0.84\pm0.13)\log\biggl[\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})\biggr]+(0.85\pm0.15)
\end{equation}
which is steeper than the WF93 best-fit, which has slope $0.68\pm0.1$. The
two fits overlap in the regime occupied by the BLS1s, and the steeper slope
of our fit is driven by the NLS1s in our sample.
A two-dimensional KS test confirms that the NLS1 and BLS1 samples
occupy a different region in the parameter
space at the 99.5\% confidence.
Figure \ref{figBumpCumulative} shows
that the NLS1 and BLS1 samples occupy similar ranges in bump strength,
but the NLS1 sample shows extended tails at both ends.
We also computed the ratio
$\biggl(\nu F_{\nu}(2271\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})\biggr)$ between
the $NUV$ and X-ray fluxes, which is analogous to $\alpha_{\rm ox}$.
The distributions of the flux ratio in both the NLS1 and BLS1
samples are shown in Figure \ref{figAlphaOx}. It is apparent
that the NLS1 sample has more objects with high flux ratios,
consistent with Figure \ref{figBumpCumulative}, and a KS test
indicates that the two distributions are different at about 97\%
confidence, which is suggestive but not especially significant.
If we assume the UV continuum is well-described by a power-law, we
can determine $\alpha_{\rm ox}$ for our AGNs by comparing the $FUV$
and $NUV$ fluxes. We find that
the mean and median of the $\alpha_{\rm ox}$ distribution of the
sample are both 1.4, consistent with the results of \citet{elvi94}.
However, we caution that this calculation requires extrapolating the
UV power-law longward of the $NUV$ effective wavelength, rendering
$\alpha_{\rm ox}$ inherently less robust than the
flux ratios shown in Figure \ref{figAlphaOx}.
In either case, our AGNs appear to be quite
typical in this respect, but there is marginal evidence that the
NLS1s have slightly stronger BBB than usual, consistent with the
results in Figure \ref{figSlope}. If BBB photons are
reprocessed to form the soft excess, a stronger BBB should be associated
with a stronger soft excess, which indeed is observed. (In order to
explain the flux ratios in Figure \ref{figSlope}, only one in
$\sim10^{6}$ BBB photons needs to be reprocessed. The associated UV flux
decrement would not be observable.)
Many of our AGNs occupy the gap between the main locus of
WF93 galaxies and their outliers, as shown in Figure
\ref{figSlope}, indicating a systematic
difference between our AGNs and those of WF93.
This difference could be caused either by weaker UV at fixed
X-ray flux or by steeper $\alpha_{\rm x}$ at fixed BBB strength.
It is apparent from
Figure \ref{figSlopeCompare} that the X-ray spectra of our galaxies are, on
average, steeper than the galaxies of WF93
($\langle\alpha_{\rm x}\rangle=2.1$, compared to
$\langle\alpha_{\rm x}\rangle=1.5$
for WF93). Comparing the far-UV and X-ray fluxes of our sample with
the fluxes of the WF93 AGNs, we find that our AGNs are fainter in both
the UV and X-ray, but the difference is larger in the UV. (The median
is shifted by a factor of 5.7 in the UV, compared to 5.0 in the X-ray.)
This, in combination with the higher average $\alpha_{\rm x}$ in our
sample accounts for the observed differences between our sample and
WF93's. The difference between the median
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$ in our sample and
WF93's might be attributable to their use of IUE observations to measure
UV fluxes. The WF93 fluxes show a fractional error near unity for fluxes below
$\sim3\times10^{-11}$, whereas the typical GALEX uncertainty is only a few
percent at these flux levels. We are therefore able to obtain
significant GALEX detections of all of our sources, and our sample
is unbiased with respect to UV flux.
While the majority of the BLS1s agree well with the WF93 best fit, the
NLS1s are shifted systematically to higher $\alpha_{\rm x}$.
In combination with the good correlation between
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$ and
$\alpha_{\rm x}$ for the full
sample, this indicates that the relation between the strength of the
BBB and the shape of the soft X-ray continuum is steeper among AGN with
the strongest soft excesses. This in turn suggests the need
for a second parameter to account for the variation in $\alpha_{\rm x}$
at fixed BBB strength.
We identified 9 AGN that lie well away from the ``main''
relation between $\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$
and $\alpha_{\rm x}$. These outliers
are listed, along with a number of important properties, in Table
\ref{tabOutliers}. Five of the outliers show UV-optical luminosity
ratios less than one, putting them well below the main locus in
Figure \ref{figLuminosity}. This suggests that the primary cause
of our outliers is UV absorption. We fit a power law to the objects
in Figure \ref{figLuminosity} with $L_{FUV}\geq L_{V}$ and found,
\begin{equation}
\log(L_{FUV}/L_{\odot})=1.09\log(L_{V}/L_{\odot})-0.65
\end{equation}
Assuming that all of the galaxies with $L_{FUV}<L_{V}$ fall exactly
on the best fit line, we require internal E(B-V) between 0.3 and 1.0
to explain the measured luminosity ratios. For the Galactic gas-to-dust
ratio, this implies
$N_{H}\approx5\times10^{21}\ {\rm cm^{-2}}$, which is far larger than the
column densities measured from X-ray spectral fits.
We note, however, that the implied ${\rm N_{H}}$
is degenerate with $\alpha_{\rm x}$, so these systems could have larger
column densities and steeper spectra than reported, though this seems
unlikely given the recorded values of $\alpha_{\rm x}$.
Also, WF93 found a small number of galaxies with significant
internal extinction despite moderate column densities inferred
from the ROSAT spectra of those systems.
The unusual luminosity ratios shown in Figure \ref{figLuminosity}
might also be an indication that the
$FUV$ and $V$ band luminosities are dominated by young stars rather than
by the AGN accretion disk. This hypothesis is supported by the unusually
low values of $\alpha_{\rm ox}$ exhibited by three of these five objects.
All three AGNs with such low $\alpha_{\rm ox}$ have
$L_{FUV}<10^{43} {\rm erg\ s^{-1}}$, which corresponds to a SFR of
$10\ M_{\odot}\ {\rm yr^{-1}}$ \citep{sali07}.
Of the 4 outliers in Table \ref{tabOutliers}
that do not appear to be strongly absorbed in Figure \ref{figLuminosity},
3 show unusually large $\alpha_{\rm x}$, and the fourth
(RX J0902-07) lies very
close to the line dividing the ``normal'' AGNs from the outliers.
This last object does not differ significantly from the ``typical''
AGNs in our sample for any of the parameters listed in Table \ref{tabOutliers},
suggesting that it should be considered normal.
The other outliers can be divided into two classes:
objects that show UV absorption and objects
that show extraordinarily high $\alpha_{\rm x}$.
Most of our AGNs
occupy the gap between the WF93 best-fit relation
and their outliers. \citet{walt93} explained
their outliers as normal objects with strong intrinsic absorption,
but few of our AGNs show evidence for UV absorption. Only 3 of the 8 objects
with $L_{FUV}/L_{V}<1$ fall into our main sample, so strong UV absorption
cannot be responsible for this difference between our sample and WF93's.
We note, however, that weak absorption is difficult to
identify from Figure \ref{figLuminosity} due to the large intrinsic
scatter about the mean relation, so weak intrinsic absorption might contribute
to the shift in our sample away from the WF93 mean.
We also examine the relation between indicators for the strength
of the BBB and its shape
$\biggl(\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})\biggr)$,
shown in Figure \ref{figXrayShape}. Like WF93, we find a
plateau accompanied by a sharp drop toward lower values
of $\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$. However,
Figure \ref{figXrayShape}
shows a broader scatter in the plateau region, plateaus at a lower
ratio, and fills in the red tail of the distribution
less completely than seen in the analogous diagram in WF93. Also,
the objects occupying the ``tail'' of the
distribution in Figure \ref{figXrayShape} are all listed as outliers
in Table \ref{tabOutliers}, which immediately suggests that
the tail in our sample is due to absorption.
The correlation between the strength and shape of the BBB
disappears if we disregard the outliers, indicating that the
shape of the BBB is largely independent of its strength.
The absence of any correlation between the shape and strength of the
BBB is a direct contradiction of the results of WF93.
We use very different methods to measure
the shape parameter of the BBB, so it is possible that the disparity
between our results and theirs are due to systematic biases, particularly
since our wavelength baseline is only half theirs.
However, the average UV flux ratio in Figure \ref{figXrayShape}
$\biggl(\langle\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})\rangle\approx1.4\biggr)$
implies a power-law continuum ($F_{\nu}\propto\nu^{-\alpha_{uv}}$)
with $\langle\alpha_{uv}\rangle\approx-0.85$, which in
turn suggests that
$\langle\nu F_{\nu}(1375\ {\rm \AA})/\nu F_{\nu}(2675\ {\rm \AA})\rangle\approx1.75$.
This is consistent with the plateau seen in WF93 Figure
11, which is at approximately 1.8.
Given this agreement and the fact that the tail
of our distribution is populated by AGNs showing probable absorption, we
suggest that WF93 were too quick to dismiss absorption as a
potential cause of their correlation.
To verify that the differences between Figure \ref{figXrayShape} and
WF93's Figure 11 are not caused by systematic differences
between $\nu F_{\nu}(1528{\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$ and
$\nu F_{\nu}(1528\AA)/\nu F_{\nu}(25\mu m)$,
we compare the two strength indicators in Figure \ref{figBumpStrength}.
Despite the differences between the UV fluxes of the two samples,
our galaxies show good agreement with the WF93 best-fit relation.
We derive a best fit relation for our sample, obtaining
\begin{equation}
\frac{\nu F_{\nu}(1528\ {\rm \AA})}{\nu F_{\nu}(25\ {\rm \mu m})}=(0.95\pm0.08)\frac{\nu F_{\nu}(1528\ {\rm \AA})}{\nu F_{\nu}(2\ {\rm keV})}-(1.16\pm0.09)
\end{equation}
which is consistent with the WF93 best fit within the uncertainties.
Thus, there is no inherent bias in
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$ compared to
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(25\ {\rm \mu m})$,
and the absence of a correlation
between the shape and strength of the BBB among our AGN sample
is not caused by differences between our strength indicator
and WF93's. It also indicates that the
steeper relation between $\alpha_{\rm x}$ and
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$ among our AGN compared
to the WF93 sample is not due to systematic errors.
This lends credence to the hypothesis that a factor besides the
strength of the BBB must
contribute to the shape of the soft X-ray continuum.
The structure of a standard thin disk, which might be reflected
in the UV color of the disk, can depend on both black
hole mass and Eddington ratio (see Eq. \ref{eqTemp}), so
We want to know whether
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})$ shows
systematic differences between the NLS1 and
BLS1 samples. A KS test reveals that the distributions
differ between the NLS1
and BLS1 samples at about 95\% confidence, but this difference disappears
when we eliminate the
outliers (Tab. \ref{tabOutliers}). Thus,
we measure no intrinsic variation in the structure of accretion disks
powering NLS1 and BLS1 AGNs.
However, the GALEX bands are sensitive only to variations in disk structure
if the Eddington ratio is well below $\dot{m}$. (See Figure
\ref{figShapeMass}.) As a result, we expect little intrinsic difference
between the BLS1 and NLS1 AGN samples.
Finally, we look for any relationships of the indicators we have already
examined with FWHM(H$\beta$), which might tend to indicate systematic
differences between the two classes of AGN.
We find two trends that might be of interest: a correlation with
$\alpha_{\rm x}$ among the merged AGN sample at
$>99.9$\% confidence and another with
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})$
among the NLS1 sample at 97\%
confidence. The second is interesting if true, because it would suggest
that the structure of the BLR is related to the UV color of the accretion
disk, but the correlation is not strong enough to
support such a claim unequivocally. Figure \ref{figWidthCorr}
shows the relation between FWHM(H$\beta$) and $\alpha_{\rm x}$ and
is consistent with the ``zone of avoidance,'' in which BLS1s generally have
$\alpha_{\rm x}\lesssim2.0$, as reported by \citet{boll96}.
The measured correlation is a result of this effect.
\subsection{Physical Parameters}\label{secPhysical}
We also examined the relationships between the observables discussed
above and the physical parameters ($M_{BH}$, $\dot{m}=L/L_{\rm edd}$
and $L_{\rm bol}$) that characterize each AGN, where the Eddington ratios were
all determined using $L_{\rm bol}$ from the Grupe et al. catalogs.
We find strong correlations ($>99$\% confidence)
of shape, strength and $\alpha_{\rm x}$ with UV luminosity among the NLS1
sample, as shown in Figure \ref{figLuminosityCorr}. We also find
correlations of both strength and shape with luminosity
in the merged sample, but the lack of correlation of $\alpha_{\rm x}$
with luminosity among BLS1s
dilutes the correlation in the merged sample to 98\% confidence.
This is significantly weaker than the same correlation
reported by \citet{kell08} for a sample of
optically-selected, radio-quiet quasars. This suggests that the
shape of the X-ray continuum is more tightly coupled to the Big Blue
Bump among optically selected AGN than among X-ray selected AGN. The
Spearman correlation coefficients and significance values for the various
parameters we examined are listed in Table \ref{tabPhysicalCorrelation}.
The strong positive correlation of
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})$ with
$\nu L_{\nu}(1528\ {\rm \AA})$ is in conflict with the
results of \citet{scot04}, who reported
that the BBB, as measured in the FUSE band (900-1200 \AA)
becomes softer in more luminous AGN. However, the GALEX $FUV$ band
does not overlap with the FUSE coverage, so the different variations
with luminosity might be strictly a wavelength effect. If this is
the case, the peak of the BBB in the average Seyfert
AGN must lie somewhere between 1500\AA and 900\AA.
The observed correlations
are weaker but still significant ($>99$\% confidence) if we consider
$\nu L_{\nu}(5100\ {\rm \AA})$. In Figures \ref{figLuminosityCorr}a and
\ref{figLuminosityCorr}b, the relations exhibited by the NLS1 and BLS1
show good agreement, which is consistent with the structure of the accretion
disks showing little variation between the two classes.
We see very different relations of $\alpha_{\rm x}$ with
luminosity between the NLS1 and BLS1 samples. This could be caused by
most NLS1s being within a factor
of a few in $M_{BH}$, causing variations in $\dot{m}$ to drive
a correlation of $\alpha_{\rm x}$ with luminosity.
From simple virial considerations, we expect that the width
of the H$\beta$ emission line should correlate with both $M_{BH}$
and $\dot{m}$. If we assume the simplest possible
relation, $R_{BLR}\propto L^{1/2}$, which is consistent with the
results of \citet{bent06}, we find that
${\rm w(H}\beta{\rm )}\propto (M_{BH}/\dot{m})^{1/4}$.
Examining the correlations in Table \ref{tabPhysicalCorrelation}, we find that
the H$\beta$ line width is indeed correlated with both $M_{BH}$
and $\dot{m}$, but the correlation is much stronger with
$M_{BH}/\dot{m}$. Fitting the FWHM to $M_{BH}/\dot{m}$ yields
\begin{equation}
\log\biggl[{\rm w(H}\beta)\biggr]=(0.24\pm0.01)\log(M_{BH}/\dot{m})+(1.5\pm0.1)
\end{equation}
with $\chi^{2}_{\nu}=1.02$,
which is consistent with the simple prediction above.
This relationship is also consistent with the
results of \citet{mcha06}, who found that the break timescale of the
power density spectrum, which is proportional to
$M_{BH}/\dot{m}$, is well correlated with line width. This good agreement
both with theory and with previous observations suggests that the
\citet{grup04c} mass measurements are, on average, robust.
Our correlation measurements also agree with \citet{pico05}, who found a strong
anti-correlation of $\Gamma_{\rm soft}$ with H$\beta$ line width
($r_{s}=-0.54$),
where $N_{\nu}\propto\nu^{-\Gamma_{\rm soft}}$ is measured
from 0.3--2.0 keV.
In fact, the strength of the correlation they report
is very similar to the strength of the correlation we find between
FWHM and $\alpha_{\rm x}$ (our $r_{s}=-0.53$),
suggesting that much of the scatter between the two variables
may be intrinsic. The errors on the line widths of NLS1s are comparable
to the errors on BLS1 widths, so the lack of correlations with
$M_{BH}$ or $\dot{m}$ among the BLS1 sample suggests
that the geometry factor $f$ varies more among the BLS1 sample than the
NLS1 sample. This might happen if the BLR becomes
more spherically symmetric at high Eddington ratio.
There is also a correlation of moderate significance (98.4\% confidence)
between $M_{BH}$ and
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})$, but correlation
is positive, which is in opposition to the trend predicted
for a standard thin disk (see Fig. \ref{figShapeMass}).
This correlation
is probably spurious, since it is driven by
a small number of AGNs with
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})<1$, three of which
are outliers in Figure \ref{figSlope}. Two additional AGNs with
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})<1$ have
$L_{FUV}<\lambda L_{\lambda}(5100\ {\rm \AA})$, suggesting
that low levels of
recent star formation could significantly influence the measured
UV flux ratio. After excluding
both of these groups, we find no significant correlation of
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})$ with $M_{BH}$.
There is no correlation of
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})$
with $\dot{m}$ regardless of whether the AGNs with
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})<1$ are considered,
which is expected given the relatively high Eddington ratios
typical of the AGNs in our sample.
\section{Theoretical Models}\label{secModels}
We would like to use the UV properties of the observed AGNs to
place constraints on theoretical models for the soft X-ray excess. We
therefore compare the UV properties of our sample to
predictions from various models.
For the standard Shakura-Sunyaev thin disk,
the temperature at the inner edge of the disk
is given by their Eq. 3.8,
\begin{equation}\label{eqTemp}
T_{\rm inner}=5\times10^{8}{\rm K\ } \alpha^{1/5} \dot{m}^{4/5} m^{-1/5} r_{ls}^{-3/2} \left(1-r_{ls}^{-1/2}\right)^{4/5}
\end{equation}
where $m=M/M_{\odot}$ and
$r_{ls}$ is the last stable radius in units of the Schwarzschild
radius. We computed $T_{\rm inner}$ for all the AGNs
displayed in Figure \ref{figShapeMass}, assuming $\alpha=0.1$,
$r_{ls}=1.5$ and $\dot{m}$ determined by the measured luminosities and
black hole masses. We found that only NGC 7214 has
a maximum disk temperature near $(1+z)T_{FUV}$. We note
that NGC 7214 falls in the ``main relation'' in Figure \ref{figShapeMass}
and has $\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})>1$,
meaning it is
essentially normal. This is consistent with our argument that GALEX is
insensitive to changes in the structure of the accretion disk.
The accretion rates implied by the UV colors of our AGNs
(Fig. \ref{figShapeMass}) are substantially
lower than the accretion rates determined using the bolometric luminosities
from the literature ($\dot{m}\gtrsim0.1$). This
implies that either the measured UV fluxes suffer from substantial intrinsic
extinction, which would naturally redden the emergent spectrum,
or the $NUV$ fluxes might contain a substantial
contribution from sources other than the accretion disk. \citet{walt93}
are able to measure the Balmer decrements for their sources, and they find
that most of their sample suffers from little to no intrinsic extinction.
Given the excellent agreement between the UV and MIR properties of their
sample and ours (Figure \ref{figBumpStrength}), intrinsic
extinction is highly unlikely to influence our results. The most likely source
of a significant contribution to the $NUV$ fluxes of our objects is
low-level star formation, but a non-standard disk
structure is also possible.
A popular class of models for non-standard accretion disks is the slim disk
model first proposed by \citet{much82}, in which super-Eddington accretion
drives the disk to puff up and change its structure.
The super-Eddington accretion rates observed in several
of our AGN suggest that this model might be applicable.
Even more objects move into the slim disk regime if
we consider the ``corrected'' black hole masses rather than the virial
products, because the geometric factor for masses determined
using the FWHM of the $H\beta$ emission line is less than 1
(e.g. \citealt{wats07}). The slim disk models of \citet{wang03} predict
that the SED of the BBB rises steeply toward higher energy in the UV
for even moderately super-Eddington accretion ($\dot{m}\gtrsim5$), so
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})$
should be greater than 1.
This is generally true for our sample, but it is unable to
explain the most unusual objects in Figure \ref{figShapeMass},
which have UV flux ratios lying below rather than above the predictions
of a standard thin disk.
Furthermore, the slim disk model predicts that $\alpha_{\rm x}$
should decrease slightly
with increasing $\dot{m}$, which has already been demonstrated to be false
(e.g. \citealt{grup04b}). Alternative slim disk models from \citet{kawa03}
and \citet{chen04} show similar failings.
Furthermore, two of the most extreme objects in Figure \ref{figShapeMass} are
BLS1s and show moderate Eddington ratios ($\dot{m}=0.08, 0.06$ respectively).
This precludes the application of slim disk theory to these objects.
Models that rely on Comptonization of thermal
photons in a hot plasma (e.g. \citealt{kawa01}) are motivated
by the strong correlation between
$\nu F_{\nu}(1375\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$
and $\alpha_{\rm x}$ reported by WF93.
Because our sample differs systematically from the WF93 best-fit,
we infer that an additional parameter
related to the strength of the soft excess may influence the
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$---$\alpha_{\rm x}$
relation. However, the underlying model is supported by the strong
correlation between the strength of the BBB and the shape of the
soft X-ray continuum in our data.
Given the significantly different
$\langle M_{BH}\rangle$ and $\langle \dot{m}\rangle$
exhibited by BLS1s and NLS1s, it is
logical to infer that the temperature or density of the disk corona
might be responsible for the different
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$---$\alpha_{\rm x}$
relations exhibited by the two samples, since both $M_{BH}$ and $\dot{m}$
can influence the structure of the corona. Since the BLS1s, on average,
agree well with the WF93 results, this could also explain the differences
between our merged sample and WF93's results.
Models that suggest an atomic origin for the soft excess,
originally proposed by \citet{gier04}, postulate that the soft excess
is actually a ``hard deficit,'' in which the X-ray flux in the range
$0.7\ {\rm keV} \lesssim E \lesssim 5\ {\rm keV}$ is subject to
significant absorption
by relativistically broadened O{\sc vii} and O{\sc viii} lines.
In a recent paper, \citet{schu07} modeled the emergent X-ray spectrum
that would be observed following
absorption by material in a UV line-driven wind. They exclude
this model based on sharp absorption features that appear in the model
spectra but not in the spectra of real AGN. They also suggest that this
could be resolved by invoking magnetically-driven outflow, which can
potentially reach much larger terminal velocities.
\citet{schu06} modeled the X-ray spectrum of
PG 1211+143 with absorption in a high-velocity wind without subjecting the
wind to any physical constraints. We want to determine whether our
UV flux measurements are consistent with a smeared absorption model,
assuming a mechanism to drive an outflow with the necessary velocity
profile could be found. Since the X-ray continua in soft
excess AGNs are generally smooth \citep{schu07}, we assume that the
multiplicative flux
decrement from an input power-law continuum to the measured flux at
2 keV is linearly proportional to the strength of the soft X-ray excess.
To relate the strength of the soft excess to the soft X-ray spectral
index ($\alpha_{\rm x}$), we fit the soft excess and
$\Gamma_{\rm x}$ measurements of by WF93, finding
\begin{equation}\label{eqWFGamma}
\log(\Gamma_{\rm x})=(1.5\pm0.2)\log(X)+(1.9\pm0.1)
\end{equation}
with $\chi^{2}_{\nu}=0.59$,
where $\Gamma_{\rm x}$ is the photon spectral index in the ROSAT band, and
$X$ is the strength of the soft excess relative to the hard X-ray continuum,
following WF93. Inverting this equation and transforming to $\alpha_{\rm x}$
yields:
\begin{equation}\label{eqStrength}
\log(X)=\frac{\alpha_{\rm x}-0.9}{1.5}
\end{equation}
We predict the flux decrements
required to produce the measured $\alpha_{\rm x}$ in each of our sources
using Equations \ref{eqWFGamma} and \ref{eqStrength} in combination with the
rest-frame 2 keV flux decrement for PG 1211+143 required by Schurch \& Done
(2006; $\alpha_{\rm cont}=1.37$, flux decrement = 1.3 from their Figure 5).
To determine the minimum
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$
required by the model, we need to know the shape of the input continuum
for each AGN in our sample.
We compute the rest-frame $F_{\nu}(5100\ {\rm \AA})$ for each of our
AGNs from the published $L_{\nu}(5100\ {\rm \AA})$ in Grupe et al.
(1998, 2004), using measured $F_{\nu}(2271\ {\rm \AA})$ to estimate
K-corrections and assuming a power-law continuum.
We calculate the continuum shape ($\alpha_{\rm cont}$) from the
measured 5100 \AA and 2 keV fluxes for each of our AGNs,
\begin{equation}\label{eqContinuum}
\alpha_{\rm cont}=-0.343\biggl(\log[F_{\nu}(2\ {\rm keV})]-\log[F_{\nu}(5100\ {\rm \AA})]\biggr)
\end{equation}
where the $F_{\nu}$ are rest-frame fluxes, and the X-ray flux has
been corrected for the appropriate flux decrement. Using $\alpha_{\rm cont}$
and the flux decrements required by our {\it ad hoc} model, we predict lower
limits on $\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$ for
each AGN.
We show the lower limits and measured flux ratios for
our objects, excluding the outliers, in Figure \ref{figRatioLimits}.
The blue triangles mark the six objects
(H0439-27, Mrk 141, MCG+08-23-067, RX J1319+52, NGC 7214, RX J2349-31)
whose lower limits exceed the measured flux ratios.
The cumulative deficit distribution of these objects,
normalized to the uncertainties in their flux ratios,
is shown in Figure \ref{figLowerCum}. This distribution is
consistent with all of the objects having flux ratios intrinsically
equal to the lower limits but scattered low by
the observational errors. Thus, we cannot rule out an origin of the
soft excess in smeared absorption based on our GALEX measurements.
While the AGNs in our sample are inconsistent with slim disk models,
our measured flux ratios are consistent with either smeared
absorption or Comptonization in a hot corona. We are therefore unable
to favor either of these competing models, though the differences between
our best-fit
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$---$\alpha_{\rm x}$
relation and WF93's
indicates the need for a second parameter in the Comptonization model. We
suggest this parameter might be the Eddington ratio.
\section{Summary \& Conclusions}\label{secConclusions}
We measure the UV fluxes of a sample of X-ray selected AGNs with
strong soft X-ray excesses. We find that our AGNs are slightly fainter
in the UV compared to the X-ray than a similar sample studied by WF93, and
we conclude that these differences are attributable to selection effects.
We examine the relationships between several observables and the
inferred physical properties of our AGN. We find that the shape
of the soft X-ray continuum shows significant
correlations with $\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$,
but the slope of the relation is steeper than that measured by WF93.
This difference appears to result from selection effects.
We conclude that the X-ray spectra of AGN with unusually steep
soft X-ray continua, which belong to the NLS1 class,
are related to their UV spectra
in a way fundamentally similar to AGN with more mundane soft
X-ray spectra. The mechanism that drives the
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$---$\alpha_{\rm x}$
correlation must also lead to steeper $\alpha_{\rm x}$ at fixed
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$ among NLS1s.
The Eddington ratio might make a good choice for this second parameter,
since the differences between our results and WF93's are largest for
the NLS1 sample.
We find a positive correlation of moderate significance between
$M_{BH}$ with the shape of the UV continuum, but this correlation
disappears if we disregard objects lying far from in main locus in
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$---$\alpha_{\rm x}$
space. We also find no evidence for a correlation of
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2271\ {\rm \AA})$ with
$L/L_{\rm edd}$. If the soft X-ray excess is caused by Comptonization
of BBB photons in the hot corona of the accretion disk,
a second parameter is needed to explain the large
intrinsic variation in $\alpha_{\rm x}$ at fixed BBB strength.
Because $\alpha_{\rm x}$ is known to depend strongly on $L/L_{\rm edd}$
while and the properties of the accretion disk vary only weakly
with accretion rate, $L/L_{\rm edd}$ is
the most obvious candidate.
We find no significant correlation between the color
and strength of the BBB, so either the luminosity of the
accretion disk relative to the underlying power law is independent
of the temperature of the disk, or the
characteristic temperature of the typical Seyfert 1 galaxy is outside
the range where GALEX colors are sensitive
($5{\rm eV}\lesssim kT\lesssim 10{\rm eV}$).
The latter hypothesis is more likely based on the limited predicted range
in GALEX colors for the black hole masses and accretion rates appropriate
for our sample. Comparisons between predicted and measured flux ratios
also suggest that the GALEX fluxes include contamination from young stars,
obscuring any underlying correlation in objects with
$\nu L_{\nu}(1528\AA)\lesssim5\times10^{43}{\rm erg\ s^{-1}}$
(estimated ${\rm SFR}\lesssim10\ M_{\odot}\ {\rm yr^{-1}}$; \citealt{sali07}).
Among our sample, there are 7(3) of 54(45) AGN in this luminosity
range including (excluding)
the outliers, so the impact of UV emission from young stars on our main
conclusions will be small. Resolving
the question of whether or not the shape and strength of the BBB are
independent will likely require UV spectroscopy from HST, which has the
resolution to separate host starlight from AGN emission and can
be used to correct the measured flux ratios for redshift.
Finally, we are unable to use the UV fluxes of the Grupe et al. AGNs to
distinguish between the absorption and Comptonization models for the
origin of the soft X-ray excess. Resolving this question could have important
implications for our understanding of AGN feedback, but the {\it ad hoc}
model we use to estimate minimum
$\nu F_{\nu}(1528\ {\rm \AA})/\nu F_{\nu}(2\ {\rm keV})$ ratios does
not provide sufficient predictive power to determine whether the absorption
model really agrees with the UV flux measurements. Further study with
a more detailed model is needed.
\acknowledgements
We thank an anonymous referee for insightful and penetrating comments which
have significantly improved this paper. We are also
grateful to G.C. Dewangan for helpful comments
and to Dirk Grupe for illuminating discussion regarding
the ROSAT spectra used to construct his AGN samples.
We also wish to thank the GALEX collaboration and the
Space Telescope Science Institute for providing access to the UV
images used in this work. GALEX is a NASA Small Explorer Class mission.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,108 |
StreamingMedia.com Industry Announcements
View Press Releases Add Your Press Release
StreamingMedia.com provides this section as a service to its readers and customers.
Press releases are subject to approval by the editorial staff of StreamingMedia.com and may be edited or altered for length and clarity, or to remove unsubstantiated and unverifiable claims.
All content presented within the press release section is that of the submitter. StreamingMedia.com does not necessarily endorse such content and bears no responsibility or liability for its accuracy.
Ooyala Enables Fast, Simple Video Syndication to Amazon Fire TV for Premium Video Providers
Santa Clara, CA(15 Apr 2015)
Ooyala, a Telstra subsidiary and the leading innovator in premium video publishing, analytics and monetization, is making it fast and simple for Ooyala customers to syndicate video to the popular Amazon Fire TV line of devices. Ooyala's syndication feeds are one of the fastest ways for publishers to distribute content to the living room, and Fire TV, which is available in the US, UK and Germany, now becomes another important channel for providers looking to reach online viewers with a lean-back experience.
By utilizing Amazon's HTML5-based Web App Starter Kit for Fire TV to create a Fire TV app, Ooyala customers can quickly create a syndication feed for the app which groups any number of live or VOD assets into desired categories, such as movies, sports or documentaries, for the viewer. PGA Tour is among the first to syndicate to Fire TV via Ooyala's video platform.
Scott Gutterman, vice president of digital operations for PGA Tour, said, "PGA Tour fans are staying connected with our content everywhere, across every kind of device. As we see more of our viewers looking for video online, making that content easily available is increasingly important. This combination of tools from Amazon and Ooyala results in a very simple and elegant solution for both PGA Tour and for our viewers - we were able to quickly deploy a rich TV experience that is rewarding for our audience and easy on our developers."
"We are thrilled that Ooyala customers can now easily syndicate video to Amazon Fire TV, directly reaching new viewers right in their living rooms," said Steve Rabuchin, Vice President, Amazon Appstore. "This brings a whole new set of content to our customers that we know they will love, and provides a fast and easy way for developers to build apps for the television experience."
Jonathan Wilner, vice president of products for Ooyala, said, "People today have a big appetite for discovering and enjoying new kinds of video on the biggest screen in the house. Fire TV is not only one of the fastest ways for publishers to get their content onto the TV, but also one of the easiest ways for people to find great content that's not available through traditional TV. We're seeing more and more customers adopting syndication to connected TV devices as a way to engage their audience in new ways, and we expect Fire TV to be another great driver of that growth."
About Ooyala
Ooyala helps deliver content that connects. A US-based subsidiary of global telecommunications and IT services company Telstra, Ooyala's comprehensive suite of offerings includes one of the world's largest premium video platforms and a leading ad serving solution. Built with superior analytics capabilities for advanced business intelligence and a strong commitment to customers success, Ooyala's industry-leading end-to-end solutions help large-scale broadcasters, operators, media companies, enterprises and brands build more engaged and more profitable audiences, and monetize video and TV with personalized, interactive experiences across any screen.
ESPN, Univision, Sky Sports (The U.K.), Foxtel (Australia), NBCUniversal, RTL Germany (Germany), M6 (France), TV4 (Sweden), Mediaset (Spain), STV (UK) and Singapore's Mediacorp: these are just a few of the hundreds of broadcasters and media companies who choose Ooyala.
Headquartered in Silicon Valley, Ooyala has offices in New York, London, Stockholm, Sydney, Tokyo, Singapore and Guadalajara, and sales operations in dozens of other countries across the globe. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,686 |
{"url":"http:\/\/www.oaj.pku.edu.cn\/wk3\/syxk\/EN\/abstract\/abstract27899.shtml","text":"ISSN 1002-1027\u3000\u3000CN 11-2952\/G2\n\n### A Generic Programmable Dual Modulus Divider\n\nHUANG Shuilong1, WANG Zhihua\n\n\u2022 Received:2006-04-11 Online:2007-01-20 Published:2007-01-20\n\nAbstract: A programmable dual modulus divider is proposed. The circuit mainly includes three building blocks: prescaler, 8-bit programmable counter and \u03a3\u0394 modulator. Two operation modes (integer\/fractional-N) are achieved by switching on\/off the output signal of the \u03a3\u0394 modulator. Only a programmable counter is needed for the swallow pulse divider. The prescaler was designed by using the improved dynamic TSPC triggers, and the other blocks were realized by the way of digital synthesis, placing and routing. Based on 0.18\u03bcm 1.8V CMOS technology, SpectreVerilog simulations verify that it can operate within the division ratio of 56-2 047 with 2GHz maximum operation frequency and <4mA current dissipation. The circuit is very simple and can be used in the high performance PLL frequency synthesizer.","date":"2020-08-03 12:44:15","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\": 0.2623694837093353, \"perplexity\": 8754.95585330467}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-34\/segments\/1596439735810.18\/warc\/CC-MAIN-20200803111838-20200803141838-00526.warc.gz\"}"} | null | null |
Q: Convexity of Bregman divergence I'm studying Bregman divergence and there is one of the properties that i dont quite understand. The definitions of the Bregman divergence is the following: $$ $$
Let $d_f : C x C $ $\xrightarrow{}$ $ [0,\infty), (\textbf{x}, \textbf{y})$ $\xrightarrow{}$ $f(\textbf{x} - f(\textbf{y} - \langle \nabla f(\textbf{y}), \textbf{x} - \textbf{y} \rangle $
My question is how can I proove the convexity property which states that $d_f (\textbf{x}, \textbf{y}) \geq 0 $ is convex in $\textbf{x} \in C $, but not generally in $\textbf{y} \in C $
A: For simplicity assume that $f$ is twice differentiable. To see that $d_{f}(x, y)$ is convex in $x$, note that by convexity of $f$ we have
$\nabla^{2}_{x} d_{f}(x,y) = \nabla^{2}f(x) \succcurlyeq 0$ by the assumption that $f$ is convex.
To see that $d_{f}$ is not necessarily convex in its second argument $y$, let $f(x) = - \sum_{i=1}^{n} \log x_{i}$, with $\mathbf{dom} f = \mathbb{R}^{n}_{++}$. Then $d_{f}$ (known as the Itakura-Saito distance) is given by $d_{f}(x, y) = \sum_{i=1}^{n}\left( \frac{x_{i}}{y_{i}} - \log \frac{x_{i}}{y_{i}} - 1 \right)$ and it is non-convex in its second argument. To see why the last claim is true, fix $n=1$, then $\frac{d^2}{dy^{2}} d_{f}(x,y) = \frac{2x-y}{y^3}$ is negative for $y > \frac{x}{2}$.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,689 |
using System;
namespace SIM.Sitecore9Installer.Validation
{
public enum ValidatorState
{
Pending,
Error,
Warning,
Success
};
public class ValidationResult
{
public ValidationResult(ValidatorState state, string message, Exception exception)
{
this.State = state;
this.Message = message;
this.Exception = exception;
}
[RenderInDataGreed]
public ValidatorState State { get; set; }
[RenderInDataGreed]
public string Message { get; set; }
[RenderInDataGreed]
public Exception Exception { get; set; }
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,173 |
{"url":"http:\/\/www.ck12.org\/geometry\/Corresponding-Parts-of-Similar-Figures\/lesson\/Corresponding-Parts-of-Similar-Figures\/r11\/","text":"<meta http-equiv=\"refresh\" content=\"1; url=\/nojavascript\/\"> Corresponding Parts of Similar Figures ( Read ) | Geometry | CK-12 Foundation\nYou are viewing an older version of this Concept. Go to the latest version.\n\n# Corresponding Parts of Similar Figures\n\n%\nProgress\nPractice Corresponding Parts of Similar Figures\nProgress\n%\nCorresponding Parts of Similar Figures\n\nRemember the geometric skateboard park from the Distinguish Between Regular and Irregular Polygons Concept? Well, the students are working on all kinds of designs for the sidewalk that leads into the park.\n\nSam is designing some figures to be painted on the sidewalk for the skateboard park.\n\n\"I am going to use all primary colors,\" Sam told his friend Kara at lunch.\n\n\"Let me see,\" Kara said looking at his drawing.\n\nHere are Sam's designs.\n\n\"Those aren't the same,\" Kara said looking at the drawing.\n\n\"I know that. These are similar figures. But I think they are cool.\"\n\n\"They are cool, but they aren't the same,\" Kara said again.\n\n\"That doesn't matter with similar figures. They have corresponding sides,\" Sam explained.\n\nKara is puzzled. She isn't sure how to identify corresponding sides of similar figures.\n\nDo you know?\n\nIn this Concept you will learn all about corresponding sides of similar figures, and you will know how to identify them too.\n\n### Guidance\n\nPreviously we worked on identifying the corresponding parts of congruent figures, and identifying the corresponding parts of similar figures. We do this in the same way.\n\nFirst, notice that all of the angle measures are the same. Whether figures are similar or congruent, the angle measures are the same in both.\n\nThe side lengths are different in similar figures. The side lengths are the same in congruent figures.\n\nTriangle $ABC$ is similar to triangle $DEF$ . This means that while they are the same shape, they aren\u2019t the same size. In fact, there is a relationship between the corresponding parts of the triangle.\n\nThe side lengths are corresponding even though they aren\u2019t congruent.\n\n$\\overline{AB} \\times \\overline{DE} \\\\\\overline{BC} \\times \\overline{EF} \\\\\\overline{AC} \\times \\overline{DF}$\n\nWe use the symbol for similar (\"~\") to show the relationship between the corresponding sides of the two triangles.\n\nUse these similar figures to answer the following questions.\n\n#### Example A\n\nHow many right angles are in the first two figures?\n\nSolution: 4 right angles\n\n#### Example B\n\nWhat makes the two squares similar if they both have four right angles?\n\nSolution: The side lengths are different.\n\n#### Example C\n\nIn the triangle pair, are the two triangles similar or congruent? why?\n\nSolution: The triangles are similar because the side lengths are different. The angle measures are the same.\n\nNow back to Kara, Sam and the similar figures. Here is the original problem once again.\n\nSam is designing some figures to be painted on the sidewalk for the skateboard park.\n\n\"I am going to use all primary colors,\" Sam told his friend Kara at lunch.\n\n\"Let me see,\" Kara said looking at his drawing.\n\nHere are Sam's designs.\n\n\"Those aren't the same,\" Kara said looking at the drawing.\n\n\"I know that. These are similar figures. But I think they are cool.\"\n\n\"They are cool, but they aren't the same,\" Kara said again.\n\n\"That doesn't matter with similar figures. They have corresponding sides,\" Sam explained.\n\nKara is puzzled. She isn't sure how to identify corresponding sides of similar figures.\n\nWhen working with congruent figures, you had to match up the sides that were the same length. Similar figures aren't the same length, but based on the position of the figures, you can figure out which sides go together. These are the corresponding sides. Corresponding sides are in the same position on two different figures.\n\nHere are the corresponding sides of these figures.\n\n$\\overline{HG}$ ~ $\\overline{XW}$\n\n$\\overline{HI}$ ~ $\\overline{XY}$\n\n$\\overline{IJ}$ ~ $\\overline{XZ}$\n\n$\\overline{GJ}$ ~ $\\overline{WZ}$\n\n### Vocabulary\n\nCongruent\nhaving the same size and shape and measurement\nSimilar\nhaving the same shape, but not the same size. Similar shapes are proportional to each other.\nCorresponding\nmatching-corresponding sides between two triangles are sides that match up\n\n### Guided Practice\n\nHere is one for you to try on your own.\n\nList all of the pairs of corresponding sides in the similar figures below.\n\nHere are the pairs of corresponding sides.\n\n$\\overline{OP}$ and $\\overline{RS}$\n\n$\\overline{NO}$ and $\\overline{QR}$\n\n$\\overline{MP}$ and $\\overline{TS}$\n\n$\\overline{MN}$ and $\\overline{TQ}$\n\n### Practice\n\nDirections : Use the following figures to answer each question.\n\n1. Are these two triangles similar or congruent?\n\n2. How do you know?\n\n3. Which side is congruent to $\\overline{AB}$ ?\n\n4. Which side is congruent to $\\overline{AC}$ ?\n\n5. Which side is congruent to $\\overline{RS}$ ?\n\n6. Which angle is congruent to angle A?\n\n7. Which angle is congruent to angle B?\n\n8. Which angle is congruent to angle C?\n\n9. Are the two figures similar or congruent?\n\n10. Why?\n\n11. Which side is congruent to $\\overline{NO}$ ?\n\n12. Which side is congruent to $\\overline{MN}$ ?\n\n13. Which side is congruent to $\\overline{ST}$ ?\n\n14. Which side is congruent to $\\overline{QT}$ ?\n\n15. Which side is congruent to $\\overline{OP}$ ?","date":"2015-02-01 16:01:32","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 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\": 27, \"texerror\": 0, \"math_score\": 0.5362765789031982, \"perplexity\": 1257.957498534574}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-06\/segments\/1422122238667.96\/warc\/CC-MAIN-20150124175718-00230-ip-10-180-212-252.ec2.internal.warc.gz\"}"} | null | null |
{"url":"http:\/\/mymathforum.com\/applied-math\/174529-height-feed-trapezoidal-trough.html","text":"My Math Forum Height of feed in a trapezoidal trough.\n User Name Remember Me? Password\n\n Applied Math Applied Math Forum\n\n September 13th, 2015, 04:03 AM #1 Member \u00a0 Joined: Jun 2015 From: Warwick Posts: 37 Thanks: 1 Height of feed in a trapezoidal trough. A trough has a cross-section in the form of a trapezium. Its base has a length of 1m, and the sides slope out at 45 degrees. to the horizontal. The trough is filled with feed to a depth of x metres. Find the value of x given that the centre of mass of the contents of the trough is 0.5m above the base. Centroid of a trapezium is (h\/3)[(b+2a)\/(b+a)], where h is the height and b is the longest (base) and a is the shortest base (although in this problem, it is a on the horizontal). The height of the trough is sin(45), if we take the length of the sloped edge to be 1m, as well. The answer should be 0.866\nSeptember 15th, 2015, 09:47 AM \u00a0 #2\nMath Team\n\nJoined: Jul 2011\nFrom: Texas\n\nPosts: 2,881\nThanks: 1503\n\n$\\displaystyle \\bar{y} = \\frac{h}{3} \\left(\\frac{2a+b}{a+b}\\right)$\n\nnote from the diagram ...\n\n$b=1$, $a-2h=1 \\implies a=2h+1$\n\n$\\displaystyle \\frac{1}{2} = \\frac{h}{3} \\left[\\frac{2(2h+1)+1}{(2h+1)+1}\\right]$\n\n$\\displaystyle \\frac{1}{2} = \\frac{h}{3} \\left(\\frac{4h+3}{2h+2}\\right)$\n\n$\\displaystyle \\frac{3}{2h} = \\frac{4h+3}{2h+2}$\n\n$\\displaystyle h = \\frac{\\sqrt{3}}{2} \\approx 0.866$\nAttached Images\n centroid_trap.jpg (31.2 KB, 5 views)\n\n September 16th, 2015, 02:54 AM #3 Newbie \u00a0 \u00a0 Joined: Aug 2015 From: USA Posts: 29 Thanks: 0 It's near to accurate. Last edited by skipjack; September 16th, 2015 at 04:16 AM.\n September 16th, 2015, 04:28 PM #4 Member \u00a0 Joined: Jun 2015 From: Warwick Posts: 37 Thanks: 1 Thanks for the reply. It is a good answer and the diagram is very clear.\n\n Tags centre of mass, feed, height, trapezoidal, trough\n\n Thread Tools Display Modes Linear Mode\n\n Similar Threads Thread Thread Starter Forum Replies Last Post kittycub4 Calculus 2 October 21st, 2011 03:55 PM aaron-math Calculus 4 October 2nd, 2011 05:37 PM\n\n Contact - Home - Forums - Cryptocurrency Forum - Top","date":"2019-04-19 16:14:20","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.5194992423057556, \"perplexity\": 4919.573032039829}, \"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-2019-18\/segments\/1555578527865.32\/warc\/CC-MAIN-20190419161226-20190419183226-00105.warc.gz\"}"} | null | null |
Orthostixis cribrata är en fjärilsart som beskrevs av Treitschke 1825. Orthostixis cribrata ingår i släktet Orthostixis och familjen mätare. Inga underarter finns listade i Catalogue of Life.
Källor
Mätare
cribrata | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,933 |
Hotel Channel Manger, is an on-line distribution solution for the Hotels to Optimize management of their distribution channels.A Hotel channel manager is a software that helps hoteliers to manage room distribution across various OTAs and their own hotel website in real-time.
It works as an excellent Revenue Management tool for the hotels, very simple, time saving and easy to use.
Hotel Channel Manager gives you the ability to manage reservation of rooms in your hotel through as many channels as you want to along with managing the inventory and giving you a clear picture of the booking dates, the rooms availability, the guests arrival/departure dates, rate management,the other promo offers etc in one dashboard.
It is a common practice for hoteliers to add their hotels to different OTAs. Now a day OTA's are the major source of online bookings, other than their own website.
But it is very hectic for hoteliers to log into multiple OTA accounts to mange hotel room rates and inventory.
With Channel Manager all the extranets of individual channels are listed under common platform. As needed the dynamic rates, inventories can be managed with a single point feed, than saving and publishing it.
This distribution solution rewrites / updates the changes on all individual channel with minutes, saving the time and efforts.
At booking hotel.co.in we help to manage online room bookings through major OTA's like booking.com ,� goibibo,� make my trip-MMT,� cleartrip ,� travelguru� ,� agoda & expedia.
Not only we manages OTA's, we also captures bookings from hoteliers own website with the help of booking engine. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,614 |
Q: How to draw a big hollow diamond in GLES on phone? I want to render a very large hollow diamond. In the fragment shader, if a point is inside the diamond, it is not rendered, otherwise it is rendered. The program runs very well on PC, but it does not work on Android phones. I guess it should be caused by accuracy problems. The size of the rhombus is changed. Sometimes it is too large, exceeding the mediump value in GLSL. Is there any other way to simply render a hollow diamond on the phone screen? The main code is as below:
uniform mediump vec4 user_DiamondCenter;
uniform mediump vec4 user_DiamondSize;
varying mediump vec4 v_worldPos;
lowp vec4 fragmentColor = v_fragmentColor;
lowp vec4 srcColor = texture2D(CC_Texture0, v_texCoord);
mediump vec4 testPoint = (v_worldPos - user_DiamondCenter);
lowp float fIn = step(user_DiamondSize.y * user_DiamondSize.x * 0.5f, abs(testPoint.x * user_DiamondSize.y) + abs(testPoint.y * user_DiamondSize.x));
fragmentColor.a = fragmentColor.a * fIn;
gl_FragColor = fragmentColor * srcColor;
The user_DiamondSize may be very large, so it cause the problem. Is there any solution, or any other simple way to render this large hollow diamond? The camera is moving, and sometimes it is necessary to render the border of this diamond.
A: If the camera is within the object, and the object is not rendered only on phone, then the obvious issue is in Face culling.
glDisable(GL_CULL_FACE)
This will disable culling so you can check if that is the issue
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,691 |
{"url":"https:\/\/ctan.org\/tex-archive\/macros\/generic\/lt3luabridge","text":"# lt3luabridge\n\nlt3luabridge is an expl3 package for plain , , and Cont that allows you to execute Lua code in Lua or any other engine that exposes the shell:\n\n\\documentclass{standalone}\n\\usepackage{lt3luabridge}\n\\begin{document}\n$1 + 2 = \\luabridgeExecute{ print(1 + 2) }$\n\\end{document}\n\n\nlt3luabridge was previously part of the Markdown package for , where it has been battle-tested since 2016. Since 2022, lt3luabridge has been available as a separate package.","date":"2022-12-06 11:48:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.7280144691467285, \"perplexity\": 2929.144748783616}, \"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\/1669446711077.50\/warc\/CC-MAIN-20221206092907-20221206122907-00184.warc.gz\"}"} | null | null |
Theodor Christian Avellan, russifié en Fiodor Karlovitch Avelan, en , né le à Loviisa (grand-duché de Finlande) (aujourd'hui république de Finlande) et décédé le à Petrograd (aujourd'hui Saint-Pétersbourg), est un marin et homme politique russe, d'origine suédoise de Finlande, qui fut amiral, ministre de la Marine impériale de Russie (1903-1905), membre du Conseil de l'Amirauté, membre du Conseil d'État (1914). Ce fut l'un des principaux responsables de la défaite de la Marine impériale pendant la guerre russo-japonaise.
Mariage et descendance
Theodor Avellan épouse Adalinda Erickson aristocrate suédoise de Finlande et luthérienne comme lui.
Trois filles sont nées de cette union :
Olga Fiodorovna Avelan
Nadejda (dite Hope) Fiodorovna Avelan
Maria Fiodorovna Avelan
Biographie
Il est isu d'une famille noble suédoise du grand-duché de Finlande et fils de Karl Avellan. Il est de confession luthérienne.
En 1855, Fiodor Avelan obtient son diplôme de l'École du Corps naval des cadets Alexandre avec le grade de garde-marine. En 1857, il est affecté à la Flotte de la mer Baltique. Entre 1869 et 1872, il sert à bord du clipper Gaydamak au grade de lieutenant de marine. En 1878, il prend part à une expédition navale le long des côtes d'Amérique du Nord et commande le croiseur Asie. Entre 1879 et 1889, il commande au cours de deux tours du monde, le clipper Herald, la corvette Rynda et la frégate Svetlana. De 1889 à 1893, il occupe les fonctions de chef d'état-major du port de Kronstadt. C'est l'amiral Avelan qui commande l'escadre russe de la Baltique rendant visite à la flotte française en à Toulon, puis à Paris, dans le cadre des festivités de l'Alliance franco-russe. Il est accueilli à Toulon par l'amiral Henri Rieunier, ministre de la marine. Cette visite eut un énorme retentissement en France, auparavant isolée d'un point de vue diplomatique. La presse est alors élogieuse à l'égard de l'amiral Avellan qui voyage à bord du Mémoire d'Azov et de l'Empereur Nicolas Ier. Il est fait officier de la Légion d'honneur cette même année.
Fiodor Karlovitch Avelan est élevé au grade de contre-amiral en 1891. De 1895 à 1896, il occupe le poste de chef adjoint de l'état-major de la marine. Il est nommé chef du personnel naval en 1896. En 1903, il est élevé au grade d'adjudant-général. Le , l'empereur Nicolas II le nomme ministre de la Marine. Il occupe cette fonction jusqu'au . La même année, Avelan est promu au grade d'amiral de la Marine impériale.
Après la défaite navale de la Marine impériale à la bataille de Tsushima, les 27 mai et , il est désigné comme l'un des principaux responsables des défaites navales de la Guerre russo-japonaise (1904-1905). Il est privé de son grade d'adjudant-général et présente sa démission à l'empereur qui rejette sa demande. En 1914, il est admis à siéger au Conseil d'État.
Décès et inhumation
Fiodor Karlovitch Avelan meurt le à Pétrograd (aujourd'hui Saint-Pétersbourg) et il est inhumé dans cette même ville au cimetière luthérien de Smolensk.
Distinctions
Ordre de Saint-Vladimir ( - avec ruban)
1884 : Ordre du Rédempteur (Ordre grec - )
1897 : Grand Croix de l'Ordre du Rédempteur
Ordre de l'Aigle blanc
1890 : Ordre de Saint-Vladimir (troisième classe)
1891 : Chevalier de la Légion d'honneur
1893 : Officier de la Légion d'honneur
1899 : Ordre de Saint-Vladimir (deuxième classe)
1896 :Ordre de Sainte-Anne (premier classe)
1897 : Grand Croix de l'Ordre François-Joseph (Autriche)
1897 : Ordre de la Couronne ( - Ordre de Prusse)
1898 : Ordre de Saint-Alexandre (Ordre de Bulgarie)
1891 : Ordre de Saint-Stanislas ()
1900 : Ordre du Soleil Levant ( - Ordre du Japon)
1902 : Ordre de l'Aigle blanc
1902 : Ordre de l'Aigle Rouge ( - Ordre de Prusse)
1902 : Ordre de l'Épée ( - Ordre de Suède)
1902 : Ordre des Saints-Maurice-et-Lazare ( - Ordre d'Italie)
1907 : Ordre de Saint-Alexandre Nevski
1912 : Ordre de Saint-Alexandre Nevski (avec diamants)
1916 : Ordre de Saint-Vladimir ()
Notes et références
Articles connexes
Bataille de Tsushima
Liens externes
Русский Биографический Словарь
Военная история в лицах
Всероссийское генеалогическое древо
Photographie
Avellan et Rojestvensky (photo)
Amiral de l'Empire russe
Ministre de la Marine impériale de Russie
Noblesse russe du XIXe siècle
Récipiendaire de l'ordre de Saint-Vladimir de 1re classe
Chevalier de l'ordre de Saint-Alexandre Nevski
Récipiendaire de l'ordre de l'Aigle blanc (russe)
Récipiendaire de l'ordre de Sainte-Anne de 1re classe
Récipiendaire de l'ordre de Saint-Stanislas (russe)
Noblesse russe du XXe siècle
Noblesse suédoise
Officier de la Légion d'honneur
Chevalier de l'ordre des Saints-Maurice-et-Lazare
Naissance à Loviisa
Naissance dans le grand-duché de Finlande
Naissance en septembre 1839
Décès en septembre 1916
Décès à 77 ans
Personnalité inhumée au cimetière luthérien de Saint-Pétersbourg
Militaire russe de la guerre russo-japonaise | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 33 |
At Siemens Switzerland Ltd, Building Technologies Division atvise® webMI is used within building automation, where it is deployed only project related in panels and Ipads to control and monitor room controls.
"Intuitive user interface with touch panels significantly simplifies the room controlling and by the use of atvise® software we can fulfill various requirements. We were convinced by the consistant usage of open standards, which we at Siemens persue for many years and the simplicity of the atvise® software", says Pius Widmer, Global Portfolio Manager Room Solutions at Siemens. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,856 |
{"url":"https:\/\/en.wikipedia.org\/wiki\/*-regular_semigroup","text":"# Semigroup with involution\n\n(Redirected from *-regular semigroup)\n\nIn mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which\u2014roughly speaking\u2014brings it closer to a group because this involution, considered as unary operator, exhibits certain fundamental properties of the operation of taking the inverse in a group: uniqueness, double application \"cancelling itself out\", and the same interaction law with the binary operation as in the case of the group inverse. It is thus not a surprise that any group is a semigroup with involution. However, there are significant natural examples of semigroups with involution that are not groups.\n\nAn example from linear algebra is the multiplicative monoid of real square matrices of order\u00a0n (called the full linear monoid). The map which sends a matrix to its transpose is an involution because the transpose is well defined for any matrix and obeys the law (AB)T = BTAT, which has the same form of interaction with multiplication as taking inverses has in the general linear group (which is a subgroup of the full linear monoid). However, for an arbitrary matrix AAT does not equal the identity element (namely the diagonal matrix). Another example, coming from formal language theory, is the free semigroup generated by a nonempty set (an alphabet), with string concatenation as the binary operation, and the involution being the map which reverses the linear order of the letters in a string. A third example, from basic set theory, is the set of all binary relations between a set and itself, with the involution being the inverse relation, and the multiplication given by the usual composition of relations.\n\nSemigroups with involution appeared explicitly named in a 1953 paper of Viktor Wagner (in Russian) as result of his attempt to bridge the theory of semigroups with that of semiheaps.[1]\n\n## Formal definition\n\nLet S be a semigroup with its binary operation written multiplicatively. An involution in S is a unary operation * on S (or, a transformation *\u00a0: SS, xx*) satisfying the following conditions:\n\n1. For all x in S, (x*)* = x.\n2. For all x, y in S we have (xy)* = y*x*.\n\nThe semigroup S with the involution * is called a semigroup with involution.\n\nSemigroups that satisfy only the first of these axioms belong to the larger class of U-semigroups.\n\nIn some applications, the second of these axioms has been called antidistributive.[2] Regarding the natural philosophy of this axiom, H.S.M. Coxeter remarked that it \"becomes clear when we think of [x] and [y] as the operations of putting on our socks and shoes, respectively.\"[3]\n\n## Examples\n\n1. If S is a commutative semigroup then the identity map of S is an involution.\n2. If S is a group then the inversion map *\u00a0: SS defined by x* = x\u22121 is an involution. Furthermore, on an abelian group both this map and the one from the previous example are involutions satisfying the axioms of semigroup with involution.[4]\n3. If S is an inverse semigroup then the inversion map is an involution which leaves the idempotents invariant. As noted in the previous example, the inversion map is not necessarily the only map with this property in an inverse semigroup; there may well be other involutions that leave all idempotents invariant; for example the identity map on a commutative regular, hence inverse, semigroup, in particular, an abelian group. A regular semigroup is an inverse semigroup if and only if it admits an involution under which each idempotent is an invariant.[5]\n4. Underlying every C*-algebra is a *-semigroup. An important instance is the algebra Mn(C) of n-by-n matrices over C, with the conjugate transpose as involution.\n5. If X is a set, the set of all binary relations on X is a *-semigroup with the * given by the inverse relation, and the multiplication given by the usual composition of relations. This is an example of a *-semigroup which is not a regular semigroup.\n6. If X is a set, then the set of all finite sequences (or strings) of members of X forms a free monoid under the operation of concatenation of sequences, with sequence reversal as an involution.\n7. A rectangular band on a Cartesian product of a set A with itself, i.e. with elements from A \u00d7 A, with the semigroup product defined as (a, b)(c, d) = (a, d), with the involution being the order reversal of the elements of a pair (a, b)* = (b, a). This semigroup is also a regular semigroup, as all bands are.[6]\n\n## Basic concepts and properties\n\nAn element x of a semigroup with involution is sometimes called hermitian (by analogy with a Hermitian matrix) when it is left invariant by the involution, meaning x* = x. Elements of the form xx* or x*x are always hermitian, and so are all powers of a hermitian element. As noted in the examples section, a semigroup S is an inverse semigroup if and only if S is a regular semigroup and admits an involution such that every idempotent is hermitian.[7]\n\nCertain basic concepts may be defined on *-semigroups in a way that parallels the notions stemming from a regular element in a semigroup. A partial isometry is an element s such that ss*s = s; the set of partial isometries of a semigroup S is usually abbreviated PI(S).[8] A projection is an idempotent element e that is also hermitian, meaning that ee = e and e* = e. Every projection is a partial isometry, and for every partial isometry s, s*s and ss* are projections. If e and f are projections, then e = ef if and only if e = fe.[9]\n\nPartial isometries can be partially ordered by st defined as holding whenever s = ss*t and ss* = ss*tt*.[9] Equivalently, st if and only if s = et and e = ett* for some projection e.[9] In a *-semigroup, PI(S) is an ordered groupoid with the partial product given by st = st if s*s = tt*.[10]\n\n### Examples\n\nIn terms of examples for these notions, in the *-semigroup of binary relations on a set, the partial isometries are the relations that are difunctional. The projections in this *-semigroup are the partial equivalence relations.[11]\n\nThe partial isometries in a C*-algebra are exactly those defined in this section. In the case of Mn(C) more can be said. If E and F are projections, then EF if and only if imE \u2286 imF. For any two projection, if EF = V, then the unique projection J with image V and kernel the orthogonal complement of V is the meet of E and F. Since projections form a meet-semilattice, the partial isometries on Mn(C) form an inverse semigroup with the product ${\\displaystyle A(A^{*}A\\wedge BB^{*})B}$.[12]\n\nAnother simple example of these notions appears in the next section.\n\n## Notions of regularity\n\nThere two related, but not identical notions of regularity in *-semigroups. They were introduced nearly simultaneously by Nordahl & Scheiblich (1978) and respectively Drazin (1979).[13]\n\n### Regular *-semigroups (Nordahl & Scheiblich)\n\nAs mentioned in the previous examples, inverse semigroups are a subclass of *-semigroups. It is also textbook knowledge that an inverse semigroup can be characterized as a regular semigroup in which any two idempotents commute. In 1963, Boris M. Schein has published the following two axioms providing an analogous characterization of inverse semigroups as a subvariety of *-semigroups:\n\n\u2022 x = xx*x\n\u2022 (xx*)(x*x) = (x*x)(xx*)\n\nThe first of these looks like the definition of a regular element, but is actually in terms of the involution. Likewise, the second axiom appears to be describing the commutation of two idempotents. It is known however that regular semigroups do not form a variety because their class does not contain free objects (a result established by D. B. McAlister in 1968). This line of reasoning motivated Nordahl and Scheiblich to begin in 1977 the study of the (variety of) *-semigroups that satisfy only the first these two axioms; because of the similarity in form with the property defining regular semigroups, they named this variety regular *-semigroups.\n\nIt is a simple calculation to establish that a regular *-semigroup is also a regular semigroup because x* turns out to be an inverse of x. The rectangular band from example 7 is a regular *-semigroup that is not an inverse semigroup.[6] It is also easy to verify that in a regular *-semigroup the product of any two projections is an idempotent.[14] In the aforementioned rectangular band example, the projections are elements of the form (x, x) and [like all elements of a band] are idempotent. However, two different projections in this band need not commute, nor is their product necessarily a projection since (a, a)(b, b) = (a, b).\n\nSemigroups that satisfy only x** = x = xx*x (but not necessarily the antidistributivity of * over multiplication) have also been studied under the name of I-semigroups.\n\n#### P-systems\n\nThe problem of characterizing when a regular semigroup is a regular *-semigroup (in the sense of Nordahl & Scheiblich) was addressed by M. Yamada (1982). He defined a P-system F(S) as subset of the idempotents of S, denoted as usual by E(S). Using the usual notation V(a) for the inverses of a, F(S) needs to satisfy the following axioms:\n\n1. For any a in S, there exists a unique a\u00b0 in V(a) such that aa\u00b0 and a\u00b0a are in F(S)\n2. For any a in S, and b in F(S), a\u00b0ba is in F(S), where \u00b0 is the well-defined operation from the previous axiom\n3. For any a, b in F(S), ab is in E(S); note: not necessarily in F(S)\n\nA regular semigroup S is a *-regular semigroup, as defined by Nordahl & Scheiblich, if and only if it has a p-system F(S). In this case F(S) is the set of projections of S with respect to the operation \u00b0 defined by F(S). In an inverse semigroup the entire semilattice of idempotents is a p-system. Also, if a regular semigroup S has a p-system that is multiplicatively closed (i.e. subsemigroup), then S is an inverse semigroup. Thus, a p-system may be regarded as a generalization of the semilattice of idempotents of an inverse semigroup.\n\n### *-regular semigroups (Drazin)\n\nA semigroup S with an involution * is called a *-regular semigroup (in the sense of Drazin) if for every x in S, x* is H-equivalent to some inverse of x, where H is the Green\u2019s relation H. This defining property can be formulated in several equivalent ways. Another is to say that every L-class contains a projection. An axiomatic definition is the condition that for every x in S there exists an element x\u2032 such that xxx\u2032 = x, xxx = x, (xx\u2032)* = xx, (xx)* = xx. Michael P. Drazin first proved that given x, the element x\u2032 satisfying these axioms is unique. It is called the Moore\u2013Penrose inverse of x. This agrees with the classical definition of the Moore\u2013Penrose inverse of a square matrix. In the multiplicative semigroup Mn(C) of square matrices of order n, the map which assigns a matrix A to its Hermitian conjugate A* is an involution. The semigroup Mn(C) is a *-regular semigroup with this involution. The Moore\u2013Penrose inverse of A in this *-regular semigroup is the classical Moore\u2013Penrose inverse of A.\n\n## Free semigroup with involution\n\nAs with all varieties, the category of semigroups with involution admits free objects. The construction of a free semigroup (or monoid) with involution is based on that of a free semigroup (and respectively that of a free monoid). Moreover, the construction of a free group can easily be derived by refining the construction of a free monoid with involution.[15]\n\nThe generators of a free semigroup with involution are the elements of the union of two (equinumerous) disjoint sets in bijective correspondence: ${\\displaystyle Y=X\\sqcup X^{\\dagger }}$. (Here the notation ${\\displaystyle \\sqcup \\,}$ emphasized that the union is actually a disjoint union.) In the case were the two sets are finite, their union Y is sometimes called an alphabet with involution[16] or a symmetric alphabet.[17] Let ${\\displaystyle \\theta :X\\rightarrow X^{\\dagger }}$ be a bijection; ${\\displaystyle \\theta }$ is naturally extended to a bijection ${\\displaystyle {}\\dagger :Y\\to Y}$ essentially by taking the disjoint union of ${\\displaystyle \\theta }$ (as a set) with its inverse, or in piecewise notation:[18]\n\n${\\displaystyle y^{\\dagger }={\\begin{cases}\\theta (y)&{\\text{if }}y\\in X\\\\\\theta ^{-1}(y)&{\\text{if }}y\\in X^{\\dagger }\\end{cases}}}$\n\nNow construct ${\\displaystyle Y^{+}\\,}$ as the free semigroup on ${\\displaystyle Y\\,}$ in the usual way with the binary (semigroup) operation on ${\\displaystyle Y^{+}\\,}$ being concatenation:\n\n${\\displaystyle w=w_{1}w_{2}\\cdots w_{k}\\in Y^{+}}$ for some letters ${\\displaystyle w_{i}\\in Y.}$\n\nThe bijection ${\\displaystyle \\dagger }$ on ${\\displaystyle Y}$ is then extended as a bijection ${\\displaystyle {}^{\\dagger }:Y^{+}\\rightarrow Y^{+}}$ defined as the string reversal of the elements of ${\\displaystyle Y^{+}\\,}$ that consist of more than one letter:[16][18]\n\n${\\displaystyle w^{\\dagger }=w_{k}^{\\dagger }w_{k-1}^{\\dagger }\\cdots w_{2}^{\\dagger }w_{1}^{\\dagger }.}$\n\nThis map is an involution on the semigroup ${\\displaystyle Y^{+}\\,}$. Thus, the semigroup ${\\displaystyle (X\\sqcup X^{\\dagger })^{+}}$ with the map ${\\displaystyle {}^{\\dagger }\\,}$ is a semigroup with involution, called a free semigroup with involution on X.[19] (The irrelevance of the concrete identity of ${\\displaystyle X^{\\dagger }}$ and of the bijection ${\\displaystyle \\theta }$ in this choice of terminology is explained below in terms of the universal property of the construction.) Note that unlike in example 6, the involution of every letter is a distinct element in an alphabet with involution, and consequently the same observation extends to a free semigroup with involution.\n\nIf in the above construction instead of ${\\displaystyle Y^{+}\\,}$ we use the free monoid ${\\displaystyle Y^{*}=Y^{+}\\cup \\{\\varepsilon \\}}$, which is just the free semigroup extended with the empty word ${\\displaystyle \\varepsilon \\,}$ (which is the identity element of the monoid ${\\displaystyle Y^{*}\\,}$), and suitably extend the involution with ${\\displaystyle \\varepsilon ^{\\dagger }=\\varepsilon }$, we obtain a free monoid with involution.[18]\n\nThe construction above is actually the only way to extend a given map ${\\displaystyle \\theta \\,}$ from ${\\displaystyle X\\,}$ to ${\\displaystyle X^{\\dagger }\\,}$, to an involution on ${\\displaystyle Y^{+}\\,}$ (and likewise on ${\\displaystyle Y^{*}\\,}$). The qualifier \"free\" for these constructions is justified in the usual sense that they are universal constructions. In the case of the free semigroup with involution, given an arbitrary semigroup with involution ${\\displaystyle S\\,}$ and a map ${\\displaystyle \\Phi :X\\rightarrow S}$, then a semigroup homomorphism ${\\displaystyle {\\overline {\\Phi }}:(X\\sqcup X^{\\dagger })^{+}\\rightarrow S}$ exists such that ${\\displaystyle \\Phi =\\iota \\circ {\\overline {\\Phi }}}$, where ${\\displaystyle \\iota :X\\rightarrow (X\\sqcup X^{\\dagger })^{+}}$ is the inclusion map and composition of functions is taken in diagram order.[19] The construction of ${\\displaystyle (X\\sqcup X^{\\dagger })^{+}}$ as a semigroup with involution is unique up to isomorphism. An analogous argument holds for the free monoid with involution in terms of monoid homomorphisms and the uniqueness up to isomorphism of the construction of ${\\displaystyle (X\\sqcup X^{\\dagger })^{*}}$ as a monoid with involution.\n\nThe construction of a free group is not very far off from that of a free monoid with involution. The additional ingredient needed is to define a notion of reduced word and a rewriting rule for producing such words simply by deleting any adjacent pairs of letter of the form ${\\displaystyle xx^{\\dagger }}$ or ${\\displaystyle x^{\\dagger }x}$. It can be shown than the order of rewriting (deleting) such pairs does not matter, i.e. any order of deletions produces the same result.[15] (Otherwise put it, these rules define a confluent rewriting system.) Equivalently, a free group is constructed from a free monoid with involution by taking the quotient of the latter by the congruence ${\\displaystyle \\{(yy^{\\dagger },\\varepsilon ):y\\in Y\\}}$, which is sometimes called the Dyck congruence\u2014in a certain sense it generalizes Dyck language to multiple kinds of \"parentheses\", however simplification in the Dyck congruence takes place regardless of order, e.g. if \")\" is the inverse of \"(\", then ${\\displaystyle ()=)(=\\varepsilon }$; the one-sided congruence that appears in the Dyck language proper ${\\displaystyle \\{(xx^{\\dagger },\\varepsilon ):x\\in X\\}}$, which instantiates only to ${\\displaystyle ()=\\varepsilon }$ is (perhaps confusingly) called the Shamir congruence. The quotient of a free monoid with involution by the Shamir congruence is not a group, but a monoid\u00a0; nevertheless it has been called the free half group by its first discoverer\u2014Eli Shamir\u2014 although more recently it has been called the involutive monoid generated by X.[17][20] (This latter choice of terminology conflicts however with the use of \"involutive\" to denote any semigroup with involution\u2014 a practice also encountered in the literature.[21][22])\n\n## Baer *-semigroups\n\nA Baer *-semigroup is a *-semigroup with (two-sided) zero in which the right annihilator of every element coincides with the right ideal of some projection; this property is expressed formally as: for all xS there exists a projection e such that\n\n{ yS | xy = 0 } = eS.[22]\n\nThe projection e is in fact uniquely determined by x.[22]\n\nMore recently, Baer *-semigroups have been also called Foulis semigroups, after David James Foulis who studied them in depth.[23][24]\n\n### Examples and applications\n\nThe set of all binary relations on a set (from example 5) is a Baer *-semigroup.[25]\n\nBaer *-semigroups are also encountered in quantum mechanics,[22] in particular as the multiplicative semigroups of Baer *-rings.\n\nIf H is a Hilbert space, then the multiplicative semigroup of all bounded operators on H is a Baer *-semigroup. The involution in this case maps an operator to its adjoint.[25]\n\nBaer *-semigroup allow the coordinatization of orthomodular lattices.[23]\n\n## Notes\n\n1. ^ Christopher Hollings (2014). Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups. American Mathematical Society. p.\u00a0265. ISBN\u00a0978-1-4704-1493-1.\n2. ^ Chris Brink; Wolfram Kahl; Gunther Schmidt (1997). Relational Methods in Computer Science. Springer. p.\u00a04. ISBN\u00a0978-3-211-82971-4.\n3. ^ H.S.M. Coxeter, Introduction to Geometry, p. 33\n4. ^ C. van den Berg; J. P. R. Christensen; P. Ressel (2012). Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions. Springer Science & Business Media. pp.\u00a087\u201388. ISBN\u00a0978-1-4612-1128-0.\n5. ^ Munn, Lemma 1\n6. ^ a b Nordahl and Scheiblich\n7. ^ Easdown, David, and W. D. Munn. \"On semigroups with involution.\" Bulletin of the Australian Mathematical Society 48.01 (1993): 93-100.\n8. ^ Lawson, p. 116\n9. ^ a b c Lawson, p. 117\n10. ^ Lawson, p. 118\n11. ^ Lawson p.122 and p.35\n12. ^ Lawson p.120\n14. ^ Nordahl and Scheiblich, Theorem 2.5\n15. ^ a b Lawson p. 51\n16. ^ a b Andrzej Ehrenfeucht; T. Harju; Grzegorz Rozenberg (1999). The Theory of 2-structures: A Framework for Decomposition and Transformation of Graphs. World Scientific. pp.\u00a013\u201314. ISBN\u00a0978-981-02-4042-4.\n17. ^ a b Jacques Sakarovitch. Elements of Automata Theory. Cambridge University Press. pp.\u00a0305\u2013306.\n18. ^ a b c Stephen Lipscomb (1996). Symmetric Inverse Semigroups. American Mathematical Soc. p.\u00a086. ISBN\u00a0978-0-8218-0627-2.\n19. ^ a b Lawson p. 172\n20. ^ Ion Petre and Arto Salomaa (2009). \"Algebraic Systems and Pushdown Automata\". In Manfred Droste, Werner Kuich, Heiko Vogler. Handbook of Weighted Automata. Springer. p.\u00a0271. ISBN\u00a0978-3-642-01492-5.\n21. ^ Karl-Hermann Neeb (2000). Holomorphy and Convexity in Lie Theory. Walter de Gruyter. p.\u00a021. ISBN\u00a0978-3-11-015669-0.\n22. ^ a b c d Enrico G. Beltrametti; Gianni Cassinelli (2010) [1981]. The Logic of Quantum Mechanics. Cambridge University Press. p.\u00a0178. ISBN\u00a0978-0-521-16849-6.\n23. ^ a b T.S. Blyth (2006). Lattices and Ordered Algebraic Structures. Springer Science & Business Media. pp.\u00a0101\u2013102. ISBN\u00a0978-1-84628-127-3.\n24. ^ Harding, John. \u201cDaggers, Kernels, Baer *-Semigroups, and Orthomodularity.\u201d Journal of Philosophical Logic. April 6, 2013. doi:10.1007\/s10992-013-9275-5\n25. ^ a b Foulis, D. J. Relative inverses in Baer *-semigroups. Michigan Math. J. 10 (1963), no. 1, 65--84. doi:10.1307\/mmj\/1028998825.","date":"2017-10-23 09:08:04","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 46, \"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\": 0.9026315212249756, \"perplexity\": 689.6623913348269}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-43\/segments\/1508187825812.89\/warc\/CC-MAIN-20171023073607-20171023093607-00447.warc.gz\"}"} | null | null |
Q: Generating dual rail power from a MAX3232? I've seen several electronics devices using MAX3232 or similar devices to generate dual rail power supplies. In my instance, I have 3.3V going in and need regulated ±5V outputs. I have three four questions.
*
*How much output current can they sink or source?
*Are they regulated or do I need an LDO?
*What noise do these give? Through an LDO, would any noise be tolerable for high speed (85 MHz) op-amps?
*What other solutions are there for this problem (dual rail power)?
A: Charge-pump based voltage generators, like the MAX3232 are generally very limited in terms of output current (it seems that all the MAX3232 datasheet guaranties is a voltage of +/-5V at 2.5 mA load). Beside, they are not very efficient at compensating output transients. If the required output current is higher than a few 10 mA, use a true step-up (boost) DC/DC converter, like the LT1300 from Linear. I even found this part: LT3582-5 (from Linear also), which seems to do exactly what you want. Other similar parts may exist as well.
If your application is noise sensitive, you have no guaranty at all regarding this point in this datasheet... I am afraid that you can't just guess what the output noise would be!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,886 |
package org.apache.geode.management.configuration;
import static org.apache.commons.lang3.StringUtils.isBlank;
import com.fasterxml.jackson.annotation.JsonIgnore;
import org.apache.geode.annotations.Experimental;
import org.apache.geode.lang.Identifiable;
import org.apache.geode.management.api.ClusterManagementService;
import org.apache.geode.management.api.CommandType;
import org.apache.geode.management.api.JsonSerializable;
import org.apache.geode.management.runtime.RuntimeInfo;
/**
* This class represents either a configuration or a filter.
* <p>
* As a configuration of a managed entity it can be used to
* either {@linkplain ClusterManagementService#create(AbstractConfiguration) create},
* {@linkplain ClusterManagementService#update(AbstractConfiguration) update},
* or {@linkplain ClusterManagementService#delete(AbstractConfiguration) delete} it,
* or to describe it in the result of
* {@linkplain ClusterManagementService#list(AbstractConfiguration) list}
* or {@linkplain ClusterManagementService#get(AbstractConfiguration) get}.
* <p>
* As a filter as input to {@linkplain ClusterManagementService#list(AbstractConfiguration) list}
* or {@linkplain ClusterManagementService#get(AbstractConfiguration) get}
* it can be used to specify what entities to return.
*
* @param <R> the RuntimeInfo that corresponds to this configuration. Each non-abstract subclass
* needs to supply this when it extends this class.
*/
@Experimental
public abstract class AbstractConfiguration<R extends RuntimeInfo>
implements Identifiable<String>, JsonSerializable {
private static final long serialVersionUID = -6612840641128145954L;
/**
* The reserved group name that represents the predefined "cluster" group.
* Every member of a cluster automatically belongs to this group.
* Note that this cluster group name is not allowed in some contexts.
* For example when creating a region, instead of setting the group to CLUSTER,
* you need to set it to NULL or just let it default.
*/
public static final String CLUSTER = "cluster";
/**
* Returns true if the given "groupName" represents the predefined "cluster" group.
* This is true if "groupName" is a case-insensitive match for {@link #CLUSTER},
* is <code>null</code>, or is an empty string.
*
* @param groupName the group name to be checked
* @return true if groupName is a case-insensitive match for {@link #CLUSTER}, is
* <code>null</code>, or is an empty string
*/
public static boolean isCluster(String groupName) {
return isBlank(groupName) || groupName.equalsIgnoreCase(CLUSTER);
}
public static String getGroupName(String group) {
return isCluster(group) ? CLUSTER : group;
}
@JsonIgnore
public String getGroup() {
return null;
}
/**
* Returns the attribute of the configuration that uniquely identifies it
*/
@Override
public abstract String getId();
/*
* for internal usage only
*/
@JsonIgnore
public abstract Links getLinks();
/**
* Returns true if the RuntimeInfo will be the same on all members;
* false if each member can have different RuntimeInfo.
*
* @return true if the RuntimeInfo will be the same on all members
*/
@JsonIgnore
public boolean isGlobalRuntime() {
return false;
}
@JsonIgnore
public CommandType getCreationCommandType() {
return CommandType.CREATE;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,516 |
Tuna is a contemporary typeface created by Felix Braden together with Alex Rütten and published by Ligature Inc which is available in 5 weights and their italics. It is characterized by low contrast, strong angle, dynamic structure derived from broad nib pen-writing, large x-height, moderate extenders, horizontal emphasis, heavy, slightly arched serif, open aperture and large counters. It is ideal for editorial use, optimized for on screen reading. With more than 700 glyphs, it supports all Western, Eastern & Central-European languages. Cannot miss it!
Price: starting from $49,00 for one font to $249,00 for all 10 fonts.
A font description published on Tuesday, January 31st, 2017 in Alex Rutten, Felix Braden, Fonts, Ligature Inc by Alexandra that has 2,842 views. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,207 |
Q: How do I programmatically show a keyboard for textbox? I have one textbox on a windows phone page and I want to show keyboard as soon as the page is loaded.
Is there any way to make this textbox already focused when I navigate to this page?
I considered using Guide.BeginShowKeyboardInput() but I don't think it's a good solution in silverlight.
A: Yeah, I wouldn't manually show the keyboard. It may be an annoyance for those that have devices with a physical keyboard. In the load event for the page you could just call the Focus method on the textbox that you want to be selected. The Keyboard should automatically show as necessary.
private void PhoneApplicationPage_Loaded(object sender, RoutedEventArgs e)
{
txtLongitude.Focus();
}
A: Override the OnNavigatedTo method for the page.
protected override void OnNavigatedTo(NavigationEventArgs e)
{
base.OnNavigatedTo(e);
// Set focus to the TextBox, this will pop up the
// virtual keyboard
myTextBox.Focus();
}
A: You could call textBox.Focus() via a Dispatcher if you use it on the OnNavigatedTo event:
protected override void OnNavigatedTo(NavigationEventArgs e)
{
base.OnNavigatedTo(e);
if (e.NavigationMode != NavigationMode.Back)
{
Dispatcher.InvokeAsync(() => ShowKeyboard());
}
}
private void ShowKeyboard()
{
textBox.Focus();
}
The if statement here makes sure the keyboard is only shown when the page is not navigated to from the Back button.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,537 |
\section{Introduction}
The robustness of cluster mass estimates has become more and more
important as galaxy clusters have been widely used as important
cosmology tools (e.g., Ebeling et al. 1998, 2000; Allen et al. 2002;
B\"ohringer et al. 2004; Vikhlinin et al. 2009a, 2009b). Precision
cluster cosmology experiments using the mass function are based on
accurately calibrated mass-observable scaling relations in terms of
their shape, scatter, and evolution (e.g., Vikhlinin et al. 2006;
Arnaud et al. 2007). To calibrate the mass-observable scaling
relations, the first necessary task is to obtain well-understood
measurements of the cluster mass and observables (e.g., B\"ohringer et
al. 2007; Zhang et al. 2006, 2008). X-ray measurements provide an
important estimate of the cluster mass. With deep X-ray observations
from \emph{XMM-Newton} and \emph{Chandra}, one can precisely trace
both temperature and electron number density distributions of the
intracluster medium and thus measure the mass distributions with
statistical uncertainties below 15\% up to $r_{500}$ (e.g., Vikhlinin
et al. 2006). However, the accuracy of X-ray cluster mass estimates
is limited by additional physical processes in the ICM and projection
effects. Although the current total cluster mass calibration between
two independent approaches, weak lensing and X-ray, shows an agreement
(e.g., Mahdavi et al. 2008, Zhang et al.2008), a radial dependence is
found in the ratio of weak lensing and X-ray mass measurements (e.g.,
Mahdavi et al. 2008). Such a radial dependence is thought to be due
to a bias in the hydrostatic mass estimates (e.g., Nagai et al. 2007).
Cluster merging is one of many effects causing biases in the X-ray
mass estimates. Previous results on X-ray cluster maps (e.g.,
Vikhlinin et al. 2001, Markevitch et al. 2003, Schuecker et al. 2004,
Finoguenov et al. 2005) show that clusters are not simple hydrostatic
equilibrium systems. Both relaxed and unrelaxed clusters may be
affected by additional non-thermal pressure processes. Particularly,
merging clusters of galaxies are often not in a hydrostatic
equilibrium state. Cluster mergers change the X-ray luminosities and
temperatures of clusters, both in a transient sense and in the long
term (e.g., Ricker \& Sarazin 2001; Poole et al. 2006, 2007), and also
dramatically affect the properties of their galaxies (e.g., Sun et al.
2007). The temperature distribution, as an important input in the
X-ray mass estimate, can cause biases in the X-ray measured mass
distribution. Mergers seriously affect both mass estimates and
observables, and thus the scaling relations of galaxy clusters
(e.g., Evrard et al. 2008). Elimination of systematic uncertainties
from the scaling relation calibration demands that major cluster
mergers are identified and effects of major mergers on cluster mass
estimates are quantified. Substructure can be used to identify and
trace the merging process and the substructure fraction can be used to
link the cluster mass systematics with the mass assembly history (e.g.,
Smith \& Taylor 2008).
Substructure studies are enormously important to understand cluster
mass estimates and the drivers of the scaling relations. Cluster
mergers create disturbances associated with both shocks and mixing of
the stripped gas. As parameters controlling their relative importance,
e.g., the viscosity, are not so well constrained (Sijacki \& Springel
2006), it is unclear how much each contributes and at which scales
each effect dominates. Observationally, we are able to provide
better constraints using spatial fluctuations of the temperature,
electron number density, entropy and pressure maps. Observational
results can be compared with numerical simulations with different
prescriptions to reveal more details of the merging physics.
We aim to perform quantitative substructure studies using X-ray
spectrally measured two-dimensional (2D) maps to access the systematic
errors in cluster mass measurements due to departures from hydrostatic
equilibrium. Substructures in galaxy clusters have been intensely
investigated since the \emph{ROSAT} era using the X-ray surface
brightness distribution from observations and simulations (e.g., Jones
\& Forman 1984; B\"ohringer et al. 2007; Ventimiglia et al. 2008;
Piffaretti \& Valdarnini 2008). However, substructures are less
obvious in the X-ray surface brightness distribution than in the
temperature distribution (Riemer-Sorensen et al. 2009; Jee \& Tyson
2009; Andersson et al. 2009). The \emph{Chandra} and
\emph{XMM-Newton} telescopes, with their high spatial resolution,
conveniently provide us the opportunity to perform substructure
studies using also the temperature map. Most such studies derive
approximate X-ray temperature maps via X-ray hardness ratio maps
(e.g., Fabian et al. 2001, 2002; Churazov et al. 2003; Markevitch et
al. 2001, 2005; Finoguenov et al. 2005; Zhang et al. 2005; Forman
et al. 2007). An alternative and more reliable way to derive X-ray
temperature maps with high precision is to perform a spectral analysis
in each spatial bin. This method avoids, for instance, spurious
temperature variations due to underlying metallicity variations
because the metallicity is determined simultaneously (e.g., Henry et
al. 2004; Reiprich et al. 2004, 2009; Belsole et al. 2004; Pratt et
al. 2005; Sanderson et al. 2005; Sakelliou \& Ponman 2006; Sanders \&
Fabian 2007; Simionescu et al. 2007; Kapferer et al. 2008).
In this paper, we use the spatial fluctuations in the ICM temperature,
electron number density, entropy, and pressure in the 2D maps as substructure
indicators and the deviation of the mass-observable data pair from the
mass-observable relations of relaxed clusters as an estimate of the mass bias.
In Sect.~\ref{s:method}, we describe the key steps in the data reduction,
particularly emphasizing the background subtraction. Our technique to measure
the spectral temperature is shown in Sect.~\ref{s:spe} and how to derive the
2D maps using the spectral analysis is shown in Sect.~\ref{s:map},
respectively. We briefly describe the mass modeling in Sect.~\ref{s:mass}, and
show our results based on spectrally measured X-ray 2D maps in
Sect.~\ref{s:scatter}. We summarize our conclusions in
Sect.~\ref{s:conclusion}. Unless explicitly stated otherwise, we adopt a flat
$\Lambda$CDM cosmology with the density parameter $\Omega_{\rm m}=0.3$ and the
Hubble constant $H_{\rm 0}=70$~km~s$^{-1}$~Mpc$^{-1}$. We adopt the solar
abundance table of Anders \& Grevesse (1989). Confidence intervals correspond
to the 68\% confidence level. The Orthogonal Distance Regression package
(ODRPACK~2.01\footnote{http://www.netlib.org/odrpack and references therein},
e.g., Boggs et al. 1987) taking into account measurement errors on both
variables is used for example, to derive
correlations between observationally derived parameters. We use Monte
Carlo simulations to evaluate the propagation of the errors in the
X-ray mass modeling on all quantities of interest.
\section{Data Reduction}
\label{s:method}
Spectrally measured 2D X-ray maps using most existing techniques
require high photon statistics and are only applied to a few very
nearby clusters/galaxies (e.g., Henry et al. 2004; Reiprich et al.
2004; Belsole et al. 2004; Pratt et al. 2005; Sakelliou \& Ponman
2006; Sanders \& Fabian 2007; Simionescu et al. 2007). In most
previous studies, a relatively simple blank sky background subtraction
was often applied. Therefore, high signal-to-noise ratio (S/N) data are
required to avoid large uncertainties caused by the background
modeling. These technical limitations make this approach applicable
only to targets with extremely good photon statistics, requiring 1-2
orders of magnitude higher exposures than the typical archival data
for nearby clusters. It is a challenge to carry out such studies on
medium quality data.
A precise background subtraction method could make spectrally measured
map analysis possible also for medium quality \emph{XMM-Newton} data
to increase the size of the cluster sampling. Snowden et al. (2008)
developed a precise background modeling method but only for the MOS
data and only to measure the radial temperature profile. We adopted
their method and developed an advanced background modeling pipeline,
which is applicable to both pn and MOS data and which can be used to
measure the spectral temperature for both the radial analysis and the
map analysis. It allows us to perform reliable spectral analysis in
each spatial bin to derive the X-ray maps, but for clusters with
\emph{XMM-Newton} data with $\ge$~120,000 source counts in total.
The XMMSAS version 7.1.0 software combined with our in-house-developed pipeline is
used for data reduction.
\subsection{Data Selection}
To demonstrate the robustness of the method and to determine the S/N
threshold for such substructure studies, we composed a sample of four
clusters showing different morphologies as well as different photon
statistics in their \emph{XMM-Newton} data. Four clusters of galaxies
are selected from the HIghest X-ray FLUx Galaxy Cluster Sample
(HIFLUGCS\footnote{The HIFLUGCS sample consists of 64 X-ray brightest
galaxy clusters in the extragalactic sky. They were selected from
the \emph{ROSAT} All-Sky Survey (RASS), irrespective of their
morphology, simply applying an X-ray flux limit.}; Reiprich \&
B\"ohringer 2002) according to the following criteria. (1) The
$r_{2500}$\footnote{$r_{\Delta}$ is the radius within which the
density contrast to the critical density is $\Delta$. $M_{\Delta}$
is the total mass within $r_{\Delta}$. For example, for
$\Delta=200$, $r_{200}$ is the radius within which the density
contrast is 200 and $M_{200}$ is the total mass within $r_{200}$.
The $r_{200}$ used here is derived from the cluster global
temperature in Reiprich \& B\"ohringer (2002) and the $M_{200}$-$T$
relation from simulations in Evrard er al. (1996).} fits the
\emph{XMM-Newton} field of view (FOV). (2) The photon statistics are
sufficient for the map analysis using spectral measurements but varies
in a small range which gives 10-60 bins, of which the uncertainty of
the spectrally measured temperature in each spatial bin is $\simeq
10$\%. (3) The background is mildly contaminated by flares. (4) The
map analysis has not already been published. The first criterion is
important to measure the temperature distribution, and thus to
guarantee reliable X-ray mass modeling to derive the mass bias. The
second and third criteria are required to guarantee robust X-ray
background modeling, particularly in the spectral analysis for the map
analysis. In addition, the reason we chose those four clusters with
slightly different photon statistics is to test how far from the
cluster center and how reliably one can perform substructure studies
with a range of data quality. Such an investigation is important to
justify the required photon statistics for substructure studies of
galaxy clusters using X-ray maps on different levels. Our empirical
results will be useful for the community to sample clusters and to
perform X-ray observations for such substructure studies. We set the
fourth criterion in order to get new scientific results out of our
tests.
\subsection{Data Preparation}
\label{s:screen}
To prepare the data, we apply iterative screening using a 2$\sigma$ clipping
as described in Zhang et al. (2006, 2007) using both the soft band
(0.3-10~keV) and the hard hand (10-12~keV for MOS and 12-14~keV for pn) to
filter flares. Hereafter, we call those light-curve screened events for the
clusters the target observations (TOs). The properties of the four clusters
are presented in Table~\ref{t:basic}.
\subsection{Point-Like Source Identification and Subtraction}
\label{s:psrc}
The ``edetect\_chain'' command is used to detect point-like sources. Point
sources in the outskirts of the cluster are subtracted. In the cluster center,
only these detected point-like sources carefully checked by eye and identified
with detected point-like sources in Chandra (Hudson et al. 2009) are
subtracted.
There is good agreement between \emph{XMM-Newton} and \emph{Chandra} detected central
point-like sources. For IIIZw54, a point source is detected by both
\emph{XMM-Newton} and \emph{Chandra} at the center (03:41:17.54, +15:23:47.61), where
a cD galaxy sits. A3391 also has a point source at the center (06:26:20.45,
-53:41:35.80) coincident with the cD, detected by both \emph{XMM-Newton} and
\emph{Chandra}. For EXO0422, there are no evident point-like sources detected by
\emph{Chandra} at the center. The \emph{XMM-Newton} image shows extremely peaked
X-ray emission similar to a point-like source (04:25:51.25, -08:33:36.97) at
the position of the cluster galaxy C1G~0422-09 (also see Belsole et al. 2005).
Conservatively, we identify it as a point-like source and subtract it. For
A0119, there are no evident point-like sources in the cluster center in either
\emph{XMM-Newton} or \emph{Chandra} data, co-spatial with a cD.
\subsection{Background Treatment}
\label{s:allbkg}
As also described in Snowden et al. (2008), the following four background
components have been taken into account in our background treatment. The first
is the quiescent particle background (QPB). The second is the fluorescent
X-ray background (FXB). The third is the soft proton - caused background
(SPB). The fourth is the cosmic X-ray background (CXB).
\subsubsection{QPB and FXB}
\label{s:qpb}
The treatment of the QPB and FXB has been documented using the filter wheel
closed (FWC) observations for MOS in Snowden et al. (2008) and for pn in
Freyberg et al. (2006).
As a first step to model the QPB and FXB, we extract the spectra using
events out of the FOV\footnote{An expression of ``\#XMMEA\_16'' in the
SAS command ``evselect'' means to select the events out of the FOV.}
from the FWC
observations\footnote{http://xmm.vilspa.esa.es/external/xmm\_sw\_cal/background/\#EPIC}
to investigate the properties of the QPB and FXB using the 2-12 keV
band as done in Snowden et al. (2008) and Freyberg et al. (2006). The
FWC MOS1/MOS2 (pn) spectrum can be well fitted by a ``powerlaw/b''
model together with six (eight) ``Gaussian/b'' models to account for
the FXB lines. The photon index of the ``powerlaw/b'' model, $\Gamma$,
is $0.154 \pm 0.006$ for MOS1 (reduced $\chi^2=1.14$ for 645 degrees
of freedom (dof)), $0.138\pm 0.008$ for MOS2 (reduced $\chi^2=1.09$
for 645 dof), and $0.345\pm 0.012$ for pn (reduced $\chi^2=0.89$
for 630 dof), respectively. The best fit provides reliable
measurements of the ``LineE'' parameter with a few percent precision
and of the ``Sigma'' parameter within a factor of 1.4 for the
``Gaussian/b'' model. Across the detectors we found the slope of the
``powerlaw/b'' is $\sim 0.15$ for MOS and $\sim 0.35$ for pn, both
varying by at most 15\%. The properties of the FWC observations are
consistent with the results found in de Plaa et al. (2006) and
Freyberg et al. (2006)
De Luca \& Molendi (2004) pointed out that a simple renormalization of
the QPB using the high energy band (e.g., 8-12~keV) count rate may
lead to systematic errors in both the continuum and the lines. We thus
checked the out of FOV - extracted spectra of $\sim 60$ TOs. The slope
of the individual TOs is indeed inconsistent (up to $\sim$50\%) with
the stack FWC observations when the full 2-12~keV band is used. A
consistency of the slope appears when the 3-10~keV band is fitted. We
therefore re-normalize the FWC observations for the QPB and FXB
subtraction using a broad band of 3-10~keV. The best fit of the
photon index ($\Gamma$) of the stack FWC observations using the
3-10~keV band is $0.144 \pm 0.016$ for MOS1 (reduced $\chi^2=1.07$ for
640 dof), $0.140\pm 0.017$ for MOS2 (reduced $\chi^2=1.03$ for 637
dof), and $0.341\pm 0.039$ for pn (reduced $\chi^2=0.89$ for 498 dof),
respectively.
As a second step, for both MOS and pn, we model and subtract the QPB for
individual observations using the stacked FWC observations with the same mode
as for the TOs. To determine the normalization, we extract the
spectra using events out of the FOV (\#XMMEA\_16) and outside of a
$15.4^{\prime}$ radius from the detector center for both FWC observations and
TOs. As De Luca \& Molendi (2004) found, both X-ray photons and low energy
particles can reach CCD~2 and CCD~7 of the MOS cameras. We exclude both CCDs
for MOS. For later observations with the MOS1 camera, we exclude CCD~6 in the
FWC data to match the loss of MOS1 CCD~6 in the TOs. As also found in Snowden
et al. (2008), some observations show occasional deviations of CCD~4 and CCD~5
for MOS1 and CCD~5 for MOS2. These CCDs are then excluded as well for those
observations. Freezing the photon index of the ``powerlaw/b'' model and the
``LineE'' and ``Sigma'' parameters of the ``Gaussian/b'' model to the best fit
derived above using all events out of the FOV from the FWC observations in the
3-10~keV, we obtained the normalization from the best fit. The
renormalization factor ($n_{\rm QPB}$) of the continuum component is derived
as the ``powerlaw/b'' normalization ratio of the TO to FWC observations. The
FWC spectrum ($S_{\rm FWC}$) is normalized by this renormalization factor,
$n_{\rm QPB}$, and subtracted from the TO spectrum ($S_{\rm TO}$) for each
instrument.
\subsubsection{SPB}
The screening procedure described in Sect.~\ref{s:screen} using both
the hard band and the soft band to prepare the data has filtered all
of the significant SPB component for most observations. The
observations with significant residual SPB found in the spectral
analysis shall be excluded. Luckily, none of the observations for the
four clusters show significant residual SPB.
\subsubsection{CXB}
\label{s:cxb}
Both RASS data and PSPC pointed data can be used to model the CXB. The
latter, of higher statistical quality, are preferred. The \emph{ROSAT}
PSPC calibration shows an accuracy of better than 5\% even for
energies lower than 0.28~keV (Beuermann 2008). Therefore we use the
\emph{ROSAT} PSPC pointed data in the 0.1-2.4~keV band to model the
CXB. The spectrum was extracted from the region just beyond $r_{200}$
for each cluster. The best fit of the spectrum shows that the CXB can
be well described by a combined model,
``mekal$+$wabs$*$(mekal$+$powerlaw)''. The temperature of the
unabsorbed thermal component is often $\sim 0.1$~keV, and of the
absorbed thermal component is often between 0.1 and 0.2~keV,
respectively. To avoid large background fluctuations, we have excluded
regions showing bright sources identified by eye. The absorbed
``powerlaw'' model, with its slope set to 1.41, accounts for
unresolved point sources (De Luca \& Molendi 2004). The ``wabs'' model
is set to the hydrogen column density from the LAB survey\footnote{The
Leiden/Argentine/Bonn Galactic HI Survey (LAB survey) contains the
final data release of observations of $\lambda$21-cm emission from
Galactic neutral hydrogen over the entire sky, merging the
Leiden/Dwingeloo Survey (LDS; Hartmann \& Burton 1997) of the sky
north of $\delta = -30^{\circ}$ with the Instituto Argentino de
Radioastronomía Survey (IARS; Arnal et al. 2000; Bajaja et al.
2005) of the sky south of $\delta = -25^{\circ}$. The angular
resolution of the combined survey is half-power beamwidth (HPBW)
$\sim 0.6^{\circ}$.
http://www.astro.uni-bonn.de/$\sim$webrai/english/tools\_labsurvey.php}
(Hartmann \& Burton 1997; Arnal et al. 2000; Bajaja et al. 2005;
Kalberla et al. 2005) at the \emph{XMM-Newton} determined cluster
center. We repeated the CXB modeling with a
``mekal$+$wabs$*$(mekal$+$mekal$+$powerlaw)'' model, which includes a
second absorbed thermal emission component, and which shows no
significant improvement of the fit. Therefore, we use the
``mekal$+$wabs$*$(mekal$+$powerlaw)'' model for the CXB.
With increasing radial distance from the cluster center, the CXB
becomes dominant over the cluster emission. We therefore use the
outskirts to model the CXB. We extract the \emph{XMM-Newton} spectra
from the outermost region ($9^{\prime}.17<R<10^{\prime}$ from the
cluster center) in the \emph{XMM-Newton} FOV, $S_{\rm TO}$. The FWC
spectrum is extracted from the same detector coordinates as for the TO
spectrum, and normalized by $n_{\rm QPB}$ (derived in
Sect.~\ref{s:qpb}). We call these spectra, $S_{\rm TO} - n_{\rm
QPB}S_{\rm FWC}$, the secondary observational (SO) spectra. To
derive the normalization of the CXB and to measure the cluster
emission, we made a joint fit of the above \emph{ROSAT} PSPC spectrum
by ``mekal$+$wabs$*$(mekal$+$powerlaw)'', and the three
\emph{XMM-Newton} EPIC spectra by
``wabs$*$mekal$+$mekal$+$wabs$*$(mekal$+$powerlaw)$+$powerlaw/b''.
Note in this co-fit analysis, we link the temperatures and
normalizations of the two ``mekal'' model and the normalization of the
``powerlaw'' model for the CXB between \emph{ROSAT} PSPC and
\emph{XMM-Newton} EPIC. The first ``wabs$*$mekal'' component in the
model for the \emph{XMM-Newton} EPIC spectra takes into account the
hydrogen column density absorption (frozen to the value from the LAB
survey) and cluster emission with its metallicity fixed to 0.3 solar
metallicity. The ``powerlaw/b'' component takes into account the
residual SPB in the \emph{XMM-Newton} spectra, which normalization
should be consistent with zero. For some TOs, the ``powerlaw/b''
normalization can be significantly higher, which is inconsistent with
zero. Due to the SPB contamination, the spectra from the corners out
of the FOV for such TOs often show completely inconsistent shape (i.e.
the slope of the ``powerlaw'' component) with that for the FWC
observations. Therefore, the designed QPB background treatment using
the FWC observations will fail for such TOs, and they should not be
used for our analysis. Luckily, the normalization of the
``powerlaw/b'' model for all four clusters is consistent with zero. This
confirms that the light curve screening procedure in
Sect.~\ref{s:screen} has removed all of the significant flares for
these four clusters.
De Luca \& Molendi (2004) derived the normalization of
0.00345~photons~keV$^{-1}$~cm$^{-2}$~s$^{-1}$~deg$^{-2}$ at 1~keV for
the ``powerlaw'' model of the CXB with a photon index of 1.41 using
\emph{XMM-Newton} EPIC data. The agreement is better than 40\%
between their value and the best-fit value from our co-fit of
\emph{ROSAT} PSPC pointed data and \emph{XMM-Newton} EPIC data for
each annulus for each cluster, i.e. within 28\% for IIIZw54, within
14\% for A3391, within 40\% for EXO0422, and within 30\% for A0119.
And the agreement becomes better with increasing radial distance from
the cluster center as the cluster emission becomes less dominant in
the outskirts. Setting the normalization to the value in De Luca \&
Molendi (2004), we observe no pronounced change in the $\chi^2$ and
measured parameters of the best fit. Note that the best fits of the
spectra also provide reasonable cluster temperatures in comparison to
previous published results.
\section{Spectral analysis for temperature profile}
\label{s:spe}
\subsection{Point-Spread Function and Vignetting}
Using the \emph{XMM-Newton} point-spread function (PSF) calibrations
in Ghizzardi (2001) we estimate the redistribution fraction of the
flux. It is 20\% for bins with widths of about $0.5^{\prime}$ and less
than 10\% for bins with widths $\ge 1^{\prime}$ neglecting energy- and
position\footnote{All four observations roughly centered on the
cluster centers.}- dependent effects. We thus require annular width
$\ge 0.5^{\prime}$ in the radial spectral analysis. The PSF effect is
important within $0.5^{\prime}$, which corresponds to $\le
0.038r_{500}$ for our four nearby clusters. The PSF effect introduces an
uncertainty only to the radial temperature measurement in the inner
bins. We made an attempt to correct for the PSF effect for
RXCJ2228$+$2037 in Jia et al. (2008), and found the PSF correction is
important mainly in the inner radii and causes effects well within
10\% level on the temperature measurements. A similar conclusion was
reached in Snowden et al. (2008) for A1795. Therefore we skip the PSF
correction in our radial spectral analysis.
X-ray telescopes often have non-azimuthally symmetric PSFs. In the temperature
map, the structure due to effects of the non-azimuthally symmetric PSF might
be interpreted as actual structure in the cluster. However, those effects
become important only an off-axis radii of larger than $10^{\prime}$. The
regions used for our studies are well within a off-axis radius of
$6^{\prime}$. Note that the regions used for 2D diagnostics are often
$\le 6^{\prime}$ for the four clusters. In addition, these effects are
significant only for regions of $1^{\prime}$ size along the radial-axis in
such outer regions. The radial axis width of the bins are all much larger than
$1^{\prime}$, particularly using the \emph{Mask-V} (defined in
Sect.~\ref{s:mask}), in the outer regions.
For both images and spectra, the vignetting is taken into account in the
extraction using the ``evigweight'' created column in the events.
\subsection{Radial Bin Size}
The blank sky accumulations of the archival \emph{XMM-Newton} observations in
the \emph{Chandra} Deep Field South (CDF-S) can be used as a rough estimate of the
background. Note that in the spectral analysis, the background is properly
treated as described in Sect.~\ref{s:allbkg}. The CDF-S observations are only
used as a rough background estimate to determine the radial bin size for the
spectral analysis.
We screen the CDF-S observation using the same threshold as for the TOs, and
normalize them to the TOs using the hard band (10-12~keV for MOS and
12-14~keV for pn) as described in Zhang et al. (2004). This former step
guarantees similar QPB levels, and the latter step guarantees similar SPB
levels. The residual SPB and the difference in the CXB and FXB are ignored in
the determination of the bin size.
For a cluster with a temperature of $\sim 4$~keV, the uncertainty in
the spectrally measured temperature is $\le $5\% (10\%) using both pn
and MOS spectra, giving net source counts of $\ge 72,000$ (24,000)
after the background subtraction. Therefore the annuli for spectral
analysis are determined by requiring (1) that the width of each
annulus is larger than $0.5^{\prime}$, (2) that the net source counts
is $\ge C$ per MOS2 spectrum in the 0.5-7.8~keV band. The threshold
$C$ is 18,000 except for the clusters with less than four annuli in total
for which $C$ is 6000. We include an outermost bin which does not
fulfill the threshold of $C$, with an outer radius truncated to give a
maximum net source counts.
\subsection{Spectral Fitting}
To obtain the projected temperature profile, the three EPIC spectra
for each annulus are normalized to the solid angle of that annulus
taking into account corrections for gaps, bad pixels and point
sources. We performed the background modeling and co-fit as described
for the outermost region in Sect.~\ref{s:cxb}. Note that we firstly
fit the \emph{ROSAT} PSPC spectrum together with one of the
\emph{XMM-Newton} EPIC spectrum and found that the fitting parameters
(temperature, abundance, and normalization) agree to within a few per
cent between different EPIC instruments. We then fit the parameters
simultaneously to the \emph{ROSAT} PSPC spectrum together with all
three \emph{XMM-Newton} EPIC spectra.
To obtain the radial temperature profile for the mass modeling, we
deproject the spectra (e.g., Zhang et al. 2007), in which the spectral
models for the background components are renormalized to the volume of
the radial shell. The deprojected EPIC spectra and \emph{ROSAT} PSPC
spectrum are then fitted simultaneously to derive the radial
temperature measurements.
\section{Mass Modeling}
\label{s:mass}
The soft band (0.7-2~keV) X-ray surface brightness profile model $S_{\rm
X}(R)$, in which $R$ is the projected radius, is linked to the ICM electron
number density profile $n_{\rm e}(r)$ and emissivity function as an integral
performed along the line of sight,
\begin{equation}
S_{\rm X}(R)\propto\int_{-\infty}^{\infty} n_{\rm p} n_{\rm e} d\ell.
\label{e:sx}
\end{equation}
The \emph{XMM-Newton} observed surface brightness profile is derived by
subtracting the renormalized (by $n_{\rm QPB}$) FWC surface brightness profile
and the CXB in the 0.7-2~keV band derived in Section~\ref{s:spe} from the TO
surface brightness profile. The truncation radii (S/N~$\ge 3$, see
Table~\ref{t:basic}) of the \emph{XMM-Newton} observed surface brightness
profiles are rather small ($<r_{500}$). The \emph{ROSAT} observed surface
brightness profiles cover radii well beyond $r_{500}$ with S/N~$\ge 3$,
although with sparse data points in the cluster core. We thus combine the
\emph{XMM-Newton} observed surface brightness within its truncation radius
($r_{\rm t}$) with the \emph{ROSAT} converted observed surface brightness
profile\footnote{The \emph{ROSAT} converted observed surface brightness
profile can be derived using the \emph{ROSAT} surface brightness model in
Reiprich \& B\"ohringer (2002) with the following two steps: (1) calculating
the electron number density profile from the \emph{ROSAT} surface brightness
model using the \emph{ROSAT} emissivity function, (2) projecting the
electron number density profile to obtain the \emph{XMM-Newton}-like surface
brightness profile using the \emph{XMM-Newton} response and convolving the
\emph{XMM-Newton} PSF. In this procedure, the scatter and the error of each
bin of the \emph{ROSAT} observed surface brightness profile are propagated.}
beyond $r_{\rm t}$ as the observed surface brightness profile (e.g., IIIZw54
in Figure~\ref{f:sx}). The observed surface brightness profile is fitted by
Eq.~\ref{e:sx} convolved with the \emph{XMM-Newton} PSF matrices to obtain the
parameters of the double-$\beta$ model of the electron number density profile,
$n_{\rm e}(r)=n_{\rm e01}(1+r^2/r_{\rm c1}^2)^{-3\beta/2}+n_{\rm
e02}(1+r^2/r_{\rm c2}^2)^{-3\beta/2}$.
We assume that, (1) the ICM is in hydrostatic equilibrium within the
gravitational potential dominated by dark matter (DM), and (2) the DM
distribution is spherically symmetric. The cluster mass is then
calculated from the X-ray measured ICM density and temperature
distributions by,
\begin{equation}
\frac{1}{\mu m_{\rm p} n_{\rm e}(r)}\frac{d[n_{\rm e}(r) k T(r)]}{dr}=
-\frac{GM(<r)}{r^2}~,
\label{e:hyd}
\end{equation}
where $\mu=0.62$ is the mean molecular weight per hydrogen atom. $k$ is the
Boltzmann constant, and $T$ is the temperature. Following the method in Zhang
et al. (2007), we use a set of input parameters of the approximation
functions, in which $\beta$, $n_{\rm e0i}$, $r_{\rm ci}$ ($i=1,2$) represent
the double-$\beta$ electron number density profile $n_{\rm e}(r)$ and $P_{\rm
i}$ ($i=1,...,7$) represent the deprojected temperature profile
$T(r)=P_3\;\exp[-(r-P_1)^2/P_2]+P_6(1+r^2/P_4^2)^{-P_5}+P_7$ (e.g., for
IIIZw54 and EXO0422 in Figure~\ref{f:tprof}), respectively, to compute the mean
cluster mass. The mass uncertainties are propagated using the uncertainties of
the electron number density and temperature measurements by Monte Carlo
simulations as described in Zhang et al. 2007, 2008). The cluster masses
$M_{2500}$ and $M_{500}$ are used in studying the scaling relations in
Sect.~\ref{s:scaling}.
\section{Spectrally Measured 2D Maps}
\label{s:map}
In our procedure, the 2D temperature, electron number density, entropy
and pressure maps\footnote{They will be made publicly available
through the German Astrophysical Virtual Observatory (GAVO) under
Multivariate Archive of X-Ray Images, http://www.g-vo.org/MAXI/~.}
are created based on the spectral measurements in each spatial bin.
The binning methods described below allow for less biased definition
of the zones for the spectral extraction compared with the zones
determined in the wavelet approach in e.g., Finoguenov et al. (2005).
The available statistics of our data are sufficient to provide
detailed 2D diagnostics, and the radial study of the fluctuations for
individual clusters - a new complementary tool to measure the
substructure.
\subsection{Mask Determination}
\label{s:mask}
We use the MOS2 data to determine the spatial bins in the mask
(e.g., for IIIZw54 in Figure~\ref{f:mask}) for the following two reasons:
(1) the pn data are seriously affected by gaps which can complicate
the analysis of cluster structure, and (2) the CCD6 is missing for
MOS1 for recent observations. We use the 0.5-2~keV band MOS2 image
binned in $4^{\prime \prime}\times 4^{\prime \prime}$ pixels to
determine the mask regions for the spectral analysis. The image is
binned to give an S/N of $\ge33$ for each spatial bin in the mask.
For a cluster with a temperature of $\sim 4$~keV, the uncertainty in
the spectrally measured temperature is $\sim$10\% (e.g., for IIIZw54,
lower panels in Figure~\ref{f:tmap}).
We adopted two methods to determine the bins (e.g., for IIIZw54 in
Figure~\ref{f:mask}), which are both based on the brightness criteria. One is
the weighted Voronoi tessellation method (Cappellari \& Copin 2003; Diehl \&
Statler 2006), whose binning shapes are geometrically unbiased giving a quasi
circle-like shape. This binning scheme is sensitive to local brightness
fluctuations (e.g., Simionescu et al. 2007). The other method was developed by
Sanders (2006), and bins the brightest pixels of the remaining region. The
mask therefore extends along the isophotal annulus centered at the cluster
core. This binning scheme is sensitive to the detection of shocks and cold
fronts (e.g., Sanders \& Fabian 2007). Hereafter we call the mask defined with
the former method as \emph{Mask-V}, and the mask defined with the latter
method as \emph{Mask-S}. The advantage of the \emph{Mask-S} binning is that
mixing of different temperature components due to a radial temperature
gradient is minimal, while the \emph{Mask-V} binning is more sensitive to
features like bright spots.
\subsection{Temperature Maps}
\label{s:2dspec}
The spectra are extracted for each bin in the mask, and normalized to the
solid angle of that bin taking into account corrections for gaps, bad pixels
and excluded point sources. The QPB and CXB models derived in
Sect.~\ref{s:spe} in the spectral fit are normalized to the solid angle of the
bin as frozen models. The MOS and pn spectra are fitted simultaneously by a
``wabs*mekal'' model for hydrogen column density absorption and cluster
emission, with the frozen models to account for the background. The best-fit
temperature and its error bar for each bin are used to create the temperature
($T$) map and its error map (e.g., for IIIZw54 shown in Figure~\ref{f:tmap}).
\subsection{Electron Number Density, Entropy and Pressure Maps}
The spectral normalization in each spatial bin can be used to derive a
quasi deprojected estimate of the electron number density ($n_{\rm
e}$) in that spatial bin (e.g., Henry et al. 2004). In XSPEC, the
normalization of the ``mekal'' model is given as $K=10^{-14} / [4\pi
D_{\rm A}^2 (1+z)^2] \int n_{\rm e} n_{\rm H} dV$, where $D_{\rm A}$
is the angular diameter distance, $z$ is the redshift, and the volume
corresponding to that spatial bin is approximated by $V \approx
(4/3)D_{\rm A}^3 \Omega \sqrt{\theta_{\rm out}^2-\theta_{\rm in}^2}$.
Here $\Omega$ is the solid angle of the corresponding spatial bin, and
$\theta_{\rm out}$ and $\theta_{\rm in}$ are the angles of the
outermost and innermost radii of that bin from the cluster center. As
mentioned in Simionescu et al. (2007), it provides a quasi
deprojection using an approximation of the three-dimensional extent
of each spatial bin and assuming a constant temperature along the line
of sight. As most emission in the bin is from the densest gas near the
innermost radius of that bin, the electron number density derived from
the spectral normalization can be used as the measurement of the
electron number density at the projected radius.
The entropy ($S$) and pressure ($P$) maps can be derived from the temperature
and electron number density maps by $S=kT n_{\rm e}^{-2/3}$ and $P=kT n_{\rm
e}$. The X-ray spectrally measured temperature, electron number density,
entropy and pressure maps for IIIZw54, A3391, EXO0422 and A0119, respectively,
are shown in Figures~\ref{f:iiizw54map}-\ref{f:a0119map}.
\section{Substructure Diagnostics with ICM $T$, $n_{\rm e}$, $S$ and $P$ Maps}
The fluctuations in the 2D maps and their scatter can be used as
substructure diagnostics. A disturbance in a cluster may appear as a
high amplitude of and/or a discontinuity in the radial profile of the
scatter of the fluctuations. Unrelaxed clusters may show larger
fluctuations and significant correlations between,
e.g., temperature and electron number density fluctuations. The
substructure diagnostics of galaxy clusters are therefore directly
linked to the scatter of the scaling relations due to the bias in
X-ray hydrostatic masses and X-ray observables caused by
substructures.
The \emph{Mask-S} method, whose bins are close to radial annuli, has the
advantage that the interpretation of a comparison to a mean temperature
profile is more straightforward because the range of radii sampled in each bin
is smaller. Therefore, we concentrate more on the results from this method,
particularly when the data quality is low.
\subsection{Scatter of the ICM $T$, $n_{\rm e}$, $S$ and $P$ Fluctuations}
\label{s:scatter}
The scatter of the fluctuations in the 2D maps from the mean profile
can be used as diagnostics of the ICM substructure. Here we briefly
describe how the scatter and error are calculated. To avoid systematic
errors due to uncertain background subtraction, we only consider bins
of radii $\le 0.6r_{\rm tr}$ ($r_{\rm tr}$ see Table~\ref{t:basic}).
To better show the asymmetries of the clusters, we use a polar
coordinate system with the cluster center as its coordinate center.
The scaled distribution of a 2D map is defined as $D(d, \theta)$, in
which ($d, \theta$) are the angle and distance in the polar coordinate
system. For example $D(d_i, \theta_i)=T(R_i, \theta_i)/T_{0.2-0.5
r_{500}}$ is the value of the 2D spatial bin ($d_i, \theta_{i}$) in
a 2D temperature map. Note that $T_{0.2-0.5 r_{500}}$ is the cluster
temperature, a volume average of the radial temperature profile
limited to the radial range of $0.2-0.5 r_{500}$ (see Appendix B.2 in
Zhang et al. 2008) and $d_i=R_i/r_{500}$ is the distance between the
cluster center and the geometric center of that 2D bin scaled by the
cluster $r_{500}$. To investigate the asymmetry, we derive an
azimuthal-averaged profile $D(d)$ of the scaled distribution
$D(d,\theta)$. A non-parametric locally weighted
regression\footnote{The procedure calls ``lowess'' in the R package,
which uses locally weighted polynomial regression (e.g., Becker et
al. 1988). We used the default smoothing span $f=2/3$. ``Local'' is
defined by the distance to the ``floor($f* n$)''{\it th} nearest
neighbor, and tricubic weighting is used for $x$ which fall within
the neighborhood. Note that ``floor'' in the R package takes a
single numeric argument $x$ and returns a numeric vector containing
the largest integers not greater than the corresponding elements of
$x$. More details are at http://CRAN.R-project.org.} (Sanderson et
al. 2005, and references therein) of the averaged profile is used to
derive the mean profile $\langle D(d)\rangle$. The absolute
fluctuation distribution is defined as $F=|D(d, \theta)/\langle
D(d)\rangle-A|$. Here, the renormalization $A$ is not equal to one only
when there is a possible bias in the mean scaled profile. In this
work, we used $A=1$. In the scatter calculation, the weighting of the
absolute fluctuation $F_i$ is the area $w_i$ of the corresponding
$i$th spatial bin in the 2D map. The cumulative scatter and error are
calculated from the area weighted absolute fluctuations as
$\sqrt{\Sigma F_i^2 w_i}/\sqrt{\Sigma w_i}$, with all bins within $d$.
The differential scatter and error are calculated from the weighted
absolute fluctuations with all bins in the range of $d_1$ and $d_2$,
in which $d=0.5(d_1+d_2)$.
\subsection{Scatter Profiles from the Azimuthal Average}
\label{s:step2}
When one single azimuthal-averaged profile $\langle D(d)\rangle$ for the four
clusters as a whole is used, the scatter and error can indicate the degree of
self-similarity of the investigated azimuthal-averaged quantities. We thus
carry out a non-parametric fit on the scaled distribution of temperature,
electron number density, entropy, and pressure, respectively, for the four
clusters as a whole (see Figure~\ref{f:tdis}). The cumulative scatter and error
for the four clusters as a whole are shown in Figure~\ref{f:tnormsca}, and the
differential scatter and error are shown in Figure~\ref{f:tnormsca_dr}. The
highest amplitude occurs in the cluster core ($\le 0.3r_{500}$) which is
caused by the known difference between cool core and non-cool core clusters.
To avoid the above scatter due to the difference between cool core and
non-cool core clusters in substructure diagnostics, we carry out a
non-parametric fit to the scaled distribution of temperature, electron
number density, entropy, and pressure, respectively, for each cluster
to derive its own azimuthally averaged scaled distribution $\langle
D(d)\rangle$. The cumulative scatter and error for the four cluster as
a whole using the individual cluster mean scaled profiles are shown in
Figure~\ref{f:tnormsca_ind}, and the differential scatter and error
are shown in Figure~\ref{f:tnormsca_dr_ind}. The cumulative scatter is
quite flat. Its amplitude indicates $\sim 10$\% fluctuations in the
temperature, electron number density, and entropy maps, and $\sim
15$\% fluctuations in the pressure map. The cumulative scatter and
error for each cluster using the individual cluster mean scaled
profiles are shown in Figure~\ref{f:tsca}, and the differential
scatter and error are shown in Figure~\ref{f:tsca_dr}. To derive the
mean profiles for each cluster, broader bins (a bin size of $0.2
r_{500}$) are used due to decreased statistics for individual clusters
compared with the statistics for the four clusters as a whole, where we use
a bin size of $0.1 r_{500}$. The scatter here can be used as
substructure diagnostics for individual clusters as shown in
Sect.~\ref{s:diag}.
\subsection{Substructure Diagnostics in Individual Clusters}
\label{s:diag}
A disturbance in the clusters appears as a high amplitude of and/or a
discontinuity in the radial profile of the scatter of the
fluctuations. The radial studies of the scatter of the fluctuations in
the 2D map for individual clusters thus provide detailed diagnostics
to identify the ICM substructures.
{\it IIIZw54}. The 2D maps ($T$, $n_{\rm e}$, $S$ and $P$) show an
azimuthally symmetric appearance (Figure~\ref{f:iiizw54map}). It has a
relatively low amplitude of the scatter, particularly for the
temperature and entropy fluctuations ($\sim 5$\%, see
Figure~\ref{f:tsca}). The cumulative scatter appears very flat. The
differential scatter (Figure~\ref{f:tsca_dr}), which describes the local
fluctuations, shows an increase for the temperature and entropy in the
radial ranges beyond $0.3r_{500}$ using the \emph{Mask-V} only. This
indicates that the substructure is roughly round clumps detectable
using the \emph{Mask-V} instead of isophotal annuli detectable using
the \emph{Mask-S}. Both the radial studies of the scatter and the 2D
map appearance shows IIIZw54 is the most relaxed cluster among the four
clusters, with mild entropy clumps beyond $0.3r_{500}$. It is peculiar
that this cluster does not host a cool core (Figure~\ref{f:tprof}).
IIIZw54 therefore is an example of a relaxed non-cool core cluster.
{\it A3391}. It shows a mild increasing amplitude (from 4\% to 10\%) with
radius in the cumulative scatter of the fluctuations (Figure~\ref{f:tsca}). The
electron number density and pressure scatter profiles show a discontinuity
around $0.2 r_{500}$ using the \emph{Mask-V}, at which radius the metallicity
also shows significant clumps as well. It has an elliptically
shaped morphology with a bi-sector feature divided by the short axis of the
elliptical as shown in Figure~\ref{f:a3391map}. It is known that A3391 is close
to the interacting cluster A3395. The sector west of the cluster core up to
$\sim 0.25 r_{500}$ shows $\sim 1$~keV higher temperature, together with low
electron number density, higher entropy and low pressure in the maps
(Figure~\ref{f:a3391map}). These substructure features are consistent with
the observed discontinuity around $0.2 r_{500}$, and all would suggest that
some merging activities are present. A3391 is therefore an unrelaxed non-cool
core cluster. The estimates of both the X-ray observables and the X-ray
cluster mass for such an unrelaxed cluster can be biased due to the observed
substructure.
{\it EXO0422}. This cluster shows the second highest scatter amplitude,
particularly for the entropy. This is somewhat surprising because the X-ray
surface brightness appears azimuthally symmetric and the radial temperature
profile even shows a drop toward the center (Figure~\ref{f:tprof}), typical of
a cool core cluster. However, the temperature maps (Figure~\ref{f:exo0422map})
clearly show a bi-sector feature divided by the southeast-northwest axis
through the cluster core. The northeastern sector shows $\sim $0.5-1~keV
higher temperature and 0.3-0.5~$Z_{\odot}$ higher metallicity than the
southwestern sector. This feature might cause a high cluster temperature
estimate, and thus a high $Y_{\rm X}$ parameter value. However, no such
significant substructure features are shown in the electron number density,
entropy and pressure maps. This indicates the cluster is almost relaxed and
that the total mass estimate for this cluster can hardly be biased. Therefore
EXO0422 is an almost relaxed cool core cluster. This seems to be a good
example of a cluster with some merging activities which would go unnoticed
without a temperature map. The scatter of the mass-observable relations for
such an almost relaxed cluster can be caused by the bias in its temperature
estimate and thus in its $Y_{\rm X}$ estimate due to the temperature
substructure.
{\it A0119}. It stands out clearly in radial studies of the scatter in
Figures.~\ref{f:tsca} and \ref{f:tsca_dr}. The scatter of the
temperature fluctuations exhibits a high amplitude, particularly in
the outskirts. We observe an elongation in its X-ray morphology with a
faint emission tail (see also Buote \& Tsai 1996, Hudson et al.
2009). Though this cluster has low-quality data, the maps show clearly
an asymmetric structure with the southwestern sector up to 1-2~keV
hotter than the northeastern sector (Figure~\ref{f:a0119map}), and the
high-temperature zone is located at a central radius of $\sim
2^{\prime}$ ($\sim 0.17r_{500}$) from the cluster center using the
\emph{Mask-S} method. As the $<0.2 r_{500}$ region is excluded in the
cluster temperature determination, the cluster temperature, and thus
the $Y_{\rm X}$ parameter, is less affected by the hot structure in
the cluster core. The pressure map shows a similar feature observed in
the temperature map, while the entropy map shows less significant
features. This suggests that the fluctuations of temperature and
density are likely isentropic, which can be produced by a low Mach
number shock, compression wave, turbulence or triaxiality in the dark
matter distribution. The appearance of A0119 is in favor of being
unrelaxed. Its total mass estimate may thus be significantly affected.
A0119 is an unrelaxed non-cool core cluster.
{\it Summary}. The application of the diagnostics on the four clusters
show the differential scatter of either entropy or temperature is a
sensitive indicator of the substructure. Particularly, the temperature
map is more sensitive to unnoticed substructure which only exists in
the temperature map for an almost relaxed cluster. For an unrelaxed
cluster, the amplitudes of the scatter profiles in the 2D maps are
likely high, with a possible discontinuity in the scatter
profiles.
\subsection{Density versus Temperature Fluctuations}
A correlation between temperature fluctuations and electron number density
fluctuations may shed light on the origin of the fluctuations, e.g., a
constant pressure solution yielding ratios of temperature fluctuations to
electron number density fluctuations, $-1$; and a constant entropy solution
yielding ratios, $2/3$.
To check whether the electron number density fluctuations show a correlation
with the temperature fluctuations, we performed a linear fit ($Y=A+B X $) to
the relation. It shows the highest Pearson correlation coefficient value for
A0119 (Table~\ref{t:dndtfit}), but is still hard to conclude a concrete
correlation. There is no trend of the fluctuations as a function of radius
except for a bump at radii of $0.35-0.45 r_{500}$ for the two unrelaxed
clusters, A3391 and A0119.
\subsection{Scaling Relations versus ICM $T$, $n_{\rm e}$, $S$ and $P$
Fluctuations}
\label{s:scaling}
The substructure diagnostics of galaxy clusters are of prime importance to the
understanding of the X-ray mass estimates and the X-ray observables. In Zhang
et al. (2008), we found the X-ray gas mass ($M_{\rm gas}$) and the X-ray
analog of the integrated SZ flux ($Y_{\rm X}= M_{\rm gas} \cdot
T_{0.2-0.5r_{500}}$) can be used as low scatter cluster mass indicators
compared with other X-ray observables. Therefore we present the mass-$Y_{\rm X}$
relation and mass-$M_{\rm gas}$ relation here (Figure~\ref{f:mymg}).
In simulations, there is a small intrinsic dispersion between the true mass
and the mass derived from the hydrostatic equilibrium equation for relaxed
clusters (e.g., Nagai et al. 2007). We therefore used the deviation of the
cluster mass from the mass-observable relations for a sample of relaxed
clusters as an indicator of the mass bias for the hydrostatic mass. Note that
the mass-observable relations for relaxed clusters could still be biased by
residual non-thermal support (e.g., Mahdavi et al. 2008, Zhang et al. 2008).
We have compiled a sample of 44 LoCuSS clusters (37 in Zhang et al. 2008), and
used the best-fit scaling relations of the subsample of all 22 relaxed
clusters as the reference. At $r_{2500}$, the four clusters are in good agreement
with the subsample of 22 relaxed LoCuSS clusters. With the cluster masses
determined in Sect.~\ref{s:mass}, we observe tantalizing hints linking the
scatter of the ICM fluctuations and the hydrostatic mass bias relative to the
expected mass based on the $M$-$Y_{\rm X}$ and $M$-$M_{\rm gas}$ relations,
particularly at $r_{500}$.
A typical example of a relaxed cluster, IIIZw54 (Figure~\ref{f:iiizw54map}),
lies on the mass-observable scaling relations. A3391 is a weakly merging
cluster (Figure~\ref{f:a3391map}), and lies significantly off from the
mass-observable scaling relations. EX0422 is a mild unrelaxed cool core
cluster. Though its pressure map has no significant substructures which means
the cluster mass may be unbiased. The hot substructure in the temperature map
could cause a high cluster temperature estimate and thus a high $Y_{\rm X}$
estimate. As a result, it lies on the mass-$M_{\rm gas}$ scaling relations but
shows a small offset toward the hot side in the $M$-$Y_{\rm X}$ relation,
particularly at $r_{500}$. A typical example of a dynamically active cluster
is A0119 (Figure~\ref{f:a0119map}). The significant feature of substructures
observed in the pressure map might cause a large bias in the cluster mass
estimate. This cluster indeed shows significant deviations in both the
$M$-$Y_{\rm X}$ and $M$-$M_{\rm gas}$ relations.
To quantify the trend between the mass bias and the scatter of the
fluctuations in the 2D maps, we defined the quasi-mass bias as follows. For
example, the quasi-true mass $M_{\Delta}^{\rm Y_{\rm X}}$ (or $M_{\Delta}^{\rm
M_{\rm gas}}$) can be derived from $Y_{\rm X}$ (or $M_{\rm gas}$) at
$r_{\Delta}$ via the $M_{\Delta}$-$Y_{\rm X}$ (or $M_{\Delta}$-$M_{\rm gas}$)
scaling relation of a subsample of 22 LoCuSS clusters characterized as
relaxed. The quasi-mass-bias is thus defined as $B_{\rm M_{\Delta}}^{\rm
Y_{\rm X}}=M_{\Delta}/M_{\Delta}^{\rm Y_{\rm X}} -1$ (or $B_{\rm
M_{\Delta}}^{\rm M_{\rm gas}}=M_{\Delta}/M_{\Delta}^{\rm M_{\rm gas}} -1$).
We carried out a simple linear fit $Y=A+B X $ to the relation of the
quasi-mass-bias at $r_{\Delta}$ versus the cumulative scatter at the outermost
radius one can measure for individual clusters. The correlation is only
significant (i.e. correlation coefficient $>0.65$) using the scatter of either
entropy or pressure fluctuations and using the quasi-mass-bias at $r_{500}$.
Therefore, we only list the best fit and Pearson correlation coefficient using
the scatter of entropy and pressure fluctuations and the quasi-mass-bias at
$r_{500}$ in Table~\ref{t:bias}. We interpret this result as tentative
evidence for an interesting correlation between mass bias and scatter
amplitude. We will constrain the parameters of these relations in more detail
using a larger cluster sample. These findings shall encourage similar studies
to be carried out using hydrodynamical simulations.
\subsection{Data Quality versus Radial Studies of ICM $T$, $n_{\rm e}$, $S$ and
$P$ Fluctuations}
As shown above, sufficient photon statistics are required to provide
quantitative diagnostics of the substructure in the ICM and to imply
detailed physics relevant to the systematics of the scaling relations.
EXO0422 has the highest data quality among the four clusters. Therefore
the ICM substructure shown in great details allows us to understand
its small offset in the scaling relations, which would have been missed
without our studies. A0119 has insufficient photon statistics to
perform such radial studies of the ICM $T$, $n_{\rm e}$, $S$ and $P$
fluctuations. Though we observed significant features indicating the
strong merging activities in the 2D maps of A0119, the radial
profiles of the scatter show large statistical error and could not
reveal possible discontinuities. Therefore $\ge 30$ bins within the
$0.6r_{\rm tr}$ region is required for such radial studies of the
fluctuations of the spectrally measured ICM $T$, $n_{\rm e}$, $S$ and
$P$ maps. In term of net counts, $\ge$~120,000 cluster photons are
required for one nearby cluster.
\section{Conclusions}
\label{s:conclusion}
Substructure diagnostics of galaxy clusters are crucial to the robustness of
the estimates of both the cluster mass and the X-ray observables. Therefore
they have enormous importance to the understanding of the systematics and
scatter of the mass-observable scaling relations. As a result, the knowledge
of the substructure directly affects the precision of the cosmological tests
using the cluster mass function. To probe possible biases in hydrostatic mass
estimates as a function of cluster dynamical state, we developed a precise
background subtraction procedure using both MOS and pn and a spectral analysis
procedure to derive the X-ray maps via spectral measurements in each spatial
bin. With \emph{XMM-Newton} observations of the four morphological different
clusters selected from the HIFLUGCS sample, we report our procedures and
strategies for the ICM substructure studies using the spectrally measured 2D
temperature, electron number density, entropy, and pressure maps with medium
quality \emph{XMM-Newton} data for nearby clusters. Our procedures provide
detailed 2D diagnostics and a new complementary tool, the radial studies of
the fluctuations in the 2D map of ICM temperature, electron number density,
pressure and entropy, to quantify the substructure in galaxy clusters, and
attempt to explain the deviation of the cluster from the mass-observable
scaling relations.
The amplitude of and the discontinuity in the scatter provide
substructure diagnostics due to merging, the physics behind the
scatter of the mass-observable scaling relations. The amplitude
indicates $\sim 10$\% fluctuations in the temperature, electron number
density, and entropy maps, and $\sim 15$\% fluctuations in the pressure
map. The differential scatter can indicate the most disturbed radial
range, e.g., $0.35-0.45 r_{500}$ for the unrelaxed clusters, A3391 and
A0119.
The temperature map is particularly unique to identify the substructure of an
almost relaxed cluster which would be unnoticed in the ICM electron number
density and pressure maps.
There is a tantalizing link between the substructure identified using the
scatter of the entropy and pressure fluctuations and the hydrostatic mass bias
relative to the expected mass based on the $M$-$Y_{\rm X}$ and $M$-$M_{\rm
gas}$ relations particularly at $r_{500}$. A typical relaxed cluster, such
as IIIZw54, lies on the mass-observable scaling relations. A weakly merging
cluster, A3391, lies significantly off from the mass-observable scaling
relations. An almost relaxed cool core cluster, EXO0422, shows a small offset
in the $M$-$Y_{\rm X}$ relation. A typical dynamical active cluster, A0119,
shows significant mass deviation in the both $M$-$Y_{\rm X}$ and $M$-$M_{\rm
gas}$ relations. The scatter of the observed scaling relations caused by an
unrelaxed cluster can be due the mass estimate being biased by the pressure
substructure and the temperature estimate biased by the temperature
substructure in this cluster, e.g., A0119. The scatter of the observed scaling
relations can also be caused by an almost relaxed cluster, due to the bias in
its temperature estimate affected by its temperature substructure, e.g.,
EXO0422.
\emph{XMM-Newton} observations with $\ge$~120,000 source photons per cluster
are sufficient to apply our method for detailed diagnostics to identify the
substructures of the clusters. More concrete conclusions require such
substructure studies using a statistically large sample, with $\ge$~120,000
source photons per cluster in their \emph{XMM-Newton} observations; this is
work in progress. It will then be interesting to make a detailed comparison of
a possible scatter - mass-bias correlation with the results of numerical
simulations.
\acknowledgments
The \emph{XMM-Newton} project is an ESA Science Mission with instruments and
contributions directly funded by ESA Member States and the USA (NASA). The
\emph{XMM-Newton} project is supported by the Bundesministerium f\"ur
Wirtschaft und Technologie/Deutsches Zentrum f\"ur Luft- und Raumfahrt
(BMWI/DLR, FKZ 50 OX 0001) and the Max-Planck Society. Y.Y.Z. acknowledges J. de
Plaa, S.L. Snowden, H. B\"ohringer, and J. S. Sanders for useful discussions.
Y.Y.Z., T.H.R. and D.S.H. acknowledge support by the DFG through Emmy Noether Research
Grant RE\,1462/2 and the Transregional Collaborative Research Centre TRR33
``The Dark Universe'' and by the German BMBF through the Verbundforschung
under grant\,50\,OR\,0601. A.F. acknowledges support from BMBF/DLR under
grant\,50\,OR\,0207 and MPG and support through the funding of the DFG
for the Excellence Cluster Universe EXC153. CLS was supported in part by NASA
\emph{XMM-Newton} grants NNX06AE76G, NNX08AZ34G, and NNX08AW83G, and by
Chandra grant GO7-8129X. This work has been partially supported from NASA
grants NNX07AV73G and NNX07AT29G. For help in the early stage of the project,
we acknowledge H. B\"ohringer, T. Clarke, T. Erben, A. Evrard, Y. Fujita,
Y. Ikebe, O.-E. Nenestyan, E. Pierpaoli, S. Randall, and P. Schuecker.
\clearpage
\begin{deluxetable}{lccccrcccccc}
\tabletypesize{\scriptsize}
\rotate
\tablecaption{Cluster Properties and
\emph{XMM-Newton} Observations.\label{t:basic}}
\tablewidth{0pt}
\tablehead{
\colhead{Name} & \colhead{OBS-ID} & \colhead{} & \colhead{Net exposure (ks)} & \colhead{} &
\colhead{Mode} & \colhead{X-ray centroid} & \colhead{(J2000)} &
\colhead{$z$} & \colhead{$N_{\rm H}$} & \colhead{$T_{0.2-0.5r_{500}}$} &
\colhead{$r_{\rm tr}$}
}
\startdata
& & MOS1 & MOS2 & pn & pn & R.A. &
Decl. & &$10^{22}{\rm cm}^{-2}$& keV & arcmin\\
\hline
IIIZw54 & 0505230401 & 23.3 & 22.3 & 30.3 & EFF &$ 03:41:18.729 $&$
+15:24:13.91 $& 0.0311 & 0.1470 & $ 2.17 \pm 0.03 $ & 13.35\\
A3391 & 0505210401 & 23.3 & 24.6 & 18.2 & EFF &$ 06:26:24.222 $&$
-53:41:24.02 $& 0.0531 & 0.0559 & $ 5.02 \pm 0.05 $ & 13.32\\
EXO0422 & 0300210401 & 31.5 & 32.2 & 32.7 & EFF &$ 04:25:51.224 $&$
-08:33:40.34 $& 0.0390 & 0.0808 & $ 2.99 \pm 0.03 $ & 13.29\\
A0119 & 0505211001 & 8.2 & 8.0 & 7.6 & FF &$ 00:56:17.119 $&$
-01:15:11.98 $& 0.0440 & 0.0328 & $ 5.47 \pm 0.11 $ & 11.00\\
\enddata
\tablecomments{The EFF mode is the extended full frame mode. The MOS data are
in FF mode. The truncation radius ($r_{\rm t}$) is the radius corresponding
to an S/N of 3.}
\end{deluxetable}
\begin{deluxetable}{lcccccc}
\tabletypesize{\scriptsize} \rotate \tablecaption{The Best Linear Fit
($Y=A+ B X$) of the Relation of Electron Number Density
Fluctuations versus Temperature Fluctuations.
\label{t:dndtfit}}
\tablewidth{0pt}
\tablehead{
\colhead{Name} & & \colhead{\emph{Mask-V}} & & & \colhead{\emph{Mask-S}} & \\
}
\startdata
& $A$ & $B$ & Coefficient & $A$ & $B$ & Coefficient \\
\hline
IIIZw54 & $0.029 \pm 0.004$ & $0.03 \pm 0.08$ & 0.154 & $0.026 \pm 0.002$ &
$0.05 \pm 0.03$ & 0.321 \\
A3391 & $0.038 \pm 0.003$ & $0.06 \pm 0.03$ & 0.335 & $0.043 \pm 0.003$ &
$0.05 \pm 0.03$ & 0.285 \\
EXO0422 & $0.028 \pm 0.002$ & $0.01 \pm 0.02$ & 0.066 & $0.029 \pm 0.001$ &
$0.03 \pm 0.02$ & 0.323 \\
A0119 & $0.046 \pm 0.003$ & $0.06 \pm 0.02$ & 0.765 & $0.052 \pm 0.003$ &
$0.08 \pm 0.02$ & 0.830 \\
\hline
All four clusters & $0.032 \pm 0.001$ & $0.03 \pm 0.02$ & 0.192 & $0.034 \pm 0.001$ &
$0.04 \pm 0.01$ & 0.263 \\
\enddata
\end{deluxetable}
\begin{deluxetable}{llcccccc}
\tabletypesize{\scriptsize} \rotate \tablecaption{The Best Linear Fit ($Y=A+
B X$) of the Relation of the Quasi-Mass Bias, Column~(1), versus the
Cumulative Scatter at the Outermost Radius One can Measure for
Individual Clusters, Column~(2).
\label{t:bias}}
\tablewidth{0pt}
\tablehead{
\colhead{Bias} & Scatter
& & \colhead{\emph{Mask-V}} &
& & \colhead{\emph{Mask-S}} & \\
}
\startdata
&
& $A$ & $B$ & coeff.
& $A$ & $B$ & coeff. \\
\hline
$B_{\rm M_{500}}^{\rm Y_{\rm X}}$ & $S$
& $1.45 \pm 0.38$ &$-14.3 \pm 3.3$ &-0.98
& $0.61 \pm 0.22$ &$-6.6 \pm 1.9$ &-0.80 \\
& $P$
& $1.07 \pm 0.29$ &$-8.0 \pm 1.9$ &-0.97
& $1.12 \pm 0.31$ &$-9.2 \pm 2.2$ &-0.97 \\
$B_{\rm M_{500}}^{\rm M_{\rm gas}}$ & $S$
& $1.06 \pm 0.41$ &$-9.8 \pm 3.6$ &-0.95
& $0.42 \pm 0.23$ &$-4.0 \pm 2.0$ &-0.69 \\
& $P$
& $0.79 \pm 0.32$ &$-5.5 \pm 2.1$ &-0.94
& $0.76 \pm 0.32$ &$-5.9 \pm 2.3$ &-0.90 \\
\enddata
\tablecomments{See details in Sect.~\ref{s:scaling}.}
\end{deluxetable}
\clearpage
\begin{figure*}
\begin{center}
\includegraphics[angle=270,width=15cm]{plots/f01.ps}
\end{center}
\caption{Observed surface brightness profile, with the \emph{ROSAT}
observed surface brightness profile (black) converted to match the
\emph{XMM-Newton} observed surface brightness profile (gray). The
continuous curve presents the best fit of the observed surface
brightness profile using a double-$\beta$ model for the electron
number density profile.
\label{f:sx}}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[angle=270,width=8.0cm]{plots/f02a.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f02b.ps}
\end{center}
\caption{Radial (deprojected) temperature (upper) and metallicity
(lower) profiles. Note that the very central region ($r\le
15^{\prime\prime}$) of EXO0422 was excluded in the spectral analysis
to avoid the possible contamination from the galaxy CIG0422-09 found
by Belsole et al. (2005).
\label{f:tprof}}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[angle=0,width=14cm]{plots/f03.ps}
\end{center}
\caption{Masks using the \emph{Mask-V} (left)
and \emph{Mask-S} (right) method for IIIZw54. The
image size is $11^{\prime} \times 11^{\prime}$.
Each gray scale (from 0 to 34) denotes one bin, but has no physical meaning.
\label{f:mask}}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[angle=0,width=14cm]{plots/f04a.ps}
\includegraphics[angle=0,width=14cm]{plots/f04b.ps}
\end{center}
\caption{Temperature maps (top) and their error maps (bottom) for IIIZw54
using \emph{Mask-V} (left) and \emph{Mask-S} (right). The color
bar is in the range of 1.5-3.2~keV in the top panels, and 0-0.2~keV in the
bottom panels. The image size is $11^{\prime} \times 11^{\prime}$.
\label{f:tmap}}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[angle=0,width=8cm]{plots/f05a.ps}
\includegraphics[angle=0,width=8cm]{plots/f05b.ps}
\includegraphics[angle=0,width=8cm]{plots/f05c.ps}
\includegraphics[angle=0,width=8cm]{plots/f05d.ps}
\end{center}
\caption{Temperature ($T$), electron number density ($n_{\rm e}$), entropy
($S$), and pressure ($P$) maps for IIIZw54 with the \emph{Mask-V} on the
left and the \emph{Mask-S} on the right in each panel. The color bars
are in the range of 1.5-3.2~keV,
0-0.0063~cm$^{-3}$, 90-400~keV~cm$^2$, and 0-0.02~keV~cm$^{-3}$ in the
$T$, $n_{\rm e}$, $S$, and $P$ panels, respectively. The image size is
$11^{\prime} \times 11^{\prime}$.
\label{f:iiizw54map}}
\end{figure*}
\clearpage
\begin{figure*}
\begin{center}
\includegraphics[angle=0,width=8cm]{plots/f06a.ps}
\includegraphics[angle=0,width=8cm]{plots/f06b.ps}
\includegraphics[angle=0,width=8cm]{plots/f06c.ps}
\includegraphics[angle=0,width=8cm]{plots/f06d.ps}
\end{center}
\caption{Temperature ($T$), electron number density ($n_{\rm e}$), entropy
($S$), and pressure ($P$) maps for A3391 with the \emph{Mask-V} on the
left and the \emph{Mask-S} on the right in each panel. The
color bars are in the range of 3.3-6.5~keV,
0-0.0046~cm$^{-3}$, 200-850~keV~cm$^2$, and 0-0.025~keV~cm$^{-3}$ in the
$T$, $n_{\rm e}$, $S$, and $P$ panels, respectively. The image size is
$11^{\prime} \times 11^{\prime}$.
\label{f:a3391map}}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[angle=0,width=8cm]{plots/f07a.ps}
\includegraphics[angle=0,width=8cm]{plots/f07b.ps}
\includegraphics[angle=0,width=8cm]{plots/f07c.ps}
\includegraphics[angle=0,width=8cm]{plots/f07d.ps}
\end{center}
\caption{Temperature ($T$), electron number density ($n_{\rm e}$), entropy
($S$), and pressure ($P$) maps for EXO0422 with the \emph{Mask-V} on the
left and the \emph{Mask-S} on the right in each panel. The
color bars are in the range of 1.5-4.2~keV,
0-0.023~cm$^{-3}$, 20-580~keV~cm$^2$, and 0-0.025~keV~cm$^{-3}$ in the
$T$, $n_{\rm e}$, $S$, and $P$ panels, respectively. The image size is
$11^{\prime} \times 11^{\prime}$. The
hole in the cluster center for EXO0422 is the region excluded in the
spectral analysis to avoid the possible contamination from the galaxy
CIG0422-09 found by Belsole et al. (2005).
\label{f:exo0422map}}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[angle=0,width=8cm]{plots/f08a.ps}
\includegraphics[angle=0,width=8cm]{plots/f08b.ps}
\includegraphics[angle=0,width=8cm]{plots/f08c.ps}
\includegraphics[angle=0,width=8cm]{plots/f08d.ps}
\end{center}
\caption{Temperature ($T$), electron number density ($n_{\rm e}$), entropy
($S$), and pressure ($P$) maps for A0119 with the \emph{Mask-V} on the
left and the \emph{Mask-S} on the right in each panel. The
color bars are in the range of 3.5-7.2~keV,
0-0.003~cm$^{-3}$, 200-900~keV~cm$^2$, and 0-0.018~keV~cm$^{-3}$ in the
$T$, $n_{\rm e}$, $S$, and $P$ panels, respectively. The image size is
$11^{\prime} \times 11^{\prime}$.
\label{f:a0119map}}
\end{figure*}
\clearpage
\begin{figure*}
\begin{center}
\includegraphics[angle=270,width=5.0cm]{plots/f09a.ps}
\includegraphics[angle=270,width=5.0cm]{plots/f09b.ps}
\includegraphics[angle=270,width=5.0cm]{plots/f09c.ps}
\includegraphics[angle=270,width=5.0cm]{plots/f09d.ps}
\includegraphics[angle=270,width=5.0cm]{plots/f09e.ps}
\includegraphics[angle=270,width=5.0cm]{plots/f09f.ps}
\includegraphics[angle=270,width=5.0cm]{plots/f09g.ps}
\includegraphics[angle=270,width=5.0cm]{plots/f09h.ps}
\end{center}
\vspace{-0.5cm}
\caption{Normalized temperature, electron number density, entropy,
and pressure distributions (from top to bottom) of the spectrally
measured 2D maps using \emph{Mask-V} (left) and \emph{Mask-S}
(right), respectively. The curves are the local regression fits of
the distributions of the four clusters as a whole.
\label{f:tdis}}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[angle=270,width=8.0cm]{plots/f10a.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f10b.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f10c.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f10d.ps}
\end{center}
\vspace{-0.5cm}
\caption{Cumulative scatter of the temperature, electron number
density, entropy, and pressure fluctuations in the 2D maps for
the four clusters as a whole using
\emph{Mask-S}. Note that for each plot, the
mean profile $\langle D(d)\rangle$ is determined for the four clusters
as a whole as described in Sect.~\ref{s:step2}.
\label{f:tnormsca}}
\end{figure*}
\clearpage
\begin{figure*}
\begin{center}
\includegraphics[angle=270,width=8.0cm]{plots/f11a.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f11b.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f11c.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f11d.ps}
\end{center}
\vspace{-0.5cm}
\caption{Differential scatter of the temperature, electron number density,
entropy, and pressure
fluctuations in the 2D maps for the four clusters
as a whole using \emph{Mask-S}. Note that for each plot,
the mean profile $\langle D(d)\rangle$
is determined for the four clusters as a whole as described in
Sect.~\ref{s:step2}.
\label{f:tnormsca_dr}}
\end{figure*}
\clearpage
\begin{figure*}
\begin{center}
\includegraphics[angle=270,width=8.0cm]{plots/f12a.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f12b.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f12c.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f12d.ps}
\end{center}
\vspace{-0.5cm}
\caption{Cumulative scatter of the temperature, electron number
density, entropy, and pressure fluctuations in the 2D maps
for the four clusters as a whole using
\emph{Mask-S}. Note that for each plot, the
mean profile $\langle D(d)\rangle$ is individually determined for
each cluster as described in Sect.~\ref{s:step2}.
\label{f:tnormsca_ind}}
\end{figure*}
\clearpage
\begin{figure*}
\begin{center}
\includegraphics[angle=270,width=8.0cm]{plots/f13a.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f13b.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f13c.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f13d.ps}
\end{center}
\vspace{-0.5cm}
\caption{Differential scatter of the temperature, electron number
density, entropy, and pressure fluctuations in the 2D maps
for the four clusters as a whole using \emph{Mask-S}.
Note that for each plot,
the mean profile $\langle D(d)\rangle$ is individually determined
for each cluster as described in Sect.~\ref{s:step2}.
\label{f:tnormsca_dr_ind}}
\end{figure*}
\clearpage
\begin{figure*}
\begin{center}
\includegraphics[angle=270,width=8.0cm]{plots/f14a.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f14b.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f14c.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f14d.ps}
\end{center}
\vspace{-0.5cm}
\caption{Cumulative scatter of the temperature, electron number
density, entropy and pressure fluctuations in the 2D maps
for each cluster using
\emph{Mask-S}. The $X$-axis has been shifted by
0.005, 0.010, and 0.015 for A3391, EXO0422 and A0119, respectively,
to avoid the overlap. Note that for each plot, the mean profile
$\langle D(d)\rangle$ is individually determined for each cluster as
described in Sect.~\ref{s:step2}.
\label{f:tsca}}
\end{figure*}
\clearpage
\begin{figure*}
\begin{center}
\includegraphics[angle=270,width=8.0cm]{plots/f15a.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f15b.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f15c.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f15d.ps}
\end{center}
\vspace{-0.5cm}
\caption{Differential scatter of the temperature, electron number
density, entropy, and pressure fluctuations in the 2D maps
for each cluster using
\emph{Mask-S}. The X-axis has been shifted by
0.005, 0.010, and 0.015 for A3391, EXO0422 and A0119, respectively,
to avoid the overlap. Note that for each plot, the mean profile
$\langle D(d)\rangle$ is individually determined for each cluster as
described in Sect.~\ref{s:step2}.
\label{f:tsca_dr}}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[angle=270,width=8.0cm]{plots/f16a.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f16b.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f16c.ps}
\includegraphics[angle=270,width=8.0cm]{plots/f16d.ps}
\end{center}
\caption{Mass-$Y_{\rm X}$ relations (left) and the mass-$M_{\rm gas}$
relations (right). We compile a sample of 44 LoCuSS clusters (37 LoCuSS
clusters are from Zhang et al. 2008) and use the best-fit scaling
relations of a subsample of 22 clusters characterized as relaxed
(black lines) at $r_{500}$ and $r_{2500}$, respectively, as the
reference for our studies. The scaling relations at $r_{500}$ from
simulations in Nagai et al. (2007; gray lines) are shown for comparison.
Clusters characterized as possibly merging/elliptical in Hudson et al.
(2009) are denoted by open squares. The cluster masses for the four
clusters are determined in Sect.~\ref{s:mass}.
\label{f:mymg}}
\end{figure*}
\clearpage
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,485 |
TV Streams
Streaming websites
Felicia May 9th, 2015
Music Cravings – 7 Tips to Enhance Your Online Music Streaming Experience
Listening music can put you in a good mood and can really make you relax you and put your mind at ease. This is especially true when you are listening to your favorite songs. Most people are oblivious to the effects of music to their health and sees it more as a hobby or a spare time to pass up the time; however, there are benefits that you can get from music and it has already been scientifically proven too!
Health benefits include decrease in back pains, improvement on memory loss and releasing more dopamine hormones to help you relax. This of course depends on the type rhythm of music as it can encourage your brain to release large amounts of Dopamine which essentially is a sedative. For fast-beat and/or rock music though they tend to change your mood, making you more hyperactive and in some cases – aggressive. But altogether, music is a lot of fun and is a great way to feed your soul and connect with
→Read More
Tinaya Mar 15th, 2015
Apple Set To Launch Streaming Music Service In June
Apple is preparing to launch its streaming music service this coming June. The service will be a complete renovation of Beats; however, it will feature iTunes branding and will be more tightly integrated with Apple's software and devices. The official debut of the new streaming music service will probably be at WWDC.
Sources have been citing a target date of June 8th as the official "date of unveiling." The premiere is scheduled for Apple's annual developer conference event. Speculation is that the event will take place sometime between the dates of June 8th and June 12th if this year, but there are no official dates set as of yet, according to Mark Gurman of 9to5Mac.
Apple's new music service plans on integrating "Beats-style personalization and possibly even recommendation features of the Beats service as well, with new software and no Beats branding. The service will be offered across platforms such as Android and the worldwide web.
The cross-platform offering may be a good decision for Apple because: the company has an extensive history when it comes to reaching out to its competition, beginning with iTunes for Windows. Additionally, Apple recently made its iWork program available for all users via iCloud over the internet, regardless of their hardware preferences. Apple can use the new service to reach out to consumers who are beyond the tech industry conglomerate's "ecosystem"
Apple is also seeking to make the service more appealing to potential customers by offering a more attractive service price. The company is planning on offering a $7.99 monthly service rate. This rate is $2.00 less than the rate of both Rdio and Spotify monthly subscription services.
Latest TV searches:
The Wire The Target
Tinaya Mar 8th, 2015
YouTube Music Key Coming soon
YouTube will be introducing a new paid subscription service called Music Key. The service is officially in its bets stages and a full launch to the general public is anticipated to be coming soon.
The Music Key subscription service will be YouTube's first venture into the area of an industry that is presently being dominated by conglomerates such as Amazon and iTunes. YouTube's new Music Key service will be operating on a monthly paid subscription basis and the monthly fees will be starting at about $7.99 per month for ad-free access.
The Music Key service is designed to be compatible with the YouTube app, which will enable various options for listening to your favorite songs and watching your favorite videos. The application will also enable music playability even while other apps are running and even when the screen is off.
Also, the app will give users the ability to listen to their music even when they are offline. Even though it is still in its beta testing stage, the new Music Key option has accumulated quite a compilation of content for future subscribers.
According to its official website, Music Key offers millions of album tracks, official music videos, concert clips, remixes and covers.
The new Music Key service is not the only addition to YouTube that is designed to help the site stay on top even while facing some mounting competition. The Google Preferred Program which was recently launched by the company, lets video makers use adverts that can't be skipped any longer. The end result of the move is higher amounts of earnings for the content providers that are seeing a 70% annual growth rate in their revenue vs. the rate increase seen by YouTube partners on the whole, which is only 50%.
No definitive launch date of the new Music Key service has been set by the company as of yet.
youtube com music
Felicia Feb 21st, 2015
Maroon 5's Music Video Sugar
Adam Levine is known as the lead vocalist of Los Angeles pop rock band Maroon 5. This band was formed in the year 1994 as Kara's Flower when the member's are still in high school. That is a very long time and until now they are still very much active. Now this band was known for their bold and unique music videos that is really eye catchy and you just can't stop but look t over. Music Video's like Misery, Moves Like Jagger, Payphone, Animal and now the latest one Sugar.
So what is so unique about this one? I mean they've already done the one were Adam is in this case like room with a girl and even the band that was being driven who knows where then the recently one was Animal with those animals and blood. If you've already watched the music video then you'll see why but if you haven't well at the start of the video Adam stared right at the camera and announced that "December 6th 2014, we're gonna drive around L.A and hit every wedding we possibly can. It's gonna be awesome." The location where they used as a setting for the video was Los Angeles and it was just brimming with joy and sunshine. Not like the other music video's where Adam is shirtless with tattoos or leather jackets, in this one he and his band mates are all in black tux and looking as elegant as they can be since they are crashing some weddings, they might as well wear formal for the occasion.
So it's the bride and groom's reception and then this people come and make some sort of stage with a curtain all together and made the bride and groom go upfront then when the chorus of the song came up, the curtains fall of and unveil Maroon 5. You could seriously see the stunned face of the bride and groom and almost everyone in the reception that recognized Maroon 5. There was screaming then almost everyone would gather at the front and dance like there is no tomorrow.
The video showed a lot of weddings actually. It is really cool of the Maroon 5 to give these couples a surprise and all those weddings that they went to are so lucky to have a free concert.
The band really did an outstanding video yet again. Almost like nothing is impossible for the Maroon 5 in making their music video. But there is also some concerns upon seeing the video and that is whether the weddings was fake or real. There were some evidence that Maroon 5 did crashed weddings for real like the bride that said WTF and even the time where the band were taking shots of cognac. The rest are still unresolved because if you ask me, I think they were all real because you can really see how overwhelm the people in the video or they are just really good actors and actresses. But you know what? It doesn't matter because ok if it was staged it was still cool if there really were some popular band that would come to your wedding and surprise the heck out of you.
maroon 5, maroon 5 sugar video, maroon 5 sugar
Mishka Jan 30th, 2015
Sony and Spotify to launch "PlayStation Music"
Spring will see the launch of "PlayStation Music". The premium music service is a joint project between Spotify and Sony Network Entertainment International (SNEI) will bring over 30 million songs to play as background music when playing PlayStation games.
PlayStation Music will be accessible worldwide to all Sony game consoles and Xperia devices. It will reach more than 64 million users logged into the PlayStation Network (PSN).
"This partnership represents the best in music and the best in gaming coming together," Sony president Andrew House said in a statement. "We're thrilled to make Spotify the foundation of our strategy with PlayStation Music."
The new music service marks the end of Sony's Music Unlimited service which will end support in March and closes doors to the 19 countries it currently supports.
Subscribers of Music Unlimited will be able to avail a month of free access to Playstation Music until March 29, 2015.
Sony noting the success of its game consoles is pushing towards the integration of existing Sony services -Music Unlimited and Video Unlimited- into the Playstation brand by converting them into PlayStation Music and PlayStation Video.
"As a gamer and PlayStation 4 user myself, I'm super excited to be able to soundtrack my FIFA 15 Arsenal matches later this spring," said Spotify founder Daniel Ek.
iHeartRadio Hits A Big Milestone – 60 Million Registered Users
Last week the radio streaming service iHeartRadio threw out some numbers to show people how quick it is growing.
The company said that it has total of 60 million registered users and almost 90 million unique visitors. The number of downloads of the iHeartRadio app is more than 500 million.
But if we compare the figures to its competitors, iHeartRadio does not impress easily. Spotify said in its latest statement that it has 60 million active users; the number of registered users exceed this figure. On the other hand, Pandora has an impressive 76.5 million active users.
American mass media company iHeartMedia -formerly known as Clear Channel- is the parent company which owns iHeartRadio.
Perhaps the success in iHeartRadio's figures comes down to the difference in the number of registered users and number of downloads of the iHeartRadio app. 500 million people have downloaded the app, but only 60 million have registered.
The app does not require registration to be used, unless one wishes to use its custom smart radio feature.
The company claims it's growing "faster than any other radio or digital music service — even faster than Facebook."
The service is completely free, in stark contrast with its competitors. Its revenue comes form serving ads, which is an option which Spotify and Pandora strive to stay away from, by offering paid ad-free options.
Games console TV
Internet Music
Internet TV Articles
Internet TV Explained
Internet TV Hardware
Internet TV news
Internet TV Reviews
Internet TV Software
Internet TV Websites
Mobile Phone TV
Movie Download reviews
P2P Software
PPstream
Sopcast
TV Torrents
TVants
TVUplayer
Twitter Facebook Email RSS
XBMC Media Player Guide
Watch Classic Movies
Reference & Help
Internet TV guide
Satellite TV on PC
Follow us and contact..
Still can't find what you're looking for? Search Site
Copyright © WorldTVPC.com 2013
Privacy policy | Legal Disclaimer | About us | Contact us | DMCA complaint | Advertise | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 103 |
The Trentham Park branch line was a railway line that ran through the Trentham area of Stoke-on-Trent. It was last branch line to be built by the North Staffordshire Railway. Intended to route traffic to Trentham Gardens, the branch was authorised in 1907 and opened on 1 April 1910. It left the main line at Trentham Junction where there was a platform connected by a short path to , although Trentham Junction itself never appeared as a separate station in the timetable.
Abortive extension
By the time of its opening, local traffic was already being carried by road. As a result, the only intermediate station, Hanford Road Halt, was closed after just three years. However, the original plan was to extend the line to Pool Dam, Newcastle-under-Lyme, to form a four mile long route around the growing suburbs. In preparation for this a steel bridge was constructed in September 1914 over London Road (now part of the A34) just beyond Trentham Park, but the extension was halted by World War I. It remained as a bridge to nowhere until 1940, when it was dismantled for scrap for the World War II effort.
World War II
During the war, the branch was at its busiest due to the Bankers' Clearing House having temporarily relocated the national cheque clearing house to the ballroom at the Trentham Estate. Numerous unpublicised passenger trains ran to serve it, along with a daily freight working.
Closure
After the war the line continued to be used for excursion trains from the Midlands, the last one running from Birmingham on 1 October 1957.
References
Closed railway lines in the West Midlands (region)
Rail transport in Stoke-on-Trent
North Staffordshire Railway
Railway lines opened in 1907
Railway stations closed in 1957 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,288 |
SYNOPSIS: Either Bush knows he's bankrupting the government and doesn't care, which is bad, or he doesn't know, which is worse.
What do Medicare and the military have in common? Both are about to be betrayed in the name of tax cuts.
Start with the military. During the campaign George W. Bush warned audiences that America's military was in decline. "Not since the years before Pearl Harbor has our investment in national defense been so low as a percentage" of the gross domestic product, he declared. Strangely, if you looked at the numbers put out by his economic team, you found that he actually proposed to reduce that percentage further, spending substantially less on defense than his opponent.
Nonetheless, the military overwhelmingly supported Mr. Bush; officers thought that they had an understanding — nudge nudge, wink wink, say no more — that defense spending would quickly expand once he reached the White House. Indeed, senior officers have been telling Congress that they need a 30 percent increase in their budget. (Do they? Not my department.)
Guess again. Last week, according to newspaper reports, Mr. Bush told lawmakers that there would be "no new money this year for defense." Karen Hughes, a counselor to Mr. Bush, conceded that "we may in fact need resources" for the military — may? after all that martial rhetoric? — but made it clear that there was no rush. One officer bitterly declared, "It sounds like campaign promise No. 1 being broken."
Then there's Medicare. The Medicare system is currently running surpluses, but almost everyone agrees that the Medicare surplus, like the Social Security surplus, should not be considered available for tax cuts or new spending. The two programs both rely on taxes paid by working-age Americans to pay for benefits to current retirees, and both face a demographic crisis as the baby boomers get older. Their current surpluses are therefore, as everyone acknowledges, a necessary, even inadequate, provision for the difficult decades ahead.
Everyone acknowledges this, except the administration, which — unlike members of its own party in Congress — refuses to rule out raiding the Medicare surplus.
But isn't the federal government awash in surpluses? Hasn't Alan Greenspan told us that our big economic problem is how to give the money away, lest politicians end up owning the stock market? If there's plenty of money for tax cuts, why won't the administration give the military at least some of what it wants and promise to keep its hand out of the Medicare cookie jar?
Because someone in the White House is aware of the truth, which is that there isn't plenty of money after all.
Here's the arithmetic: the Congressional Budget Office has projected a 10-year surplus of $5.6 trillion. (I don't believe it, but never mind.) Take the Social Security and Medicare surpluses off the table, however, and you are left with only $2.7 trillion. That may sound like a lot, but the projected cost of Mr. Bush's tax cut has also grown, for reasons that are important but too boring to explain. It would now use up around $2 trillion of that surplus.
And what's left depends on the totally unrealistic assumption that federal spending, including defense spending, will not grow at all over the next decade, despite a growing population and a growing economy. Give the military what it says it needs, and we're already well into deficit — and that doesn't include missile defense, not to mention prescription drug coverage, new education programs and all that. Oh, and what about the trillion dollars of Social Security money that Mr. Bush has proposed to spend twice?
Nonetheless, Congress is about to go into a tax-cut feeding frenzy, adding huge tax breaks for corporations to Mr. Bush's proposal. The spectacle will be distressing, but it will be over quickly. Pretty soon, quite possibly as soon as this summer, we'll be worrying about deficits, not surpluses.
Of course, some conservatives would say that's the point, that we need to starve the government to shrink it. But what the federal government actually spends its money on is retirement, health care and defense; the rest is small change. So guess what gets shrunk? And if the military elite is shocked to find that this administration considers eliminating the inheritance tax more important than providing new weapons systems, that it is more concerned with the security of estates than the security of the state — well, that's what you get when you trust in winks and nudges instead of checking the numbers. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,752 |
\section{Details of One-Loop Calculations}
\label{app:appendix}
In this appendix we provide the one-loop diagram-by-diagram results of the hadronic amplitude for the unpolarized PDF, helicity PDF and pseudoscalar meson LCDA cases. We only show the explicit expressions of the UV and IR divergent parts, and the expressions for finite parts can be found in the supplementary Mathematica notebook file.
\subsection{Unpolarized PDF}
\label{app:pdf}
The one-loop hadronic amplitude can be expressed as
\begin{align}\label{eq:upnloapp}
T_q^{\{\mu\nu\}(1)}\Big/ {\alpha_SC_F\over 4\pi}
&={4i \bar{u}(p)q^{\{\mu} \gamma^{\nu\}} u(p)\over \tilde Q^2} H_{1}^{(1)} + {4 i \bar{u}(p)p^{\{\mu} \gamma^{\nu\}}u(p)\over \tilde Q^2} H_{2}^{(1)}\nonumber\\
&\qquad-{ 2ig^{\mu\nu}_\perp \bar{u}(p) \slashed q u(p)\over \tilde Q^2} H_{3}^{(1)} + {2i q^\mu q^\nu \bar{u}(p) \slashed q u(p)\over \tilde Q^2} H_{4}^{(1)}\,.
\end{align}
The diagrammatic contributions are shown as follows:
The box diagram in \fig{box}.
\begin{align}
H^{(1)}_{1, \rm box}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\mu,\epsilon)&= \left({1\over \epsilon'_{\rm ir}} + \ln{\mu^2\over \tilde Q^2}\right) {-2\tilde \omega - (1-\tilde \omega) \ln(1-\tilde \omega) + (1+\tilde \omega) \ln(1+\tilde \omega)\over \tilde \omega^2} + h^{(1)}_{1, \rm box}(\tau,\tilde \omega)\,,
\end{align}
\begin{align}
H^{(1)}_{2, \rm box}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\mu,\epsilon)
&= \left({1\over \epsilon'_{\rm ir}} + \ln{\mu^2\over \tilde Q^2}\right) {-2\tilde \omega - (1-\tilde \omega) \ln(1-\tilde \omega) + (1+\tilde \omega) \ln(1+\tilde \omega)\over \tilde \omega^3} + h^{(1)}_{2, \rm box}(\tau,\tilde \omega)\,,
\end{align}
\begin{align}
H^{(1)}_{3, \rm box}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\mu,\epsilon)
&= \left({1\over \epsilon'_{\rm ir}} + \ln{\mu^2\over \tilde Q^2}\right) {-2\tilde \omega - (1-\tilde \omega) \ln(1-\tilde \omega) + (1+\tilde \omega) \ln(1+\tilde \omega)\over \tilde \omega^2} + h^{(1)}_{3, \rm box}(\tau,\tilde \omega)\,,
\end{align}
\begin{align}
H^{(1)}_{4, \rm box}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\mu,\epsilon)
&= h^{(1)}_{4, \rm box}(\tau,\tilde \omega)\,.
\end{align}
As one can see, the box diagram is UV finite but collinearly divergent.
The vertex diagrams in \figs{v1}{v2}.
\begin{align}
H^{(1)}_{1, \rm vertex}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon)
&= \left({1\over \epsilon'_{\rm uv}} + \ln{\mu^2\over \tilde Q^2}\right) {2\tilde \omega\over 1- \tilde \omega^2}+ h^{(1)}_{1, \rm vertex}(\tau,\tilde \omega) \nonumber\\
&\qquad -\left({1\over \epsilon'_{\rm ir}} + \ln{\mu^2\over \tilde Q^2}\right) \frac{2 \left[2 \tilde \omega ^2+\ln (1-\tilde \omega^2)-2 \tilde \omega \tanh ^{-1}(\tilde \omega )\right]}{\tilde \omega \left(1- \tilde \omega ^2\right)}\,,
\end{align}
\begin{align}
H^{(1)}_{2, \rm vertex}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon) &= \left({1\over \epsilon'_{\rm uv}} + \ln{\mu^2\over \tilde Q^2}\right) {2\over 1- \tilde \omega^2}+ h^{(1)}_{2, \rm vertex}(\tau,\tilde \omega)\nonumber\\
&\qquad -\left({1\over \epsilon'_{\rm ir}} + \ln{\mu^2\over \tilde Q^2}\right) \frac{2 \left[2 \tilde \omega ^2+\ln (1-\tilde \omega^2)-2 \tilde \omega \tanh ^{-1}(\tilde \omega )\right]}{\tilde \omega ^2 \left(1- \tilde \omega ^2\right)}\,,
\end{align}
\begin{align}
H^{(1)}_{3, \rm vertex}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon)&= \left({1\over \epsilon'_{\rm uv}} + \ln{\mu^2\over \tilde Q^2}\right) {2\tilde \omega\over 1- \tilde \omega^2}+ h^{(1)}_{3, \rm vertex}(\tau,\tilde \omega)\nonumber\\
&\qquad -\left({1\over \epsilon'_{\rm ir}} + \ln{\mu^2\over \tilde Q^2}\right) \frac{2 \left[2 \tilde \omega ^2+\ln (1-\tilde \omega^2)-2 \tilde \omega \tanh ^{-1}(\tilde \omega )\right]}{\tilde \omega \left(1- \tilde \omega ^2\right)}\,,
\end{align}
\begin{align}
H^{(1)}_{4, \rm vertex}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon) &= 0\,.
\end{align}
The self-energy diagrams in \fig{self} and \fig{self2}.
\begin{align}
H^{(1)}_{1, \rm self}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon) &=- \left({1\over \epsilon'_{\rm uv}} - {1\over \epsilon'_{\rm ir}}\right) {\tilde \omega \over 1-\tilde \omega^2} - \left({1\over \epsilon'_{\rm uv}} + \ln{\mu^2\over \tilde Q^2}\right) {\tilde \omega \over 1- \tilde \omega^2} - (1-\tau)\left({3\over \epsilon'_{\rm uv}} + 3\ln{\mu^2\over \tilde Q^2}\right) {4\tilde \omega \over (1-\tilde \omega^2)^2} \nonumber\\
& \qquad + h^{(1)}_{1, \rm self}(\tau,\tilde \omega)\,,
\end{align}
where the first term comes from the light-quark self-energy, while the second and third terms originate fom the heavy-quark self-energy.
\begin{align}
H^{(1)}_{2, \rm self}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon)&=- \left({1\over \epsilon'_{\rm uv}} - {1\over \epsilon'_{\rm ir}}\right) {1\over 1-\tilde \omega^2} - \left({1\over \epsilon'_{\rm uv}} + \ln{\mu^2\over \tilde Q^2}\right) {1\over 1- \tilde \omega^2} - (1-\tau)\left({3\over \epsilon'_{\rm uv}} + 3\ln{\mu^2\over \tilde Q^2}\right) {2(1+\tilde \omega^2)\over (1-\tilde \omega^2)^2}\nonumber\\
&\qquad + h^{(1)}_{2, \rm self}(\tau,\tilde \omega)\,,
\end{align}
\begin{align}
H^{(1)}_{3, \rm self}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon) &=- \left({1\over \epsilon'_{\rm uv}} - {1\over \epsilon'_{\rm ir}}\right) {\tilde \omega \over 1-\tilde \omega^2} - \left({1\over \epsilon'_{\rm uv}} + \ln{\mu^2\over \tilde Q^2}\right) {\tilde \omega \over 1- \tilde \omega^2} - (1-\tau)\left({3\over \epsilon'_{\rm uv}} + 3\ln{\mu^2\over \tilde Q^2}\right) {4\tilde \omega \over (1-\tilde \omega^2)^2} \nonumber\\
& \qquad + h^{(1)}_{3, \rm self}(\tau,\tilde \omega)\,,
\end{align}
\begin{align}
H^{(1)}_{4, \rm self}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon) &= 0 \,.
\end{align}
The heavy-quark mass needs renormalization, and the corresponding counter-terms in the ${\overline{\mathrm{MS}}}$ and on-shell schemes are
\begin{align}
\delta H_{1,m}^{{\overline{\mathrm{MS}}}(1)} &= \delta H_{3,m}^{{\overline{\mathrm{MS}}}(1)} = (1-\tau){3\over \epsilon'_{\rm uv}} {4\tilde \omega \over (1-\tilde \omega^2)^2} \,,\\
\delta H_{1,m}^{\rm OS(1)} &= \delta H_{3,m}^{\rm OS(1)} = (1-\tau)\left[{3\over \epsilon'_{\rm uv}} +4 + 3\ln{\mu^2\over m_\Psi^2}\right] {4\tilde \omega \over (1-\tilde \omega^2)^2}\,.
\end{align}
\begin{align}
\delta H_{2,m}^{{\overline{\mathrm{MS}}}(1)} &= (1-\tau){3\over \epsilon'_{\rm uv}} {2(1+\tilde \omega^2)\over (1-\tilde \omega^2)^2} \,,\\
\delta H_{2,m}^{\rm OS(1)} &= (1-\tau)\left[{3\over \epsilon'_{\rm uv}} +4 + 3\ln{\mu^2\over m_\Psi^2}\right] {2(1+\tilde \omega^2)\over (1-\tilde \omega^2)^2}\,.
\end{align}
By summing all the one-loop diagrams, one finds out that the UV divergences regulated by $\epsilon'_{\rm uv}$ cancel except for that from the heavy-quark mass correction. The collinear divergences regulated by $\epsilon'$ add up to
\begin{align}
- {1\over\epsilon'}\frac{\tilde \omega \left(2+\tilde \omega ^2\right)+\left(1+\tilde \omega ^2\right) \left[\tilde \omega \ln{(1-\tilde \omega^2)}-2 \tanh ^{-1}(\tilde \omega )\right]}{\tilde \omega ^2 \left(1-\tilde \omega ^2\right)}
\end{align}
in $H^{(1)}_{1}$ and $H^{(1)}_{3}$ and
\begin{align}
- {1\over\epsilon'}\frac{\tilde \omega \left(2+\tilde \omega ^2\right)+\left(1+\tilde \omega ^2\right) \left[\tilde \omega \ln{(1-\tilde \omega^2)}-2 \tanh ^{-1}(\tilde \omega )\right]}{\tilde \omega ^3 \left(1-\tilde \omega ^2\right)}
\end{align}
in $H^{(1)}_{2}$, whose Taylor expansions in $\tilde \omega$ exactly reproduce the collinear divergences in the Mellin moments in the OPE in \eq{tnlo}. This is an important consistency check of our results.
In the limit of massless heavy-quark, i.e., $\tau\to1$, the hadronic amplitude no longer depends on the heavy-quark mass renormalization. Moreover, it satisfies the chiral ward identity
\begin{align}
q_\mu T_q^{\mu\nu}(q,p,m_\Psi=0,\mu,\epsilon) = q_\nu T_q^{\mu\nu}(q,p,m_\Psi=0,\mu,\epsilon) = 0\,,
\end{align}
which leads to the relations
\begin{align}
H_1 &=\tilde \omega H_2\,,\ \ \ \ \ \ \ \ H_1 = H_3+H_4\,,
\end{align}
as we have also checked.
All the finite parts, $h^{(1)}_{i, \rm box}$, $h^{(1)}_{i, \rm vertex}$ and $h^{(1)}_{i, \rm self}$ are provided in the supplementary material. Therefore, the finite non-logarithmic part of the hadronic amplitudes in the ${\overline{\mathrm{MS}}}$ scheme are
\begin{align}
h^{{\overline{\mathrm{MS}}} (1)}_1(\tilde Q^2, \mu^2, \tau, \tilde \omega) &= h^{(1)}_{1,\rm box}(\tau,\tilde \omega)+h^{(1)}_{1,\rm vertex}(\tau,\tilde \omega)+h^{(1)}_{1,\rm self}(\tau,\tilde \omega) { - (1-\tau)\left(3\ln{\mu^2\over \tilde Q^2}\right) {4\tilde \omega \over (1-\tilde \omega^2)^2}}\,, \nonumber\\
h^{{\overline{\mathrm{MS}}} (1)}_2(\tilde Q^2, \mu^2, \tau, \tilde \omega) &= h^{(1)}_{2,\rm box}(\tau,\tilde \omega)+h^{(1)}_{2,\rm vertex}(\tau,\tilde \omega)+h^{(1)}_{2,\rm self}(\tau,\tilde \omega) { - (1-\tau)\left(3\ln{\mu^2\over \tilde Q^2}\right) {2(1+\tilde \omega^2)\over (1-\tilde \omega^2)^2}}\,, \nonumber\\
h^{{\overline{\mathrm{MS}}} (1)}_3(\tilde Q^2, \mu^2, \tau, \tilde \omega) &= h^{(1)}_{3,\rm box}(\tau,\tilde \omega)+h^{(1)}_{3,\rm vertex}(\tau,\tilde \omega)+h^{(1)}_{3,\rm self}(\tau,\tilde \omega) { - (1-\tau)\left(3\ln{\mu^2\over \tilde Q^2}\right) {4\tilde \omega \over (1-\tilde \omega^2)^2}}\,, \nonumber\\
h^{{\overline{\mathrm{MS}}} (1)}_4(\tau, \tilde \omega) &= h^{(1)}_{4,\rm box}(\tau,\tilde \omega)\,,
\end{align}
whose Taylor expansion in $\tilde \omega$ gives the ${\overline{\mathrm{MS}}}$ Wilson coefficients. The on-shell scheme result is related to $h^{{\overline{\mathrm{MS}}} (1)}$ by
\begin{align}
h^{{\rm OS} (1)}_1(\tau, \tilde \omega) - h^{{\overline{\mathrm{MS}}} (1)}_1(\tilde Q^2, \mu^2, \tau, \tilde \omega) &= h^{{\rm OS} (1)}_3(\tau, \tilde \omega) - h^{{\overline{\mathrm{MS}}} (1)}_3(\tilde Q^2, \mu^2, \tau, \tilde \omega) = (1-\tau){4\tilde \omega \over (1-\tilde \omega^2)^2} \Big(4 { + 3\ln{\mu^2\over m_\Psi^2}}\Big) \,.\\
h^{{\rm OS} (1)}_2(\tau, \tilde \omega) - h^{{\overline{\mathrm{MS}}} (1)}_2(\tilde Q^2, \mu^2, \tau, \tilde \omega) &= (1-\tau){2(1+\tilde \omega^2)\over (1-\tilde \omega^2)^2} \Big(4 {+ 3\ln{\mu^2\over m_\Psi^2}}\Big) \,,\\
h^{{\rm OS} (1)}_4(\tau, \tilde \omega) - h^{{\overline{\mathrm{MS}}} (1)}_4(\tilde Q^2, \mu^2, \tau, \tilde \omega) &= 0 \,.
\end{align}
\subsection{Helicity PDF}
\label{app:hpdf}
The one-loop correction to the hadronic amplitude for the helicity PDF case can be expressed as
\begin{align}
T_q^{[\mu\nu](1)}&= -{2\epsilon^{\mu\nu\rho\sigma}q_\rho \over \tilde Q^2} \ \bar{u}(p)\gamma_\sigma \gamma_5 u(p)\ {\alpha_SC_F\over 4\pi}H^{(1)}\,.
\end{align}
To simplify the calculation, we can choose $p^\mu=(p^z,0,0,p^z)$ and $\mu, \nu = 1, 2$ without loss of generality.
The diagrammatic contributions are as follows:
The box diagram in \fig{box}.
\begin{align}
H^{(1)}_{\rm box}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon)
&= - \left({1\over \epsilon'_{\rm ir}} + \ln{\mu^2\over \tilde Q^2}\right) {(1-\tilde \omega) \ln(1-\tilde \omega) + (1+\tilde \omega) \ln(1+\tilde \omega)\over \tilde \omega^2} + h^{(1)}_{\rm box}(\tau,\tilde \omega)\,,
\end{align}
which is UV finite but collinearly divergent.
Note that since the helicity PDF is defined with the axial vector current, we must treat the definition of $\gamma_5$ with care. In our calculation, we adopt the scheme used in Refs.~\cite{delAguila:1981nk,Braaten:1982yp}, where the treatment of $\gamma_5$ is determined by calibrating the Wilson coefficients to those obtained with quark off-shellness $p^2<0$ as the regulator for collinear divergence. Within this scheme, the moments of the helicity PDF are the same as the unpolarized case in \eq{moment1}, while only the box diagram must be modified, as one has to introduce a finite counter-term that is equivalent to the replacement,
\begin{align}\label{eq:gamma5}
{1\over \epsilon'_{\rm ir}} \to {1\over \epsilon'_{\rm ir}} - 4\,.
\end{align}
This finite counter-term induced by the factor $(-4)$ has been absorbed into $h^{(1)}_{\rm box}(\tau,\tilde \omega)$.
The vertex diagrams in \figs{v1}{v2}.
\begin{align}
H^{(1)}_{\rm vertex}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon)
&= \left({1\over \epsilon'_{\rm uv}} + \ln{\mu^2\over \tilde Q^2}\right) {2\over 1- \tilde \omega^2} + h^{(1)}_{\rm vertex}(\tau,\tilde \omega)\nonumber\\
&\qquad \!-\! \left({1\over \epsilon'_{\rm ir}} + \ln{\mu^2\over \tilde Q^2}\right) \left[{4\over 1-\tilde \omega^2} \!+\! {2\over \tilde \omega}\left({\ln(1-\tilde \omega)\over 1-\tilde \omega} \!-\! {\ln(1+\tilde \omega)\over 1+\tilde \omega}\right)\right] \,.
\end{align}
The self-energy diagrams in \fig{self} and \fig{self2}.
\begin{align}
H^{(1)}_{\rm self}(\tilde Q^2, \mu^2, \tau,\tilde \omega,\epsilon)
&=- \left({1\over \epsilon'_{\rm uv}} - {1\over \epsilon'_{\rm ir}}\right) {1\over 1-\tilde \omega^2} - \left({1\over \epsilon'_{\rm uv}} + \ln{\mu^2\over \tilde Q^2}\right) {1\over 1- \tilde \omega^2} - (1-\tau)\left({3\over \epsilon'_{\rm uv}} + 3\ln{\mu^2\over \tilde Q^2}\right) {2(1+\tilde \omega^2)\over (1-\tilde \omega^2)^2} \nonumber\\
& \qquad + h^{(1)}_{\rm self}(\tau,\tilde \omega)\,.
\end{align}
The heavy-quark mass needs renormalization, and the corresponding counter-terms in the ${\overline{\mathrm{MS}}}$ and on-shell schemes are
\begin{align}
\delta H_m^{{\overline{\mathrm{MS}}}(1)} &= (1-\tau){3\over \epsilon'_{\rm uv}} {2(1+\tilde \omega^2)\over (1-\tilde \omega^2)^2} \,,\\
\delta H_m^{\rm OS(1)} &= (1-\tau)\left[{3\over \epsilon'_{\rm uv}} +4 + 3\ln{\mu^2\over m_\Psi^2}\right] {2(1+\tilde \omega^2)\over (1-\tilde \omega^2)^2}\,.
\end{align}
Again, one finds that the UV divergences regulated by $\epsilon'_{\rm uv}$ cancel except for that from the heavy-quark mass correction. Besides, collinear divergences regulated by $\epsilon'$ add up to
\begin{align}
-{1\over\epsilon'}\left[{3\over 1-\tilde \omega^2} + {1+\tilde \omega^2\over \tilde \omega^2}\left({\ln(1-\tilde \omega)\over 1-\tilde \omega} + {\ln(1+\tilde \omega)\over 1+\tilde \omega}\right) \right]\,,
\end{align}
whose Taylor expansion in $\tilde \omega$ exactly reproduces the collinear divergences of the Mellin moments in \eq{tnlo2}.
All the finite parts, $h^{(1)}_{\rm box}$, $h^{(1)}_{\rm vertex}$ and $h^{(1)}_{\rm self}$ are provided in the supplementary material. Therefore, the finite non-logarithmic part of the hadonic amplitude is
\begin{align}
h^{{\overline{\mathrm{MS}}} (1)}(\tilde Q^2, \mu^2, \tau, \tilde \omega) &= h^{(1)}_{\rm box}(\tau,\tilde \omega)+h^{(1)}_{\rm vertex}(\tau,\tilde \omega)+h^{(1)}_{\rm self}(\tau,\tilde \omega) { - (1-\tau)\left( 3\ln{\mu^2\over \tilde Q^2}\right) {2(1+\tilde \omega^2)\over (1-\tilde \omega^2)^2}}
\end{align}
in the ${\overline{\mathrm{MS}}}$ scheme, whose Taylor expansion in $\tilde \omega$ gives the ${\overline{\mathrm{MS}}}$ Wilson coefficients. The on-shell scheme result is related to $h^{{\overline{\mathrm{MS}}} (1)}$ by
\begin{align}
h^{{\rm OS} (1)}(\tau, \tilde \omega) - h^{{\overline{\mathrm{MS}}} (1)}(\tilde Q^2, \mu^2, \tau, \tilde \omega) &= (1-\tau){2(1+\tilde \omega^2)\over (1-\tilde \omega^2)^2} \Big(4 { + 3\ln{\mu^2\over m_\Psi^2}}\Big) \,.
\end{align}
\subsection{LCDA}
\label{app:lcda}
The one-loop correction to the hadronic amplitude for the LCDA case can be expressed as
\begin{align}
V^{[\mu\nu](1)}&= -{\alpha_sC_F\over 4\pi} {2 \epsilon^{\mu\nu\rho\sigma}q_\rho \over \tilde{Q}^2}\bar{v}\gamma_\sigma \gamma_5 u\ H^{(1)}\,.
\end{align}
To simplify the calculation, we can choose $p^\mu=(p^z,0,0,p^z)$, $q^\mu=(q^0,0,0,q^z)$ and $\mu, \nu = 1, 2$ without loss of generality.
The one-loop contributions are as follows:
The box diagram in \fig{box}.
\begin{align}
H^{(1)}_{\rm box}(\tilde Q^2, \mu^2, \tau,\tilde \omega, x_0,\epsilon)
&= - \left({1\over \epsilon'_{\rm ir}} + \ln{\mu^2\over \tilde Q^2}\right) {4\over (1-x_0^2) \tilde \omega^2}\left[\ln \frac{4-\tilde \omega^2}{4-x^2_0 \tilde \omega^2} \!-\! x_0 \tilde \omega \tanh ^{-1}\left(\frac{x_0 \tilde \omega }{2}\right) \!+\!\tilde \omega \tanh ^{-1}\left(\frac{\tilde \omega }{2}\right)\right] \nonumber\\
&\qquad + h^{(1)}_{\rm box}(\tau,\tilde \omega,x_0)\,,
\end{align}
where we treat $\gamma_5$ with the same prescription for the helicity PDF case by making the substitution in \eq{gamma5}.
The vertex diagrams in \figs{v1}{v2}.
\begin{align}
H^{(1)}_{\rm vertex}(\tilde Q^2, \mu^2, \tau,\tilde \omega, x_0,\epsilon)
&= \left({1\over \epsilon'_{\rm uv}} + \ln{\mu^2\over \tilde Q^2}\right) {8\over 4- x_0^2\tilde \omega^2}+ h^{(1)}_{\rm vertex}(\tau,\tilde \omega,x_0)\\
&\quad + \left({1\over \epsilon'_{\rm ir}} + \ln{\mu^2\over \tilde Q^2}\right) {8\over (1-x^2_0) \tilde \omega (4-x_0^2 \tilde \omega^2)}\nonumber\\
&\quad \times \left[-(1-x^2_0) \tilde \omega \left(\ln \frac{4-x^2_0 \tilde \omega ^2}{4-\tilde \omega ^2}+2\right) +\left(4\!-\!x^2_0 \tilde \omega ^2\right) \tanh ^{-1}\left(\frac{\tilde \omega }{2}\right) \!-\! x_0 (4\!-\!\tilde \omega ^2) \tanh ^{-1}\left(\frac{x_0 \tilde \omega }{2}\right)\right]\,.\nonumber
\end{align}
The self-energy diagrams in \fig{self} and \fig{self2}.
\begin{align}
H^{(1)}_{\rm self}(\tilde Q^2, \mu^2, \tau,\tilde \omega,x_0,\epsilon)
&=- \left({1\over \epsilon'_{\rm uv}} - {1\over \epsilon'_{\rm ir}}\right) {4\over 4- x_0^2\tilde \omega^2} - \left({1\over \epsilon'_{\rm uv}} + \ln{\mu^2\over \tilde Q^2}\right) {4\over 4- x_0^2\tilde \omega^2} - (1-\tau)\left({3\over \epsilon'_{\rm uv}} + 3\ln{\mu^2\over \tilde Q^2}\right) {8(4+x_0^2\tilde \omega^2)\over (4-x_0^2\tilde \omega^2)^2} \nonumber\\
& \qquad + h^{(1)}_{\rm self}(\tau,\tilde \omega,x_0)\,.
\end{align}
The heavy-quark mass needs renormalization, and the corresponding counter-terms in the ${\overline{\mathrm{MS}}}$ and on-shell schemes are
\begin{align}
\delta H_m^{{\overline{\mathrm{MS}}}(1)} &= (1-\tau){3\over \epsilon'_{\rm uv}}{8(4+x_0^2\tilde \omega^2)\over (4-x_0^2\tilde \omega^2)^2} \,,\\
\delta H_m^{\rm OS(1)} &= (1-\tau)\left[{3\over \epsilon'_{\rm uv}} +4 + 3\ln{\mu^2\over m_\Psi^2}\right]{8(4+x_0^2\tilde \omega^2)\over (4-x_0^2\tilde \omega^2)^2}\,.
\end{align}
Same as the PDF cases, the UV divergences regulated by $\epsilon'_{\rm uv}$ cancel except for that from the heavy-quark mass correction. The collinear divergences add up to \eq{lcdall}, which also passes the consistency check that its conformal expansion reproduces the collinear divergences of the Gegenbauer moments.
All the finite parts, $h^{(1)}_{\rm box}$, $h^{(1)}_{\rm vertex}$ and $h^{(1)}_{\rm self}$, as well as their massless limits when $\tau\to1$, are provided in the supplementary material. We can identify that the finite term ${\mathbf R}^{(1)}(\tau, \tilde \omega, x_0)$ in \eq{oneloop} is
\begin{align}
{\mathbf R}^{{\overline{\mathrm{MS}}} (1)}(\tilde Q^2, \mu^2, \tau, \tilde \omega, x_0) &= h^{(1)}_{\rm box}(\tau,\tilde \omega,x_0)+h^{(1)}_{\rm vertex}(\tau,\tilde \omega,x_0)+h^{(1)}_{\rm self}(\tau,\tilde \omega,x_0) { - (1-\tau)\left( 3\ln{\mu^2\over \tilde Q^2}\right) {8(4+x_0^2\tilde \omega^2)\over (4-x_0^2\tilde \omega^2)^2}}
\end{align}
in the ${\overline{\mathrm{MS}}}$ scheme. The on-shell scheme result is related to ${\mathbf R}^{{\overline{\mathrm{MS}}} (1)}$ by
\begin{align}
{\mathbf R}^{{\rm OS} (1)}(\tau, \tilde \omega, x_0) - {\mathbf R}^{{\overline{\mathrm{MS}}} (1)}(\tilde Q^2, \mu^2, \tau, \tilde \omega, x_0) &= (1-\tau){8(4+x_0^2\tilde \omega^2)\over (4-x_0^2\tilde \omega^2)^2} \Big(4 {+3\ln{\mu^2\over m_\Psi^2}}\Big) \,.
\end{align}
Notably, in the massless limit, our result of ${\mathbf R}^{(1)}(1, \tilde \omega, x_0)$
reproduces Eq.~(5.2) in the literature~\cite{Braaten:1982yp} if make the replacements
\begin{align}
Q^2\to 2Q^2\,,\ \ \ \ \ x\to {1\over 2}(1-x_0)\,,\ \ \ \ \ w\to {1\over2} - {\omega\over4}.
\end{align}
\section{Conclusion}
\label{sec:summary}
This paper contains novel and important information for applying the HOPE strategy to determine directly the $\xi$-dependence and moments for the PDFs and LCDAs. In particular, we discuss the theoretical details of the HOPE method applied to the PDF and LCDA. After introducing the unpolarised PDF, helicity PDF and LCDA we begin with a general overview of the HOPE strategy. This approach is a modified OPE relation where the conventional current operators are replaced with heavy-light flavour changing currents. Importantly the use of a fictitious heavy quark species allows for suppression of higher-twist effects. In the regime $\tilde{Q}\sim m_\Psi$, the effects of the heavy quark mass can be incorporated into the Wilson coefficients, and thus the resulting moments are the standard QCD moments.
The HOPE method was first proposed in Ref.~\cite{Detmold:2005gg} for computing higher moments of the PDFs with lattice QCD. The results presented in this article extend this proposal for direct determinations of $\xi$-dependence of the PDFs and LCDAs. As demonstrated in Sec.~\ref{sec:Hope_qPDF}, the PDFs and LCDAs can be related to appropriate HOPE hadronic amplitudes through a perturbative matching condition. This offers a novel, future direction for analysing these HOPE hadronic amplitudes.
Our work contains new ingredients required for a precise lattice determination of higher moments of the PDFs and LCD. First, as noted in Sec.~\ref{sec:convg}, we investigate carefully the convergence radius of the HOPE. The analysis shown there also advances our understanding of the HOPE strategy, by indicating that large hadron momentum is required for the extraction of these higher moments. Secondly, in this paper we report calculations for the one-loop Wilson coefficients which are required for a precise determination of the moments of the unpolarised and helicity PDFs and meson LCDAs. The Wilson coefficients for the PDFs can be extracted using the existing results~\cite{Gottschalk:1980rv,Gluck:1996ve} of cross sections of heavy-qaurk production in DIS involving flavour-changing currents. Nevertheless, we perform independent calculations, as described in Secs.~\ref{sec:nlopdf} and \ref{sec:helicity}, and confirm these previous computations. We emphasize that the one-loop Wilson coefficients for the LCDAs, presented in Sec.\ref{sec:danlo}, have not been previously calculated in the literature, and are thus new to this work.
\section*{Acknowledgements}
CJL and RJP were supported by the Taiwanese MoST Grant No. 109-2112-M-009-006-MY3 and MoST Grant No. 109-2811-M-009-516. The work of IK is partially supported by the MEXT as ``Program for Promoting Researches on the Supercomputer Fugaku'' (Simulation for basic science: from fundamental laws of particles to creation of nuclei) and JICFuS. YZ is supported in part by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under grant Contract No. DE-SC0012704, No.~DE-AC02-06CH11357 and within the framework of the TMD Topical Collaboration. YZ is also supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics and Office of Advanced Scientific Computing Research within the framework of Scientific Discovery through Advance Computing (ScIDAC) award Computing the Properties of Matter with Leadership Computing Resources. WD and AVG acknowledge support from the U.S.~Department of Energy (DOE) grant DE-SC0011090. WD is also supported within the framework of the TMD Topical Collaboration of the U.S.~DOE Office of Nuclear Physics, and by the SciDAC4 award DE-SC0018121.
\section{The HOPE Method}
\label{sec:the_hope}
The HOPE method was originally proposed in Ref.~\cite{Detmold:2005gg} as a way to extract information about the moments of PDFs and LCDAs via an analysis of matrix elements which we refer to as \textit{hadronic amplitudes}. We define these as
\begin{align}
T^{\mu\nu}(p,q)&=\int d^4z\ e^{iq\cdot z}\bra{H(\mathbf{p},\mathbf{s})}\mathcal{T}\{J_A^\mu(z/2)J_A^\nu(-z/2)\}\ket{H(\mathbf{p},\mathbf{s})},\label{eq:compton_amplitude}
\\
V^{\mu\nu}(p,q)&=\int d^4z\ e^{iq\cdot z}\bra{\Omega}\mathcal{T}\{J_A^\mu(z/2)J_A^\nu(-z/2)\}\ket{M(\mathbf{p})},\label{eq:lcda_amplitude}
\end{align}
where $\mathcal{T}$ is the time-ordering symbol and the heavy-light axial-vector current $J_A^\mu(z)$ is given by
\begin{equation}
J_A^\mu(z)=\overline{\Psi}(z)\gamma^\mu \gamma_5 \psi(z)+\overline{\psi}(z)\gamma^\mu \gamma_5 \Psi(z).\label{eq:hope_current}
\end{equation}
We denote the fictitious heavy quark species as $\Psi$ and the light quark species as $\psi$. Note that other choices for the Dirac matrix structure in the current are also possible. The application of the HOPE method to $T^{\mu\nu}(p,q)$ enables one to extract the moments of the unpolarized and helicity PDFs. The matrix element $V^{\mu\nu}(p,q)$ allows a determination of the LCDA moments since both the current-current operator shown above and the operator in Eq.~\eqref{eq:lcda} can be expanded in terms of the same local operators~\cite{Brodsky:1980ny}.
The HOPE strategy is characterized by its use of a fictitious flavor-changing heavy-light current (Eq.~\eqref{eq:hope_current}). The heavy quark is quenched and as a result only propagates between the two currents~\cite{Detmold:2005gg}. We note that the use of a quenched heavy quark removes certain higher-twist diagrams entirely from the calculation and also provides a source of higher-twist suppression beyond the large momentum transfer at the currents due to the the heavy quark mass, $m_\Psi$. In order for the heavy quark mass to be considered a `large' scale we require that
\begin{equation}
\Lambda_\text{QCD}\ll m_\Psi\sim \sqrt{Q^2},
\end{equation}
where $Q^2=-q^2$.
To apply the HOPE method, we define the operator
\begin{equation}
t^{\mu\nu}(q;m_\Psi)=\int d^4z\ e^{iq\cdot z}\mathcal{T}\{J_A^\mu(z/2)J_A^\nu(-z/2)\}.
\end{equation}
and perform an OPE. In the case of the symmetrized isovector operator, this yields~\cite{Detmold:2005gg}
\begin{align}
t^{\{\mu\nu\}}(q;m_\Psi)&=\frac{4i}{\tilde{Q}^2} \sum_{\substack{n=0\\ \text{even}}}^\infty \frac{(2q_{\mu_1})\dots (2q_{\mu_n})}{\tilde{Q}^{2n}}C_{1,n}(\tilde{Q}^2,m_\Psi^2,\mu^2)\mathcal{O}_{n+2,V}^{\mu\nu \mu_1\dots\mu_{n}}(\mu)
\nonumber\\
&\qquad +i g^{\mu\nu}\sum_{\substack{n=2\\ \text{even}}}^\infty\frac{(2q_{\mu_1})\dots (2q_{\mu_n})}{\tilde{Q}^{2n}}C_{2,n}(\tilde{Q}^2,m_\Psi^2,\mu^2)\mathcal{O}_{n,V}^{\mu_1\dots\mu_{n}}(\mu)\nonumber\\
&\qquad -{2\over \tilde Q^2}g^{\mu\nu}m_\Psi \sum_{\substack{n=0\\ \text{even}}}^\infty\frac{(2q_{\mu_1})\dots (2q_{\mu_n})}{\tilde{Q}^{2n}}C_{3,n}(\tilde{Q}^2,m_\Psi^2,\mu^2)\hat{\mathcal{O}}_{n}^{\mu_1\dots\mu_{n}}(\mu) \nonumber\\
&\qquad -{4i\over \tilde Q^2}q^{\{\mu }\sum_{\substack{n=1\\ \text{odd}}}^\infty\frac{(2q_{\mu_1})\dots (2q_{\mu_n})}{\tilde{Q}^{2n}}C_{4,n}(\tilde{Q}^2,m_\Psi^2,\mu^2)\mathcal{O}_{n+1,V}^{\nu\}\mu_1\dots\mu_{n}} +\text{higher twist}(\mu)
,\label{eq:hope_compton}
\end{align}
where $C_{i,n}$ are the Wilson coefficients and we have defined
\begin{equation}
\tilde{Q}^2=-q^2+m_\Psi^2.\label{eq:hope_twist_suppression}
\end{equation}
Higher twist contributions are supressed by at least one extra inverse power of $\tilde{Q}$. The operators occurring on the right hand side of Eq.~\eqref{eq:hope_compton} are the well-known standard twist-two operators:
\begin{align}
\mathcal{O}_{n,V}^{\mu_1\dots \mu_n}&=\overline{\psi}\gamma^{\{\mu_1}(i\overset{\leftrightarrow}{D}\vphantom{D}^{\,\mu_2})\dots(\overset{\leftrightarrow}{D}\vphantom{D}^{\,\mu_n\}})\psi-\tr,\label{eq:ov}
\\
\mathcal{O}_{n,A}^{\mu_1\dots \mu_n}&=\overline{\psi}\gamma^{\{\mu_1}\gamma_5(i\overset{\leftrightarrow}{D}\vphantom{D}^{\,\mu_2})\dots(i\overset{\leftrightarrow}{D}\vphantom{D}^{\,\mu_n\}})\psi-\tr,\label{eq:oa}
\end{align}
and the twist-three operators:
\begin{equation}
\hat{\mathcal{O}}_{n}^{\mu_1\dots \mu_n}=\overline{\psi}(i\overset{\leftrightarrow}{D}\vphantom{D}^{\,\{\mu_1})(i\overset{\leftrightarrow}{D}\vphantom{D}^{\,\mu_2})\dots(i\overset{\leftrightarrow}{D}\vphantom{D}^{\,\mu_n\}})\psi-\tr,
\end{equation}
where $i$ is the quark flavor, $\{\cdots\}$ denotes total symmetrization of the Lorentz indices and trace subtraction, and
\begin{equation}
\overset{\leftrightarrow}{D}\vphantom{D}^{\,\mu}=\frac{1}{2}(\overset{\rightarrow}{D}\vphantom{D}^{\,\mu}-\overset{\leftarrow}{D}\vphantom{D}^{\,\mu}).
\end{equation}
Lorentz covariance allows us to write the general form for the twist-two matrix elements as
\begin{align}
\bra{H(\mathbf{p},\mathbf{s})}\mathcal{O}_{n,V}^{\mu_1\dots \mu_n}\ket{H(\mathbf{p},\mathbf{s})}&=2a_{n,V}^{H}(\mu^2)[p^{\mu_1}\dots p^{\mu_n}-\tr],\label{eq:localops_vector}
\\
\bra{H(\mathbf{p,s})}\mathcal{O}_{n,A}^{\mu_1\dots \mu_n}\ket{H(\mathbf{p,s})}&=2a_{n,A}^{H}(\mu^2)[s^{\{\mu_1}p^{\mu_2}\dots p^{\mu_n\}}-\tr],
\\
\bra{H(\mathbf{p},\mathbf{s})}\hat{\mathcal{O}}_{n}^{\mu_1\dots \mu_n}\ket{H(\mathbf{p},\mathbf{s})}&=2b_{n}^{H}(\mu^2)[p^{\mu_1}\dots p^{\mu_n}-\tr],
\\
\bra{\Omega}\mathcal{O}_{n,A}^{\mu_1\dots \mu_n}\ket{M(\mathbf{p})}&=f_M\expval{\xi^{n-1}}_M(\mu^2)[p^{\mu_1}p^{\mu_2}\dots p^{\mu_n}-\tr],
\end{align}
where $\ket{H(\mathbf{p},\mathbf{s})}$ is a general hadronic state $H$ with mometum $\mathbf{p}$ and spin $\mathbf{s}$, $\ket{M(\mathbf{p})}$ is a general pseudoscalar mesonic state with momentum $\mathbf{p}$, $a_{n,V}^{H}$, $a_{n,A}^{H}$, $b_{n}^{H}$ and $\expval{\xi^{n}}_M$ are the Mellin moments, and $f_M$ is the meson decay constant.
Explicitly, for the symmetric case of Eq.~\eqref{eq:compton_amplitude} in a pion, we have
\begin{align}\label{eq:hope_compton2}
T^{\{\mu\nu\}}(p,q)&=\bra{\pi(\mathbf{p})}t^{\{\mu\nu\}}(q;m_\Psi)\ket{\pi(\mathbf{p})}
\\
&=\frac{i}{\tilde{Q}^2}\bigg(4p^\mu p^\nu\sum_{\substack{n=0\\ \text{even}}}^\infty \tilde{\omega}^n {C}_{1,n}(\tilde{Q}^2,m_\Psi^2,\mu^2)2a_{n+2,V}^{\pi}(\mu^2)
+\tilde{Q}^2 g^{\mu\nu}\sum_{\substack{n=2\\ \text{even}}}^\infty\tilde{\omega}^n{C}_{2,n}(\tilde{Q}^2,m_\Psi^2,\mu^2)2a^{\pi}_{n,V}(\mu^2)\nonumber
\\
&+2ig^{\mu\nu}m_\Psi\sum_{\substack{n=0\\ \text{even}}}^\infty\tilde{\omega}^n{C}_{3,n}(\tilde{Q}^2,m_\Psi^2,\mu^2)2b_n^{\pi}(\mu^2)-2(p^\mu q^\nu+q^\mu p^\nu) \sum_{\substack{n=1\\ \text{odd}}}^\infty\tilde{\omega}^n{C}_{4,n}(\tilde{Q}^2,m_\Psi^2,\mu^2)2a_{n+1,V}^{\pi}(\mu^2)
\bigg)\nonumber,
\end{align}
where our expansion parameter is
\begin{equation}
\tilde{\omega}=\frac{1}{\tilde{x}_B}=\frac{2p\cdot q}{\tilde{Q}^2},\label{eq:hope_expansion_parameter}
\end{equation}
and $p^\mu$ is the momentum of the external hadronic state. Target mass corrections can be resummed using the standard techniques~\cite{Nachtmann:1973mr,Georgi:1976vf,Georgi:1976ve,Wandzura:1977ce}, and the explicitly resummed expression for \eq{hope_compton2} can be found in Ref.~\cite{Detmold:2005gg}. In either case, the application of the formalism to lattice QCD is as follows: first, numerically calculate the required hadronic amplitude, then fit the HOPE expression to lattice data with the moments as free parameters. Note that the applicability of the approach requires $|\tilde{\omega}| < 1$, leading to kinematical suppression of higher moments. Successful application of the HOPE method requires $\tilde{Q}^2\gg\Lambda_\text{QCD}^2$, so in order to enhance the contributions from higher moments for fixed $q^\mu$, one must increase the hadron momentum $|\mathbf{p}|$. This point has been discussed previously in Ref.~\cite{Detmold:2020lev}.
\input{hope_qPDF}
\subsection{Convergence and Analytic Structure of HOPE Hadronic Amplitude}
\label{sec:convg}
In this section, we shall analyze the convergence properties of the
HOPE hadronic amplitude $T^{\mu\nu}(p,q)$. A similar analysis can also
be made for the matrix element $V^{\mu\nu}(p,q)$.
The materials presented in this section are
important for examining the validity of the HOPE method, and they
complement the discussion in Ref.~\cite{Detmold:2005gg} where the
approach was first proposed.
To begin with, we note that $T^{\mu\nu}(p,q)$ is a rank-2 tensor and thus the most general Lorentz covariant decomposition is
\begin{align}
T^{\mu\nu}(p,q)&= g^{\mu\nu}A_1(q^2,p\cdot q;m_\Psi)+p^\mu p^\nu A_2(q^2,p\cdot q;m_\Psi)+p^\mu q^\nu A_3(q^2,p\cdot q;m_\Psi)+q^\mu p^\nu A_4(q^2,p\cdot q;m_\Psi)\nonumber
\\
&\qquad+q^\mu q^\nu A_5(q^2,p\cdot q;m_\Psi)
+i\epsilon^{\mu\nu\alpha\beta}q_\alpha p_\beta A_6(q^2,p\cdot q;m_\Psi),
\end{align}
where the $A_i$ are scalar functions which are dependent on all possible kinematic variables. In the HOPE method, one performs an OPE as described in Ref~\cite{Detmold:2005gg}. We may equivalently express the scalar functions $A_i$ in terms of the variables
\begin{equation}
\tau=Q^2/\tilde{Q}^2,\label{eq:tau}
\end{equation}
$\tilde{Q}^2$ and $\tilde{\omega}$ (defined in Eq.~\eqref{eq:hope_twist_suppression} and Eq.~\eqref{eq:hope_expansion_parameter}, respectively) as
\begin{equation}
A_i=A_i(\tilde{Q}^2,\tilde{\omega},\tau).
\end{equation}
Understanding the analytic properties of these scalar functions will enable us to understand the radius of convergence for the HOPE strategy in terms of the expansion variable $\tilde{\omega}$. Since the intention of this work is to describe the theoretical background for a numerical calculation using lattice QCD, we note that the relevant Euclidean constraint can be found by taking $q_0\to iq_4$ in $\tilde{\omega}$, provided the amplitude is analytic for this value of $q_0$. Since $\tilde{\omega}$ is in general complex, we seek to determine the radius of convergence in the complex plane. To study this, we must analyze the general analytical properties of the amplitude without recourse to perturbation theory. We shall consider the amplitude purely in Minkowski space and derive relations for the physical poles and branch points. Information regarding the locations of these singularities is important for determining the radius of convergence.
To discuss the analytic properties of the scalar functions $A_i(\tilde{Q}^2,\tilde{\omega},\tau)$, it is useful to express these amplitudes in terms of standard Mandelstam variables. Noting that the matrix element we consider is in the forward limit, we write
\begin{align}
s&=(p+q)^2\,,\ \ \ \ \ t=0\,,\ \ \ \ \ u=(p-q)^2\,.
\end{align}
Conservation of momentum allows us to relate $u$ to $q^2$ and $s$. We may express $s$ in terms of the HOPE variables:
\begin{align}
s&=m_\pi^2+\tau \tilde{Q}^2(\tau^{-1}\tilde{\omega}-1) =m_\pi^2+\tilde{Q}^2(\tilde{\omega}-\tau)\,.
\end{align}
The lowest pole $\tilde{\omega}_\text{pole}$ in $A_i(\tilde{Q}^2,\tilde{\omega},\tau)$ appears at a value of $s=m_\text{HL}^2$ corresponding to the propagation of a heavy-light axial-vector meson with mass $m_{\rm HL}$ between the two inserted currents:
\begin{align}
\tilde{\omega}_\text{pole}&=\tau+\frac{m_\text{HL}^2-m_\pi^2}{\tilde{Q}^2} =1-\frac{m_\pi^2+m_\Psi^2-m_\text{HL}^2}{\tilde{Q}^2}\,.
\end{align}
The first hadronic branch point which will appear is due to the two-body threshold ($s=(m_\pi+m_\text{HL})^2$). The corresponding position of the branch point in terms of $\tilde{\omega}$ is
\begin{align}
\tilde{\omega}_\text{b.p.}&=\tau+\frac{(m_\text{HL}+m_\pi)^2-m_\pi^2}{\tilde{Q}^2} =1+\frac{(m_\text{HL}+m_\pi)^2-m_\Psi^2-m_\pi^2}{\tilde{Q}^2}\,.
\end{align}
Further branch points appear due to the opening of more channels as the energy increases. Finally, from Eq.~\eqref{eq:compton_amplitude} it is possible to see that the amplitude is invariant under the combined interchange
\begin{equation}
q\leftrightarrow -q,\, \ \ \ \ \mu\leftrightarrow\nu.
\end{equation}
Under this interchange the roles of $s$ and $u$ are reversed. Above threshold this corresponds to the physical region of the $u$-channel process. In terms of $\tilde{\omega}$, this leads to
\begin{equation}
\tilde{\omega}\leftrightarrow -\tilde{\omega},
\end{equation}
and thus for each singularity or branch point we have discussed in $\tilde{\omega}$ due to a physical process in the $s$-channel there will be a corresponding singularity or branch point at $-\tilde{\omega}$ for the $u$-channel process. The resulting analytic structure of the amplitude is shown in Fig.~\ref{fig:analytic_structure}.
From this discussion of the analytic properties of the hadronic amplitude one may be assured that the HOPE method converges when performing numerical simulations provided one chooses kinematics such that
\begin{equation}
|\tilde{\omega}|<\tilde{\omega}_\text{pole}=1-\frac{m_\pi^2+m_\Psi^2-m_\text{HL}^2}{\tilde{Q}^2}.
\end{equation}
Note that in the limit that the heavy quark mass becomes infinite, $\tilde{\omega}_\text{pole}\to1$ and $\tilde{\omega}_\text{b.p.}\to1$.
\begin{figure}
\centering
\includegraphics[scale=1,trim={5cm 18cm 8cm 2cm},clip]{re_im}
\caption{The analytic structure of HOPE Compton amplitude. The radius of convergence is determined by the location of the nearest singularity, which is represented as a cross. The first branch point appears at $|\tilde{\omega}_\text{b.p.}|=1+[(m_\text{HL}+m_\pi)^2-m_\Psi^2-m_\pi^2]/\tilde{Q}^2$ and the branch cut is represented by the zigzag.
In order to ensure a convergent expression one should choose a value of $|\tilde{\omega}|<\tilde{\omega}_\text{pole}=1-(m_\pi^2+m_\Psi^2-m_\text{HL}^2)/\tilde{Q}^2$.}
\label{fig:analytic_structure}
\end{figure}
\subsection{Relationship to Other Approaches}
\label{sec:Hope_qPDF}
The HOPE method allows extraction of information about light-cone quantities from a current-current correlator where the standard current operator is replaced by that given in Eq.~\eqref{eq:hope_current}. While the use of this fictitious flavor changing current implies that the resulting matrix elements are not observables of standard QCD, the quenching of the heavy quark ensures the modifications may be wholly absorbed into the Wilson coefficients and thus the resulting moments correspond to those of QCD. As a result it is possible to show that the amplitude may be written in a factorized form as is done in the quasi-PDF~\cite{Ji:2013dva,Ji:2014gla,Ji:2020ect}, ``lattice cross section''~\cite{Ma:2017pxb} (LCS) or pseudo-PDF~\cite{Radyushkin:2017cyf,Orginos:2017kos} approaches. To do this, we start from Eq.~\eqref{eq:compton_amplitude} and use the HOPE expression for the operator given in Eq.~\eqref{eq:hope_compton}. By taking $\mu=3$, $\nu=0$, we can remove contributions from the twist-3 operators and as a result the HOPE expression for the pion hadronic amplitude $T^{\mu\nu}(p,q)$ is~\cite{Detmold:2005gg}:
\begin{align}
T^{\{30\}}(p,q)&=8i\frac{p^3p^0}{\tilde{Q}^2}\sum_{n=0,\text{even}}^\infty \tilde{\omega}^n {C}_{1,n}(\tilde{Q}^2,m_\Psi^2,\mu^2) a_{n+2,V}^{\pi}(\mu^2)-4i\frac{p^0q^3+p^3q^0}{\tilde{Q}^2}\sum_{n=1,\text{odd}}\tilde{\omega}^n {C}_{4,n}(\tilde{Q}^2,m_\Psi^2,\mu^2)a_{n+1,V}^{\pi}(\mu^2)\nonumber
\\
&\qquad+\text{higher-twist}.
\end{align}
Importantly, this relation is valid to twist-two accuracy, with higher-twist contributions being suppressed by at least an extra factor of $\Lambda_{\text{QCD}}/\tilde{Q}$.
When the momentum of the hadron becomes large, it also serves to suppress the target-mass effects which are of higher twist. To see this, let us compare the twist-two operator ${\cal O}_{n,V}^{\mu_0\mu_1}$ to the twist-four counter-part $g^{\mu_0\mu_1}{\cal O}_{n,V}^{(4)}$, which is given by
\begin{equation}
{\cal O}^{(4)}_{n,V}=\overline{\psi} (i\overset{\leftrightarrow}{\slashed{D}})\psi.
\end{equation}
Their contributions to the OPE are
\begin{align}
(2q_{\mu_0})(2q_{\mu_1})\bra{H(\mathbf{p},\mathbf{s})}\mathcal{O}_{n,V}^{\mu_0\mu_1}\ket{H(\mathbf{p},\mathbf{s})} &= 2a_{n,V}^{H} \left[(2q\cdot p) ^2 - q^2 m_H^2\right]\,,\\
(2q_{\mu_0})(2q_{\mu_1})g^{\mu_0\mu_1}\bra{H(\mathbf{p},\mathbf{s})}\mathcal{O}^{(4)}_{n,V}\ket{H(\mathbf{p},\mathbf{s})} &= 2a_{n,V}^{(4)}[4q^2 m_H^2]\,.
\end{align}
where $a_{n,V}^{(4)}$ is the Mellin moment for the twist-four operator ${\cal O}^{(4)}_{n,V}$. Thus we see that for kinematics where $q\cdot p \sim -q^2 \gg m_H^2$, both the target mass corrections and twist-four corrections are suppressed.
Using Eq.~\eqref{eq:anvH}, we may write
\begin{align}
T^{30}(p,q)&=\int_{0}^1 d\xi\ f_{H}(\xi,\mu^2) K(\xi,\tilde{\omega},\tilde{Q}^2,\mu^2)+\text{higher-twist},\label{eq:compton_factorized}
\end{align}
where the matching kernel is
\begin{align}\label{eq:kernel}
K(\xi,\tilde{\omega},\tilde{Q}^2,&\mu^2)=\sum_{n=0,\text{even}}^\infty\bigg[8i\frac{p^3p^0}{\tilde{Q}^2} \xi^2(\xi\tilde{\omega})^n {C}_{1,n}(\tilde{Q}^2,m_\Psi^2,\mu^2)-4i\frac{p^0q^3+p^3q^0}{\tilde{Q}^2}\xi(\xi\tilde{\omega})^{n+1} {C}_{4,n+1}(\tilde{Q}^2,m_\Psi^2,\mu^2)\bigg],
\end{align}
and we again emphasize that the flavor labels have been suppressed in the above definitions of the PDF and matching kernel.
Assuming $|\tilde{\omega}|<1$, we can re-sum the resulting geometric series to find a closed-form expression for the matching kernel~\cite{Martinelli:1998hz,Chambers:2017dov}. More generally, one may express the amplitude as the convolution of the PDF and the short-range kernel $K$. Importantly, one must ensure that $\tilde{Q}$ is large enough to isolate the twist-two contribution, and so that the matching coefficients can be calculated using perturbation theory.
According to Eq.~\eqref{eq:compton_factorized}, the hadronic amplitude defined by Eq.~\eqref{eq:compton_amplitude} may also be analyzed using a factorization theorem similar to the quasi-PDF, LCS or pseudo-PDF approaches. If we obtain the hadron amplitude as a continuous function in $\tilde\omega$ in its full range, then in principle we can invert \eq{compton_factorized} as is done in the quasi-PDF approach. Note that the kinematics we require to ensure a valid OPE is equivalent to that for the factorization of the amplitude into the light-cone quantity of interest and a perturbatively calculable matching kernel. To obtain large $\tilde \omega \sim 1$, we need large pion momentum. With a limited range of $\tilde \omega$, it is difficult to perform the inversion, so we have to rely on either a model fit of the PDF to the hadronic amplitude data using \eq{compton_factorized}, or we can fit the lowest moments using the OPE formula. In this regard, both strategies allow us to extract the same amount of information about the PDF, but the latter is model independent because the it does not introduce uncontrollable systematic effects from modeling the PDF to perform the inversion.
Generically, fitting lattice data to OPE formulae allows for the extraction of higher moments of the PDFs and LCDAs.
This evades the need for the direct evaluation of matrix elements of local operators, which involve the subtraction of power divergences in the renormalisation procedure. In principle, having information for all moments enables one to reconstruct the PDFs and LCDAs. Indeed, as demonstrated in the above section, the HOPE hadronic amplitudes allow us to determine directly the $\xi$-dependence
in these latter quantities, since the matching kernel, $K$, in Eqs.~(\ref{eq:compton_factorized}) and (\ref{eq:kernel}) is perturbatively computable. The same general idea has been realised in different practical ways. For example, similar proposals for obtaining information about parton physics can also be found in Refs.~\cite{Braun:2003rp,Chambers:2017dov}. Compared to these other proposals, the introduction of the fictitious (valence) heavy quark in the
HOPE strategy provides several advantages \footnote{The presence of an extra large mass scale modifies the Wilson coefficients $C_{j,n} (j=1,2,3,4)$ that have been derived in the massless case~\cite{Gross:1973ju,Gross:1974cs,Georgi:1951sr,Calvo:1977ba,DeRujula:1976baf,Altarelli:1978id,Kodaira:1978sh,Kodaira:1979ib,Kodaira:1979pa}. Therefore, a precise determination of the PDF or LCDA would necessitate the recalculation of $C_{j,n}$ and $K$ with the explicit dependence on the heavy quark mass. One can determine $K$ from the the Wilson coefficients $C_{j,n}$ presented in~\sec{oneloop}.}. As already explained in Ref.~\cite{Detmold:2005gg}, the heavy quark provides a large scale that offers an additional parameter to control the OPE, and its valence nature is crucial for suppressing higher-twist effects. Here we would like to point out two other assets that arise from the introduction of this heavy quark. First, in the setting where $m_{\Psi}^{2}\gtrsim (p+q)^{2}$, it is natural that no on-shell state can
appear between the two currents in the Minkowski-space counterpart of the HOPE hadronic amplitudes. This means that their analytic continuation is straightforward.
Secondly, the presence of the heavy quark serves to suppress the matrix element at large distances, and thus ensure that the effect of truncating the finite numerical data when performing the temporal Fourier transform is negligible.
\section{Introduction}
Factorization in Quantum Chromodynamics (QCD) allows one to describe many hard hadronic reactions as a convolution of a short-range (high-energy) perturbative kernel and a long-range (low-energy) process-independent function~\cite{Collins:1989gx}.
Historically, the approach used to describe high-energy hadronic processes has been to calculate the short-range kernel using perturbation theory and to extract the long-distance piece from experimental data.
The validity of this approach is established by the universality of the long-range contributions, which are intrinsic properties of the hadron.
While the low-energy functions in QCD factorization can be measured from experimental data, they are also calculable within a non-perturbative field theoretic framework. Currently, the only non-perturbative first-principles approach to QCD is through lattice regularization, and such low-energy functions are prime candidates for a direct calculation using this framework. Recently the advances in computational power, numerical algorithms and theoretical understanding have enabled these quantities to be computed. The two simplest examples of these long-distance functions are the parton distribution functions (PDFs) introduced to explain deep inelastic scattering (DIS)~\cite{Bjorken:1968dy,Feynman:1969ej,Bjorken:1969ja}, and the light-cone distribution amplitudes (LCDAs) introduced to describe high-energy exclusive processes~\cite{Radyushkin:1977gp,Lepage:1980fj}.
Direct evaluations of the PDFs and LCDAs require the computation of matrix elements involving non-perturbative dynamics on the light-cone, and hence are not possible in a Euclidean formulation of field theory like lattice QCD. Historically, this problem in lattice calculations has been addressed using Wilson's operator product expansion (OPE)~\cite{Wilson:1969zs,Wilson:1972ee} to express the non-local operator as an infinite sum of local operators. Matrix elements of these local operators are directly calculable within the framework of lattice QCD, and are related to moments of the PDFs and LCDAs. In principle, knowledge of these moments facilitates the reconstruction of the PDFs and LCDAs. See, for example, Refs~\cite{Kronfeld:1984zv,Martinelli:1987si,Best:1997qp} for earlier works employing this strategy. Nevertheless, the renormalisation procedure for the local operators appearing in this approach requires subtractions of power divergences that arise from the breaking of the $O(4)$ Euclidean space-time symmetry. As a result, the method is practically applicable only to the determination of a few leading moments.
Over the past two decades, various alternative strategies have been proposed to extract PDFs and LCDAs using lattice QCD~\cite{Aglietti:1998ur,Liu:1999ak,Detmold:2005gg,Braun:2007wv,Davoudi:2012ya,Ji:2013dva,Chambers:2017dov,Radyushkin:2017cyf,Ma:2017pxb}. All of these strategies involve lattice computations for matrix elements of non-local operators. In this article, we expand the theoretical details of the proposal suggested in Ref.~\cite{Detmold:2005gg}. This proposal is originally designed to allow access to higher moments with lattice QCD. Its key ingredient is the introduction of a fictitious, valence heavy quark that enables additional control of an OPE for calculating higher moments. Here we call this the heavy-quark operator product expansion (HOPE) method. In the current paper we show how one may extend the HOPE method to enable the direct determination of $\xi$-dependence of the PDFs and LCDAs. This is achieved, as explained in detail in Sec.~\ref{sec:Hope_qPDF}, by demonstrating that the hadronic amplitudes appearing in the HOPE approach can be expressed as the convolution of a perturbative matching kernel and either a PDF or LCDA. Concerning the computation of the moments, we complement the discussions in Ref.~\cite{Detmold:2005gg} by analysing the convergence properties of the HOPE. This analysis is presented in Sec.~\ref{sec:convg} below. Furthermore, in this work we provide the relevant one-loop Wilson coefficients for extracting moments of the unpolarised and helicity PDFs, as well as the meson LCDAs. This allows one to account for renormalisation scheme and scale dependence in the moments more precisely. Although the Wilson coefficients for the PDFs can be inferred from results in Refs.~\cite{Gottschalk:1980rv,Gluck:1996ve} where the cross sections for heavy-quark production in charged-current DIS are computed, we perform alternative calculations and describe them in Secs.~\ref{sec:nlopdf} and \ref{sec:helicity}. Finally, in Sec.~\ref{sec:danlo} we give one-loop results for the LCDAs, which are new.
\section{Definitions and Elementary Properties}
In order to make this paper self-contained, we give formal definitions for the PDF and LCDA, summarize their uses and motivate the necessity for computing these quantities from first principles. Although we intend this calculation to be used for a determination of moments of the LCDA using Euclidean lattice field theory, in this work we proceed in Minkowski space and utilize the ``mostly negative'' metric: $g^{\mu\nu}=\ensuremath{\text{diag}}(+1,-1,-1,-1)$. Results in Euclidean space can be obtained straightforwardly provided the analytic continuation of the matrix element considered is possible. Further discussion of this point is found in \sec{convg}.
\subsection{Parton Distribution Function}
Parton distribution functions were introduced in the context of the study of DIS~\cite{Bjorken:1968dy,Feynman:1969ej,Bjorken:1969ja} and are an important input in the Standard Model predictions of collisions at high-energy hadronic colliders like the LHC. Currently nucleon PDFs are extracted through global fits to a number of different cross sections~\cite{Harland-Lang:2014zoa,Ball:2017nwa,Alekhin:2017kpj,Hou:2019efy,Sato:2019yez}. However, it is a goal of lattice field theory to produce predictions of the PDFs from first-principle calculations in QCD of similar or better precision to those extracted from experiments. Formally the unpolarized PDF, $f_{i/H}(\xi,\mu^2)$ and helicity PDF, $\Delta f_{i/H}(\xi,\mu^2)$ for a quark of flavor $i$ carrying a fraction $\xi$ of momentum in a hadron $H$ are defined as
\begin{align}
\begin{split}
f_{i/H}(\xi,\mu^2)&=\int \frac{dx^-}{(4\pi)}\ e^{-i\xi P^+ x^-}\bra{H(\mathbf{p},\mathbf{s})}\overline{\psi}_i(x^-)\gamma^+ W[x^-,0]\psi_i(0)\ket{H(\mathbf{p},\mathbf{s})},
\end{split}
\\
\begin{split}
\Delta f_{i/H}(\xi,\mu^2)&=\frac{1}{s^+}\int \frac{dx^-}{(4\pi)}\ e^{-i\xi P^+ x^-}\bra{H(\mathbf{p},\mathbf{s})}\overline{\psi}_i(x^-)\gamma^+ \gamma_5 W[x^-,0]\psi_i(0)\ket{H(\mathbf{p},\mathbf{s})},
\end{split}
\end{align}
where $\mu^2$ is the renormalization scale of the light-cone separated operator, $s^\mu$ is the spin vector of the hadron of mass $m_H$, with $s^2=-m_H^2$ and $s\cdot p=0$, and
\begin{equation}
W[x,y]=\mathcal{P}\exp(ig\int_x^y dz_\mu\ A_a^\mu(z)t_a)
\end{equation}
is a Wilson line which ensures gauge invariance of the matrix element. We use light-cone coordinates where for a general four-vector $V^\mu$ the ``plus'' and ``minus'' components are defined as
\begin{align}
V^\pm&=\frac{1}{\sqrt{2}}(V^0\pm V^3)\,.
\end{align}
In order to keep the notation relatively simple, in what follows we shall drop explicit flavor labels unless they are necessary. Correspondingly, $f_{i/H}$ and $\Delta f_{i/H}$ will be denoted as $f_{H}$ and $\Delta f_{H}$, respectively.
\subsection{Light-cone Distribution Amplitude}
The LCDA was originally introduced in order to study the asymptotically large momentum transfer limit of the pion electromagnetic form factor~\cite{Radyushkin:1977gp}. At around the same time, it was realized~\cite{Lepage:1980fj} that meson and baryon LCDAs were the central objects of interest in describing a number of exclusive process at high energy. In light-cone gauge where $A^+=0$, the LCDA $\phi_M(\xi,\mu^2)$ of a meson $M$ is interpreted as the probability amplitude for converting the meson into a collinear quark-antiquark pair with longitudinal momentum fractions $(1+\xi)/2$ and $(1-\xi)/2$, respectively, at the renormalization scale $\mu^2$. For pseudoscalar mesons, the LCDA is defined by the matrix element~\cite{Radyushkin:1977gp,Lepage:1980fj}
\begin{align}
\bra{\Omega}\overline{\psi}(z)\gamma_\mu \gamma_5 W[z,-z]\psi(-z)\ket{M(\mathbf{p})} = if_M p_\mu\int_{-1}^1 d\xi\ e^{-i\xi p\cdot z }\phi_M(\xi,\mu^2)\,,
\label{eq:lcda}
\end{align}
where $\bra{\Omega}$ is the physical vacuum state, $z^2=0$ is a light-like separation and $f_M$ is the pseudoscalar meson decay constant defined by the $z\to0$ limit of Eq.~\eqref{eq:lcda}. The most studied of the LCDAs is that of the pion. In the isospin limit where the masses of the up and down quarks are degenerate, the pion LCDA is symmetric under the interchange $\xi\to -\xi$, that is
\begin{equation}
\phi_\pi(\xi,\mu^2)=\phi_\pi(-\xi,\mu^2).
\end{equation}
We shall assume isospin symmetry in this work. At leading logarithmic accuracy, the natural orthogonal polynomial basis for the LCDA is the set of Gegenbauer polynomials~\cite{Lepage:1980fj,Efremov:1979qk},
\begin{equation}
\mathcal{C}=\{\mathcal{C}_n^{(3/2)}(\xi)\,|\,n=0,1,2\dots\}.
\end{equation}
The pion LCDA can thus be expressed as
\begin{equation}
\phi_\pi(\xi,\mu^2)=\frac{3}{4}(1-\xi^2)\sum_{n=0,2,\dots}^\infty \phi_n^\pi(\mu^2)\mathcal{C}_n^{(3/2)}(\xi).
\end{equation}
From this decomposition, it is clear that knowledge of the Gegenbauer moments $\phi_n^\pi(\mu^2)$ is sufficient to reconstruct the LCDA. In the limit that $\mu^2\to\infty$, $\phi_0(\mu^2)\to1$ and the higher moments go logarithmically to zero. As a result
\begin{equation}
\phi_\pi(\xi,\mu^2\to\infty)=\frac{3}{4}(1-\xi^2).\label{eq:lcda_asymp}
\end{equation}
The high-energy behavior of certain exclusive processes in QCD are controlled by this asymptotic form of the distribution amplitude given in Eq.~\eqref{eq:lcda_asymp}. In particular, in Ref.~\cite{Lepage:1980fj}, predictions are given for transition and electromagnetic form factors of the pion. The success of this formalism is particularly clear for the case of the $\gamma\gamma^*\to\pi^0$ transition form factor, where experimental data from Belle~\cite{Uehara:2012ag} appears to show the predicted asymptotic form, although previous experiments appeared to suggest that this prediction underestimated the data~\cite{Gronberg:1997fj,Aubert:2009mc}. For the case of the pion electromagnetic form factor, the situation is less clear. The most recent experimental data~\cite{Blok:2008jy,Huber:2008id} does not agree with the prediction of Ref.~\cite{Lepage:1980fj}. Although the extracted values of the pion form factor are in principle model dependent~\cite{Guidal:1997by,Vanderhaeghen:1997ts}, it has been shown that they are relatively insensitive to the model used~\cite{Perry:2018kok,Perry:2020hli}. Since the asymptotic form of the distribution amplitude is only expected to be valid at very high photon virtualities, it has been suggested that the discrepancy between theory and experiment can be traced to the use of Eq.~\eqref{eq:lcda_asymp} at energy scales where the LCDA has not yet evolved to its asymptotic form.
While further high-energy measurements of the pion electromagnetic form factor are certainly required, it is clear that precise determinations of the pion LCDA are also necessary to fully understand this discrepancy.
\subsection{Current Theoretical Approaches}
Due to the importance of having accurate calculations of PDFs and LCDAs, much work has been done to obtain information about the these quantities using many different phenomenological approaches. As we have previously emphasized, the most reliable theoretical determinations of such non-perturbative objects are obtained from lattice QCD. The `traditional' approach involves a determination of the Mellin moments of either the PDF or LCDA. These moments may be written as linear combinations of the Gegenbauer moments. The Mellin moments of the unpolarized PDF $f$, helicity PDF $\Delta f$ and LCDA $\phi_M$ for meson $M$ are defined respectively as
\begin{align}
a_{n,V}^{H}(\mu^2)&=
\int_0^1d\xi\ \xi^n f_{H}(\xi,\mu^2) \,,\label{eq:anvH}
\\
a_{n,A}^{H}(\mu^2)&=
\int_0^1d\xi\ \xi^n \Delta f_{H}(\xi,\mu^2)\,,
\\
\expval{\xi^n}_{M}(\mu^2)&=\int_{-1}^1 d\xi\ \xi^n\phi_M(\xi,\mu^2).\label{eq:phiM}
\end{align}
With exact knowledge of all the Mellin moments, one is able to reconstruct the full $\xi$-dependence of the distributions.
In practice, numerical determinations restrict one to calculating a finite set of moments, and further difficulties appear when one attempts to compute matrix elements of twist-two operators with spin greater than four in a lattice regularized field theory~\cite{Gockeler:1996mu}. This is because the lattice regularization breaks the full rotation group $\text{SO}(4)$ and leads to mixing of operators with different mass dimensions, hence the appearance of power divergences. These power divergences make the determination of the higher moments difficult. Nevertheless, this approach has been well studied and has yielded results for the lowest three moments of the pion PDF~\cite{Best:1997qp,Guagnelli:2004ga,Capitani:2005jp,Abdel-Rehim:2015owa,Oehm:2018jvm,Alexandrou:2020gxs} (for the lattice calculations of nucleon PDF moments see a recent review in Ref.~\cite{Lin:2020rut}), as well as the first non-trivial moment of the pion LCDA and the first two moments of the kaon LCDA~\cite{Kronfeld:1984zv,Martinelli:1987si,Braun:2015axa,Oehm:2018jvm,Bali:2019dqc}
To go beyond the calculation of the lowest moments of the PDF or LCDA, several alternative approaches have been proposed. One method is based on the short-distance operator product expansion (OPE) of a current-current correlator~\cite{Braun:2007wv,Bali:2017gfr}, where the issue of power-divergent operator mixing can be avoided since the currents have a well-defined continuum limit, and one can in principle extract the $n\ge4$ moments of the LCDA given sufficient numerical precision. The current-current correlator has also been used in the calculation of PDFs in recent studies~\cite{Ma:2017pxb,Sufian:2020vzb}.
A method has been proposed to restore the broken rotational symmetry~\cite{Davoudi:2012ya} which would reduce the power-divergent mixing so that the higher moments can be directly computed on the lattice. More recently, the formalism of large-momentum effective theory (LaMET)~\cite{Ji:2013dva,Ji:2014gla,Ji:2020ect} was proposed as a method to determine the $\xi$-dependence of the PDF~\cite{Alexandrou:2018pbm,Lin:2018pvv,Izubuchi:2019lyk}. In this approach, one calculates the ``quasi-PDF'' which is defined as the Fourier transform of equal-time quark bilinear corrrelators in a hadron state with large momentum. The LaMET approach has also been applied to the lattice calculation of the LCDAs for light mesons~\cite{Zhang:2017bzy,Chen:2017gck,Zhang:2020gaj}. The same matrix element that defines the quasi-PDF can also be used in a short-distance coordinate space expansion known as the ``Ioffe-time pseudo distribution'' approach~\cite{Radyushkin:2017cyf,Orginos:2017kos}. Using this formalism, several moments of the PDF have been determined, and the $\xi$-dependence has been determined via a fit to a parametrized {\it ansatz}~\cite{Joo:2019bzr,Gao:2020ito,Joo:2020spy}. A direct lattice calculation of the hadronic tensor has also been proposed and explored~\cite{Liu:1993cv,Liang:2019frk}. In a similar vein, an application of the Feynman-Hellman theorem allows indirect access to the hadronic tensor via a determination of two-point correlators coupled to external fields~\cite{Chambers:2017dov,Can:2020sxc}.
In this work we pursue a different approach: the HOPE method~\cite{Detmold:2005gg,Detmold:2018kwu,Detmold:2020lev}. This procedure was first proposed in Ref.~\cite{Detmold:2005gg} and builds on the conventional OPE by performing the numerical simulation of a current-current correlator with the currents containing a fictitious heavy quark species which leads to a number of advantages over the standard treatment~\cite{Detmold:2005gg}. In the next section, we review this strategy and provide more details about its theoretical foundation and practical implementation.
\section{One-Loop Wilson Coefficients for PDF and LCDA}
\label{sec:oneloop}
In this section, we derive the one-loop Wilson coefficients in the HOPE of the hadronic amplitude in \eqs{compton_amplitude}{lcda_amplitude} for both the PDF and pseudoscalar meson LCDA cases. Compared to the OPE for the hadronic amplitude from light-quark current-current correlators which has been previously studied~\cite{Gross:1973ju,Gross:1974cs,Georgi:1951sr,Calvo:1977ba,DeRujula:1976baf,Altarelli:1978id,Bardeen:1978yd,Kodaira:1978sh,Kodaira:1979ib,Kodaira:1979pa,Braaten:1982yp,Mueller:1997ak,Braun:2003rp,Braun:2007wv}, the heavy-quark mass in the HOPE method modifies the Wilson coefficients. Note that for the unpolarized and helicity PDF cases, the Wilson coefficents can be extracted from the cross section for heavy quark production through the charged current in neutrino DIS~\cite{Gottschalk:1980rv,Gluck:1996ve}, while for the LCDA case there is no known results in the literature. Therefore, our calculation of the latter is new in this work.
We carry out calculations of such Wilson coefficients with asymptotic massless external quarks, where both the ultraviolet (UV) and infrared (IR, or collinear) divergences are regulated using dimensional regularization. The OPEs for the PDF and LCDA cases expand in terms of Mellin and Gegenbauer moments, respectively, so we treat them differently with different external states. The Feynman diagrams contributing to the one-loop corrections are shown in \figs{oneloop}{self}.
\begin{figure}
\centering
\subfigure[]{\label{fig:tree}
\includegraphics[width=0.25\linewidth]{treeleveluncrossed}
}
\subfigure[]{\label{fig:box}
\includegraphics[width=0.25\linewidth]{boxdiagramuncrossed}
}
\subfigure[]{\label{fig:v1}
\includegraphics[width=0.25\linewidth]{vertexdiagramuncrossed1}
}
\subfigure[]{\label{fig:v2}
\includegraphics[width=0.25\linewidth]{vertexdiagramuncrossed2}
}
\subfigure[]{\label{fig:self2}
\includegraphics[width=0.25\linewidth]{hquncrossed}
}
\caption{The hard scattering kernel up to $\mathcal{O}(\alpha_s)$. One must also sum crossed versions of these diagrams.}
\label{fig:oneloop}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.3\linewidth]{lqself}
\caption{Self energy correction to the light quark.}
\label{fig:self}
\end{figure}
\subsection{Parton Distribution Functions}
\label{sec:nlopdf}
The physical process that corresponds to the hadronic amplitude for the PDF case is heavy quark production through the charged current in neutrino DIS~\cite{Gottschalk:1980rv,Gluck:1996ve}, except that the latter only involves left-handed fermions. The next-to-leading order correction to the cross section was first calculated in Ref.~\cite{Gottschalk:1980rv}, and a mistake in that calculation was corrected in Ref.~\cite{Gluck:1996ve}. Currently, the QCD correction has been computed up to ${\cal O}(\alpha_s^3)$~\cite{Blumlein:2011zu,Hasselhuhn:2013swa,Blumlein:2014fqa,Behring:2015roa,Behring:2016hpa}, and power corrections due to heavy quark mass have also been obtained at ${\cal O}(\alpha_s^2)$~\cite{Blumlein:2016xcy}.
In principle we can derive the dispersion relation~\cite{Christ:1972ms} for HOPE and the neutrino DIS structure functions, which can be used to extract the Wilson coefficients~\cite{Blumlein:2011zu}.
Nevertheless, in this work we directly calculate the Wilson coefficients from the hadronic amplitude using the standard method in field theory. To be specific, we first compute the one-loop quark matrix element of the current-current correlator, and then compare the coefficients in its Taylor expansion in $\tilde \omega$ to the matrix elements of the corresponding Mellin moments. The IR divergences between the two at each order of $\tilde \omega$ must be identical, and their difference gives the perturbative Wilson coefficient. In the end, we compare our results to those extracted from the one-loop neutrino DIS cross section formula~\cite{Gottschalk:1980rv,Gluck:1996ve,Blumlein:2011zu}.
For the PDF case, we set $p_1=p_2=p$ in \fig{oneloop}. The tree-level
hadronic amplitude is
\begin{align}
T_q^{\mu\nu}(q,p) &= \int d^4x\ e^{iq\cdot x}\langle p| {\cal T}\left\{J^\mu_A({x/2})J^\nu_A(-{x/2})\right\}|p\rangle\nonumber\\
&=i \bar{u}(p) \left[\gamma^\mu{ \slashed q + \slashed p+m_\Psi\over (q + p)^2 \!- \! m_\Psi^2}\gamma^\nu \!+\! \gamma^\nu {-\slashed q + \slashed p+m_\Psi\over (q - p)^2 \!-\! m_\Psi^2}\gamma^\mu \right]u(p)\,,
\end{align}
where $|p\rangle$ is a free quark state and $u(p)$ is a quark Dirac spinor.
Due to chiral symmetry, the terms linear in $m_\Psi$ vanish between the light-quark spinors as they are proportional to $\bar{u}(p)\gamma^{\mu}\gamma^\nu u(p)$ or $\bar{u}(p)\gamma^{\nu}\gamma^\mu u(p)$, and therefore
\begin{align}\label{eq:unpol}
T_q^{\{\mu\nu\}}(q,p) &= {T_q^{\mu\nu}(q,p)+T_q^{\nu\mu}(q,p)\over2}\nonumber\\
&= 2i \bar{u}(p)q^{\{\mu} \gamma^{\nu\}}u(p) \left[{ 1 \over (q + p)^2 \!- \! m_\Psi^2} \!-\! {1 \over (q - p)^2 \!-\! m_\Psi^2} \right] + 2i \bar{u}(p)p^{\{\mu} \gamma^{\nu\}} u(p) \left[{ 1 \over (q + p)^2 \!- \! m_\Psi^2} \!+\! {1 \over (q - p)^2 \!-\! m_\Psi^2} \right]\nonumber\\
&\quad -ig^{\mu\nu} \bar{u}(p) \slashed q u(p) \left[{ 1 \over q^2+2q\cdot p \!- \! m_\Psi^2} \!-\! {1 \over q^2-2q\cdot p \!-\! m_\Psi^2} \right]\nonumber\\
&= -4i\sum_{\substack{n=1,\\\rm odd}}^\infty \left({2 q_{\mu_1}\over \tilde Q^2}\right)\cdots \left({2 q_{\mu_n}\over \tilde Q^2}\right) \langle p| q^{\{\mu}{\cal O}_{n+1,V}^{\nu \mu_1\ldots \mu_n\}}|p\rangle - 4i\sum_{\substack{n=0,\\\rm even}}^\infty \left({2 q_{\mu_1}\over \tilde Q^2}\right)\cdots \left({2 q_{\mu_n}\over \tilde Q^2}\right) \langle p| {\cal O}_{n+2,V}^{\mu\nu \mu_1\ldots \mu_n}|p\rangle \nonumber\\
&\quad + ig^{\mu\nu}\sum_{\substack{n=2,\\\rm even}}^\infty \left({2 q_{\mu_1}\over \tilde Q^2}\right)\cdots \left({2 q_{\mu_n}\over \tilde Q^2}\right) \langle p| {\cal O}_{n,V}^{\mu_1\ldots \mu_n}|p\rangle \,.
\end{align}
Since the heavy-to-light currents we use are not conserved due to the nonzero quark mass, the hadronic amplitude $T_q^{\{\mu\nu\}}(q,p)$ does not satisfy the chiral Ward identity,
\begin{align}
q_\mu T_q^{\{\mu\nu\}}(q,p) \neq 0\,
\end{align}
Therefore, $T_q^{\{\mu\nu\}}(q,p)$ can include up to four independent Lorentz tensor structures,
\begin{align}
g^{\mu\nu}\,,\ \ p^\mu p^\nu\,,\ \ (p^\mu q^\nu + p^\nu q^\mu)\,,\ \ q^\mu q^\nu\,,
\end{align}
where the first three structures are present at tree level, as seen in \eq{unpol}, while the last one enters at ${\cal O}(\alpha_s)$.
In perturbative QCD, the hadronic amplitude $T_q^{\{\mu\nu\}}$ includes collinear divergences which are regulated by dimensional regularization with $d=4-2\epsilon$.
At one-loop order, all UV divergences in the Feynman diagrams in \figs{oneloop}{self} cancel, except for that from the heavy quark mass correction. Therefore, the hadronic amplitude is independent of the wave function renormalization scheme for the quarks, but depends on the scheme for heavy-quark mass renormalization. In our calculation, we consider the heavy-quark mass in both on-shell and ${\overline{\mathrm{MS}}}$ schemes.
The OPE of the hadronic amplitude $T_q^{\{\mu\nu\}}$ to all orders in perturbation theory takes the form~\cite{Gottschalk:1980rv}
\begin{align}\label{eq:tnlo}
T_q^{\{\mu\nu\}}(q,p,m_\Psi,\mu_{\tiny\rm uv},\mu_{\tiny\rm ir},\epsilon_{\tiny\rm ir})
&={4i \bar{u}(p)q^{\{\mu} \gamma^{\nu\}} u(p) \over \tilde Q^2}\sum_{\substack{n=1,\\\rm odd}}^\infty \tilde \omega^{n}C_{1,n}(\tilde Q^2, \tau,\mu^2_{\rm uv}) a_{n,V}(\epsilon_{\tiny \rm ir},\mu^2_{\rm uv},\mu^2_{\rm ir}) \nonumber\\
&\quad+{4 i \bar{u}(p)p^{\{\mu} \gamma^{\nu\}}u(p) \over \tilde Q^2} \sum_{\substack{n=1,\\\rm odd}}^\infty \tilde \omega^{n-1}C_{2,n}(\tilde Q^2, \tau,\mu^2_{\rm uv}) a_{n,V}(\epsilon_{\tiny \rm ir},\mu^2_{\rm uv},\mu^2_{\rm ir}) \nonumber\\
&\quad- {2ig^{\mu\nu}\bar{u}(p) \slashed q u(p)\over \tilde Q^2} \sum_{\substack{n=1,\\\rm odd}}^\infty \tilde \omega^{n}C_{3,n}(\tilde Q^2, \tau,\mu^2_{\rm uv}) a_{n,V}(\epsilon_{\tiny \rm ir},\mu^2_{\rm uv},\mu^2_{\rm ir})\nonumber\\
&\quad + {2i q^\mu q^\nu \bar{u}(p) \slashed q u(p) \over \tilde Q^4} \sum_{\substack{n=1,\\\rm odd}}^\infty \tilde \omega^{n}C_{4,n}(\tilde Q^2, \tau,\mu^2_{\rm uv}) a_{n,V}(\epsilon_{\tiny \rm ir},\mu^2_{\rm uv},\mu^2_{\rm ir}) \,,
\end{align}
where $C_{i,n}(\tilde Q^2, \tau,\mu^2_{\tiny\rm uv})$ are the Wilson coefficients, and $a_{n,V}(\epsilon_{\tiny \rm ir},\mu^2_{\rm uv},\mu^2_{\rm ir})$ are the Mellin moments in perturbation theory. We use $\epsilon_{\tiny \rm uv}$ and $\epsilon_{\tiny \rm ir}$ to differentiate the UV and IR divergences, and $\mu_{\tiny\rm uv}$ and $\mu_{\tiny\rm ir}$ are the ${\overline{\mathrm{MS}}}$ scales for UV renormalization and IR regularization.
The Mellin moments in the massless quark state are
\begin{align}\label{eq:moment1}
a_{n,V}(\epsilon_{\rm ir},\mu^2_{\rm uv},\mu^2_{\rm ir}) &=1+ {\alpha_s C_F\over 4\pi}\gamma_n^{(0)}\Big({1\over\epsilon'_{\tiny\rm ir}} - \ln{\mu^2_{\tiny\rm uv} \over \mu^2_{\tiny\rm ir}}\Big) + {\cal O}(\alpha_s^2)\,,
\end{align}
where $1/\epsilon'_{\tiny\rm ir}=1/\epsilon_{\tiny\rm ir}-\gamma_E+ \ln(4\pi )$, and the factor
\begin{align}
\gamma_n^{(0)} &= 2\left[{3+2n\over 2+3n+n^2} + 2H_n -{3\over2} \right]
\end{align}
is the minus one-loop anomalous dimension of $a_{n,V}$
with the harmonic number
\begin{align}
H_n=\sum_{j=1}^n {1\over j}\,.
\end{align}
Note that the regulator $\epsilon_{\tiny \rm ir}$ is introduced to bookkeep the IR divergence in our perturbative calculation, but it is not a prediction for the IR contribution in the hadron state, which is intrinsically nonperturbative. Due to the cancellation of $\epsilon_{\tiny \rm ir}$-dependence between the hadronic amplitude and the Mellin moments, the Wilson coefficients only depend on the UV scales and are thus perturbatively calculable, which allows us to make predictions for the Mellin moments once the hadronic amplitude are computed from lattice QCD.
For convenience, from now on we will not differentiate $\epsilon_{\tiny \rm uv}$ and $\epsilon_{\tiny \rm ir}$, and we set $\mu_{\tiny \rm uv}=\mu_{\tiny \rm ir}=\mu$, which is the factorization scale. Therefore, the hadronic amplitude is denoted as $T_q^{\{\mu\nu\}}(q,p,m_\Psi,\mu,\epsilon)$, while the Mellin monents are denoted $a_{n,V}(\epsilon)$.\\
The Wilson coefficients $C_{i,n}(\tilde Q^2, \tau,\mu^2)$ are also series expansions in $\alpha_s$ given by
\begin{align}\label{eq:cnexp1}
C_{i,n}& = 1 + {\alpha_sC_F\over 4\pi}C_{i,n}^{(1)}+{\cal O}(\alpha_s^2)\,,\ \ \ {\rm for }\ i=1\,,2\,,3\,,\\
C_{4,n}& = {\alpha_sC_F\over 4\pi}C_{4,n}^{(1)}+{\cal O}(\alpha_s^2)\,.
\end{align}
Therefore, at ${\cal O}(\alpha_s)$,
\begin{align}\label{eq:nlo2}
C_{i,n} a_{n,V}(\epsilon) &= 1 + {\alpha_s C_F\over 4\pi}\left[ {\gamma_{n}^{(0)}\over\epsilon'} + C^{(1)}_{i,n}\right]+ {\cal O}(\alpha_s^2) \,,
\end{align}
for $i=1,2,3$, and
\begin{align}\label{eq:nlo3}
C_{4,n} a_{n,V}(\epsilon) &= {\alpha_s C_F\over 4\pi} C^{(1)}_{4,n} \!+\! {\cal O}(\alpha_s^2) \,.
\end{align}
The one-loop Wilson coefficients $C^{(1)}_{i,n}(\tilde Q^2, \tau,\mu^2)$ have the structure
\begin{align}\label{eq:cnexp2}
C^{(1)}_{i,n}(\tilde Q^2, \tau,\mu^2) &= \gamma_{n}^{(0)} \ln{\mu^2\over \tilde Q^2} \!+\! R_{i,n}^{(1)}(\tilde Q^2, \mu^2, \tau)\,,\ {\rm for}\ i=1\,,2\,,3\,,\\
C^{(1)}_{4,n}(\tilde Q^2, \tau,\mu^2) &= R_{4,n}^{(1)}(\tau)\,,
\end{align}
following the renormalization group equation of the Mellin moments. Therefore, by Taylor expanding the one-loop matrix element of the hadronic amplitude $T_q^{\{\mu\nu\}}(q,p,m_\Psi,\mu,\epsilon)$ in $\tilde \omega$, we can read off the finite term $R_{i,n}^{(1)}(\tau)$ by comparing to \eqs{tnlo}{nlo2}. This can be achieved by employing the formulae provided in the supplementary material.
The full one-loop result of $T_q^{\{\mu\nu\}}(q,p,m_\Psi,\mu,\epsilon)$ can be found in \app{pdf}. Here, we provide the Wilson coefficients for the first few moments.
In the on-shell scheme for heavy-quark mass renormalization, which we denote by ``OS'' in the superscripts of $R^{{\rm OS}}_{i,n}(\tau)$ below, there is no dependence on $\ln(\mu^2/\tilde Q^2)$, and
\begin{align}
R_{1,1}^{{\rm OS}(1)}(\tau) &= - {12-22 \tau+20 \tau^2-11 \tau^3 \over 3\tau^3} - {2(1-\tau)(6 - 8 \tau + 7 \tau^2 + 13 \tau^3)\ln(1-\tau) \over 3\tau^4}\,,\\
R_{1,3}^{{\rm OS}(1)}(\tau) &= -{480 - 696 \tau + 262 \tau^2 + 173 \tau^3 + 332 \tau^4 -
824 \tau^5 \over 60\tau^5} \nonumber\\
&\qquad - {(1-\tau)(240 - 228 \tau + 57 \tau^2 + 97 \tau^3 + 217 \tau^4 +
337 \tau^5) \ln(1-\tau) \over 30 \tau^6}\,.
\end{align}
\begin{align}
R_{2,1}^{{\rm OS}(1)}(\tau) &= - {2 - 5 \tau + 2 \tau^2 \over 3\tau^2 } - {2(1-\tau)(1 - 2 \tau + 10 \tau^2) \ln(1-\tau) \over 3\tau^3} \,,\\
R_{2,3}^{{\rm OS}(1)}(\tau) &=- {144 - 198 \tau + 233 \tau^2 + 226 \tau^3 - 678 \tau^4 \over 60\tau^4} - {(1-\tau)(72 - 63 \tau + 97 \tau^2 + 157 \tau^3 + 277 \tau^4) \ln(1-\tau) \over 30 \tau^5}\,.
\end{align}
\begin{align}
R_{3,1}^{{\rm OS}(1)}(\tau) &= {6 - 11 \tau - 5 \tau^2 + 7 \tau^3 \over 3\tau^3} + {2(1-\tau)(3 - 4 \tau - 4 \tau^2 - 13 \tau^3)\ln(1-\tau) \over 3\tau^4}\,,\\
R_{3,3}^{{\rm OS}(1)}(\tau) &= {120 - 324 \tau - 2 \tau^2 - 103 \tau^3 - 182 \tau^4 +
716 \tau^5 \over 60\tau^5} \nonumber\\
&\qquad + {(1-\tau)(60 - 132 \tau - 57 \tau^2 - 97 \tau^3 - 157 \tau^4 -
337 \tau^5) \ln(1-\tau) \over 30 \tau^6}\,.
\end{align}
\begin{align}
R_{4,1}^{{\rm OS}(1)}(\tau) &= - {4(12 - 18 \tau + 4 \tau^2 + \tau^3) \over 3\tau^4} - {16(1-\tau)^2\ln(1-\tau) \over \tau^5}\,,\\
R_{4,3}^{{\rm OS}(1)}(\tau) &= - {2(60 - 90 \tau + 20 \tau^2 + 5 \tau^3 + 2 \tau^4 + \tau^5) \over 5\tau^6} - {24(1-\tau)^2\ln(1-\tau) \over \tau^7}\,.
\end{align}
The ${\overline{\mathrm{MS}}}$ Wilson coefficients are related to the on-shell scheme ones through
\begin{align}
R_{1,n}^{{\overline{\mathrm{MS}}} (1)}(\tilde Q^2, \mu^2, \tau) - R_{1,n}^{{\rm OS}(1)}(\tau) &= R_{3,n}^{{\overline{\mathrm{MS}}} (1)}(\tilde Q^2, \mu^2, \tau) - R_{3,n}^{{\rm OS}(1)}(\tau) = -2(n+1)(1-\tau)\Big(4 + 3\ln{\mu^2\over m_\Psi^2}\Big)\,,\\
R_{2,n}^{{\overline{\mathrm{MS}}} (1)}(\tilde Q^2, \mu^2, \tau) - R_{2,n}^{{\rm OS}(1)}(\tau) &= -2n(1-\tau)\Big(4 + 3\ln{\mu^2\over m_\Psi^2}\Big)\,, \\
R_{4,n}^{{\overline{\mathrm{MS}}} (1)}(\tau) - R_{4,n}^{{\rm OS}(1)}(\tau) &= 0\,.
\end{align}
Finally, we compare our results to those derived from the Mellin moments of the hard coefficient functions in Eq.~(42) of Ref.~\cite{Gottschalk:1980rv} for heavy-quark production from neutrino DIS, with a correction in Ref.~\cite{Gluck:1996ve}. Both $R_{2,n}^{{\rm OS}(1)}(\tau)$ and $R_{3,n}^{{\rm OS}(1)}(\tau)$ were presented as $h_2^q(\tau,n+2)$ and $h_1^q(\tau,n+2)$ in compact forms for arbitrary $n$ in Ref.~\cite{Blumlein:2011zu}. We found agreement in the on-shell scheme for all the $R_{i,n}^{{\rm OS}(1)}(\tau)$, except that the factor $A_5$ in Table I in Ref.~\cite{Gottschalk:1980rv} must be corrected by a factor of two. Since the factor $A_2$ in Table I in Ref.~\cite{Gottschalk:1980rv} is also missing a factor of two, as was pointed out in Ref.~\cite{Gluck:1996ve}, we believe that $A_5$ has the same problem.
In the heavy-quark massless limit $m_\Psi\to0$ or $\tau\to1$, the above results no longer depend on the heavy-quark mass renormalization scheme and agree with those in the literature~\cite{Gross:1973ju,Gross:1974cs,Georgi:1951sr,Calvo:1977ba,DeRujula:1976baf,Altarelli:1978id,Bardeen:1978yd},
\begin{align}
R_{1,n}^{(1)}(1) &= R_{2,n}^{(1)}(1) = 3H_{n+1} - 4 H_{n+1}^{(2)} - {2H_{n+1}\over (n+1)(n+2)} + 4 \sum_{s=1}^{n+1}{1\over s} \sum_{j=1}^s {1\over j} + {3\over n+1} + {4\over n+2} + {2\over (n+1)^2 } -9 \,,\nonumber\\
R_{3,n}^{(1)}(1) &= R_{1,n}^{(1)}(1) - {4\over n+2}\,,\ \ \ \ \ \ \ \ \ R_{4,n}^{(1)}(\tau) = {4\over n+2}\,,
\end{align}
where
\begin{align}
H_n^{(2)}=\sum_{j=1}^n {1\over j^2}\,.
\end{align}
\subsection{Helicity Parton Distribution Functions}
\label{sec:helicity}
To calculate the helicity PDF, we use the anti-symmetrized hadronic amplitude
\begin{align}
T_q^{[\mu\nu]}(q,p) &= {T_q^{\mu\nu}(q,p)-T_q^{\nu\mu}(q,p)\over2}\,.
\end{align}
The HOPE of $T^{[\mu\nu]}_q$ takes a similar form to \eq{tnlo},
\begin{align}\label{eq:tnlo2}
T_q^{[\mu\nu]}(q,p,m_\Psi,\mu,\epsilon)&= -{2\epsilon^{\mu\nu\rho\sigma}q_\rho \over \tilde Q^2} \ \bar{u}(p)\gamma_\sigma \gamma_5 u(p) \sum_{\substack{n=0,\\\rm even}}^\infty \tilde \omega^n \tilde C_n(\tilde Q^2, \tau,\mu^2) a_{n,A}(\epsilon)\,
\end{align}
The Wilson coefficients $\tilde C_n$ have the same perturbative expansion as in \eqs{cnexp1}{cnexp2}, i.e.,
\begin{align}
\tilde C^{(1)}_{n}(\tilde Q^2, \tau,\mu^2) &= \gamma_{n}^{(0)} \ln{\mu^2\over \tilde Q^2} + \tilde R^{(1)}_{n}(\tilde Q^2, \mu^2, \tau)\,,
\end{align}
so they can be extracted following exactly the same procedure as the unpolarized PDF.
The full one-loop result of $T_q^{[\mu\nu]}(q,p,m_\Psi,\mu,\epsilon)$ can be found in \app{hpdf}. Here we provide results for the lowest four Wilson coefficients:
\begin{align}
\tilde R^{{\rm OS}(1)}_0(\tau) &=-3 -\frac{6 (1-\tau ) \ln (1-\tau )}{\tau}\,,\\
\tilde R^{{\rm OS}(1)}_2(\tau) &= -\frac{18 + 17 \tau + 34 \tau^2 - 84 \tau^3}{12 \tau ^3} -\frac{(1-\tau)(9 + 13 \tau + 25 \tau^2 + 61 \tau^3) \ln (1-\tau )}{6 \tau ^4}\,,\\
\tilde R^{{\rm OS}(1)}_4(\tau) &= -\frac{300 + 6 \tau + 118 \tau^2 + 192 \tau^3 + 294 \tau^4 -
1433 \tau^5}{90 \tau ^5} \nonumber\\
&\qquad - \frac{(1-\tau)(50 + 26 \tau + 41 \tau^2 + 61 \tau^3 + 91 \tau^4 +
181 \tau^5) \ln (1-\tau )}{15 \tau ^6}\,,
\end{align}
and
\begin{align}
\tilde R^{{\overline{\mathrm{MS}}} (1)}_n(\tilde Q^2, \mu^2, \tau) - \tilde R^{{\rm OS}(1)}_n(\tau) &= -2(n+1)(1-\tau)\Big(4 + 3\ln{\mu^2\over m_\Psi^2}\Big) \,.
\end{align}
Again, we also find agreement between our results and those from the neutrino DIS cross section for heavy-quark production~\cite{Gottschalk:1980rv,Gluck:1996ve,Blumlein:2011zu} in the on-shell scheme. In particular, the reader can find a compact form of $\tilde R_{n}^{{\rm OS}(1)}(\tau)$ for arbitrary $n$ in Ref.~\cite{Blumlein:2011zu}, where it was presented as $h_3^q(\tau,n+1)$.
In the massless limit $m_\Psi\to0$ or $\tau\to1$, the above results become independent of the heavy-quark mass renormalizaiton scheme and agree with those in the literature~\cite{Kodaira:1978sh,Kodaira:1979ib,Kodaira:1979pa},
\begin{align}\label{eq:forwardpdf}
\tilde R^{(1)}_n(1) & = 2H_{n+1}^2 - 2H_{n+1}^{(2)} + 3H_{n+2} + {3-2H_n\over (n+1)(n+2)} - 9\,.
\end{align}
\subsection{Light-Cone Distribution Amplitude}
\label{sec:danlo}
For the pseudoscalar meson LCDA defined in \eq{lcda}, we calculate the transition amplitude of the heavy-quark hadronic amplitude from vacuum to the asymptotic state composed of a quark and antiquark, that is,
\begin{equation}
\ket{\pi(\mathbf{p})}\rightarrow |u({1\over2}(1+x_0)p,\uparrow) \bar{d}({1\over2}(1-x_0)p,\downarrow)\rangle
\end{equation}
with $-1< x_0 < 1$.
In \fig{oneloop}, this corresponds to choosing
\begin{equation}
p_1={1\over2}(1+x_0)p \,, \ \ \ \ \ \ \ \ \ p_2=-{1\over2}(1-x_0)p\,,
\end{equation}
so the external line carrying $p_2$ stands for the antiquark. In this simple model, the LCDA at tree level is
\begin{align}
\phi_\pi^{(0)}(x,x_0) &= \delta(x-x_0)\,,
\end{align}
The Gegenbauer moments~\cite{Radyushkin:1977gp} for fixed $x_0$ are therefore
\begin{align}
\phi_n^{(0)}(x_0) &\equiv {4(n+{3\over2})\over 3(n+1)(n+2)}\int_{-1}^{1} dx\ {\cal C}_n^{3/2}(x) \phi_\pi^{(0)}(x,x_0) = {4(n+{3\over2})\over 3(n+1)(n+2)} {\cal C}_n^{3/2}(x_0) \,.
\end{align}
At tree level, the hadronic amplitude
\begin{align}
V_q^{\mu\nu(0)}(q,p)
&=\bar{v}({1\over2}(1-x_0)p,\downarrow)\left[\gamma^\mu\gamma_5 {i\over \slashed q + {x_0\slashed p\over2}-m_\Psi}\gamma^\nu\gamma_5 + \gamma^\nu\gamma_5 {i\over -\slashed q +{x_0\slashed p\over2}-m_\Psi}\gamma^\mu\gamma_5 \right]u({1\over2}(1+x_0)p,\uparrow)\,.
\end{align}
After antisymmetrization of $\mu$ and $\nu$, the conformal or Gegenbauer OPE of the hadronic amplitude is~\cite{Braun:2007wv},
\begin{align}
V_q^{[\mu\nu](0)}(q,p,m_\Psi,x_0)
&= \epsilon^{\mu\nu\rho\sigma}q_\rho \bar{v}\gamma_\sigma \gamma_5 u \left[{1\over q^2 + x_0 p\cdot q-m_\Psi^2} +{1\over q^2 -x_0p\cdot q-m_\Psi^2}\right]\nonumber\\
&=-{2\epsilon^{\mu\nu\rho\sigma}q_\rho \over \tilde{Q}^2}\bar{v}\gamma_\sigma \gamma_5 u \sum_{\substack{n=0,\\\rm even}}^\infty {\cal F}^{(0)}_n(\tilde \omega) \phi_n^{(0)}(x_0)\,,
\end{align}
where
\begin{align}
{\cal F}^{(0)}_n(\tilde \omega) &={3\over2}\frac{\sqrt{\pi } (n+1) (n+2) n! }{2^{n+2} \Gamma \left(n+\frac{5}{2}\right)}\left(\frac{\tilde \omega}{2}\right)^n \, _2F_1\left(\frac{n+1}{2},\frac{n+2}{2};n+\frac{5}{2};\frac{\tilde \omega^2}{4}\right)\,.
\end{align}
At one-loop order, the Gegenbauer moments and the Mellin moments, as defined in \eq{phiM}, share the same anomalous dimensions.
Therefore,
\begin{align}
\phi_n (x_0,\epsilon) &= \phi_n^{(0)}(x_0) \left[1+{\alpha_s C_F\over 4\pi} {\gamma_n^{(0)}\over\epsilon'} + {\cal O}(\alpha_s^2)\right]\,.
\end{align}
Using the renormalization group equation of the Gegenbauer moments, the hadronic amplitude should be expanded in the same fashion as that in Eq.~\eqref{eq:tnlo},
\begin{align}
&V_q^{[\mu\nu]}(q,p,m_\Psi,x_0,\mu,\epsilon) \nonumber\\
&=-{2 \epsilon^{\mu\nu\rho\sigma}q_\rho \over \tilde{Q}^2}\bar{v}\gamma_\sigma \gamma_5 u \sum_{\substack{n=0,\\\rm even}}^\infty {\cal F}_n(\tilde Q^2,\mu^2,\tilde \omega,\tau) \phi_n(x_0,\epsilon)\nonumber\\
&=-{2 \epsilon^{\mu\nu\rho\sigma}q_\rho \over \tilde{Q}^2}\bar{v}\gamma_\sigma \gamma_5 u \sum_{\substack{n=0,\\\rm even}}^\infty \Bigg[ {\cal F}^{(0)}_n(\tilde \omega) \Big(1 + {\alpha_sC_F\over 4\pi}\gamma_n^{(0)}\Big({1\over \epsilon'} + \ln{\mu^2\over \tilde Q^2} \Big)\Big) +\frac{\alpha_S C_F}{4\pi}{\cal R}^{(1)}_n(\tilde Q^2, \mu^2, \tau,\tilde \omega)\Bigg] \phi_n^{(0)}(x_0) +{\cal O}(\alpha_s^2)\,,
\end{align}
where the coefficient function ${\cal F}_n$ is expanded to one-loop order as
\begin{align}
{\cal F}_n(\tilde Q^2,\mu^2,\tilde \omega,\tau) &= {\cal F}^{(0)}_n(\tilde \omega) \left[1+ {\alpha_s C_F\over 4\pi} \gamma_n^{(0)} \ln{\mu^2\over \tilde Q^2} \right]+{\alpha_s C_F\over 4\pi} {\cal R}^{(1)}_n(\tilde Q^2, \mu^2, \tau,\tilde \omega) +{\cal O}(\alpha_s^2)\,.
\end{align}
As one can see, the logarithmic part of ${\cal F}_n$ is proportional to the tree-level coefficient function ${\cal F}^{(0)}_n(\tilde \omega) $, because at leading logarithmic accuracy QCD is conformal and the Gegenbauer moments do not mix with each other.
Beyond leading logarithm, the conformal symmetry is broken, so the Gegenbauer moments start to mix.
In the conformal approximation, the OPE of the current-current correlator for the pion LCDA has been derived for massless quarks in Refs.~\cite{Mueller:1997ak,Braun:2003rp,Braun:2007wv}. The coefficient functions in the conformal OPE are
\begin{align}
{\cal F}^{\rm conf}_n(Q^2,\mu^2,\tilde \omega,\delta) &= {3\over2}\frac{\sqrt{\pi } (n+1) (n+2) n! }{2^{n+2} \Gamma \left(n+\frac{5}{2}\right)}\left(\frac{\tilde \omega}{2}\right)^n \left({\mu^2\over Q^2}\right)^{\delta} \ _2F_1\left({n+1+\delta\over2}, {n+2+\delta\over2}, n+{5\over2}+\delta, {\omega^2\over4}\right)c_n(\alpha_s)\,,
\end{align}
where the logarithms of $\mu^2/Q^2$ have been resummed with the anomalous dimension
\begin{align}
\delta = {\alpha_s\over 4\pi}\gamma^{(0)}_n+ {\cal O}(\alpha_s^2)\,,
\end{align}
and the factor
\begin{align}
c_n(\alpha_s) &= 1 + {\alpha_sC_F\over 4\pi}\tilde R^{(1)}_n(1) + {\cal O}(\alpha_s^2)\,,
\end{align}
with $\tilde R^{(1)}_n(1)$ beging the same as those in the Wilson coefficients for the helicity PDF case~\cite{Kodaira:1978sh,Kodaira:1979ib,Kodaira:1979pa}, which has been given in \eq{forwardpdf}.
If we expand ${\cal F}^{\rm conf}_n(Q^2,\mu^2,\tilde \omega,\delta)$ to ${\cal O}(\alpha_s)$,
\begin{align}
{\cal F}^{\rm conf}_n(Q^2,\mu^2,\tilde \omega,\delta) &= {\cal F}^{\rm conf}_n(Q^2,\mu^2,\tilde \omega,0) + \delta {\partial \over \partial \delta'}{\cal F}^{\rm conf}_n(Q^2,\mu^2,\tilde \omega,\delta')\Big|_{\delta'=0} + {\cal O}(\alpha_s^2)\,,
\end{align}
and compare it to ${\cal F}_n(\tilde Q^2,\mu^2,\tilde \omega,\tau)$ in the massless heavy-quark limit $\tau\to1$, we find that they are not equal, which leads to the breaking of conformal symmetry in addition to the nonzero $\beta$-function that enters at ${\cal O}(\alpha_s^2)$.
Such conformal symmetry breaking effects in the ${\overline{\mathrm{MS}}}$ scheme have been observed in the literature~\cite{Melic:2002ij}, and it was proposed to rotate the ${\overline{\mathrm{MS}}}$ factorization scheme to the so-called ``conformal subtraction'' scheme where the new Gegenbauer moments evolve autonomously without mixing~\cite{Melic:2002ij}.
Nevertheless, the numerical difference between ${\cal F}_n(\tilde Q^2,\mu^2,\tilde \omega,1) $ and ${\cal F}^{\rm conf}_n(Q^2,\mu^2,\tilde \omega,\delta) $ turns out to be small. Since in our calculation we use a massive quark, the conformal symmetry is explicitly broken anyway, so we use the exact ${\overline{\mathrm{MS}}}$ result of ${\cal F}_n(\tilde Q^2,\mu^2,\tilde \omega,\tau)$.\\
The full one-loop correction for the hadronic amplitude from \figs{oneloop}{self} is
\begin{align}\label{eq:oneloop}
V_q^{[\mu\nu](1)}(q,p,m_\Psi,x_0,\mu,\epsilon)
&= - {\alpha_sC_F\over 4\pi} {2 \epsilon^{\mu\nu\rho\sigma}q_\rho \over \tilde{Q}^2}\bar{v}\gamma_\sigma \gamma_5 u \Big[\Big({1\over \epsilon'} + \ln{\mu^2\over \tilde Q^2}\Big) F^{(1)}(\tilde \omega, x_0) + {\mathbf R}^{(1)}(\tilde Q^2, \mu^2, \tau,\tilde \omega,x_0)\Big]\,,
\end{align}
where
\begin{align}\label{eq:lcdall}
F^{(1)}(\tilde \omega, x_0) &={4\over (1 - x_0^2) \tilde \omega^2 (4 - x^2_0 \tilde \omega^2)}\Bigg\{3 \left(x_0^2-1\right) \tilde \omega^2 +\big[\left(x^2_0-2\right) \tilde \omega^2+4\big] \ln \frac{ 4-x_0^2 \tilde \omega^2}{4-\tilde \omega^2}\nonumber\\
&\qquad +\tilde \omega \Big[\left(4- x_0^2 \tilde \omega^2\right)\tanh ^{-1}\big(\frac{\tilde \omega}{2}\big)+ x_0\left((2- x_0^2) \tilde \omega^2-4\right) \tanh ^{-1}\big({x_0 \tilde \omega\over2}\big)\Big]\Bigg\}\,,
\end{align}
and the finite part ${\mathbf R}^{(1)}$ is provided in the supplementary material. The details of calculating $V_q^{[\mu\nu](1)}(q,p,m_\Psi,x_0,\mu,\epsilon)$ in both the on-shell and ${\overline{\mathrm{MS}}}$ schemes can be found in \app{lcda}.
Using the orthonomality of Gegenbauer polynomials, we can verify that
\begin{align}
{\cal F}^{(0)}_n(\tilde \omega)\gamma_n^{(0)} & ={3\over4} \int_{-1}^{1}dx_0 (1-x_0^2) F^{(1)}(\tilde \omega, x_0) {\cal C}_n^{3/2}(x_0)\,,
\end{align}
and obtain ${\cal R}^{(1)}_n(\tilde Q^2, \mu^2, \tau,\tilde \omega)$ as
\begin{align}\label{eq:Rn1}
{\cal R}^{(1)}_n(\tilde Q^2, \mu^2, \tau, \tilde \omega) & ={3\over4} \int_{-1}^{1}dx_0\ (1-x_0^2) {\mathbf R}^{(1)}(\tilde Q^2, \mu^2, \tau, \tilde \omega, x_0) {\cal C}_n^{3/2}(x_0)\,,
\end{align}
The results of ${\mathbf R}^{(1)}(\tilde Q^2, \mu^2, \tau, \tilde \omega, x_0)$ and ${\cal R}^{(1)}_n(\tilde Q^2, \mu^2, \tau,\tilde \omega)$ are new in this work.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,764 |
\section{INTRODUCTION}
\label{sec:introduction}
The subject of exchange-correlation-induced phase
transitions has proven to be a rich field of research
which has revealed many intriguing phenomena.
Normal Fermi-liquid-state instabilities occur when the kinetic energy
of the particles in a quantum system is of the same order or
smaller than the inter-particle exchange and correlation
energies. The instabilities lead to a variety of new electronic
states. In Coulombic systems, this situation obtains at low densities
and instabilities are more likely in systems of
reduced dimensionality or, especially in two dimensions, in an applied
magnetic field.
Perhaps the best known examples of such new states occur
in the in the fractional-quantum-Hall, strong-field regime of two-dimensional
electronic systems.\cite{fqhe}
The interest in exchange-correlation-induced phase transitions
can be traced in part to the availability of high-quality
semiconductor quantum wells, quantum wires, and superlattices.
These artificial structures may be fabricated with
remarkable precision and quality and possess electron
densities that can be varied over a large range through a
combination of modulation doping and judicious gating.
The one- or two-dimensional nature of the resulting
electronic systems, and the low densities realizable
in devices of this kind, make them ideal for studies of
interaction-driven physics.
Another feature of these devices of importance to the
current work is the extra degree of freedom available when
multiple layers are present, as in multiple quantum wells or
superlattices.
This new degree of freedom allows transitions to states
with order not only in the intra-layer electronic degrees of
freedom but also in diagonal or off diagonal inter-layer
charge \cite{MacDonald,Ruden,nei,Varma,Katayama,Ying,Patel,Conti,Zheng,Wen-Zee_double,ezawa,iu_double}
or spin\cite{Zheng,das-tam,rad-das,Pinczuk,Zheng-Rad-Das,Plaut}
observables.
In particular, a great deal of attention has recently focussed
on the possibility of inter-layer spin ordering in wide
single or double quantum wells.
This attention is motivated by studies of quantum
well structures in which the lowest two subbands are well
separated in energy from the higher subbands and the density
is sufficiently low so that only these two subbands are
occupied.
In these structures, an earlier theoretical calculation of the
collective spin-density excitations (SDEs) in the
absence of a magnetic field showed a complete softening of
the inter-subband SDE in a range of densities around that
at which the second subband begins to populate.\cite{das-tam}
Subsequent analysis indicated that this softening
corresponded to a phase transition to a state in which each
well in the double quantum well (or the electron gases on
each side of a wide single quantum well) was spin
polarized with the polarization vectors
antiparallel; i.e., a transition to an antiferromagnetic
order in the well spin densities.\cite{rad-das}
Further work predicted that a similar transition to a canted
antiferromagnetic phase should occur in the presence of a
magnetic field at $\nu = 2$,\cite{Zheng-Rad-Das} and this
transition seems to have been observed
experimentally.\cite{Pinczuk}
However, the predicted transition in the zero-field case has
not yet been observed.\cite{Plaut}
Several possibilities exist which may explain the absence
of the zero-field antiferromagnetic phase in these
experiments.
The calculations predicting this phase\cite{rad-das} are
based on a mean-field treatment of the interacting system,
which is known to overestimate the densities and temperatures
at which such symmetry-breaking transitions occur.
In addition, electronic scattering by disorder or impurities
generally has a detrimental effect on correlation-induced
phases.
Both of these difficulties are exacerbated by the low
dimensionality of the double quantum well system considered.
Thus, the zero-field antiferromagnetic phase may exist but
may not have been observed due to measurements made at
temperatures which are too large in samples of insufficiently
high quality.
The fact that the $\nu = 2$ transition is observed\cite{Pinczuk}
as predicted by the mean-field calculations\cite{Zheng-Rad-Das}
does not contradict this point of view, since the magnetic
field completely quenches the kinetic energy and makes the
mean-field theory a controlled approximation to the interacting
system.
Alternative explanations for the absence of the zero-field
phase lie in the structure of the theory itself,\cite{rad-das}
which was derived to explore the qualitative features
of the antiferromagnetic phase without considering
several confounding effects which may nonetheless be
important. In particular, the previous calculation\cite{rad-das}
did not account for interactions between
electrons in the same subband, which should be of the
same size or stronger than the interactions between electrons
in different subbands which were included. This omission can become
especially important when the intersubband excitation softens.
These interactions could introduce ferromagnetic
or charge-ordered phases into the model which are not probed
by the current experiments.
More seriously, the slight asymmetry present in any
realistic double quantum well structure will couple the
intra- and inter-subband SDEs, potentially preventing the
latter from softening.
As this softening was expected to be a hallmark of the
antiferromagnetic phase transition,\cite{das-tam,rad-das}
it seemed reasonable to hypothesize that any asymmetry in
the structure might suppress the antiferromagnetic phase entirely.
In this paper, we address the question of the robustness of
the zero-field antiferromagnetic phase in the presence of
intra-subband interactions and asymmetry in the double
quantum well structure.
First, we argue on general grounds that the antiferromagnetic phase
is a direct consequence of the importance of the intra-well
exchange interaction at low densities and is stabilized by the
inter-well hopping, which leads to an effective
superexchange interaction.
Thus, this phase should obtain in a suitably constructed
heterostructure.
Second, we extend the self-consistent Hartree-Fock
calculations of earlier work\cite{rad-das} to include both
intra- and inter-subband matrix elements of the model
interaction and the effects of an asymmetric double
quantum well.
These calculations demonstrate that, while the intra-subband
interaction does introduce ferromagnetic phases and
asymmetry does reduce the region of the phase diagram
occupied by the antiferromagnetic phase, the
antiferromagnetic phase does not disappear.
By examining the collective mode spectrum in the asymmetric
structure, we also find that the inter-subband SDE does not
soften due to the mode coupling between the intra- and
inter-subband SDEs.
The antiferromagnetic transition nevertheless occurs as a
result of the collapse of the {\it intra}-subband SDE which,
through the mode-coupling, has a strongly antiferromagnetic character.
The outline of this paper is as follows.
In the next Section, we employ a simple model for two weakly
coupled two-dimensional electron gases to examine the energetics
of the antiferromagnetic transition.
Sec.~\ref{sec:formalism} contains the formalism for the
extended self-consistent Hartree-Fock theory used in the
remainder of the paper.
This formalism includes asymmetry and all matrix elements
of the interaction and is used to compute both the ground
state and collective mode properties in what follows.
In Sec.~\ref{sec:results}, we present the results of our
computations for the matrix elements, phase diagram, and
collective modes in this model and discuss their
implications.
Finally, in Sec.~\ref{sec:conclusion}, we summarize our
results and conclude.
\section{ORIGIN AND STABILITY OF THE ANTIFERROMAGNETIC PHASE}
\label{sec:origin}
In this Section, we examine a simple model of a
double quantum well in order to extract the basic
physics underlying the zero-field antiferromagnetic phase.
To that end, consider two two-dimensional electron gases
separated by a barrier constructed so that the interaction
between them is negligible.
This would be the case if the two-dimensional layers were
widely separated or the barrier were very high and if the
dielectric constant of the barrier were large.
Suppose the electrons in each layer move freely
except for a Hubbard-like point-contact interaction
$V({\bf r}) = V_0 \delta({\bf r})$, as used in textbook
treatments of itinerant magnetism.\cite{Doniach}
For equal charge density in the two layers,
the Hartree-Fock energy $E_{\rm HF}$ of the
two-layer system can be derived following
Refs.~\onlinecite{MacDonald,Ruden,Zheng} and may be expressed
in the form
\begin{equation}
\frac{E_{\rm HF}}{A} =
\frac{n^2}{8 N_0}\,(1-N_0 V_0)
\left( \frac{1 + m_1^2}{2} + \frac{1 + m_2^2}{2} \right)
+ \frac{1}{4} V_0 n^2,
\label{eq:Ehf}
\end{equation}
where $n$ is the total electronic density in both layers,
$N_0$ is the single-spin, two-dimensional density of states,
and
\begin{equation}
m_i =
\frac{n_{i\uparrow}-n_{i\downarrow}}
{n_{i\uparrow}+n_{i\downarrow}}
\label{eq:m}
\end{equation}
is the relative spin polarization in layer $i = 1,2$ with
partial spin-dependent densities $n_{i\sigma}$.
In this equation, the first term represents the contribution
to the energy from combined kinetic and exchange effects,
and the last term is the Hartree contribution.
As is clear from Eq.~(\ref{eq:Ehf}), when $N_0 V_0 > 1$, it
is energetically favorable for both layers to acquire a
spontaneous spin polarization $|m_1| = |m_2| = 1$, while for
$N_0 V_0 < 1$, the layer remain unpolarized.
This result is simply the Stoner criterion for 2D itinerant
magnetism.\cite{Doniach}
This description of spontaneous
spin-polarization in two-dimensional electron systems
is unrealistic both in the use of a point-contact interaction
and in the use of the Hartree-Fock approximation.
Our objective in this section is to obtain a qualitative
understanding of the influence of
weak electronic tunneling between the layers on
a double-layer system when isolated single
layer systems are close to their ferromagnetic instabilities.
We postpone a realistic discussion of
the system parameters for which the physics we address
in this paper is likely to realized to Sec.~\ref{sec:conclusion}.
For a sufficiently strong intra-layer repulsion, then, the
exchange interaction forces both layers to spin polarize,
but the relative orientation of the polarizations is unknown.
For simplicity, let us restrict our attention to two
possibilities for the relative orientation:
parallel (ferromagnetic) alignment or antiparallel
(antiferromagnetic) alignment.
With the spin unpolarized (paramagnetic) phase, the three
possible phases for the two-layer system are shown in
Fig.~\ref{fig:phases}.
\begin{figure}
\psfig{file=fig1.eps,width=0.95\linewidth}
\caption{Population of spin and well states for the phases of
a double quantum well considered in Sec.~\protect\ref{sec:origin}.
In the paramagnetic phase, there is no spin polarization in either
well.
In the magnetic phases, each well is completely spin-polarized
with the polarization vectors parallel in the ferromagnetic phase
and antiparallel in the antiferromagnetic phase.
\label{fig:phases}}
\end{figure}
In the absence of any inter-layer coupling, the
ferromagnetic and antiferromagnetic phases are degenerate,
but this situation changes if we introduce a small amplitude
for hopping between the layers.
Writing $c_{i{\bf k}\sigma}$ for the annihilation operator
of an electron in layer $i=1,2$ with two-dimensional wave vector
${\bf k}$ and spin projection $\sigma$, this inter-layer
hopping is governed by the Hamiltonian
\begin{equation}
H_{\bot} =
-\frac{\Delta_0}{2} \, \sum_{{\bf k}\sigma} \left[
c^{\dag}_{1{\bf k}\sigma} c^{~}_{2{\bf k}\sigma}
+ {\rm h.c.} \right]
\label{eq:Hbot}
\end{equation}
where $\Delta_0$ is the splitting between the symmetric and
antisymmetric single-particle eigenstates.
The leading order change in the ground state energy due to
$H_{\bot}$ can be calculated using linear response theory,
and is proportional to the transverse pseudospin susceptibility
of double-layer systems defined in Ref.~\onlinecite{leszek}.
For the present model with no inter-layer interactions and contact
intra-layer interactions, the time-dependent Hartree-Fock
approximation for the susceptibility gives
\begin{equation}
\frac{\delta E }{A} = \left\{
\begin{array}{ll}
-\frac{1}{2} N_0 \Delta_0^2 & {\rm (paramagnetic)} \\
-\frac{1}{4} N_0 \Delta_0^2 & {\rm (ferromagnetic)} \\
-\frac{1}{2} \Delta_0^2/V_0 & {\rm (antiferromagnetic)}
\end{array} \right.
\label{eq:Ebot}
\end{equation}
The fact that the results for paramagnetic and ferromagnetic
states are independent of the interaction strength is
a special property of the present model related to both the
absence of interlayer interactions and the wave vector
independence of the exchange self-energy.
We see that, in all cases, introducing inter-layer hopping
reduces the ground state energy,
as one might expect when the confinement of the electrons
to the layers is weakened.
Comparing the energies of the ferromagnetic and
antiferromagnetic phases, we also observe that the
degeneracy between these phases is broken by the hopping term.
Specifically, the antiferromagnetic phase is found to be more
stable than the ferromagnetic phase if $N_0 V_0 < 2$,
implying that the inter-layer hopping opens up a region of
antiferromagnetic order between the paramagnetic and
ferromagnetic phases.
The mechanism for this stabilization can be deduced from the
form of $\delta E / A$ to be a superexchange
interaction; that is, an electron is able to hop from one
layer to the other and back at the cost of a Hubbard energy
in the intermediate state, yielding an energy savings of
$\Delta_0^2 / 2 V_0$.
A similar mechanism is blocked by the Pauli exclusion principle
in the ferromagnetic phase , since the hopping
Hamiltonian preserves spin [Eq.~(\ref{eq:Hbot})].
We argue that this mechanism favoring an antiferromagnetic arrangement
of the ordered moments in the two layers will be dominant
in most circumstances.
The calculations described below indicate that an effective
superexchange interaction between the wells should
stabilize an antiferromagnetic phase for moderate
interaction strengths.
This explanation of the zero-field antiferromagnetic phase
suggests why the presence of asymmetry and additional
interaction matrix elements may not eliminate this phase:
both the two-dimensional ferromagnetism within each well
and the superexchange interaction between the wells should
be fairly insensitive to these perturbations.
In the remainder of the paper, we perform a more
detailed self-consistent Hartree-Fock calculation to support
this statement and to explore the consequences of these
perturbations.
\section{FORMALISM}
\label{sec:formalism}
To accomplish the goal of investigating matrix element
and asymmetry effects, we employ an extension of the
point-contact model described in Ref.~\onlinecite{rad-das}.
In the original calculation, the full Coulomb interaction
between the electrons in the double quantum well was
approximated by a delta function in real space with only the
matrix elements of this interaction between the lowest two
subbands being kept and the remainder being set to zero.\cite{rad-das}
The use of a delta-function or point-contact interaction is
based primarily on a desire to create a simple, solvable
model which mimics the qualitative features of the fully
interacting system. A quantitative theory would require
that the interaction be made realistic, and also that the
interactions be treated more accurately than in the
Hartree-Fock approximation. In practise this would require
quantum Monte-Carlo calculations of some type, which would involve
an enormous amount of effort and would not be able to address
the excitation spectrum which provides the experimental signature
for the state we are proposing.
We therefore maintain the point-contact form of the interaction here.
However, there is no reason to set matrix elements
of this interaction other than those between the lowest subbands
to zero, as in previous work.
Indeed, we shall see below that these other matrix elements
are of the same order as the inter-subband ones.
Thus, we shall include all the matrix elements between the
lowest two subbands in our calculations.
In addition to the issue of intra-subband repulsion, we would
also like to study the effects of quantum well asymmetry on
the phase diagram and collective modes of this system.
This asymmetry arises in real quantum wells through alloy
fluctuations across the profile of the well or fluctuations
in the well thickness, and we model it by allowing one of
the wells to be deeper than the other, as illustrated in
Fig.~\ref{fig:dqw}.
Although we have assumed the effective asymmetry to enter
through the well depth, the results of our calculations for
systems with asymmetric well widths should be qualitatively
similar.
\begin{figure}
\psfig{file=fig2.eps,width=0.95\linewidth}
\caption{Diagram of the asymmetric double quantum well
considered in this paper indicating the well width $w$, barrier
width $b$, confining potential $U$, and potential asymmetry
$dU$.
The values of the parameters used here and in previous
studies of magnetic instabilities of these
systems\protect\cite{das-tam,rad-das} model a typical
GaAs/Al$_x$Ga$_{1-x}$As double quantum well with
$w$ = 140~\AA, $b$ = 30~\AA, and $U$ = 220~meV.
We consider both symmetric ($dU = 0$) and weakly
asymmetric ($dU = 0.5$~meV) double quantum wells in what
follows.
\label{fig:dqw}}
\end{figure}
We therefore consider a three-dimensional electron gas confined along
the $z$-direction by a potential $V_{CONF}(z)$ of the type
shown in Fig.~\ref{fig:dqw} which interacts through
a {\it three dimensional}
point-contact potential $V({\bf R}) = V \delta({\bf R})$.
In the absence of the interaction $V({\bf R})$, the
electronic eigenstates are given by the solution of the
time-independent Schr\"{o}dinger equation
\begin{equation}
\left[ -\frac{\hbar^2}{2m^*} \frac{d^2}{dz^2} + V_{CONF} (z) \right]
\xi_n (z) = \epsilon_n \xi_n (z),
\label{eq:xidef}
\end{equation}
where $m^*$ is the effective mass, which is assumed to be
constant throughout the heterostructure.
Normalizing these eigenfunctions by
\begin{equation}
\int dz \left| \xi_n(z) \right|^2 = 1,
\label{eq:norm}
\end{equation}
we write the electron annihilation operator
$\psi_{\sigma} ({\bf R})$ as
\begin{equation}
\psi_{\sigma} ({\bf R}) =
\frac{1}{\sqrt{A}} \sum_{n{\bf k}} e^{i{\bf k \cdot r}} \xi_n (z)
c_{n{\bf k}\sigma},
\label{eq:basis}
\end{equation}
where ${\bf R} = ({\bf r},z) = (x,y,z)$, ${\bf k} = (k_x, k_y)$,
$A$ is the transverse area of the sample, and $c_{n{\bf k}\sigma}$
annihilates a quasiparticle in subband $n$, of transverse wave vector
${\bf k}$, and with spin projection $\sigma$ (these conventions will
be used throughout this paper).
Defining a composite subband and spin index $a = (n_a, \sigma_a)$
with summation over repeated indices implied, the Hamiltonian
for this system is
\begin{eqnarray}
H &=& \sum_{\bf k} \, \epsilon_{a{\bf k}}^{~} \,
c^{\dag}_{a {\bf k}} c^{~}_{a {\bf k}} \nonumber \\
&&+ \frac{1}{2 A} \, \sum_{{\bf k} {\bf k'} {\bf q}}
\, V_{ad,bc} \,
c^{\dag}_{a {\bf k + q}} c^{\dag}_{b {\bf k' - q}}
c^{ }_{c {\bf k'}} c^{ }_{d {\bf k}} .
\label{eq:H}
\end{eqnarray}
Here, the quasiparticle energy
\begin{equation}
\epsilon_{a{\bf k}} = \epsilon_n + \frac{\hbar^2 k^2}{2m^*} - \mu
\label{eq:ea}
\end{equation}
is measured with respect to the chemical potential $\mu$
and the matrix elements of the interaction are
\begin{eqnarray}
V_{ab,cd} &=&
\delta_{\sigma_a \sigma_b} \delta_{\sigma_c \sigma_d} \,
V \, \int dz \,\xi_{n_a}^{*} (z) \xi_{n_b}^{~} (z) \,
\xi_{n_c}^{*} (z) \xi_{n_d}^{~} (z) .
\label{eq:V}
\end{eqnarray}
We treat this Hamiltonian within self-consistent
Hartree-Fock theory allowing for the possibility of
phases with broken symmetry in subband and spin indices,
but imposing translational invariance within each layer.
The electronic Green's function in the interacting system can
therefore be written
\begin{equation}
G_{ab} (k_n) = - \int_0^{\beta} d\tau \, e^{i\omega_n \tau} \,
\left< T_\tau \left[ c_{a{\bf k}} (\tau) c_{b{\bf k}}^{\dag} (0)
\right] \right>,
\label{eq:G}
\end{equation}
where $k_n = ({\bf k},i\omega_n)$, $\beta = 1 / T$
($\hbar = k_B = 1$ throughout this paper), and the rest of the
notation is standard.\cite{Mahan}
This Green's function is determined self-consistently from
the self-energy in the Hartree-Fock approximation,
\begin{equation}
\Sigma_{ab} =
\left[ V_{ab,dc} - V_{ac,db} \right] \,
\frac{T}{A} \sum_{k^{\prime}_m} e^{-i \omega_m 0-} \,
G_{cd} (k^{\prime}_m),
\label{eq:Sigma}
\end{equation}
and the Dyson equation,
\begin{equation}
\left[ \left( i\omega_n - \epsilon_{a{\bf k}} \right) \delta_{ab}
- \Sigma_{ab} \right] \, G_{bc} (k_n) = \delta_{ac},
\label{eq:Dyson}
\end{equation}
under the constraint of constant sheet density $N_s$,
\begin{equation}
N_s = \frac{T}{A} \sum_{k_m} e^{-i \omega_m 0-} \, G_{aa} (k_m) ,
\label{eq:filling}
\end{equation}
which determines the chemical potential.
We solve these equations in the following way.
Given a double quantum well structure defined by the
effective mass $m^*$, sheet density $N_s$, and the
structural parameters shown in Fig.~\ref{fig:dqw}, we
compute the eigenfunctions and eigenenergies by solving
Eq.~(\ref{eq:xidef}) with the normalization condition
Eq.~(\ref{eq:norm}).
These eigenfunctions are used to compute the matrix elements
of the interaction via Eq.~(\ref{eq:V}) in terms of a single
parameter V.
The resulting matrix elements and eigenenergies are employed
to solve Eqs.~(\ref{eq:G})-(\ref{eq:filling}) self-consistently
at $T = 0$ following the procedure outlined in Sec.~II.B of
Ref.~\onlinecite{rad-das} and including {\it all} matrix
elements of the interaction between the lowest two subbands.
This procedure yields the ground state properties of the
system as a function of the sheet density $N_s$, the
interaction parameter $V$, and the structural parameters of
the double quantum well [Fig.~\ref{fig:dqw}].
To illuminate the properties of the interacting system further,
we also compute the generalized density-density response function,
which is defined by the analytic continuation of
\begin{eqnarray}
\Pi^{\mu} ({\bf Q},i\nu_n) &=&
- \int \frac{d{\bf R}}{\cal V} \, e^{-i{\bf Q \cdot R}} \,
\int_0^{\beta} d\tau \, e^{i\nu_n\tau} \times \nonumber \\
&& \left< T_{\tau} \left[ \rho^{\mu}({\bf R},\tau) \,
\rho^{\mu}({\bf 0},0) \right] \right>
\label{eq:Pi}
\end{eqnarray}
to real frequencies.
In this expression, ${\cal V}$ is the system volume and the
generalized density operator is
\begin{equation}
\rho^{\mu}({\bf R}) =
\sum_{\sigma\sigma'} \, \psi^{\dag}_{\sigma}({\bf R})
\sigma^{\mu}_{\sigma\sigma'} \psi^{~}_{\sigma'}({\bf R})
\label{eq:dop}
\end{equation}
with $ \psi_{\sigma}({\bf R})$ given by
Eq.~(\ref{eq:basis}) and
$\sigma^{\mu} = (1,\sigma^x,\sigma^y,\sigma^z)$ are the
Pauli matrices.
This response function is computed from the non-interacting
response function in subband and spin space within the
conserving approximation described in
Sec.~V.A of Ref.~\onlinecite{rad-das} but with the inclusion
of all interaction matrix elements.
In addition to the information this response function
reveals about the excitations of the interacting system,
its imaginary part is proportional to the intensity observed
in resonant inelastic light scattering
measurements,\cite{pin-abs,das:ils} allowing us to make
contact with experiment.
This is particularly relevant here, because searches for
the antiferromagnetic phase in both finite\cite{Pinczuk} and
zero\cite{Plaut} magnetic field have employed this
technique.
\section{RESULTS}
\label{sec:results}
In this Section, we apply the formalism described in
Sec.~\ref{sec:formalism} to compute the ground state phase
diagram and collective modes in a typical GaAs/Al$_x$Ga$_{1-x}$As
double quantum well structure which is expected to exhibit
the zero-field antiferromagnetic instability.
The structure has a well width of 140~\AA, a barrier width
of 30~\AA, and a well depth of 220~meV [cf.
Fig.~\ref{fig:dqw}], and an electronic effective mass
$m^* = 0.067\,m_e$.
For the moment, we leave the asymmetry unspecified.
\subsection{Matrix Elements}
\label{sec:me}
As a first step in obtaining the phase diagram for this
structure, we must solve the time-independent
Schr\"{o}dinger equaution [Eq.~(\ref{eq:xidef})] for the
lowest two eigenfunctions $\xi_n (z)$ and eigenenergies
$\epsilon_n$ at a fixed value of the asymmetry parameter
$dU$ [cf. Fig.~\ref{fig:dqw}] and then compute the matrix
elements of the interaction through Eq.~(\ref{eq:V}).
Solving Eq.~(\ref{eq:xidef}) is straightforward and yields a
splitting of the non-interacting eigenstates of
$\Delta^0_{\rm SAS} = \epsilon_2 - \epsilon_1 = 2.25$~meV
for $dU = 0$.
As $dU$ is increased, this splitting increases to a
maximum of 18.5~meV at $dU = 9.4$~meV; for larger $dU$, the
lowest eigenfunction is localized in one well.
Since the structures examined experimentally have subband
splittings on the order of 1~meV,\cite{Pinczuk,Plaut}
we restrict our attention to small $dU$ values.
The dependence of the matrix elements on the asymmetry
parameter is somewhat more interesting and merits a brief
discussion.
Since our model interaction is a delta function in real
space and we have chosen the wave functions to be real,
the matrix elements defined by Eq.~(\ref{eq:V}) are invariant
under permutation of the indices.
Thus, there are only five independent matrix elements,
$V_{11,11}$, $V_{22,22}$, $V_{11,22}$, $V_{11,12}$, and
$V_{22,21}$, which are displayed in Fig.~\ref{fig:me} as a
function of the asymmetry parameter $dU$.
In a symmetric double quantum well ($dU = 0$), the
$V_{11,12}$ and $V_{22,21}$ matrix elements vanish by
symmetry, but the remaining inter-subband ($V_{11,22}$) and
intra-subband ($V_{11,11}$ and $V_{22,22}$) matrix elements
are equal to within 5~\%. We remark that for more
realistic interaction models $V_{11,22}$, which is
roughly\cite{boebinger} proportional to the difference of
intra-layer and inter-layer interactions, is weaker
than $V_{11,11}$ and $V_{22,22}$ which are roughly
proportional to the sum.
The latter matrix elements would be equal if the
electrons were localized to the wells; the fact that they
are nearly so indicates that the wave function overlap
between the wells is small.
Additionally, this calculation provides direct evidence that
the neglect of the intra-subband repulsion employed in
earlier work\cite{rad-das} is not generally
justified for these double quantum well structures.
We shall see, however, that their inclusion in the
calculation changes the qualitative picture only slightly.
\begin{figure}
\psfig{file=fig3.eps,width=0.95\linewidth}
\caption{Dependence of the interaction matrix elements
$V_{ij,kl} / V$ [Eq.~(\protect\ref{eq:V})] on the double
quantum well asymmetry parameter $dU$ [cf.
Fig.~\protect\ref{fig:dqw}].
Shown are the intra-subband matrix elements $V_{11,11}$
(dot-dashed line) and $V_{22,22}$ (dotted line), the
inter-subband matrix element $V_{11,22}$ (solid line),
and the asymmetry-induced matrix elements $V_{11,12}$
(long dashed line) and $V_{22,21}$ (short-dashed line).
For the point-contact interaction employed in this paper,
the matrix elements are invariant under permutation of the
indices, so these matrix elements span the entire set.
\label{fig:me}}
\end{figure}
As the asymmetry is increased from zero, we discern several
features.
We see that the intra-subband matrix elements $V_{11,11}$ and
$V_{22,22}$ are approximately equal and increase with increasing
$dU$ to saturate at a value about twice the $dU = 0$ one.
The approximate equality of these diagonal matrix elements
follows from the normalization condition, Eq.~(\ref{eq:norm}),
imposed on the two eigenfunctions.
The increase in these matrix elements with $dU$, on the
other hand, can be attributed to the increasing confinement
of the wave functions of the two subbands to opposite wells,
similar to what occurs in the presence of an applied electric
field.\cite{Katayama,Ying}
Thus, at large $dU$, the two subband wave functions are almost
completely localized in opposite wells, enhancing the
magnitude of the diagonal matrix elements.
For the same reason, the inter-subband matrix element
$V_{11,22}$ decreases with increasing asymmetry:
as the wave functions from different subbands are
increasingly localized, their overlap, and hence $V_{11,22}$,
decreases to zero.
Since the zero-field antiferromagnetic transition depends on
this matrix element, it is clear that large asymmetry is
inimical to this phase.
Based on the small values of the observed
splitting of the lowest two subbands in the experimental
samples,\cite{Pinczuk,Plaut} however, we expect the actual
samples to be in a regime in which $V_{11,22}$ is still non-negligible.
Hence, the antiferromagnetic phase is not immediately excluded.
Finally, we note that the mixing terms $V_{11,12}$ and
$V_{22,21}$ have opposite signs and increase in magnitude
with $dU$ to a maximum around $dU = 1$~meV.
The wave function for the lowest ($n = 1$) subband has
no nodes and we chose it to be
positive. Orthogonality requires that the
$n = 2$ wave function have a node and we choose it to
be negative in the well where
$|\xi_1(z)|^2$ is largest; with this convention $V_{11,12}$ is
negative and $V_{22,21}$ is positive, as observed in
Fig.~\ref{fig:me}.
In addition, since these matrix elements must vanish both
in the symmetric ($dU = 0$) limit and when $dU$ is large and the
subband wave functions are localized in different wells, the
maximum seen in this figure is also expected.
These results suggest that the mode coupling between intra-
and inter-subband excitations induced by these matrix
elements will be maximal around $dU = 1$~meV.
Taken together, the behavior of the interaction matrix
elements presented in Fig.~\ref{fig:me} indicate that the
zero-field antiferromagnetic phase will probably not be
stable against large asymmetry in the quantum wells.
However, the current experimental samples have subband
splittings more consistent with small asymmetry,
and therefore these samples may be of high enough quality
to observe this phase, at least in principle.
To examine this situation further, we shall compute the phase
diagram and collective modes for two choices of $dU$ in the
weak asymmetry regime: $dU = 0$ (the symmetric case) and
$dU = 0.5$~meV (the asymmetric case).
The following subsections discuss the results of these
calculations.
\subsection{Phase Diagram}
\label{sec:phases}
As described in the preceding subsection, the structure of
the double quantum well yields the eigenenergies and
eigenfunctions of the non-interacting system which are then
used to compute the interaction matrix elements up to an
overall factor $V$ [Eq.~(\ref{eq:V})].
To be consistent with earlier work,\cite{rad-das} we choose
to parameterize the interaction strength by the magnitude of
the inter-subband repulsion $V_{11,22} = V_{12}$ rather than
by $V$, but all the matrix elements are uniquely determined
by either parameter.
With the structure and interaction strength fixed, the only
other parameter in our model is the sheet density $N_s$.
Given these parameters, Eqs.~(\ref{eq:G})-(\ref{eq:filling})
can be solved at $T = 0$ to yield the interacting ground state
of the system.
The resulting phase diagrams in terms of the dimensionless
interaction strength $N_0 V_{12}$ and sheet density $N_s / 2
N_0 \Delta^0_{\rm SAS}$ are presented in
Fig.~\ref{fig:phasediagram} for the double quantum well
structure of Fig.~\ref{fig:dqw}.
In these figures, $N_0$ is the single-spin, two-dimensional
density of states, and $\Delta^0_{\rm SAS} = \epsilon_2 -
\epsilon_1$ is the subband splitting in the non-interacting
system.
\begin{figure}
\psfig{file=fig4a.eps,width=0.95\linewidth}
\psfig{file=fig4b.eps,width=0.95\linewidth}
\caption{Phase diagram of (a) a symmetric and (b) an asymmetric
double quantum well in terms of the sheet density $N_s$ and
the interaction parameter $V_{12}$ for the point-contact model
described in Sec.~\protect\ref{sec:formalism}.
The points are the numerically computed boundaries
between the various phases of this model which are labeled
as follows:
$N_1$ and $N_2$ are paramagnetic phases with one and two
spin-degenerate subbands occupied, respectively;
$FM_i$ are ferromagnetic phases with $i$ non-degenerate
subbands occupied; and
$AF$ is the antiferromagnetic phase.
See Fig.~\protect\ref{fig:phases} for a real-space depiction of
these phases and Fig.~\protect\ref{fig:dqw} for the
structural parameters of the double quantum well.
In the figure, $N_0$ is the single-spin, 2D electronic
density of states, and $\Delta^0_{\rm SAS}$ is the
splitting between the lowest two states in the non-interacting
system.
Note that asymmetry reduces the extent of the antiferromagnetic
phase in (b) but does not destroy it altogether.
\label{fig:phasediagram}}
\end{figure}
Consider the symmetric ($dU = 0$) case first
[Fig.~\ref{fig:phasediagram}(a)].
At first glance, this phase diagram is very similar to the
one obtained from the neglect of intra-subband
repulsion,\cite{rad-das} even though this repulsion is
included in our calculations.
At low density, the paramagnetic phase with one
spin-degenerate subband occupied (labeled $N_1$ in the
figure) is stable, while at higher densities ($N_s /
2N_0\Delta^0_{\rm SAS} > 1$) but weak interaction ($N_0
V_{12} < 1/2$) the paramagnetic phase with two
spin-degenerate subbands occupied (labeled $N_2$) is stable.
For larger interaction strengths and intermediate densities,
we see a broad region in which the antiferromagnetic ($AF$)
phase obtains.
Thus, the inclusion of intra-subband repulsion
does not eliminate the zero-field antiferromagnetic phase
from the phase diagram of the model, despite the fact that
the intra- and inter-subband repulsions are of the same
order [Fig.~\ref{fig:me}].
These matrix elements do have an effect on the phase
diagram, however.
At higher densities ($N_s/2N_0\Delta^0_{\rm SAS}$ larger
than approximately 2) and strong interaction ($N_0V_{12} >
1/2$), two different ferromagnetic phases appear.
In these phases, each quantum well is spin polarized, and
the polarization vectors are parallel.
They differ in the arrangement and filling of the
interacting bands, as indicated by the labels in
the figure: the phase $FM_i$ corresponds to an interacting
band structure with $i$ spin-split subbands occupied.
The presence of the ferromagnetic phases is expected when
intra-subband repulsion in present; what is surprising is
that the ferromagnetic phases do not exclude the presence of
the antiferromagnetic phase.
As argued in Sec.~\ref{sec:origin} based on a weak-coupling
model, the antiferromagnetic phase is stabilized by a
superexchange interaction for intermediate interaction
strengths.
Similar behavior is seen in Fig.~\ref{fig:phasediagram}(a)
based on our strong-coupling computations and presumably
originates from the same mechanism.
Note that, in the limit of vanishing hopping between the
wells, $V_{12}$ may be associated with $V_0/2$ in the model
of Sec.~\ref{sec:origin}, implying that the phase boundary
$N_0 V_{12} = 1/2$ in Fig.~\ref{fig:phasediagram}(a) is nothing
but the Stoner criterion for the related Hubbard model.
The fact that the model of Sec.~\ref{sec:origin} does not
have a closer correspondence to
Fig.~\ref{fig:phasediagram}(a) suggests that the
relative magnitudes of the intra- and inter-subband
interaction matrix elements, which are all equal in
the model of Sec.~\ref{sec:origin}, are important for
determining whether ferro- or antiferromagnetic phases
obtain in a specific region of the phase diagram.
With the introduction of weak asymmetry ($dU = 0.5$~meV),
the qualitative features of the phase diagram do not change,
as seen in Fig.~\ref{fig:phasediagram}(b).
As before, we find paramagnetic phases at small interaction
strengths, the antiferromagnetic phase at larger interaction
strengths and intermediate densities, and ferromagnetic
phases at larger interaction strengths and higher densities.
The identification of these phases precisely matches those
in the symmetric case of Fig.~\ref{fig:phasediagram}(a),
although the position of the phase boundaries have shifted
somewhat.
An apparently new feature occurs at low density and large
interaction strength, where an $FM_1$ ferromagnetic phase has
replaced the paramagnetic $N_1$ phase.
However, this phase also occurs in the symmetric structure
when $N_0 V_{12}>1$, but is cut-off in
Fig.~\ref{fig:phasediagram}(a).
It corresponds to the usual ferromagnetic instability in a
single, spin-degenerate band which obtains when the
interaction is sufficiently strong.\cite{Doniach}
Although weak asymmetry clearly does not destroy the
antiferromagnetic phase, it does have observable
consequences.
The most noticeable effect of the asymmetry on the ground
state is that the spin polarizations in the magnetic phases,
which can be obtained from the expectation value of the
density operator, Eq.~(\ref{eq:dop}), are no longer of equal
magnitude in the wells.
This is an obvious consequence of an asymmetric structure
which nonetheless does not disturb the identification of
ferro- and antiferromagnetic phases, since one can determine
whether the spin polarizations are parallel or antiparallel
without referring to their magnitudes.
\subsection{Collective Modes}
\label{sec:modes}
The effects of asymmetry on the antiferromagnetic phase
cannot be fully appreciated based on the ground-state
properties alone, but must be augmented by an examination of
the excitation spectrum of the system.
We focus on the spin-density excitations in what follows,
since they are the excitations most strongly coupled to the
magnetic nature of the ground state and can also be probed
experimentally by Raman scattering.\cite{pin-abs,das:ils}
For these calculations, we compute the spin-spin
response function ($\mu = 3$ in Eq.~(\ref{eq:Pi}))
for the appropriate ground state as discussed in
Sec.~\ref{sec:formalism} and identify the collective modes
by peaks in the imaginary part of this response function.
Since this procedure is used in the Raman scattering
measurements, our results have direct implications
for experiment and we shall discuss them in this context.
For concreteness, we fix the interaction strength and sweep
the sheet density through the second-order transition from
the $N_1$ to the $AF$ phase in these calculations [cf.
Fig.~\ref{fig:phasediagram}].
As an introduction to the general phenomenology of
spin-density excitations in double quantum wells, consider
the symmetric ($dU = 0$) case first.
By appropriately arranging the light scattering geometry,
Raman scattering can selectively probe the intersubband
spin-density excitations,\cite{Pinczuk,Plaut} which, in our
approximation, have the
form shown in Fig.~\ref{fig:symmode}(a).
In addition to a continuum of inter-subband particle-hole
excitations, there is a collective spin-density excitation
(SDE) with a finite energy at $q = 0$ which disperses with
increasing $q$ toward the particle-hole continuum.
The magnitude of the $q = 0$ SDE energy is reduced from the
subband splitting $\Delta_{\rm SAS}$ by vertex corrections
appearing in the response function due the the exchange
interaction.\cite{Ando-RMP,pinczuk89}
In addition, there is an intra-subband SDE which has a
linear-in-q dispersion in our model, shown by the dashed
line in Fig.~\ref{fig:symmode}(a).
If the well is symmetric, this mode will not appear in
Raman spectra taken in a scattering geometry meant to
observe inter-subband excitations.
A symmetric system with identical quantum wells is
invariant under inversion about the mid-point between
the wells so that all
states can be classified by a parity quantum number.
Inter-subband excitations, which are odd, and intrasubband
excitations, which are even, do not interact and can cross as seen
in Fig.~\ref{fig:symmode}(a).
\begin{figure}
\psfig{file=fig5a.eps,width=0.95\linewidth}
\psfig{file=fig5b.eps,width=0.95\linewidth}
\caption{Collective spin-density excitations in a symmetric
double quantum well of the type shown in Fig.~\protect\ref{fig:dqw}
with $dU = 0$.
(a) Collective mode spectrum in terms of excitation energy
$E$ and intra-well wave vector $q$ showing the
inter- (solid line) and intra- (dashed line) collective spin-density
excitations as well as the continuum of inter-subband particle-hole
excitations (shaded area).
Although not apparent in the figure, the inter-subband
collective mode does disperse with $q$.
(b) $q = 0$ inter-subband spin density excitation (SDE) energy
$E$ as the sheet density $N_s$ is tuned through the $N_1$ to $AF$
transition at fixed interaction strength $N_0 V_{12} = 0.55$
[cf. Fig.~\protect\ref{fig:phasediagram}(a)].
Note that the SDE (solid line) softens completely at the
transition point and that the collective mode appearing on the
antiferromagnetic side ($N_s / 2N_0\Delta^0_{\rm SAS} >
0.919$) is the amplitude mode of the antiferromagnetic order
parameter (dashed line).
The dot indicates the point in parameter space presented in
(a).
In this figure, $N_0$ is the single-spin, 2D electronic
density of states, $\Delta^0_{\rm SAS}$ is the
energy separation of the lowest two subbands
in a non-interacting double quantum well, $\Delta_{\rm SAS}$
is the splitting in the interacting system, and
$q_\Delta^2 = 2 m^* \Delta^0_{\rm SAS} / \hbar^2$. The
intra-band particle-hole continuum is not indicated.
\label{fig:symmode}}
\end{figure}
As the density increases in our model, the exchange-induced
reduction in the $q=0$ inter-subband SDE energy increases
until the mode softens entirely, as illustrated in
Fig.~\ref{fig:symmode}(b).
This complete softening was seen initially in time-dependent,
local density approximation calculations of the SDE spectrum in
these systems and was the first evidence for the zero-field
antiferromagnetic phase.\cite{das-tam}
An analysis of the real-space spin response identified this
softening as an antiferromagnetic transition of the
well spin polarizations.\cite{rad-das}
As the density is increased past the antiferromagnetic
transition, the inter-subband SDE turns into the collective
mode associated with amplitude fluctuations of the
antiferromagnetic order parameter.\cite{rad-das}
Experimentally, then, one expects to see a complete
softening of the inter-subband SDE and the recovery of
this amplitude mode as the density is tuned through
the transition.
The presence of asymmetry in the double quantum well
complicates this picture somewhat.
The SDE spectrum for our asymmetric ($dU = 0.5$~meV) double
quantum well illustrates these complications and
is shown in Fig.~\ref{fig:asymmode}(a).
Most noticeably, the asymmetry mixes the intra- and
inter-subband excitations, so that even in scattering
geometries designed to measure only inter-subband
response, both intra- and inter-subband excitations will
appear.\cite{note}
This effect is seen through both an enlarged particle-hole
continuum and the presence of a damped mode in the
inter-subband spectrum corresponding to the
intra-subband SDE.
Furthermore, the asymmetry couples the intra- and
inter-subband SDEs themselves, leading to an avoided
crossing which may be seen by comparing
Fig.~\ref{fig:asymmode}(a) to Fig.~\ref{fig:symmode}(a).
\begin{figure}
\psfig{file=fig6a.eps,width=0.95\linewidth}
\psfig{file=fig6b.eps,width=0.95\linewidth}
\caption{Collective spin-density excitations in a weakly
asymmetric double quantum well of the type shown in
Fig.~\protect\ref{fig:dqw} with $dU = 0.5$~meV.
The organization of and notation in the figure are the same
as Fig.~\protect\ref{fig:symmode} with the interaction strength
fixed at $N_0 V_{12} = 0.55$ and the antiferromagnetic
transition occurring at $N_s / 2N_0\Delta^0_{\rm SAS} = 0.698$.
As seen in (a), the asymmetry induces a coupling between
the inter- and intra-subband spin-density excitations which
results in the avoided crossing of inter- and intra-subband
spin-density dispersions and a mixing of intra-subband particle-hole
excitations with the inter-subband continuum.
In (b), one sees that this mode coupling also prevents the
inter-subband SDE from softening when going from the
paramagnetic to the antiferromagnetic phase.
\label{fig:asymmode}}
\end{figure}
This avoided crossing effectively prevents the inter-subband
SDE from completely softening on entering the
antiferromagnetic phase, as shown in Fig.~\ref{fig:asymmode}(b).
In this figure, ones sees that, as the density is tuned
toward the antiferromagnetic transition, the $q=0$
inter-subband SDE energy decreases to a finite value.
Further increase of the density into the antiferromagnetic
phase reverses this trend, and the energy of the amplitude
mode of the antiferromagnetic order parameter increases,
resulting in a cusp.
Despite the fact that the inter-subband SDE does not
completely soften, the antiferromagnetic phase appears,
demonstrating that this softening is a sufficient but not
necessary signature of the zero-field phase transition.
We expect some mode to soften at this transition, however,
and it turns out that it is the {\it intra}-subband SDE which
collapses.
Specifically, the mode coupling between inter- and intra-subband
SDEs pushes the latter mode down in energy at all
$q$, effectively reducing the group velocity of this mode.
Approaching the antiferromagnetic transition, the
$q \rightarrow 0$ group velocity of the intra-subband SDE
decreases until it vanishes at the transition point.
The resulting phase has the character of the real-space
spin density profile of the intra-subband mode, which direct
calculation reveals to be antiferromagnetic.
The character of the intra-subband excitation at small $q$
is therefore very similar to the inter-subband excitation
in the symmetric well due to the mode coupling between
the two excitations.
Thus, its softening can lead to an antiferromagnetic
transition without inconsistency.
\section{CONCLUSION}
\label{sec:conclusion}
In this paper, we have examined the origin and robustness
of a zero-field antiferromagnetic phase in double quantum
wells predicted in previous calculations.\cite{das-tam,rad-das}
Based on a simple model, we determined that such
magnetic phases are a direct consequence of the
magnetism expected at low densities in two-dimensional
systems where interaction effects dominate.
In particular, magnetic phases with either ferro- or
antiferromagnetic spin polarizations
are possible, and a superexchange interaction between the wells
leads to a region at intermediate densities and interaction
strengths where the antiferromagnetic phase is preferred.
By performing a detailed self-consistent Hartree-Fock
calculation on a model of these double quantum well systems,
we addressed two features left out of preceding
work:\cite{rad-das} intra-subband repulsion and asymmetry
of the heterostructure.
Our results support and extend those of Ref.~\onlinecite{rad-das}.
Specifically, we found that the antiferromagnetic phase is
stable in a large region of the model phase diagram despite
the presence of intra-subband repulsion that is as strong as
the inter-subband repulsion which drives the antiferromagnetic
instability.
The intra-subband repulsion does, however, introduce
ferromagnetic phases, producing a rich phase diagram.
Note, however, that no charge ordering phases of the type
discussed in
Refs.~\onlinecite{MacDonald,Ruden,nei,Varma,Katayama,Ying,Patel,Conti,Zheng}
were observed, even though our formalism did allow for that
possibility.
In addition, both ferro- and antiferromagnetic phases persist
in the presence of asymmetry in the quantum well structure;
indeed, the phase diagram is qualitatively unaffected by its
introduction.
Asymmetry does have a strong influence on the collective
mode spectrum, though, and induces a mode-coupling between
inter- and intra-subband spin-density excitations which
prevents the latter from completely softening at the
antiferromagnetic phase transition.
Instead, the inter-subband spin-density excitation exhibits
a cusp at the transition while the $q \rightarrow 0$ group
velocity of the {\it intra}-subband excitation vanishes.
The coupling between these two modes nonetheless lends an
antiferromagnetic character to the intra-subband excitation
in the asymmetric system and enables the collapse of its
group velocity to yield the antiferromagnetic phase.
Taken together, these results strongly indicate that, if an
exchange-correlation-induced ferromagnetic transition occurs
in a single-layer system at sufficiently low density, then
the antiferromagnetic phase in a double-layer system should
also occur.
However, the issue of whether or not the ferromagnetic phase
obtains in a single two-dimensional layer is not settled.
Variational Monte Carlo calculations\cite{cep-ald,tan-cep}
show the presence of a ferromagnetic phase between the
paramagnetic and Wigner crystal phases, but Green's function
Monte Carlo computations\cite{tan-cep} find no intervening
ferromagnetism.
More recent numerical work based on the Monte Carlo
technique\cite{cep-unp,RS,Conti} once again favors the
existence of a ferromagnetic transition.
Other calculations using density-functional theory in
the local-spin-density approximation\cite{rad-das,Zheng} also
support the existence of a ferromagnetic transition at
sufficiently low density.
Thus, although a definitive demonstration of ferromagnetism
in a single, two-dimensional layer is lacking, a large body
of evidence exists which firmly supports this hypothesis.
The precise conditions under which these phases would be
observable are somewhat harder to elucidate based on the
mean-field theory presented in this paper.
The principle difficulty is that mean-field
calculations will tend to overestimate the temperatures
and densities at which exchange-correlation-induced phase
transitions occur.
The source of this difficulty lies in the neglect of
fluctuations in the theory, which play an important role
in the low-dimensional structures considered.
If one goes to densities and temperatures deep below the
critical values of these parameters, we expect that the
mean-field theory will give an accurate qualitative
picture of the phase.\cite{MW}
In sum, work on the single layer system indicates
that its ferromagnetic state is unlikely to occur for
electron-gas density parameters smaller than $r_s \approx 10$,
a much lower density than would be indicated by the
Hartree-Fock approximation, for which the transition to the
ferromagnetic state occurs at $r_s \approx 2$.
The present work suggests that the two-layer antiferromagnetic
phase, as well as two-layer ferromagnetic phases, are likely
to be present in double-layer
systems when the density per layer approaches the low value
at which the single-layer ferromagnetic instability occurs.
For the GaAs systems studied experimentally
it therefore seems unlikely that the antiferromagnetic state will
occur for densities per layer substantially larger than
$ \approx 10^{10} {\rm cm}^{-2}$.
However, it is exceedingly difficult to estimate the
transition density theoretically and one must rely on experiment.
Currently, a single experimental publication regarding a
search for the antiferromagnetic phase has appeared in the
literature,\cite{Plaut} and the results are equivocal.
The authors of this study report inelastic light scattering
measurements of the long-wavelength inter-subband collective
spin-density excitations as a function of density in a double
quantum well which was expected, on the basis of
the original theoretical work, to show the antiferromagnetic
instability.\cite{Plaut}
Instead of completely softening at a finite density, as
predicted in earlier work,\cite{das-tam,rad-das} the
inter-subband SDE shows no dramatic structure down to the
lowest densities measured.\cite{Plaut}
These results could be accounted for in at least two different
ways. The most likely explanation is that the
electron density of the sample, of order
$10^{11}/{\rm cm}^2$,\cite{Plaut} is above the critical
density for the antiferromagnetic transition.
Alternatively, the calculations in this paper demonstrate
that slight asymmetry in the double quantum well will
prevent a complete softening of the inter-subband SDE and
yield a cusp as a function of density.
Since the energy of the amplitude mode in the
antiferromagnetic phase is similar to that of the
inter-subband SDE away from the critical density
[cf. Fig.~\ref{fig:asymmode}(b)], measurements at a closely
spaced grid of densities may be required to detect this cusp.
In addition, the cusp may be broadened by impurity or
fluctuation effects which are beyond our mean-field
theory, further increasing the difficulty of detecting the
transition. Thus, the current experimental results cannot exclude the
existence of the zero-field antiferromagnetic state, and its
robustness as demonstrated by the calculations in this paper
leaves us optimistic that such a unique exchange-driven phase
can occur in nature.
\section*{ACKNOWLEDGMENTS}
RJR would like to acknowledge stimulating discussions
with H.~Ehrenreich regarding the superexchange mechanism
in this system.
The work of RJR and SDS work was supported by the US-ARO
and the US-ONR.
The work of AHM was supported by the
National Science Foundation under grant DMR-9416906.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,488 |
Q: IOS HttpPost with parameters I want to send http post with parameters and then retrieve cookies from response.
In android I use the following:
HttpPost request = new HttpPost("http://stackoverflow.com/");
List<NameValuePair> nameValuePairs = new ArrayList<NameValuePair>(1);
nameValuePairs.add(new BasicNameValuePair("parameter", parameter));
request.setEntity(new UrlEncodedFormEntity(nameValuePairs));
HttpResponse response = client.execute(request);
List<Cookie> cookies = client.getCookieStore().getCookies();
I tried to use the following in IOS but it did not work for me:
NSURL *authUrl = [[NSURL alloc] initWithString:@"http://stackoverflow.com/"];
NSMutableURLRequest *request = [[NSMutableURLRequest alloc] initWithURL:authUrl];
[request setHTTPMethod:@"POST"];
NSString * parameters = [NSString stringWithFormat:@"login=%@&password=%@",login,password];
NSData *requestData = [NSData dataWithBytes:[parameters UTF8String] length:[parameters length]];
[request setHTTPBody:requestData];
[request setTimeoutInterval:15.0];
NSURLConnection * connection = [[NSURLConnection alloc] initWithRequest:request delegate:self];
[connection start];
In delegate method I receive the data. But the data look like the post have been sent without parameters. It sends the link but does not sends the parameters, I guess. I also tried to setup a header and it didn't help me.
[request addValue:VALUE forHTTPHeaderField:@"login"];
And use of sendSynchronousRequest didn't help either.
NSData *urlData=[NSURLConnection sendSynchronousRequest:request returningResponse:&response error:&error];
What did I do wrong?
A: The source works correctly, but I was sending request to the wrong website.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,249 |
4 Star Hotel, 2 minutes from Hobart airport. Free shuttle to and from the Airport between the hours of 7am - 5pm. Spacious studios and 1 bedroom suites all with king or twin beds. Excellent disabled access property and rooms. Air-conditioned. Licenced Restaurant, Cafe and Bar open daily from 6.30am - 9.00pm. Meeting room.
78 room AAA 4 star, well appointed hotel. King and Twin beds, walk in showers and spas, Spacious Std Rooms, 1 Bedroom Executive rooms. "Flight" restaurant, bar and cafe open daily from 6.30am - 9.00 pm. Room service, Free wireless. Don't worry about catching your flight. Ideal property for 1st night in the state or last night on the way out. Excellent Corporate faciities and ideal for leisure and group business. Reception 24 hour.
From Hobart - cross the Tasman bridge and proceed approx 10 km on the Tasman Highway to the Hobart Airport roundabout. Take the Airport exit and turn 1st left into the hotel driveway. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,856 |
Q: Litecoin/Bitcoin how divide uint256 target value on difficulty in C++ i'm almost done in implementating litecoin/bitcoin miner in js just for fun, i just don't know ho to find target hex. As docs says, it is max / difficulty, but if difficulty is (for example) 62, how can I perform a division between 0x00000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF and 62?
So i get unit256 class from litecoin wallet source, but this class dont have divide operator. So i convert uint256 to double which have implemintation in uint256 class
double getdouble() const
{
double ret = 0.0;
double fact = 1.0;
for (int i = 0; i < WIDTH; i++) {
ret += fact * pn[i];
fact *= 4294967296.0;
}
return ret;
}
But now i need convert this huge double to hex string. This string will be represent target for miner, as far i understand. Or i need this double variable converts back to uint256 and thet get hex from it. Any advise? Thanks!
A: So solution is simple:
void setdouble(double val)
{
double ret = val;
double fact = 1.0;
for (int i = 0; i < WIDTH; i++) {
double a = ret / fact;
pn[i] = (uint32_t)a;
fact *= 4294967296.0;
}
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,825 |
As a leader in rigging and machinery moving, we provide businesses nationwide with the lifting and heavy hauling services they need. With vast industry experience and a commitment to quality service, we have the right team and equipment to tackle your most challenging projects.
CEI performs hoisting and rigging for commercial and industrial clients across the county and around the globe. From planned projects to emergency crane service, we provide an experienced team with the right equipment to get the job done.
Let CEI move your heaviest machinery. With a focus on quality and safety, our experienced crew provides end-to-end service for your move – from dismantling and rigging to transportation and installation.
Whether you're relocating an entire factory or moving a single piece of equipment, CEI can oversee your project from start to finish. Beyond project management, we offer value-add services for our customers such as millwrighting and crating.
We would like to extend our appreciation for a job well done. Without a doubt, your organization was a major factor in the success of this project. Throughout the entire project your staff met every challenge as an opportunity to excel.
As an integrated supplier to our company we relied on your expertise to meet schedule, maintain budget, and provide a quality product. This was accomplished with your quality programs, work ethic, and project management. There is no question that your company has the best interests of The Timken Company in mind.
We contacted CEI to help us move our manufacturing plant to its new home. Everyone I worked with was friendly and helpful and the job was done ahead of their promised deadline.
Through the outstanding efforts of your employees we were able to meet the deadline with room to spare.
We would like to express our appreciate to your comapny and those key employees who made it happen. You are fortunate to have such devoted and productive employees in your organization.
Chris Shelpuk / Project Manger, Waste Management DivisionLockheed Martin Energy Systems, Inc. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,777 |
With these themed specials, hotels are scoring major points with luxury travelers who love soccer.
If you're joining the rest of the soccer-crazed planet in Brazil, pack this scouting report to the city at the center of it all.
Soccer and boxing fans around the Southeast Asian nation have lots to cheer about this month.
Our soccer-loving editors put together a guide to everything on and off the pitch, ensuring you'll meet your goal of having a great weekend.
Though Manchester United has won the Premier League crown, correspondent Joseph Reaney says there's great action still to see in the capital. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,065 |
Jerusalem Post Magazine Opinion
Palestine: Violating Vatican vows
Following the Pope's meeting with Abbas, relations between Israel and the Vatican are on shaky ground.
By DAVID SINGER
Published: DECEMBER 30, 2012 16:40
Pope Benedict XVI and PA President Abbas at Vatican 311 (R)
(photo credit: REUTERS/Andrew Medichini)
Diplomatic relations between Israel and the Vatican are set to considerably cool following Pope Benedict XVI granting a private audience to Palestinian Authority President Mahmoud Abbas on December 17th.
Their meeting came at a time of growing political crisis engendered by the passage of the UN General Assembly resolution on November 29th that reaffirmed "the right of the Palestinian people to self-determination and to independence in their State of Palestine on the Palestinian territory occupied since 1967."
The Pope seemingly overlooked any discussion of the implications of this integral part of the resolution that also recognized the State of Palestine as a non-member observer state in the General Assembly - a view confirmed by the following communique issued by the Vatican:
The cordial discussions made reference to the recent Resolution approved by the General Assembly of the United Nations by which Palestine was recognized as a Non-member Observer State of the aforementioned Organization. It is hoped that this initiative will encourage the commitment of the international community to finding a fair and lasting solution to the Israeli-Palestinian conflict, which may be reached only by resuming the negotiations between the Parties, in good faith and according due respect to the rights of both.
The Pope was apparently unaware that the only matter left to be negotiated between the parties as a result of "this initiative" was the timing of the eviction of 500,000 Jews currently living in this "State of Palestine" as defined by the General Assembly.
Abbas had made this racist view very clear on July 28, 2010 when Wafa - the official Palestinian news agency - reported the following remark by Abbas in Cairo:
I'm willing to agree to a third party that would supervise the agreement, such as Nato forces, but I would not agree to having Jews among the Nato forces, or that there will live among us even a single Israeli on Palestinian land.
Could the Pope have failed to understand that the Resolution also left no room for negotiating the boundaries of this "State of Palestine" - that the General Assembly had preemptively determined that it should comprise 100% of the territory won from Jordan by Israel in the 1967 Six Day War?
Would cordial discussions have occurred had the Pope taken the opportunity to urge Abbas to recognize Israel as the Jewish National Home and offer Palestinian citizenship to those Jews who did not want to leave their current homes?
Resumption of negotiations by "the Parties in good faith and according due respect to the rights of both" in such circumstances is a pure pipe dream.
The Abbas audience was a papal faux pas for several reasons.
First, the Pope should not have blessed the audience with overt political significance by accepting from Abbas the gift of a mosaic of the Church of the Holy Sepulchre in Jerusalem bearing the inscription that it was presented to him by "the President of the State of Palestine" - a farcical nomenclature that had only been sanctioned that very day by the Chief of Protocol at the UN - Yeocheol Yoon.
Second, the Pope was clearly violating clause 11(2) of the 1993 Fundamental Agreement between The Holy See and The State Of Israel which provides:
The Holy See, while maintaining in every case the right to exercise its moral and spiritual teaching-office, deems it opportune to recall that owing to its own character, it is solemnly committed to remaining a stranger to all merely temporal conflicts, which principle applies specifically to disputed territories and unsettled borders.
Remaining a stranger to this temporal conflict would have allowed the Pope to escape any criticism as a result of this inappropriate audience.
Third, Article 2.2 of the Fundamental Agreement further avers:
The Holy See takes this occasion to reiterate its condemnation of hatred, persecution and all other manifestations of antisemitism directed against the Jewish people and individual Jews anywhere, at any time and by anyone.
Failing to condemn the "President of the State of Palestine" during the audience for his known manifestations of anti-semitism makes a mockery of the Fundamental Agreement.
Fourth, The Pope's political foray no doubt inspired his own appointed nominee as the top Roman Catholic cleric in the Holy Land - the Latin Patriarch Archbishop Fouad Twal - to also make a political statement in his annual pre-Christmas homily.
Twal told his followers at his headquarters in Jerusalem's Old City that this year's festivities were doubly joyful, celebrating:
The birth of Christ our Lord and the birth of the state of Palestine. The path (to statehood) remains long, and will require a united effort.
Twal - who was born in Jordan - had told Vatican Radio on June 21, 2008:
The majority of our priests, nuns, schools families are in Jordan. We need a link to Jordan.
That link will certainly not come from the State of Palestine designated by the UN General Assembly - since its realization is simply not going to eventuate.
Twal also told www.custodia.org in an interview on June 22, 2008:
If you want to touch Jews, Muslims, Christians, Jordanians, Palestinians, Cypriots, Europeans all together...then you have to consider every comma.
The Archbishop would have done well to have remembered this sage advice before uttering his Christmas Eve message - understanding that what he said would not touch at least 500,000 Jews - but cause them immeasurable hurt.
Indeed those who are playing charades with the newly crowned President of the State of Palestine are engaging in a world of make believe - where the words and commas in the Mandate for Palestine, the Montevideo Convention, Article 80 of the United Nations Charter, Security Council Resolution 242, the Oslo Accords and the Bush Roadmap - are apparently no longer worth the paper they are written on.
One can now add the Fundamental Agreement between the Holy See and the State of Israel to these discarded international agreements.
This does not bode well for any possible peaceful resolution of the long running conflict between Jews and Arabs.
The last Pope to bear Pope Benedict's name - Benedict XV - enthusiastically endorsed the Jews' right to reconstitute their national home in what was then Palestine. He told Zionist leader Nahum Sokolov at an audience in 1917:
Nineteen hundred years ago Rome destroyed your homeland and when you seek to rebuild it, you seek a path which leads via Rome…Yes this is the will of Divine Providence, this is what the Almighty desires.
Violating Vatican vows this time round is certainly not going to entice Israel to beat a path to Rome as it continues to reconstitute the Jewish National Home in its ancient, biblical and internationally sanctioned homeland. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,536 |
package com.monovore.example.coast
import com.monovore.coast.flow.{Flow, Topic}
import com.monovore.coast.wire.Protocol
import scala.collection.immutable.SortedSet
/**
* A sketch of a denormalization flow -- normalized models come in at the top,
* and denormalized versions appear at the bottom.
*/
object Denormalize extends ExampleMain {
import Protocol.native._
case class ID(value: Long)
type GroupID = ID
type UserID = ID
implicit val IDOrdering = Ordering.by { id: ID => id.value }
case class Group(name: String)
case class User(name: String, groupIDs: SortedSet[GroupID])
case class DenormalizedGroup(name: String, memberNames: Set[String])
// 'Changelog' for users and groups
// We expect None when the data is missing or deleted, and Some(user) otherwise
val Users = Topic[UserID, Option[User]]("users")
val Groups = Topic[GroupID, Option[Group]]("groups")
val Denormalized = Topic[GroupID, Option[DenormalizedGroup]]("denormalized-groups")
val graph = Flow.build { implicit builder =>
val usersPool =
Flow.source(Users)
.map { userOpt =>
userOpt
.map { user =>
user.groupIDs.map { _ -> user.name }.toMap
}
.getOrElse(Map.empty)
}
.latestByKey("users-changes")
val groups = Flow.source(Groups).latestOr(None)
(groups join usersPool)
.map { case (groupOption, members) =>
for (group <- groupOption) yield {
DenormalizedGroup(group.name, members.values.toSet)
}
}
.updates
.sinkTo(Denormalized)
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,226 |
To understand the evolution ladder of the operator theory, one must learn to distinguish between three types of structural complexity.
The first type (also 'direction' or 'dimension') describes the different ways by which existing operators (physical particles or organisms) interact and create systems ('interaction systems') which are not operators. Examples include stars, planets, the global ecosystem, bee colonies, populations, etc.
The second type describes the arrangement of elements inside existing operators ('internal differentiation'). Examples include organelles in cells and tissues and organs in multicellulars.
The third type, the 'operator dimension', describes an evolution ladder. This ladder starts with the quarks and continues with the steps towards the hadrons, atoms, molecules, prokaryotic cells (the bacteria sl), endosymbiontic cells (also considered as eukaryotes), multicellular organisms and multicellulars with brains. Every step on the ladder must involve the shortest route nature allows (it must be the 'first-next possibility'). A step can either be based on interactions, or on internal differentiation. Every step causes a new closure type and a new operator. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,350 |
#import "NSTextViewDelegate.h"
@protocol IDEAttributedStringControlTextViewDelegate <NSTextViewDelegate>
- (void)textViewDidCommitEditing:(id)arg1;
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 330 |
{"url":"https:\/\/11011110.github.io\/blog\/2009\/06\/22\/copyright-permanence-jossage.html","text":"Via Michael Nielsen: Don't Ask, Don't Tell: Rights Retention for Scholarly Articles. My mother, a poet, thinks it very strange when she hears about the system of scientific publishing in which we give away the copyrights for all our papers. In poetry, the authors retain their copyrights, and give permission to publishers to publish their poems; the same is true in fiction writing. The system works without problems: it doesn't prevent publishers from going after people who illicitly copy their works, and it doesn't prevent them from getting exclusive publication rights to the works in question. So what, exactly, do we gain by giving away our copyrights? What we lose is the right to distribute our own works online for free; but as this Harvard Law blog post observes, many of us do that anyway, hoping that the publishers won't demand that we take them down again or sue us for noncompliance with their contracts. And mostly it works, but there's always that risk...\n\nFortunately, there is a solution: free online journals. The Journal of Graph Algorithms and Applications and the new Journal of Computational Geometry both are free as in free beer (no cost to access the papers, no publication fees) but also free in the sense that authors retain copyright and grant the publisher a license to print the paper. Therefore, I am happy to echo Suresh and Ernie Jeff and announce that JoCG is now open for business and accepting submissions.\n\nOne question I had with the new journal was, if it's online-only, how permanent are its archives? If whoever's running the journal gets hit by a bus, what happens to all the old papers? In today's business climate one should wonder about that for commercial journals too, I suppose. JGAA has been handling the issue by collecting its old issues into printed volumes, but as I understand it that arrangement has run into difficulties, so I was curious to hear what JoCG intended. Anyway, the answer is that they're using the Open Journal Systems software and LOCKSS data security model, in which university libraries maintain local copies of open content in order to assure its permanence. So I am greatly reassured on that front.\n\nTherefore, as Samir exhorts us, get those SoCG papers into a journal. And now that we finally have a noncommercial alternative to DCG, CGTA, and IJCGA, let's support it by sending our papers there.\n\nNone: Don't accept their terms\n2009-06-22T18:26:46Z\nI now have a policy of signing a different form from the ones that the publishers send me. They end up with a form in hand but its terms are different from the terms that they offer. I do not draw their attention to my revision of the terms but I have never had a problem with a publisher refusing my revised terms which replace copyright by license to publish.\n11011110:\n2009-06-22T18:31:41Z\nAt least one of my papers was with a publisher with such ridiculous terms that I refused to sign their copyright form at all. They published it anyway (with no indication that it wasn't under their own copyright), which I think is an acceptable outcome: my paper gets published, but they have no leg to stand on if they try to tell me not to make preprints available. But I'm not sure what fraction of the time this would work and what fraction of the time they would tell me no signature no publication.\nNone:\n2009-06-23T06:02:09Z\n\nDid you actually tell them explicitly that you refused to sign, or did you just do nothing and let them publish the paper while they expected that your form was in the mail? I'd be worried in the latter case (although I'm not a lawyer), that by letting them publish the paper without objecting to the terms you were implicitly agreeing to them.\n\nThis is definitely the way it used to work many years ago. Various journals had policies saying that by submitting a paper, you were implicitly transferring copyright if the paper was accepted. I suspect this might have ended when the US signed the Berne convention in 1989, but once again I'm not a lawyer.\n\n11011110:\n2009-06-23T11:20:12Z\nIt was actually an edited collection (a book) rather than a journal, and I'm pretty sure we discussed this with the collection's editor, but I don't remember the details.\nNone: Refusing to accept their terms\n2009-06-25T05:53:41Z\nI had a case (with Elsevier) where I explicitly refused in e-mail to sign their form and they published the paper anyway with their copyright on it.\n11011110: Re: Refusing to accept their terms\n2009-06-29T18:31:18Z\nSince I've been so down on Elsevier lately, I should point out that my situation of this type wasn't with them, but with a different publisher, Marcel Dekker. The sticking point was that they wanted me to agree that my paper was a work for hire.\nNone: Re: LOCKSS\n2009-06-23T01:57:32Z\n\nThanks for the plug David.\n\nOne point about LOCKSS: It's not just for open content. Some (semi-)commercial publishers support LOCKSS on their journals:\n\nhttp:\/\/lockss.stanford.edu\/lockss\/Publishers_and_Titles\n\nHere's a list of LOCKSS participating libraries:\n\nhttp:\/\/lockss.org\/lockss\/Libraries\n\nIf your library doesn't run a LOCKSS box, you should consider suggesting to someone in charge that they do so. It's a tiny investment (less than the cost of 1 year's subscription to many journals) and will ensure continued access to lots of resources.\n\nUnfortunately, the LOCKSS access policy, which can be summarized as \"if you had a good copy of the data in the past you have the right to restore that copy in the future\" is a little too open for some commercial publishers, who seem to have come up with their own system named CLOCKSS.\n\nhttp:\/\/www.clockss.org\/clockss\/Participating_Publishers\n\nThere are fees for everyone (libraries and publishers) involved. It's not clear if it's even online yet, but please don't confuse it with LOCKSS.\n\nPat (Morin)\n\n11011110: Re: LOCKSS\n2009-06-23T04:15:01Z\nYou're welcome! And thanks for the additional information on this system.\nchouyu_31:\n2009-06-24T06:45:20Z\nDo you think that the dissertation version of our tree drawing paper and\/or my simultaneous source location paper might fit into the Graph Algorithms journal? And if so on our tree drawing paper, would it bother you to see me submit it?\n11011110:\n2009-06-24T14:45:28Z\nYes, they should both fit well, I think. Sounds like a good idea.\nNone: Poetry DOES NOT pay!\n2009-06-29T00:53:07Z\n\n\"system works without problems\" -- oh really?\n\nI have a degree in Mathematics from Caltech, and a degree in English Literature (primary Poetry) from Caltech. I publish a lot in each field.\n\nPoetry DOES NOT PAY as a publishing genre. There are fewer that a dozen poets making a middle-class living or better in the USA from Poetry publishing as such. Songwriting doesn't count. Being \"Writer in Residence\" doesn't count. I mean making a living by royalties of book sales, or magazine publication.\n\nYou don't need to believe me. Check with the National Writers Union. They have the numbers.\n\nIn a civilized country, a major poet can fill a soccer stadium for a reading. In the USA, one can win awards (I have) and have hundreds of publications (I have) and still earn no more from publishing poetry than pays for the pstage stamps to submit poems to magazines and anthologies.\n\nIn conclusion: \"system works without problems\" -- Yeah, right!\n\n-- Prof. Jonathan Vos Post\n\nhttp:\/\/magicdragon.com\n\n11011110: Re: Poetry DOES NOT pay!\n2009-06-29T01:20:41Z\nAre you claiming that it's possible to make a living writing scientific journal articles? Holding a faculty position, sure, but that's a different thing. If you're not claiming that, then in what way is poetry a bad example of a system where publication is more for fame than for money but the copyright system works?\nNone: \"Crime doesn't pay -- enough!\"; Re: Poetry DOES NOT pay!\n2009-06-30T18:54:24Z\n\nFor the economically rational Mathematician or Scientist, there MUST be significant value in having a scientific publication for which one is not paid and, indeed, may have had to pay from grant or departmental resources (\"Page charges.\") My friend professor Geoffrey Landis (Hugo & Nebula Award winning author, NASA scientist) agrees that the value is probably approximately $5,000 per paper, in increased likelihood of getting promotion, tenure, research grant. Note that this applies even if one is currently NOT embedded in an academic institution. I am between professorships, and took a 4 year detour through teaching High School, where the students so fiercely needed me. Freelance Scientist is a real niche, as in Freelance Poet. The scientist is orders of magnitude more likely to reap financial reward for her work. -- Prof. Jonathan Vos Post http:\/\/www.facebook.com\/jvpost None: Re: \"Crime doesn't pay -- enough!\"; Re: Poetry DOES NOT pay! 2009-07-01T19:25:40Z Dr. Landis emailed me to clarify: Actually, I think that the number I'd heard was more like 50 thousand dollars. It varies significantly between minor publication and major publications, of course, and the first dozen are worth a lot more than any following ones. Here's a back of the envelope calculation. For a newly-minted PhD, I'm guessing that the dividing line between a community-college instructor gig at maybe$40K per year and an assistant professorship at a research institution at maybe $60 K per year is something like five publications in respected journals. If that difference in salary holds for, say, a ten year period (after ten years that assistant prof had better produce some more...), then (ignoring npv calculations), those five publications were worth$40K each.\n\nAssistant professor at $60K per year to tenured professor at, say, 100K per year might be another ten publications. Assume that the salary difference is effective for twenty years, and that comes to$80K per publication.\n\nOnce the professor has tenure, they don't need to publish, so additional publications beyond that have a marginal value of zero. Not really quite true, of course-- professors continue to move up the ladder to full professor, endowed chair, etc., and can also move to a higher-paying institution. But at this point it's probably more about the quality of the work (i.e., getting famous) than the mere existence of papers).\n\nI may be way off in my guesses about what professorships pay these days-- probably not orders of magnitude wrong, though.","date":"2022-09-27 23:49:18","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\": 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\": 0.23693494498729706, \"perplexity\": 2155.1920647967354}, \"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-2022-40\/segments\/1664030335059.31\/warc\/CC-MAIN-20220927225413-20220928015413-00033.warc.gz\"}"} | null | null |
Death to Traitors is the second studio album by the American grunge band Paw. It was released in 1995 through A&M Records. While the album received favorable reviews from the press, sales quickly fizzled due to a lack of promotional support from the band's label. Paw was dropped by A&M in 1996, before their contract was fulfilled.
Singles from the album include "Hope I Die Tonight," "Seasoned Glove," "Max the Silent," and the five-track promotional EP "Traitors and Covers."
Track listing
"No Such Luck" – 4:25
"Seasoned Glove" – 3:58
"Hope I Die Tonight" – 4:48
"Swollen" – 3:00
"Last One" (G. Fitch, P. Fitch) – 3:49
"Death to Traitors" – 4:45
"Built Low" – 5:52
"Glue Mouth Kid" – 3:39
"Texas" – 3:29
"Max the Silent" – 3:52
"Sweet Sally Brown" (G. Fitch, P. Fitch, Mark Hennessy, John Licardello) – 5:50
"Badger" – 4:28
"Peach" (G. Fitch, P. Fitch) – 2:28
"Sunflower" – 4:02
UK version
15."Cowpoke" - 4:22
Vinyl Version
15. "I Know Where You Sleep" - 4:35
All songs were written by Mark Hennessy, Grant Fitch, and Peter Fitch, except where noted.
Personnel
Mark Hennessy - Vocals
Paul Boblett - Bass
Grant Fitch - Guitars, Lap Steel, Vocals, Additional Bass
Peter Fitch - Drums, Percussion
John Licardello - Additional Bass
References
1995 albums
Paw (band) albums
A&M Records albums | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,111 |
\section*{Methods}
\noindent \textbf{Optical circuit.} The
transformation of the optical circuit consists of BS and HWP
operations. The BS operation describes the following transformation
of the annihilation operators of the modes $\hat{a}_{k}$ and
$\hat{b}_{k}$ (note that we use annihilation operators to denote the
corresponding modes):
$\hat{a}_{k}=\sqrt{R}\hat{c}_{k}+\sqrt{T}\hat{e}_{k}$ and
$\hat{b}_{k}=\sqrt{R}\hat{d}_{k}+\sqrt{T}\hat{f}_{k}$, for $k=x,y$.
$R$ ($T$) is the amplitude reflection (transmission) coefficient of
the BS. For the modes $\hat{f}_{x}$ and $\hat{f}_{y}$, the
transformation of HWP at $-22.5^{\circ}$ is defined by:
$\hat{f}_{x}=(\hat{f}_{x'}-\hat{f}_{y'})/\sqrt{2}$ and
$\hat{f}_{y}=(\hat{f}_{x'}+\hat{f}_{y'})/\sqrt{2}$. The optical circuit is able to prevent false signals rising from
two-pair emission. This is an important feature of the scheme\cite{SliwaBanaszek} since
the creation probabilities for two pairs are much larger than for
three pairs. Furthermore, contributions from the higher order terms
of SPDC can be limited by controlling the corresponding creation
probabilities\cite{SliwaBanaszek}. It is also worth noting that for
a given three-pair photon state, the probability of creating a
heralded entangled state, i.e., $T^{4}R^{2}/2$, is controllable by
changing the transmission coefficients of the BS, which can be up to
$\sim0.011$\cite{SliwaBanaszek}.
\noindent \textbf{Photon source.} The required photon pairs are generated by type-II SPDC from a
pulsed laser in a $\beta$-Barium-Borate (BBO) crystal. Here, we use
a pulsed high-intensity ultraviolet (UV) laser with a central
wavelength of $390$ nm, a pulse duration of $180$ fs and repetition
rate of $76$ MHz. For an average power of $880$ mW UV light and
after improvements in collection efficiency and stability of the
photon sources, we observe $\sim80\times10^{3}$ photon pairs per
second with a visibility of $\mathcal{V}=(91\pm 3) \%$
measured in the diagonal ($+/-$) basis.
(The visibility is defined by
$\mathcal{V}=(N_{d}-N_{ud})/(N_{d}+N_{ud})$, were $N_{d}$ ($N_{ud}$)
denotes the number of two-fold desired (undesired) coincidence
counts. Then there exists a direct connection between visibility and
fidelity of a measured state $\hat{\rho}$:
$F=\text{Tr}(\hat{\rho}\left|\Psi^{-}\right\rangle\!\!\left\langle
\Psi^{-}\right|)=\frac{1}{4}(1+\mathcal{V}_{x}+\mathcal{V}_{y}+\mathcal{V}_{z})$,
where $\mathcal{V}_{k}$ for $k=x,y,z$ denotes the visibility of
photon pair in the diagonal, circular, and linear bases,
respectively. Here $\left|\Psi^{-}\right\rangle$ is the singlet Bell
state.) Then the probability of
creating three photon pairs is about $5.7\times10^{-5}$ per pulse,
which is $\sim33$ times larger than that of the next leading order
term. The estimation of the three-pair creation probability per
pulse is based on the experimental pair generation rate and the
theoretical $n$-pair creation probability\cite{kok00-61}
$p_{n}=(n+1)\tanh^{2n}r/\cosh^{4}r$, where $r$ is a real-valued
coupling coefficient. From the two-fold coincidence measurement
result, the experimental pair generation rate is
$p'=(80\times10^{3})/(0.15^{2}\times76\times10^{6})\approx4.7\%$. We
assume that $p_{1}=p'$, $r$ can directly be derived from $p_{1}$.
Thus the estimated creation probability $p_{3}$ and $p_{4}$ are
obtained.
\noindent \textbf{Experimental imperfections.} With single photon resolving detectors and $100 \%$ detection
efficiency, one can see that the three-pair state can provide a maximally entangled photon pair in the output modes
deterministically with a 100\% probability, if and only if the remaining photons give rise to a fourfold
coincidence among the four trigger modes. With the widely used standard SPCM, one cannot discriminate pure single
photons from multi-photons which in reality leads to a significant problem of under counting photons. Accordingly,
the trigger detectors can herald a successful event even though more than two photons from either mode
$(\hat{a}_x,\hat{a}_y)$ or $(\hat{b}_x,\hat{b}_y)$ or both have been transmitted to the trigger channels.
Furthermore, experimentally we were only able to obtain an average detection efficiency of about $\eta=15\%$
resulting from limited collection and detector efficiencies. Here the mean detection efficiency is averaged over
the coupling efficiency of eight fibre couplers and the quantum efficiency of the detectors. In addition to the
imperfect detections, there are two other factors that affect the performance of our source: the non-ideal quality
of the initially prepared pairs and the higher-order terms of down-converted photons. For perfectly created pairs,
destructive two-photon interference effects\cite{Shih-Alley,Hong-Ou-Mandel,LamasLinares} will extinguish the
contribution of two-pair emission to the trigger signal. With an experimental visibility of $(91\pm 3) \%$
imperfectly created states may still give rise to a contribution of two-pair events that leads to the detection of
the auxiliary triggers. In addition, four-pair emission can again contribute to both the triggers and the output.
Although the experimentally estimated creation probability for a four-pair emission is only $\sim1.7\times 10^{-6}$
per pulse and is much smaller than the probability for a three-pair photon state $\sim5.7\times 10^{-5}$ per pulse,
four-pair contribution can lead to an error of the theoretical estimation of the expected preparation efficiency of
about $4.5 \%$. The four-pair contribution is evaluated in the same way as the three-pair state, where the limited
detection efficiency of the trigger detectors is considered in the calculation (see Supplementary Information). In
Fig.~3, the fluctuations of our experimental data mainly result from the intrinsic statistics of detector counts,
and the stability of optical alignment.
\noindent \textbf{Experimental fidelity $F$.} Every expectation value for a correlation function is
obtained by making a local measurement along a specific polarization
basis and computing the probability over all the possible events.
For instance, to get the expectation value of $RR$ correlation
$\text{Tr}(\hat{\rho}\left|RR\right\rangle\!\!\left\langle
RR\right|)$, we perform measurements along the circular basis and
then get the result by the number of coincidence counts of $RR$ over
the sum of all coincidence counts of $RR$, $RL$, $LR$ and $LL$. All
the other correlation settings are performed in the same way. The
fidelity $F$ can then directly be evaluated.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,089 |
Suprnova commented on: Arsenal tactic help?
Suprnova added a topic: Arsenal tactic help?
Hey guys no skin is working since the 15.2 update, does anyone know how to make it work?
Anyway to get the kit back and move the bans box? | {
"redpajama_set_name": "RedPajamaC4"
} | 304 |
{"url":"https:\/\/math.stackexchange.com\/questions\/1942500\/decomposing-field-extentions-into-algebraic-and-purely-trancendental-extentions","text":"# Decomposing field extentions into algebraic and purely trancendental extentions\n\nGiven a field extension $K\/k$ we can take the algebraic (integral) closure of $F \/ k$ in $K$ and then $F\/K$ only has transcendental elements. However in this MO post the top answer talks about the 'reverse': where $K$ is an algebraic extension of some intermediate field that is purely transcendental over $k$. In the context of the post $k$ is the prime subfield, but I don't believe that should matter and the notion should apply an extension of any field.\n\nThe problem is I do not see how this is constructed. We cannot simply take the collection of all elements transcendental over $k$ as the field it generates will contain algebraic elements assuming $K$ has them to begin with. Actually as I was writting this I realized we can use AC to construct a chain $k < k(\\gamma_0) < k(\\gamma_0, \\gamma_1) ...$ of purely trancendental extentions which must terminate and then $F = \\lim k_{\\alpha}$ is our desired field. Still I would like to know what the differences\/advantages between these two constructions are and the situations in which they are each useful.\n\nIt seems to me that you are looking for the notions of transcendence degree and\/or transcendence basis.\n\nIf $K\/k$ is an extension of fields, then we say that a subset $B\\subset K$ is a transcendence basis of $K\/k$, if\n\n\u2022 $B$ is algebraically independent over $k$, i.e. the elements of $B$ do not satisfy any non-trivial multivariable polynomial equation with coefficients from $k$, and\n\u2022 The extension $K\/k(B)$ is algebraic. In other words, every element of $K$ is algebraic over $k(B)$.\n\nIt turns out that all transcendence bases of a given extension $K\/k$ have the same cardinality. But, there is nothing canonical about the intermediate field $k(B)$. In particular the degrees $[K:k(B)]$ can vary wildly when we vary the basis $B$.\n\nFor a specific example consider the function field $K=k(x,y)$ of an elliptic curve $$y^2=x^3+ax+b$$ defined over a field $k$ such that $6\\cdot1_k\\neq0_k$. Clearly $K$ is algebraic over either $k(x)$ or $k(y)$, so either $x$ or $y$ (they are both transcendental over $k$ by definition) will form a transcendence basis of $K\/k$. So does any monomial $x^m$ or $y^n$. The transcendence degree $\\operatorname{tr.deg}(K\/k)=1$. But $[K:k(x)]=2$, $[K:k(y)]=3$, $[K:k(x^n)]=2n$ et cetera.\n\nIn this example case a nice geometric result is that the field $K\/k$ is not purely transcendental. IOW there cannot be an element $z\\in K$, transcendental over $k$, such that $K=k(z)$. This is possible only for function fields of curves of genus zero. As the elliptic curves have genus one, such an element $z$ cannot exist.\n\n\u2022 Is there any significance of a choice of basis where $[K:k(B)]$ is minimal? \u2013\u00a0basket Sep 26 '16 at 18:57\n\u2022 May be? That is a good question, @basket, but I don't know the answer. \u2013\u00a0Jyrki Lahtonen Sep 26 '16 at 18:58","date":"2019-05-26 09:03:54","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8536689281463623, \"perplexity\": 123.63384212877018}, \"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-2019-22\/segments\/1558232259015.92\/warc\/CC-MAIN-20190526085156-20190526111156-00502.warc.gz\"}"} | null | null |
Electrical Fixtures – WaterSaver Faucet Co.
WaterSaver electrical boxes are UL-listed under standard UL514A, are machined for both standard and ground fault receptacles, and are furnished complete with grounding screws, a 3/4″ IPS mounting shank and locknut.
Cast aluminum boxes are polished to remove the rough cast surface. Boxes have an attractive brushed finished. To order, add suffix "SA" to model number.
Cast aluminum boxes are polished and buffed to a chrome-like surface finish. To order, add suffix "PB" to model number.
and satin aluminum pedestal boxes, face plates are furnished with a satin (brushed) finish. On polished aluminum pedestal boxes, face plates are furnished with a polished (bright) finish. Receptacles are black.
Select the desired electrical box from below.
Select the desired receptacle from below. Read across and down to find the appropriate fixture number. Note that, unless specified otherwise, receptacles are furnished in black.
Wrinkle black epoxy powder-coated finish (standard).
Satin (brushed) aluminum finish (suffix "SA").
Polished (bright) aluminum finish (suffix "PB").
Note: Satin and polished electrical boxes can be furnished with clear epoxy coating for enhanced chemical resistance. Add suffix "CLR" when ordering. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,584 |
Calejão ou Caleijão est un village du Cap-Vert sur l'île de São Nicolau.
Géographie
Il est situé à de Ribeira Brava.
Histoire
Le premier lycée séminaire d'Afrique de l'Ouest y fut construit par les portugais en 1869. Il a fermé ses portes en 1968.
Personnalités
Baltasar Lopes da Silva, écrivain, y est né et y a fait ses études.
Notes et références
Ville au Cap-Vert
São Nicolau (Cap-Vert) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,889 |
Q: Dual Booting issue I dual booted my new computer build with ubuntu 12.04 and windows 8. Now my ubuntu boots up but my windows will not. It sites and invalid EFI path error. Can some help? I've tried to use a boot repair disk with no luck. It's my first build and I'm super new to ubuntu and don't know my way around much at all.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,353 |
Гали́на Дми́триевна Кара́мышева () — советский учёный, геоморфолог. Специалист в области изучения россыпей благородных металлов в целях их прогнозирования, поисков и оценки.
Биография
Происходила из дворянского рода Карамышевых; отец, Дмитрий Дмитриевич — участник Русско-японской войны, кавалер ордена Св. Георгия.
После окончания геологического факультета МГУ в 1936 г. поступила в институт НИГРИ-золото — ЦНИГРИ, в котором проработала более 30 лет. В годы Великой отечественной войны находилась в эвакуации в посёлке Макарак.
Большой вклад Г. Д. Карамышева внесла в изучение геоморфологии и россыпной золотоносности Урала, Кузнецкого Алатау, Салаирского кряжа, Бурятии, Северного Кавказа, юга Западной Сибири и Ленского района. Для этих территорий ею составлены мелко- и крупномасштабные геоморфологические карты с данными по золотоносности россыпей, которые способствовали повышению уровня геологоразведочных работ. Участница первой и второй Ленских экспедиций, Г. Д. Карамышева проводила детальные исследования геоморфологии и стратиграфии четвертичных отложений Кропоткинского золотоносного района в бассейне реки Вачи, которые позволили обосновать выявление уникальных россыпей золота. Прогнозные рекомендации Г. Д. Карамышевой, в том числе по месторождению Сухой Лог, не утратили своей актуальности до настоящего времени и успешно реализуются золотодобытчиками.
В 1941 году, незадолго до начала Великой Отечественной войны вышла замуж. Галина Дмитриевна воспитала четверых детей. Сейчас у неё пять внуков и пять правнуков. Проживала в Мытищах.
Умерла 13 июня 2013 года в Мытищах.
Основные научные труды
Г. Д. Карамышева. К вопросу о строении и генезисе рыхлых отложений центральной части Патомского нагорья (1960)
А. И. Григорьева, Г. Д. Карамышева, С. В. Яблокова. Особенности геологии и условия формирования погребенных прибрежных россыпей на примере одного из регионов юго-восточной части Западно-Сибирской низменности (1961)
Примечания
Ссылки
100 лет геоморфологу-россыпнику Г. Д. Карамышевой // Федеральное агентство по недропользованию (Роснедра), 10.02.2008.
Геологи России
Геологи СССР
Стодесятилетние долгожительницы
Долгожительницы России
Геоморфологи СССР | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,035 |
tarea:
* separar las rutas de el archivo de servidor
* crear ruta de home, esta ruta va a tener un titulo, un header, un body con informacion acerca del proyecto
* investigar MongoDb (base de datos no relacional, basada en archivos)
* crear conexion a base de datos Mongo en archivo independiente
* vincular servidor con base de datos
* empezar a investigar.... CSS(sass o less)
---------- luego de base de datos ------------
* crear una ruta para registrarse
* crear una ruta para hacer login
* en el momento de estar logueado, la pagina del home deberia mostrar la persona que esta logueada
* crear ruta para crar "posts" se entiende como post a modo de blog donde tendras diferentes parrafor por fecha de entrada
-----------------------------------------------
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,472 |
"The best place I know to keep up with Regional Mexican stuff."
— Chuck Eddy, author of Rock and Roll Always Forgets: A Quarter Century of Music Criticism and Terminated for Reasons of Taste: Other Ways to Hear Essential and Inessential Music
"You should read NorteñoBlog regularly, as I do."
— Phil Freeman, founder of Burning Ambulance and the Burning Ambulance Podcast, jazz columnist at Stereogum, and author of New York Is Now!: The New Wave of Free Jazz and Running the Voodoo Down: The Electric Music of Miles Davis
— Ben Ratliff, New York Times critic and author of Every Song Ever: Twenty Ways to Listen In an Age of Musical Plenty and The Jazz Ear: Conversations Over Music
"I absolutely love it."
— Jennifer Bull, Sr. Marketing Manager at Sony Music Latin
"Devoted fanboy taste."
— Milo Miles, critic for NPR, Rolling Stone, The Village Voice, The New York Times, others
A curious gabacho, NorteñoBlog founder Josh Langhoff has written about Mexican and Caribbean music for Pitchfork, the Village Voice, PopMatters, The Singles Jukebox, Maura, and the 2014 EMP Pop Conference. He lives near Chicago, whose residents enjoy three two Regional Mexican FM stations — as many as they have for country or Top 40.
Originally from Yonkers, Manuel Martinez-Luna grew up in a very diverse neighborhood listening to mostly hip hop, pop, and rock. He started listening to corridos around 2006, and has become a huge fan of the genre and is excited to see what new groups pop up and where music is headed. His day job is working for Sony under the Orchard division creating compilation albums, mainly focusing on the Regional Mexican catalog. When not working in the office, he spends time with his family or works on video projects like the one he's working on right now, explaining Russia's role in Syria. Check out his NorteñoBlog articles here.
Edel lopez
I want to buy your website either that or ask me what i can do to improve it and get you a bigger fanbase.
Sean G
more please! Wish I could hear your paper at the conference.
Thanks, Sean! As you've probably guessed, much of my time that would've otherwise been spent here has gone into the conference paper, or into other freelance work. But your support means quite a bit. In the meantime, I recommend the new Intocable, which is better than their last one (sounds a lot like Maná, actually), and you might dig this Banda MS concert preview I wrote for City Pages: http://citypages.com/music/10-times-banda-ms-the-worlds-biggest-brass-band-didnt-totally-blow/507447221
¡Feliz 2016! (y ¡Lo Mejor de 2015!) | NorteñoBlog | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,253 |
Q: Amazon IVS - Reliable way to match streams to local records I'm currently using IVS to handle a live streaming solution.
As it stands, I allocate a IVS Channel to every "streaming user". I then create a record on my local database for every stream that is broadcasted.
I then begin a broadcast session on a specific channel. This would then send me a webhook notification that a stream/recording has begun on Channel X.
What I'm having trouble with, is having a foolproof way of matching the webhook payload to the locally created Stream in my database.
I could have a number of streams for that channel in my local database, and I would have liked to pass a parameter when initiating a broadcast that would be received in the webhook payload in order to match them 1:1.
Alternatively, I would have liked to call an API such as "Create Stream for channel", and then get the ID back in the response, and allocate it to my local record... however there is no "Create Stream" endpoint.
Any ideas on how I can manage to achieve a reliable match?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,137 |
Q: Keras: what is the difference between model.evaluate_generator and model.predict_generator I used keras data augmentation to perform image classification (ten-class images). The last training epoch gives the results as follows:
Epoch 50/50
4544/4545 [============================>.] - ETA: 0s - loss: 0.7628 - acc: 0.7359 loss: 0.762710434054
New learning rate: 0.00214407973866
4545/4545 [==============================] - 115s - loss: 0.7627 - acc: 0.7360 - val_loss: 0.5563 - val_acc: 0.8124
Then evaluate the trained model by:
scores = model.evaluate_generator(test_generator,1514) #1514 testing images
print("Accuracy = ", scores[1])
It leads to the following results:
('Accuracy = ', 0.80713342132152621)
The accuracy is not exactly the same as that obtained in the last training epoch. I don't understand the difference, even though it is marginal.
Further, model.predict_generator gives totally different result that is an array shown as follows:
array([[ 4.98306963e-06, 1.83774697e-04, 5.49453034e-05, ...,
9.25193787e-01, 7.74697517e-04, 5.79946618e-06],
[ 2.06657965e-02, 2.35974863e-01, 2.66802781e-05, ...,
2.16283044e-03, 8.42395966e-05, 2.46680051e-04],
[ 1.40222355e-05, 1.22740224e-03, 7.52218883e-04, ...,
3.76749843e-01, 3.85622412e-01, 6.47417846e-06],
...,
[ 9.94064331e-01, 1.30184961e-03, 1.08694976e-05, ...,
1.25828717e-06, 2.29093766e-05, 9.01326363e-04],
[ 7.10375488e-01, 2.01397449e-01, 3.10241080e-06, ...,
3.66877168e-10, 1.66322934e-05, 1.93767438e-08],
[ 8.13350256e-04, 2.67575349e-04, 6.79878794e-05, ...,
8.63052785e-01, 9.70983761e-04, 8.54507030e-04]], dtype=float32)
I don't know what the matrix represents, and what is the difference between model.evaluate_generator and model.predict_generator.
It is noted that the resultant array has a shape of 1514*10. The array should be the prediction probabilities at each class for the set of testing images. If so how to compute a confusion matrix based on the result?
A: predict_generator takes your test data and gives you the output.
evaluate_generator uses both your test input and output. It first predicts output using training input and then evaluates performance by comparing it against your test output. So it gives out a measure of performance, i.e. accuracy in your case.
A: I had similar issue and I solved setting shuffle = False in the generator.
My guess is that if the train batch isn't a multiply of elements, the last incomplete batch is not considered and having shuffle the excluded elements are random and that change sigthly the result.
A: To plot a confusion matrix you need to import the said from sklearn
from sklearn.metrics import confusion_matrix
import itertools
import matplotlib.pyplot as plt
To plot the confusion matrix, the test_labels, classes (number of output of the last fully connected layer, the output layer). It seems you have got this part figured out. Next you need both the test_labels and predictions to be of the same dimension for which you can use np.reshape and np.transpose to get the desired results. For syntax and definition you can follow the below mentioned links
https://docs.scipy.org/doc/numpy/reference/generated/numpy.reshape.html
https://docs.scipy.org/doc/numpy/reference/generated/numpy.transpose.html
Now to plot the confusion matrix you can use the code from sklearns documentation
https://scikit-learn.org/stable/auto_examples/model_selection/plot_confusion_matrix.html
Thank you. Hoping that would help you.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 563 |
\section{Introduction}
The evolution of the first stars in the universe is one of the frontiers of modern cosmology.
Primordial stars synthesized the first heavy elements in the universe, and their energetic
feedback influenced the formation of later generations of stars and the first galaxies \citep{
wet08a,wet08b,greif2010}. Early numerical models predicted that Pop III stars formed with
masses of 100-1000 {\ensuremath{\mathrm{M}_{\odot}}}{} \citep{bromm2009,abel2002}. New studies have found that
$\sim$ 20\% of Pop III stars form in binaries or multiples \citep{turk2009,stacy2010} so the
first stars could be less massive than originally thought. However, even today observations
support the existence of stars with initial masses over 150 {\ensuremath{\mathrm{M}_{\odot}}}\ \citep{r136}. Stellar
evolution models predict that Pop III stars with initial masses of 140 - 260 {\ensuremath{\mathrm{M}_{\odot}}}{} develop
oxygen cores of $\gtrsim$ 50
{\ensuremath{\mathrm{M}_{\odot}}}{} after central carbon burning \citep{heger2002}. At this point the core reaches sufficiently
high temperatures ($\sim$ $10^9$ K) and low densities ($\sim$ $10^6$ g/cc) that the creation
of electron-positron pairs is favored. Radiation pressure support then quickly decreases, triggering
a rapid contraction of the core. During contraction, core temperatures and densities sharply rise
and oxygen and silicon begin to burn explosively. The resulting thermonuclear explosion, known
as a pair-instability supernova (PSN), reverses the contraction and completely unbinds the star,
leaving no compact remnant and forming up to 50 {\ensuremath{\mathrm{M}_{\odot}}}\ of {\ensuremath{^{56}\mathrm{Ni}}}{}. One possible PSN candidate,
SN 2007bi, has recently found by \citep{2007bi}.
Most current theoretical models of PSNe are based on one-dimensional calculations \citep{
heger2002}. However, in the initial stages of a supernova spherical symmetry is
broken by fluid instabilities generated by burning, which cannot be captured in 1D.
Two-dimensional simulations of Pop III PSNe have recently been done by \citet{candace2010-2}
in which only mild dynamical instabilities were found to form, but they proceeded from 1D KEPLER
models in which explosive burning had already occurred and thus exclude instabilities driven by
burning. Such instabilities, if they form, may alter the energetics and nucleosynthesis of the SN
by vigorously mixing its fuel and must be included in simulations to understand the true evolution
of PSNe. We have performed 2D simulations of Pop III PSNe that follow the initial contraction of the
core until most of the energy due to explosive burning has been released, in contrast to
\citet{candace2010-2}, who only follow the post-nucleosynthesis hydrodynamics. Our goal is to study any
fluid instabilities that arise and how mixing alters nucleosynthesis and the energetics of the explosion.
\section{Numerical Methods}
\lSect{method}
We evolve zero-metallicity stars in \texttt{KEPLER}{} \citep{kepler}, a one-dimensional Lagrangian
stellar evolution code. In \texttt{KEPLER}{} we solve evolution equations for mass, momentum, and
energy and include physics relevant to stellar evolution such as nuclear burning and artificial
mixing. When the star comes to the end of central oxygen burning, we map its profile onto a
2D Cartesian grid in \texttt{CASTRO}{}. The procedure for mapping and seeding initial perturbations
in these profiles is discussed in detail in \citet{chen2011-2}. We evolve the star in \texttt{CASTRO}{}
through the end of explosive burning.
\texttt{CASTRO}{} \citep{ann2010,zhang2011} is a massively parallel, multidimensional Eulerian
adaptive mesh refinement (AMR) radiation-hydrodynamics code for astrophysical applications.
Its time integration of the hydrodynamics equations is based on a higher-order, unsplit Godunov
scheme. Block-structured AMR with subcycling in time enables the use of high spatial resolution
where it is most needed. We use the Helmholtz equation of state (EOS) \citep{timmes2000} with
density, temperature, and species mass fractions as inputs. The gravitational field is
calculated using a monopole approximation constructed from a radial average of the 2D density
field on the grid.
\begin{figure}
\begin{center}
\includegraphics[width=6 cm]{Chen_K_Fig1.eps}
\end{center}
\caption{Fluid instabilities at early stages of the explosion. We show oxygen mass fraction 100
sec after the reversal of core collapse. Dynamical instabilities appear at the lower boundary of
the O shell because of oxygen burning and at the upper boundary of the shell because of He
burning. The red lines indicate the location of shock. \lFig{PSN-1}}
\end{figure}
\section{2D Simulations}
\lSect{results}
In \Fig{PSN-1} we show the formation of dynamical instabilities at the base of the oxygen burning
shell during the contraction of the core \citep{chen2011-3}. They are relatively mild and do not
penetrate the central {\ensuremath{^{56}\mathrm{Ni}}}\ region, so no {\ensuremath{^{56}\mathrm{Ni}}}\ is mixed into the upper layers of the star at this stage.
After explosive burning reverses the contraction of the core, fluid instabilities driven by helium
burning also appear in the outer layers of the oxygen shell. Minor mixing caused by these
instabilities begins about 100 sec after reversal of the collapse.
As we show in \Fig{PSN-2}, when the shock propagates into the hydrogen envelope the
formation of a strong reverse shock creates additional Rayleigh-Taylor instabilities (RTI). Their
amplitudes are sufficient to mix oxygen with the surrounding shells: H, He, and Si. Some mixing
also occurs at the outer edge of the {\ensuremath{^{56}\mathrm{Ni}}}{} core. Our results demonstrate that dynamical instabilities
form at several stages of the explosion and that they are mainly driven by RTI at the interfaces of
contact discontinuities in density or species abundance. Mixing is important to the observational
signatures of Pop III PSNe because it can cause absorption lines of heavy elements to appear in
spectra sooner after shock breakout than when mixing is absent. The instabilities can also lead
to the formation of clumps in the ejecta that can strongly affect its luminosity at later times.
\begin{figure}
\begin{center}
\includegraphics[width=6 cm]{Chen_K_Fig2.eps}
\end{center}
\caption{Fluid instabilities prior to shock breakout. Here, we show the density when the shock is
about to break out from the stellar surface. The fluid instabilities are driven by the reverse shock
and lead to significant mixing. \lFig{PSN-2}}
\end{figure}
\section{Conclusions}
\lSect{con}
In contrast to earlier multidimensional simulations, we find that mixing can occur at several stages
in Pop III PSNe prior to shock breakout when core contraction and explosive nuclear burning is
followed in 2D. Mixing appears in PSN spectra by introducing absorption lines of heavy elements
at early times and by changing its luminosity. Our 2D simulations are the first in a numerical campaign
to investigate the evolution of PSNe from their earliest stages as pre-supernova progenitors. We are
currently preparing to post-process our simulations to compute light curves and spectra in order to
provide useful predictions for the James Webb Space Telescope, which may soon detect these
primordial explosions.
\acknowledgements
The authors would like to thank Daniel Whalen for reviewing the earlier manuscript and providing
many insightful comments. We thank members of the CCSE at LBNL for their assistance with CASTRO.
We also thank John Bell, Adam Burrows, Volker Bromm, and Stan Woosley for many useful discussions.
This project has been supported by the DOE SciDAC program under grants DOE-FC02-01ER41176, DOE-FC02-06ER41438, and DE-FC02-09ER41618. Finally, we acknowledge support from the AAS and NSF in the form of an International Travel Grant and from the 2011 Cefalu Meeting SOC/LOC in the form of the Best Abstract Prize, which enabled KC to attend this conference.
\bibliographystyle{asp2010}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,157 |
{"url":"https:\/\/bird.bcamath.org\/handle\/20.500.11824\/235?show=full","text":"dc.contributor.author Biccari, U. dc.date.accessioned 2016-06-13T13:33:49Z dc.date.available 2016-06-13T13:33:49Z dc.date.issued 2014-12-31 dc.identifier.issn 0363-0129 dc.identifier.uri http:\/\/hdl.handle.net\/20.500.11824\/235 dc.description.abstract We analyse the interior controllability problem for a non-local Schr\\\"odinger equation involving the fractional Laplace operator $(-\\Delta)^s$, $s\\in(0,1)$, on a bounded $C^{1,1}$ domain $\\Omega\\subset\\mathbb{R}^n$. The controllability from a neighbourhood of the boundary of the domain is obtained for exponents $s$ in the interval $[1\/2,1)$, while for $s<1\/2$ the equation is shown to be not controllable. As a consequence of that, we obtain the controllability for a non-local wave equation involving the higher order fractional Laplace operator $(-\\Delta)^{2s}=(-\\Delta)^s(-\\Delta)^s$, $s\\in[1\/2,1)$. The results follow from a new Pohozaev-type identity for the fractional Laplacian recently proved by X. Ros-Oton and J. Serra and from an explicit computation of the spectrum of the operator in the one dimensional case. dc.format application\/pdf dc.language.iso eng en_US dc.publisher dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 Espa\u00f1a en_US dc.rights.uri http:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/es\/ en_US dc.title Internal control for non-local Schrodinger and wave equations involving the fractional Laplace operator dc.type info:eu-repo\/semantics\/article en_US dc.rights.accessRights info:eu-repo\/semantics\/openAccess en_US dc.type.hasVersion info:eu-repo\/semantics\/acceptedVersion en_US\n\ufeff\n\n### This item appears in the following Collection(s)\n\nExcept where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 Espa\u00f1a","date":"2022-08-14 07:14:59","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\": 0.712319016456604, \"perplexity\": 2553.51839236571}, \"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-2022-33\/segments\/1659882571996.63\/warc\/CC-MAIN-20220814052950-20220814082950-00759.warc.gz\"}"} | null | null |
Varsan () may refer to:
Varsan, Golestan (ورسن)
Varsan, Markazi (ورسان - Varsān) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,758 |
I hope that you will find this site to be a useful resource. Here, you will find the schedule for all quizzes, tests, projects, etc. You will find a link to yearbook information, as well. Finally, you will find a contact form so you can reach me by email. Let me know if I can ever be of any help. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,601 |
Nasr Ibrahim Alean was murdered by Israel Thursday
By Nathan Stuckey | November 7, 2011 | International Solidarity Movement, Gaza
Nasr Ibrahim Alean was a 23 year old farmer from Beit Lahia. He was murdered on November 3, 2011. He was picking strawberries in his field when he was shot in the leg by the Israeli army. He called his friend Muhammad Abu Helmeyyah, 22 years old, to help him. Muhammed tried to take him to safety, but they were both killed by a missile from an Apache helicopter. Nasr was not the first farmer in Gaza murdered by the IDF, and he will probably not be the last.
When Nasr was killed he was working in a field 500 meters from the border. Outside of the Israeli imposed "buffer zone" which is in reality a 300 meter zone of death that surrounds Gaza. This isn't uncommon; the high risk area around the border extends as far as one or two kilometers according to the UN. Nasr knew that he risked his life when he went to work, but he had no choice. He needed money to get married, and working on the land was the only work that he could find. Gaza is under siege, and unemployment is rife. Not only are many imports banned, but most exports are banned as well.
We sat in the mourning tent talking with Nasr's family, hearing their stories, seeing their pictures of Nasser. A cousin showed us a video of them picking up the body. There was a giant hole in his head. They tell us that Israel did not allow the Red Cross to pick up the body immediately; it sat for several hours, until finally the ambulances came. Too late, Nasr was already dead. Muhammad was already dead. They told us worse stories, of bodies that no one was allowed to pick up, bodies that the IDF left to rot, everyone forbidden to claim them.
Nasr's brother was getting married in two days. One of his aunts heard the story as she had her eyebrows done in preparation for the wedding. She says of him, "He wasn't in the resistance, he was just trying to work," and continues "They don't even want us to work. If it wasn't for the United Nations, I don't know what we would do." His uncle tells us about how he used to work in Israel. He worked as a driver. One day a woman got in with her young child. She abused him in front of the child. He asks, "How can people who abuse you in front of their children teach their children about peace?" He doesn't seem to have much hope. They talk of going to human rights organizations to complain about Nasr's murder, but they do not really believe that they will help. Nasr hadn't given up though, he went to pick strawberries on Thursday because he wanted to live, because he wanted to get married and have children and a house of his own.
November 6, 2011 Posted by aletho | Subjugation - Torture | Comments Off on Nasr Ibrahim Alean was murdered by Israel Thursday
Occupy Building 7
March from Liberty Plaza to WTC 7 at noon each day.
Occupy the park in front of WTC 7 until nightfall.
General Assemblies will be held at 2pm each day to discuss the direction and continuation of the Occupy Building 7 occupation after 11/20.
To all those who continue to fight for the truth about 9/11 to be revealed:
It is time for us to occupy.
The Occupy Wall Street movement is a much needed response to decades of growing inequality, financial deregulation, and zero accountability for the crimes that brought about our current economic crisis. Millions throughout the nation and across globe who feel they have no voice in our political system have come to embrace "Occupy" as an expression of their anger, frustration and hope.
Ten years later, it is time for us to give voice to our own growing frustration by aligning firmly with the Occupy movement and making 9/11 one of the key issues the Occupy movement stands for.
On Saturday November 19 and Sunday November 20, we will march from Liberty Plaza to Building 7 and occupy the park in front of Building 7 until nightfall. We hope this will mark the beginning of a sustained Occupy Building 7 movement that will grow and finally bring meaningful attention to the obvious demolition of World Trade Center Building 7 and the dire need for a new 9/11 investigation. At 2pm each day we will hold a General Assembly to discuss the direction and continuation of the Occupy Building 7 occupation after November 20.
Go to OccupyBuilding7.org to learn more and to start following #OccupyBuilding7 on Twitter. On the website you will find fliers that you can print and hand out at Liberty Plaza as well as web banners that you can post on your website to help spread the word.
We are attempting to get Occupy Building 7 on the official Occupy Wall Street calendar, and we anticipate being joined by hundreds of Occupy Wall Street protesters. Most of the protesters at Liberty Plaza are keenly aware of 9/11. A lot of them already knew about it; others have been educated over the last several weeks thanks to the 9/11 activists who have given their time and energy to be there. Let us hope that by the time November 19 rolls around, there will be hundreds, if not thousands of Occupy activists eager to help us make Occupy Building 7 a part of the broader Occupy movement.
If you can make it to New York on November 19, please meet us at Liberty Plaza at noon, and let's make history.
OccupyBuilding7.org
November 6, 2011 Posted by aletho | False Flag Terrorism, Solidarity and Activism | 2 Comments
Was 'Arab Spring' Coined by a Guardian of Zion?
By Maidhc Ó Cathail | The Passionate Attachment | November 6, 2011
Writing in Foreign Policy, Joshua Keating asks, "Who first used the term Arab Spring?" As Keating points out:
It's not well remembered at this point, but the term "Arab Spring" was originally used, primarily by U.S. conservative commentators, to refer to a short-lived flowering of Middle Eastern democracy movements in 2005.
The reference to "conservative commentators" is supported by a link to an article entitled "The Arab Spring of 2005″ by none other than Charles Krauthammer — a recipient in 2002 of the prestigious Guardian of Zion award, "an annual award given since 1997 to Jews who have been supportive of the State of Israel." In that 2005 piece, the Guardian of Zion opined:
The democracy project is, of course, just beginning. We do not yet know whether the Middle East today is Europe 1989 or Europe 1848. 1989 saw the swift collapse of the Soviet empire. 1848 saw a flowering of liberal revolutions throughout Europe that, within a short time, were all suppressed.
Nonetheless, 1848 did presage the coming of the liberal idea throughout Europe. (By 1871, it had been restored to France, for example.) It marked a turning point from which there was no going back. The Arab Spring of 2005 will be noted by history as a similar turning point for the Arab world.
That year was indeed a "turning point" for Arab democracy, as AP reported on March 12:
The American democracy promotion campaign dates back to the 1980s, when Poland's Solidarity movement was one beneficiary. But for Egypt, 2005 was the watershed year, when Campbell's NDI opened a Cairo office and through Egyptian groups trained 5,500 election observers to monitor a referendum giving Mubarak another six-year term, his fifth.
From Egypt's polling places that September, NDI-paid teams reported election violations via innovative cell-phone texting in code, deciphered by headquarters computers.
The report was immediate: Widespread manipulation of the polls, and a turnout of a mere 23 percent, shattering the myth of 90-percent landslides for the "popular" Mubarak.
"It had the effect of showing the emperor had no clothes," Campbell said. "Egyptians could make a difference. They could change things."
The government reacted, restricting NDI and IRI operations in Cairo, ordering host hotels to cancel training sessions, putting security men in institute offices.
But Mubarak couldn't be too tough on the Americans, donors of $1.5 billion in annual military and economic aid. And the democracy promoters carried on, often sending Egyptian proteges abroad for sessions.
November 6, 2011 Posted by aletho | Deception, Wars for Israel | 2 Comments
The new land grab in Africa
By Agazit Abate | PAMBAZUKA NEWS | 03 November 2011
The recent phenomenon of land grab, as outlined in the extensive research of the Oakland Institute, has resulted in the sale of enormous portions of land throughout Africa. In 2009 alone, nearly 60 million hectares of land were purchased or leased throughout the continent for the production and export of food, cut flowers and agrofuel crops.
Land grab was in part spurred by the food and financial crisis of 2008 when international bodies, corporations, investment funds, wealthy individuals, and governments began to re-focus their attention on agriculture and food as a profitable commodity. As outlined in the reports, the consequences of land grab include increased food insecurity, environmental degradation, community repression and displacement, and increased reliance on aid.
MEET THE INVESTORS
While media coverage has focused on the role of countries like India and China in land deals, the Oakland Institute's investigation reveals the role of Western firms, wealthy US and European individuals, and investment funds with ties to major banks such as Goldman Sachs and JP Morgan. Investors include alternative investment firms like the London-based Emergent that works to attract speculators, and various universities like Harvard, Spelman and Vanderbilt.
Several Texas-based interests are associated with a major 600,000 hectares South Sudan deal which involves Kinyeti Development LLC, an Austin, Texas-based 'global business development partnership and holding company' managed by Howard Eugene Douglas, a former United States Ambassador at Large and Coordinator for Refugee Affairs. A key player in the largest land deal in Tanzania is Iowa agribusiness entrepreneur and Republican Party stalwart, Bruce Rastetter.
US companies are often below the radar, using subsidiaries registered in other countries, like Petrotech-ffn Agro Mali which is a subsidiary of Petrotech-ffn USA. Many European countries are also involved, often with support provided by their governments and embassies in African countries. For instance, Swedish and German firms have interests in the production of biofuels in Tanzanian. Addax Bioenergy from Switzerland and Quifel International Holdings (QIH) from Portugal are major investors in Sierra Leone. Sierra Leone Agriculture (SLA) is actually a subsidiary of the UK based Crad-1 (CAPARO Renewable Agriculture Developments Ltd.), associated with the Tony Blair African Governance Initiative.
As the media has reported, Indian firms are involved in land grab with relation to Ethiopia in particular. Food insecure nations like those of the gulf region are also participating in these land deals for the purpose of food production for their home countries.
ECONOMIC DEVELOPMENT?
A major argument by governments and investors is that these investments will lead to economic development for the home countries. The Oakland Institute reports reveal, however, that the land transactions are either for free (in the case of Mali) or very cheap (in the cases of Ethiopia and Sierra Leone). These transactions are largely unregulated with no stipulation or guarantees that they will help the local populations or create infrastructure. While land grab actors focus their rhetoric on foreign direct investment, there is no evidence to show that foreign direct investment will come into the countries in any substantial amount.
Most of these deals come with huge tax breaks and other investment incentives which is a great deal for the investors, but means less money coming into the country that could possibly go to infrastructure or social services. For instance, Sierra Leone allows 100 percent foreign ownership; there are no restrictions on foreign exchange, full repatriation of profits, dividends and royalties and no limits on expatriate employees.
Another justification for the land deals includes the idea that they will increase employment in the areas involved. Again, the lack of stipulation and on-the-ground research reveals that this is overstated at best and completely untrue at worst. The Emvest Matuba investment project summary and staff at Emergent and Emvest promise job creation with majority employment from the local community. A recent head count provided by Emergent reveals that currently only 17 permanent positions are in security (36 staff). In Mali, the area targeted by recent large land deals which could easily sustain 112,537 farm families (over half a million people, 686,478) is instead in the hands of 22 investors and will create at best a few thousand jobs.
To make matters worse, the limited employment created by these land deals is low wage, seasonal and primarily benefits the investors with cheap labour to compliment cheap land.
COMMUNITY DISPLACEMENT
While those involved firmly contend that communities are not being forcibly removed from their lands and those that are asked to move are being compensated, the opposite proves true. Ethiopian government officials, for instance, have stated that the lands being leased are unused or abandoned. Meanwhile, there is a villagisation process that has relocated 700,000 indigenous people who lived in a land that was targeted for investment.
In 2010 in Samana Dugu, Mali, bulldozers came in to clear the land and when the community protested, they were met by police forces who beat and arrested them. In Tanzania, the land investments of AgriSol Energy are focused on Katumba and Mishamo refugee settlements. The MOU between AgriSol Energy and the local government stipulates that these settlements, which house 162,000 refugees that fled Burundi in 1972 and have been farming the land for 40 years, have to be closed. In June 2009, Amnesty International reported refugees being pressured to leave camps. Some of them lost their homes to a fire set by individuals acting under the instructions of the Tanzanian authorities to get them to vacate the camp. Refugee leaders who have attempted to organize affected refugees have been arrested and detained.
Investment sites in various African countries visited by the Oakland Institute revealed a loss of local farmland where the lands held a variety of different uses and social/ecological value. Some of the lands that are claimed to be unused are those where the communities practice shifting cultivation (where plots of land are left idle after periods of cultivation in order to re-vegetate), pastoralism, and those considered communally used areas.
Forests and national reserves that are home to vital animal, fish and plant species and are a place where communities have found alternative sustenance in times of food scarcity have been burned and cleared out. These lands are being destroyed without an understanding of their significance and without assessments to determine how this will affect local communities.
Many of the communities interviewed stated that there was no prior notification of the land investments. They only realized what was happening when the bulldozers arrived in their communities.
While most of the countries and regions targeted suffer from food insecurity, these land deals focus on producing export commodities, including food, biofuels and cut flowers for foreign consumption. In Mali, half of the investors with large land holdings in the Office du Niger intend to grow plants used to produce agrofuels such as sugarcane, jatropha or other oleaginous crops. In Mozambique, most of the investments concern timber industry and agrofuels rather than food crops. Food crops represented only 32,000 hectares of the 433,000 hectares that were approved for agricultural investments between 2007 and 2009.
In Ethiopia, much of large scale land deals have focused on food production for a foreign market. Because land grab throughout Ethiopia has led to the clearing of communal lands and plots used for shifting cultivation as well as forests, the communities' primary source of sustenance along with their buffer systems are threatened. Additionally, commercial farming on these lands will affect fish habitats and other wildlife hunted in times of food scarcity and the loss and degradation of grazing lands will further increase food insecurity.
Water is of a particular concern as runoff from commercial farms will lead to the contamination and reduction of water supplies. Dam construction in investment site areas like the proposed Alwero River dam spark additional concern of the consequential uncertainty of access to water for local and downstream communities. No clause has been found in the lease agreements that discusses water use and there is no evidence that water use from commercial agriculture is managed, monitored or regulated.
In Ethiopia, not only is there no clause in any of the lease agreements that require investors to improve local food security conditions or make food available for the local populations, the federal government has actually provided incentives for those investors that grow cash crops for a foreign market. Abera Deressa, federal minister for agriculture stated that, 'If we get money we can buy food anywhere. Then we can solve the food problem.' A major concern of the communities interviewed is that they believe the government is intentionally creating a situation where communities must rely solely on the government for their food, in an attempt to marginalize and disempower them.
THE ENVIRONMENTAL FACTOR
Environmental degradation is a major concern in these land deals that have limited transparency and regulations in terms of their environmental impact. Forests have many uses for the local communities including as food, medicine, fuel wood and building materials. Forests also retain cultural and historical significance. Expected outcomes of clearing the lands and forests include loss and degradation of wetlands, decrease in wildlife populations and habitat, proliferation of invasive species and loss of biodiversity.
These environmental concerns are exemplified in Ethiopia's Gambela National Park where the Ethiopian Wildlife Conservation Authority (EWCA) estimates that 438,000 hectares of land have been leased in the vicinity of the park. While the park boundaries are not set, lands that the local population considers a part of the park have been cleared by large-scale investors, including Karuturi and Saudi Star. Wetlands have been altered and forests have been cleared. According to recent surveys, the Gambela National Park is home to 69 mammal species, valuable wetland habitat, hundreds of bird species and 92 fish species.
To compound matters, the practice of industrial agriculture will lead to increased toxicity, disruption of nature's system of pest control, creation of new weeds or virus strains, loss of biodiversity, and the spread of genetically-engineered genes to indigenous plants. […]
Instead of supporting small farmers, these land deals support industrial agriculture while displacing and disempowering the very people that have the ability to shift their communities from insecure to sustainable populations and environments. Land grab puts these countries on a path that will surely lead to increased food insecurity, environmental degradation, increased reliance on aid and the marginalisation of farming and pastoralist communities. With regards to food, the issue at stake is not only one of increased food insecurity, but an attack on food sovereignty or peoples' right to produce their own food.
Land grab is irrational at best and violent at worst. It's a violent act to take away peoples' right to food, access to their ancestral land, their social and historical ties, and their overall right for human dignity. It's a violent act to strip them of their future and the land of its fertility.
While land deals are going on behind closed doors, communities are resisting. The 2008 food uprisings, the revolt in Madagascar against land grab, and the recent protests in Guinea, all show communities who are standing up for their right for food sovereignty. In fact, in all of the countries visited, the land deals were met by community organising. Knowing what we know, resisting these land deals on all fronts and working towards investments in sustainable agriculture and empowering local populations points to the only rational and humane way forward.
November 6, 2011 Posted by aletho | Economics, Environmentalism | 2 Comments
Violent and dangerous Israeli piracy
Update on the Freedom Waves to Gaza Boats November 6, 2011
The take over of the Tahrir and the Saoirse was violent and dangerous. Despite very clear protests from the occupants of the two boats that they did not want to be taken to Israel, they were forcibly removed from the boats in a violent manner. The whole take over took about 3 hours. Many of those on the Canadian boat were beaten.
It began with Israeli forces hosing down the boats with high pressure hoses and pointing guns at the passengers through the windows. Fintan Lane, on the Saoirse, was hosed down the stairs of the boat. Windows where smashed and the bridge of that boat nearly caught fire. The boats were corralled to such an extent that the two boats, the Saoirse and the Tahrir collided with each and were damaged, with most of the damage happening to the MV Saoirse. The boats nearly sunk, the method used in the take over was very dangerous.
The Israeli forces initially wanted to leave the boats at sea but the abductees demanded that they not be left to float unmanned at sea, for they would have been lost and possibly sunk. David Heap, a Canadian delegate, was tasered and beaten. All belongings of the passengers were taken off them and crew and they still do not know if and what they will get back. 6 prisoners were released-both of the Greek Captains, 2 of the journalists and 2 delegates. The passengers remain in Givon detention center and many, including Kit Kittredge of the U.S., have not been able to make phone calls.
Those remaining are being asked to sign deportation papers which state that they came into Israel illegally and that they will not attempt another effort to break the Gaza blockade. If they sign they will not be allowed into Palestine, through Israel, for 10 years. Obviously their goal was to go to Gaza not Israel, and a signature could validate Israel's right to blockade Gaza, so they refuse to sign. This will mean longer detention. Their continued detention is designed to force them to agree to abandon their legal rights and has nothing to do with the security of Israeli civilians – just like the blockade of Gaza's civilians is clearly punitive and has nothing to do with the security of Israeli civilians
Our State Department has not been an advocate for its citizens. They would rather join Israel in stating that we are terrorists. Obama on Thursday said the passengers on these boats are defying Israeli and American law. He must have been confused. It's the other way around. State Department spokeswoman Victoria Nuland said the U.S. was renewing its call to Americans "not to involve themselves in this activity," and warned of possible consequences.
WE NEED ALL OF YOU TO GET ON THE PHONE TODAY AND CALL:
U.S. Emergency Consular Services 202-647-4000
and the U.S. Embassy in Tel Aviv 011-972-3-519-7575
Tell them you want them to insist Israel free the prisoners immediately and end its siege of Gaza.
Just a few phone calls can make a difference.
November 6, 2011 Posted by aletho | Solidarity and Activism, Subjugation - Torture, War Crimes | Comments Off on Violent and dangerous Israeli piracy
I write to you from cell 9 of the Apartheid State of Israel
Canadian Boat to Gaza
Dear sisters and brothers, friends and loved ones,
I write to you from cell 9, block 59 Givon Prison near Ramla in Occupied Palestine. Although I was tasered during the assault on the Tahrir, and bruised during forcible removal dockside (I am limping slightly as a result) I am basically ok. We, Ehab, Michael, Karen from Tahrir, as well as Karen, Kit (US) and Jihan who we saw briefly this morning. We are most concerned about our Tahrir shipmate, Palestinian Majd Kayyal from Haifa, last seen by us at Ashdod being photographed and put in a police car.*
Although Michael and I (among others) were transported in handcuffs and leg shackles, let me stress that we are neither criminals nor illegal immigrants but rather political prisoners of the apartheid state of Israel. Four from the Tahrir are imprisoned with 12 Irish comrades from the Saoirse, who have more experience with such issues. The four of us, Ehab and I (Cdn), Michael (Aus) and Hassan (UK) have joined with the Irish in their political prisoners' committee in order to press our collective demands:
association in the block – i.e. open cells
adequate writing and reading material
free communication with outside world – i.e. regular phone calls
information about shipmate women held at same prison
We add one Tahrir-specific demand: that Israeli state recognize the professional status of Democracy Now journalist Jihan Hafiz in accordance with her credentials from the US government. All political incarceration is unjust but let me stress that in duration and conditions, our situation pales in comparison to the plight of thousands of Palestinian political prisoners and to the open air prison of Gaza.
If you have energy to devote to solidarity actions in the coming days, please concentrate on them. We must get Tahrir back and hope Freedom Waves continue.
Free Majd Kayyal! Free all political prisoners! Free Gaza! Free Palestine!
Anishnabe-debuewin, restons humaine, stay human, in love and struggle,
* Majd Kayyal was released, but it appears David the other political prisoners weren't told where he was taken.
November 6, 2011 Posted by aletho | Solidarity and Activism, Subjugation - Torture, War Crimes | 1 Comment
Egypt and the IMF
Topple Their Debts
By ERIC WALBERG | CounterPunch | November 4, 2011
The Popular Campaign to Drop Egypt's Debts was launched at the Journalists' Union 31 October, with a colourful panel of speakers, including Al-Ahram Centre for Political & Strategic Studies Editor-in-Chief Ahmed Al-Naggar, Independent Trade Union head Kamal Abbas, legendary anti-corruption crusader Khaled Ali, and the head of the Tunisia twin campaign Dr Fathi Chamkhi.
Moderator Wael Gamal, a financial journalist, described how he and a core of revolutionaries after 25 January started the campaign with a facebook page DropEgyptsDebt. The IMF offer of a multi-billion dollar loan in June was like a red flag in front of a bull for Gamal, and their campaign really got underway after that, culminating in the formal launch this week, just as election fever is rising.
"Just servicing Egypt's debt costs close to $3 billion a year, more than all the food subsidies that the IMF harps about, more than our health expenditures," Gamal said angrily. "We are burdened with a $35 billion debt to foreign banks, mostly borrowed under the Hosni Mubarak regime, none of it to help the people."
Ali explained the basis of the campaign, which does not call for wholesale cancellation of the debt, but for a line-by-line review of the loan terms and useage to determine: whether the loan was made with the consent of the people of Egypt, whether it serves the interests of the people, and to what extent it was wasted through corruption. He explained that the foreign lending institutions knew full well that Mubarak was a dictator conducting phoney elections and thus not reflecting the will of the people when they showered him with money, and they should face the consequences — not the Egyptian people.
These are the internationally accepted conditions behind the legitimate practice of repudiating "odious debt", which were used by the US (though mutedly) in 2003 to tear up Iraq's debt, and by Ecuador in 2009. "Ecuador had an uprising much like our revolution and after the next election the president formed an audit committee and managed to cancel two-thirds of the $13 billion debt," noted Gamal, leaving the conferencees to ponder what a truly revolutionary government in Egypt could do for the health sector and for employment.
Al-Naggar told how the loans propped up the economy as it was being gutted under an IMF-supervised privatisation programme from 1990 on, allowing foreign companies and Mubarak cronies to pocket hundreds of millions of dollars and spirit them abroad. Meanwhile, what investment that trickled down from the loans went to financing prestige infrastructure projects like the Cairo airport expansion, which was riddled with corruption and serves only the Egyptian elite. Virtually all the loans from this period should be considered liable for writing off.
No government officials deigned — or dared — to come to the conference. On the contrary, Egypt's Finance Minister Hazem Al-Biblawi told Al-Sharouk that it defames Egypt in the world's eyes, saying, "like the proverb 'It looks like a blessing on the outside, but is hell on the inside'."
Both Gamal and Al-Naggar criticised Biblawi for distorting their intent, which is not to portray Egypt as bankrupt, like Greece, but to shift the burden of the bad loans to the guilty parties — the lenders, and thereby to help the revolution. "It is the counter-revolution that is discrediting Egypt. And they are the old regime that got the loans and misused them, and are now trying to discredit the revolution. The international community should willingly write off the odious loans if it wants the revolution to succeed," exhorted Al-Naggar.
The enthusiasm and sense of purpose at the conference was infectious. Indeed, this campaign is arguably the key to whether or not the revolution succeeds. But it requires a political backbone that only an elected government can hope to muster. The fawning of Al-Bablawi — this week he hosted another IMF mission — looks like the performance of someone from the Mubarak era, not someone delegated to protect the revolution. He welcomed the delegation and "the possibility of their offering aid to Egypt".
Al-Naggar pointed out that the purpose of the IMF is not to aid the Egyptian people, but to tie the government to international dictate. Rating agencies are part of this, downgrading Egypt's credit rating after the revolution. Why? Because Egypt is less democratic? Or because it will be harder to ply Egypt with more loans to benefit Western corporations, and to keep the Egyptian government in line with the Western political agenda. "Silence is golden," Al-Naggar advised Biblawi, meaning, "If you don't have something good to say, don't say anything."
Chamkhi brought Tunisian warmth to the meeting, though he further incensed listeners as he explained how the Western debt scheming is directly the result of 19th century colonialism. He told how France colonised Tunisia, stole the best agricultural land, and then how the quasi-independent government in 1956 had to take out French loans to buy back the land that the French had stolen, thereby indenturing Tunisia yet again, in a new neocolonial guise. The foreign debt really exploded with Zine Al-Abidine Ben Ali's kleptocracy, just as did Egypt's under Mubarak. Shamati eloquently expressed how "debts are not for our development, but to make us poor. To create a dictatorship of debts."
Tunisia's first democratic elections brought the Congress for the Republic, which supports the debt revision campaign, 30 seats. So far in Egypt, according to organiser Salmaa Hussein, Tagammu, the Nasserists and Karama support their efforts, along with presidential hopefuls Hamdeen Sabhi and Abdul Monem Abul Fotouh.
There is an international campaign dating from the 1990s, the 2000 Jubilee debt relief movement, and the Cairo conference heard a report from London about efforts on behalf of many third world countries — now including Egypt and Tunisia — by public-spirited Brits. The Arab Spring success stories now have a determined and politically savvy core of activists who know what the score is and will be pushing their respectively revolutionary governments to repudiate the debts from the corrupt regimes they overthrew at the cost of hundreds of lives. As the fiery Independent Trade Union head Abbas cried, adding an apt phrase to Egypt's revolutionary slogan: "Topple the regime, topple their debts!"
Eric Walberg writes for Al-Ahram Weekly. You can reach him at http://ericwalberg.com/
November 6, 2011 Posted by aletho | Corruption, Economics | Comments Off on Egypt and the IMF
Tom Friedman pushed Iraq war as 'radical liberal revolution'
By Philip Weiss on November 6, 2011
I sometimes forget what happened to our country. But Belén Fernández has a new book out on Tom Friedman called The Imperial Messenger, and she reminds us of Friedman's achievement, in an interview in the NY Times Examiner:
Friedman sells the Iraq war as "the most radical-liberal revolutionary war the U.S. has ever launched" despite making subsequent assessments such as "The neocon strategy may have been necessary to trigger reform in Iraq and the wider Arab world, but it will not be sufficient unless it is followed up by what I call a 'geo-green' strategy." As I point out in my book, it is difficult to determine how many true "geo-greens" would advocate for the tactical contamination of the earth's soil with depleted uranium munitions; why not introduce a doctrine of neoconservationism?
Fernández links to Tom Friedman cheerleading the Iraq war in 2003. Wow, I forgot about his stuff! Or thankfully never read it in the first place. The question arises, Did Tom Friedman make any difference with this kind of talk? And I say of course he did, he helped convince the liberal Establishment to go along with this foolish war. Friedman and Ken Pollack and Bill Keller and David Remnick– the pen is mightier than the sword.
[T]he Baathists and Arab dictators are opposing the U.S. in Iraq because — unlike many leftists — they understand exactly what this war is about. … They understand that this is the most radical-liberal revolutionary war the U.S. has ever launched — a war of choice to install some democracy in the heart of the Arab-Muslim world. […]
Many liberals oppose this war because they can't believe that someone as radically conservative as George W. Bush could be mounting such a radically liberal war.
November 6, 2011 Posted by aletho | Mainstream Media, Warmongering, Timeless or most popular | 3 Comments
Haaretz Lies About IAEA Inspections In Parchin
Moon of Alabama | November 6, 2011
Repeating the last piece of U.S. propaganda about a "nuclear Iran", Haaretz lies about the history of IAEA inspections in Iran:
Iran is pursuing its nuclear weapons program at the Parchin military base about 30 kilometers from Tehran, diplomatic sources in Vienna say.
According to recent leaks, Iran has carried out experiments in the final, critical stage for developing nuclear weapons – weaponization. This includes explosions and computer simulations of explosions. The Associated Press and other media outlets have reported that satellite photos of the site reveal a bus-sized container for conducting experiments. Parchin serves as a base for research and development of missile weaponry and explosive material.
As far back as eight years ago, U.S. intelligence sources received information indicating that the bunkers would also be suitable to develop nuclear weapons.
The Iranians rejected an IAEA request to visit Parchin, saying that IAEA rules permitted the organization's member states to deny such visits to military bases.
The last sentence is false and pure propaganda. Iran allowed two IAEA visit to Parchin in January 2005 and again in November 2005. The IAEA took environment samples there but found nothing that pointed to nuclear weapon research. Globalsecurity.org kept the records:
On 17 September 2004 IAEA head Muhammad El Baradei said his organization had found no sign of nuclear-related activity at the Parchin site in Iran, which several US officials had said might be tied to secret nuclear weapons research. "We are aware of this new site that has been referred to," he said. "We do not have any indication that this site has any nuclear-related activities. However, we will continue to investigate this and other sites, we'll continue to have a dialogue with Iran." El Baradei also dismissed allegations that he had supressed information about Parchin in his latest report on inspections in Iran.On 5 January 2005 Mohamed El Baradei said "we expect to visit Parchin within the next days or a few weeks." Iran allowed IAEA inspectors to visit the Parchin military site in January 2005 in the interests of transparency following the allegations of secret nuclear weapons related activity, but the visit was limited to only one of four areas identified as being of potential interest and to only five buildings in that area.
On 1 March 2005 Iran turned down a request by the IAEA to make a second visit to the Parchin military site, which has been linked in allegations to nuclear weapons testing. The IAEA was finally allowed access to the Parchin facility in November 2005. The IAEA reported in 2006 that they did not observe any unusual activities in the buildings visited at Parchin, and the results of the analysis of environmental samples did not indicate the presence of nuclear material at those locations. No further mention of Parchin as a suspected nuclear site had been made by the IAEA as of July 2008.
We can expect more such obvious lies in the coming weeks as the White House builds up its propaganda campaign for more sanctions on Iran.
November 6, 2011 Posted by aletho | Deception, Mainstream Media, Warmongering, Wars for Israel | 1 Comment
Syria Releases 553 Prisoners
Al-Manar | November 6, 2011
Syria releases 553 prisoners detained during the eight-month long unrest in the country, in line with the Arab League (AL) proposal to end the violence gripping the nation.
The Syrian state news agency (SANA) reported that "553 detainees who were involved in the current events with no blood on their hands were released."
SANA also said that another 119 prisoners had earlier been released.
Damascus accepted a peace plan proposed by the 22-member AL on Wednesday.
The plan calls for dialogue to take place between the government and the opposition and urges all parties to stop violence against Syrian citizens.
It also calls upon the government to both release those who were arrested during the unrest as well as to withdraw its military forces from residential areas. Syria has agreed to allow international journalists, human rights groups and AL representatives to observe the situation in the country.
On Friday, the Syrian interior ministry granted amnesty to those who would surrender their weapons from November 5 to 12, 2011. In addition, the military began pulling out its forces from urban areas.
Syria has been experiencing unrest since mid-March. Hundreds of Syrian security forces were killed.
Damascus blames the violence on outlaws, saboteurs and armed terrorist groups sponsored by foreign countries.
November 6, 2011 Posted by aletho | Civil Liberties | Comments Off on Syria Releases 553 Prisoners
Saving Syria from Pro-Israeli 'Humanitarians'
Middle East Today | November 6, 2011
November 6, 2011 Posted by aletho | Mainstream Media, Warmongering, Video, Wars for Israel | 1 Comment
U.S. State Department training Mubarak's would-be successors
Wasn't the Egyptian revolution supposed to be about getting rid of an American-backed dictator? Well, the Egyptians may have gotten rid of the dictator but the Americans appear to be there to stay. Writing in Foreign Policy , Josh Rogin confirms that the U.S. State Department is now schooling Mubarak's would-be successors in the ways of liberal democracy:
U.S. assistance to Egypt is helping political parties of all ideologies prepare for the upcoming elections — even Islamic parties that may have anti-Western agendas.
"We don't do party support. What we do is party training…. And we do it to whoever comes," William Taylor, the State Department's director of its new office for Middle East Transitions, said in a briefing with reporters today. "Sometimes, Islamist parties show up, sometimes they don't. But it has been provided on a nonpartisan basis, not to individual parties."
The programs, contracted through the National Democratic Institute for International Affairs (NDI) and the International Republican Institute (IRI), include helping political parties in Egypt conduct polling, provide constituent services, and prepare for election season. NDI's chairwoman is former Secretary of State Madeleine Albright. IRI's chairman is Sen. John McCain (R-AZ).
This, of course, is not the first time that newly-liberated peoples have received such generous support from the National Endowment for Democracy to help them make the expected democratic transition:
Taylor led a similar office in the 1990s that coordinated policy in Eastern Europe after the fall of the Soviet Union. He is pressing for $2 billion in new aid to Egypt, half in loans and half in debt forgiveness, but acknowledged that the U.S. fiscal situation is not nearly as good now as it was then.
"This is a tight time on budgets here, as we all know. And when [State Department spokeswoman] Toria [Nuland] and I worked together earlier, we had a lot more money to put in to the former Soviet Union, Eastern Europe," he said. "Now, that having been said, we recognize that there are other countries that are eager to provide support, and we support that."
Victoria Nuland is the wife of Robert Kagan, the influential pro-Israeli hawk who, as a February 12 New York Times report noted, "long before the revolution helped assemble a nonpartisan group of policy experts to press for democratic change in Egypt."
Plus ça change…
November 6, 2011 Posted by aletho | Corruption | 1 Comment
AAP greenlights dangerous drugs & aggressive surgeries for obese kids
For more videos go to the Aletho News – Video Category
or go to
Aletho News Archives – Video-Images
1988: Maldives completely under water in 30 years
Agence France Press, September 26, 1988
Subscribe to Aletho News
Visits Since December 2009
Aletho News Civil Liberties Corruption Deception Economics Environmentalism Ethnic Cleansing, Racism, Zionism Fake News False Flag Terrorism Full Spectrum Dominance Illegal Occupation Mainstream Media, Warmongering Malthusian Ideology, Phony Scarcity Militarism Progressive Hypocrite Russophobia Science and Pseudo-Science Solidarity and Activism Subjugation - Torture Supremacism, Social Darwinism Timeless or most popular Video War Crimes Wars for Israel
9/11 Afghanistan Africa AIPAC al-Qaeda Argentina Australia BBC Benjamin Netanyahu Brazil Canada CDC Central Intelligence Agency China CIA CNN Colombia Covid-19 COVID-19 Vaccine Da'esh Donald Trump Egypt European Union Facebook FBI France Gaza Germany Google Hamas Hebron Hezbollah Hillary Clinton Human rights India Iran Iraq ISIS Israel Israeli settlement Japan Jerusalem Joe Biden Korea Latin America Lebanon Libya Middle East National Security Agency NATO New York Times North Korea NSA Obama Pakistan Palestine Qatar Russia Sanctions against Iran Saudi Arabia Syria The Guardian Turkey Twitter UAE UK Ukraine United Nations United States USA Venezuela Washington Post West Bank Yemen Zionism
tracy on Plan to blockade Russian shipp…
brianharryaustralia on Let the Crow Eating Begin
Peter on Joe Biden Says "Our Work Is Fa…
Mr Reynard on Plan to blockade Russian shipp…
brianharryaustralia on Plan to blockade Russian shipp…
jbthring on Joe Biden Says "Our Work Is Fa…
brianharryaustralia on Joe Biden Says "Our Work Is Fa…
Kyle Smile WINNING (… on Timeline: The Crimean Ref…
brianharryaustralia on Amount of frozen Russian inves…
Let the Crow Eating Begin February 1, 2023
Lauterbach in 2020: "Schools drive the pandemic, the research is clear." Lauterbach in 2023: The belief that many infections occur in schools and day-care centres "did not prove to be correct" January 31, 2023
Acute Psychosis after COVID-19 Vaccination January 31, 2023
Joe Biden Says "Our Work Is Far from Over!" January 31, 2023
Croatia's President Doesn't Want Be West's 'Circus Poodle' in Ukraine Crisis January 31, 2023
Amount of frozen Russian investments revealed January 31, 2023
Plan to blockade Russian shipping in Baltic Sea breaks international law and could provoke war January 31, 2023
Pentagon's prediction of 'inevitable' conflict with China shows war is America's primary 'export' January 31, 2023
US, South Korea vow to expand war games amid tensions in Korean Peninsula January 31, 2023
MbS urged Baghdad to set up Iran-Saudi meeting: Iraqi FM January 31, 2023
Isfahan incident may have been foreign provocation January 31, 2023
American Academy of Pediatrics greenlights dangerous drugs & aggressive surgeries for obese kids January 31, 2023
The Censorship of Mercola — A Timeline January 31, 2023
The Real Disinformation Was The 'Russia Disinformation' Hoax January 31, 2023
UK government asked Facebook to remove a post that was restricted to be seen by "Friends Only" January 30, 2023
Russia names people behind US-backed Ukraine biological projects January 30, 2023
New Study: COVID Vaccines 'Profoundly Impair' Protective Immunity, 'Probably Enhance Disease Severity' January 30, 2023
How to Memory-Hole a PSYOP January 31, 2023
Down Cricket Road January 30, 2023
WATCH: The 6th Annual Fake News Awards January 29, 2023
Richie Allen
1 in 4 UK Adults Can't Get GP Appointment January 31, 2023
Uni Cancels Lent & Easter To Be More Inclusive January 30, 2023
Woke Players Boycott Hogwarts Game Over JK Rowling Trans Stance January 30, 2023
Sturgeon U-Turn On Trans Prisoners January 30, 2023
Consent Factory
If Americans Knew
Author Martin Sandler says Mossad may have assassinated JFK January 31, 2023
3 more Palestinians dead – one shot in the head for honking his horn January 30, 2023
Israeli government: stories you may have missed January 28, 2023
Not A Lot Of People Know That
5 charts explain gas & power price slump into 2023 January 30, 2023
Why Environmentalists May Make This Whale Species Extinct January 30, 2023
Forget Net Zero: Oil and gas investment needed for another 30 years, BP warns January 30, 2023
India to use emergency law to maximise coal power output January 30, 2023
1969 Cold Record Broken In China -53°C…Snow In The Mediterranean…Japan Hard Hit January 31, 2023
Observation: Removing Water Vapor (Greenhouse Gas) Leads To Warming…Adding It Leads To Cooling January 30, 2023
Reclaim The Net
Al-Manar
atheonews (at) gmail.com
This site is provided as a research and reference tool. Although we make every reasonable effort to ensure that the information and data provided at this site are useful, accurate, and current, we cannot guarantee that the information and data provided here will be error-free. By using this site, you assume all responsibility for and risk arising from your use of and reliance upon the contents of this site.
This site and the information available through it do not, and are not intended to constitute legal advice. Should you require legal advice, you should consult your own attorney.
Nothing within this site or linked to by this site constitutes investment advice or medical advice.
Materials accessible from or added to this site by third parties, such as comments posted, are strictly the responsibility of the third party who added such materials or made them accessible and we neither endorse nor undertake to control, monitor, edit or assume responsibility for any such third-party material.
The posting of stories, commentaries, reports, documents and links (embedded or otherwise) on this site does not in any way, shape or form, implied or otherwise, necessarily express or suggest endorsement or support of any of such posted material or parts therein.
The word "alleged" is deemed to occur before the word "fraud." Since the rule of law still applies. To peasants, at least.
This site contains copyrighted material the use of which has not always been specifically authorized by the copyright owner. We are making such material available in our efforts to advance understanding of environmental, political, human rights, economic, democracy, scientific, and social justice issues, etc. We believe this constitutes a 'fair use' of any such copyrighted material as provided for in section 107 of the US Copyright Law. In accordance with Title 17 U.S.C. Section 107, the material on this site is distributed without profit to those who have expressed a prior interest in receiving the included information for research and educational purposes. For more info go to: http://www.law.cornell.edu/uscode/17/107.shtml. If you wish to use copyrighted material from this site for purposes of your own that go beyond 'fair use', you must obtain permission from the copyright owner.
DMCA Contact
This is information for anyone that wishes to challenge our "fair use" of copyrighted material.
If you are a legal copyright holder or a designated agent for such and you believe that content residing on or accessible through our website infringes a copyright and falls outside the boundaries of "Fair Use", please send a notice of infringement by contacting atheonews@gmail.com.
We will respond and take necessary action immediately.
If notice is given of an alleged copyright violation we will act expeditiously to remove or disable access to the material(s) in question.
All 3rd party material posted on this website is copyright the respective owners / authors. Aletho News makes no claim of copyright on such material. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,094 |
I am young, well presented, athletic, educated, and offer warm and authentic company, As well being very Confident and dominate I'm here to fulfill your fantasies so don't be shy to say what satisfies you the most I aim to please your every need.
I am north Manchester based, but can travel subject to expenses and the notice period. Everyone I met so far has been amazing and lovely.
•ALWAYS AVAILABLE FEEL FREE TO CONTACT ME ANYTIME. IF I DO NOT ANSWER, PLEASE TEXT ME AND I WILL GET BACK TO YOU AS SOON AS POSSIBLE.
I CAN VISIT YOU AT YOUR HOTEL OR APARTMENT. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,870 |
We face many big challenges when it comes to global food production. Resources like fresh water availability, arable land and oil are limited, and we must produce enough food to feed over 7 billion people. Yet, one third of the food we produce globally is wasted. All the while, we're encountering more volatile, changing climates, which increase agricultural instability.
To overcome these obstacles, we must build new and innovative solutions to the way we grow, distribute and consume food. Over the past few months, I have had the opportunity to interview food startups who are working to solve these challenges on the Food Startups Podcast. Some are thriving already, while others are still in the early stages scraping and clawing to make it happen. Learn more about them below.
Two Berkley undergrads graduated in 2009 and almost went into corporate America, but they decided to take a leap of faith and launch an at-home mushroom growing kit that uses recycled coffee grounds. What started out as a fun idea has grown into a nationally distributed brand that aims to be the "Pixar of food". Its line of products, which now includs a self-cleaning fish tank, a garden in a can and a cereal brand with only 3 ingredients, are in Target, Home Depot and Whole Foods, among other retailers. Learn more about the startup's growth in my interview with co-founder Nikhil Arora.
This app alerts consumers when food is close to going bad so that they can swoop in and purchase it at a discount. It's a win-win for grocers and buyers and it prevents food from being wasted. No Food Wasted is live in Holland in 25 stores and is debating whether to enter the U.S. market in the near future.
U.S. startup FoodStar, which FTC covered in 2013, had a nearly identical business model and did not succeed. However, two years later, tech acceptance and global consciousness around food waste have both increased significantly.
Corigin is a B2B company that converts forest and farm waste into bio-sustainable products for farmers including broad spectrum organic pesticides, organic amendments to neutralize alkaline water and soil amendments that help growers cut water and fertilizer use and increase crop yields. Check out my radio interview with Mike Woelk from Corigin here.
This Maryland-based startup collects and delivers produce to consumers that may never makes it to grocery stores because it's considered "ugly". And for every bag of product it sells, it makes a matching donation to a local family in need. In the U.S., over 6 billion pounds of edible produce is wasted each year because it looks funny. Hungry Harvest is working to change our perception of what fruits and vegetables can and "should" look like. Learn more in my interview with co-founder Evan Lutz.
Former UN Secretary General Kofi Annan advocates that we should eat bugs to stop global warming. Eating bugs over beef saves water, space and methane gas emissions. Tiny Farms founder Daniel Imrie-Situnayake and his team are pioneering the insect-eating movement. They developed an open source grow-at-home bug farming kit. Based out of Oakland, Tiny Farms is on a mission to help the average joe grow edible insects.
Overfishing in our oceans has become a major problem. How big? A staple in international cuisine, the blue-fin tuna is heading towards extinction, to name one example. Headquartered in Maine, Acadia Harvest produces sustainable farm-raised fish using cutting edge aquaculture techniques in a "low to zero waste" facility. The startup currently farms California yellow tail and black sea bass.
Matt Aaron, a food entrepreneur since 2012, is sharing organic and exotic superfoods from South America. He is also producer and host of the Food Startups Podcast. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,426 |
## Contents
Epigraph
Author's Note
Perseverance
Showing Up
Grit and Gratitude
Competition
Get Caught Trying
Getting Started
A Day in the Life
Sisterhood
On Being a Woman in Politics
Motherhood, Wifehood, Daughterhood, Sisterhood
Turning Mourning into a Movement
Idealism and Realism
Change Makers
Sweating the Details
Making History
Frustration
Country Roads
Those Damn Emails
Trolls, Bots, Fake News, and Real Russians
Election Night
Why
Resilience
Love and Kindness
Onward Together
Acknowledgments
About the Author
Index
For the team who stood with me in 2016 and worked their hearts out for a better, stronger, fairer America. Being your candidate was one of the greatest honors of my life.
If you are tired, keep going.
If you are scared, keep going.
If you are hungry, keep going.
If you want to taste freedom, keep going.
—Harriet Tubman
## Author's Note
This is my story of what happened.
It's the story of what I saw, felt, and thought during two of the most intense years I've ever experienced.
It's the story of what led me to this crossroads of American history and how I kept going after a shocking defeat; how I reconnected with the things that matter most to me and began to look ahead with hope, instead of backward with regret.
It's also the story of what happened to our country, why we're so divided, and what we can do about it.
I don't have all the answers, and this isn't a comprehensive account of the 2016 race. That's not for me to write—I have too little distance and too great a stake in it. Instead, this is my story. I want to pull back the curtain on an experience that was exhilarating, joyful, humbling, infuriating, and just plain baffling.
Writing this wasn't easy. Every day that I was a candidate for President, I knew that millions of people were counting on me, and I couldn't bear the idea of letting them down. But I did. I couldn't get the job done, and I'll have to live with that for the rest of my life.
In this book, I write about moments from the campaign that I wish I could go back and do over. If the Russians could hack my subconscious, they'd find a long list. I also capture some moments I want to remember forever, like when my tiny granddaughter raced into the room while I was practicing my convention speech, and what it was like hours later to step onstage to deliver that speech as the first woman ever nominated by a major political party for President of the United States.
I write about people who inspired me, from a minister in South Carolina who talked with me about love and kindness, to residents who banded together in a town poisoned by lead, to tireless campaign volunteers giving everything they had for a better future. And I share my thoughts on big challenges I've grappled with for decades that have taken on new urgency, such as the roles that gender, race, and class play in our politics and the importance of empathy in our national life.
I've tried to learn from my own mistakes. There are plenty, as you'll see in this book, and they are mine and mine alone.
But that's not the end of the story. We can't understand what happened in 2016 without confronting the audacious information warfare waged from the Kremlin, the unprecedented intervention in our election by the director of the FBI, a political press that told voters that my emails were the most important story, and deep currents of anger and resentment flowing through our culture.
I know some people don't want to hear about these things, especially from me. But we have to get this right. The lessons we draw from 2016 could help determine whether we can heal our democracy and protect it in the future, and whether we as citizens can begin to bridge our divides. I want my grandchildren and all future generations to know what really happened. We have a responsibility to history—and to a concerned world—to set the record straight.
I also share with you the painful days that followed the election. A lot of people have asked me, "How did you even get out of bed?" Reading the news every morning was like ripping off a scab. Each new revelation and outrage made it worse. It has been maddening to watch our country's standing in the world plummet and to see Americans live in fear that their health care might be taken away so that the superrich can get a tax cut. There are times when all I want to do is scream into a pillow.
But slowly, on a personal level, it has gotten better—or at least less terrible. I did quite a bit of thinking and writing, some praying, some stewing, and, in time, a good deal of laughing. I went on a lot of long walks in the woods with my husband and our dogs, Tally and Maisie, who took all this much better than we did. I surrounded myself with friends and caught up on some of the shows that people have been telling me about for years, as well as a lot of HGTV. Best of all, I spent time with my wonderful grandchildren, making up for all the bedtime stories and songs in the bathtub I missed during my long months on the campaign trail. I believe this is what some call "self-care." It turns out, it's pretty great.
Now when people ask how I'm doing, I say that, as an American, I'm more worried than ever—but as a person, I'm doing okay.
This book is the story of that journey. Writing it has been cathartic. I got angry and sad all over again. At times, I've had to step away, lie down, close my eyes, and try to empty my mind. This book has been hard to write for another reason: I've lost count of the number of times that I've sat at my kitchen table working on these pages, been interrupted by a breaking news alert, hung my head and sighed, and then took out my red pen and started revising.
I've tried to make my peace with painful memories and recapture some of the fun that filled more days on the campaign than you might think. In the past, for reasons that I try to explain, I've often felt I had to be careful in public, like I was up on a wire without a net. Now I'm letting down my guard.
By the time I finished writing, I felt ready to face the future again. I hope that, by the final page, you'll be right there with me.
I will always be grateful to have been the Democratic Party's nominee and to have earned 65,844,610 votes from my fellow Americans. That number—more votes than any candidate for President has ever received, other than Barack Obama—is proof that the ugliness we faced in 2016 does not define our country.
I want to thank everyone who welcomed me into their homes, businesses, schools, and churches over those two long, crazy years; every little girl and boy who ran into my arms at full speed or high-fived me with all their might; and the long chain of brave, adventurous people, stretching back generations, whose love and strength made it possible for me to lead such a rewarding life in the country I love. Thanks to them, despite everything else, my heart is full.
I started this book with some words attributed to one of those pathbreakers, Harriet Tubman. Twenty years ago, I watched a group of children perform a play about her life at her former homestead in Auburn, New York. They were so excited about this courageous, determined woman who led slaves to freedom against all odds. Despite everything she faced, she never lost her faith in a simple but powerful motto: Keep going. That's what we have to do now, too.
In 2016, the U.S. government announced that Harriet Tubman will become the face of the $20 bill. If you need proof that America can still get it right, there it is.
It's supposed to be hard. If it wasn't hard, everyone would do it. The hard is what makes it great.
—A League of Their Own
## Perseverance
That which does not kill us makes us stronger.
—Friedrich Nietzsche (and Kelly Clarkson)
## Showing Up
Deep breath. Feel the air fill my lungs. This is the right thing to do. The country needs to see that our democracy still works, no matter how painful this is. Breathe out. Scream later.
I'm standing just inside the door at the top of the steps leading down to the inaugural platform, waiting for the announcer to call Bill and me to our seats. I'm imagining that I'm anywhere but here. Bali maybe? Bali would be good.
It's tradition for Bill and me, as a former President and First Lady, to attend the swearing-in of the new President. I had struggled for weeks with whether or not to go. John Lewis wasn't going. The civil rights hero and Congressman said that the President Elect was not legitimate because of the mounting evidence of Russian interference in the election. Other members of Congress were joining him in boycotting a President Elect they saw as divisive. A lot of my supporters and close friends urged me to stay home, too.
My friends understood how painful it would be to sit on the platform and watch Donald Trump sworn in as our next Commander in Chief. I had campaigned relentlessly to make sure that never happened. I was convinced he represented a clear and present danger to the country and the world. Now the worst had happened, and he was going to take the oath of office.
Plus, after the mean-spirited campaign Trump ran, there was a decent chance I'd get booed or be met with "Lock her up!" chants if I went.
Still, I felt a responsibility to be there. The peaceful transfer of power is one of our country's most important traditions. I had touted it around the world as Secretary of State, hoping that more countries would follow our example. If I really believed in it, I had to put my feelings aside and go.
Bill and I checked with the Bushes and the Carters to see what they were thinking. George W. and Jimmy had been among the first to call me after the election, which meant a lot to me. George actually called just minutes after I finished my concession speech, and graciously waited on the line while I hugged my team and supporters one last time. When we talked, he suggested we find time to get burgers together. I think that's Texan for "I feel your pain." Both he and Jimmy knew what it felt like to put yourself on the line in front of the whole country, and Jimmy knew the sting of rejection. He and I commiserated over that a bit. ("Jimmy, this is the worst." "Yes, Hillary, it is.") It was no secret that these former Presidents weren't fans of Donald Trump. He had been absolutely vicious to George's brother Jeb in particular. But were they going to the inauguration? Yes.
That gave me the push I needed. Bill and I would go.
That's how I ended up right inside the door of the Capitol on January 20, waiting to be announced. It had been such a long journey to get here. Now I just had to take a few more steps. I took Bill's arm and squeezed it, grateful to have him by my side. I took a deep breath and walked out the door with as big a smile as I could muster.
* * *
* * *
On the platform, we sat next to the Bushes. The four of us had caught up inside a few minutes earlier, trading updates about our daughters and grandchildren. We chatted like it was any other day. George and Laura gave us the latest news about the health of George's parents, former President George H. W. and Barbara, both of whom had been in the hospital recently but, happily, were now on the mend.
As we sat waiting for the President Elect to arrive, my mind wandered back to that incredible day twenty-four years earlier when Bill took the oath of office for the first time. It could not have been easy for George H. W. and Barbara to watch, but they had been extraordinarily gracious to us. The outgoing President left a letter for Bill in the Oval Office that is one of the most decent and patriotic things I've ever read. "Your success now is our country's success. I am rooting hard for you," he wrote. We did our best to show the same graciousness to George W. and Laura eight years later. At this moment, I was trying to summon a similar attitude about the incoming President. As I had said in my concession speech, he deserved an open mind and the chance to lead.
I also thought about Al Gore, who in 2001 sat stoically through George W.'s inauguration despite having won more votes. Five members of the Supreme Court decided that election. That must have been awful to bear. I realized I was inventing a new pastime: imagining the pain of past electoral losses. John Adams, our second Commander in Chief, suffered the indignity of being the first President ever voted out of office, losing to Thomas Jefferson in 1800, but he got a measure of revenge twenty-five years later when his son John Quincy was elected. In 1972, George McGovern lost forty-nine out of fifty states to Richard Nixon—Bill and I worked hard on McGovern's campaign and have indelible memories of that defeat. And let's not forget William Howard Taft, whom Teddy Roosevelt had groomed to succeed him. Four years later, in 1912, Teddy decided Taft wasn't doing a good enough job as President, so he ran as a third-party candidate, split the electorate, and Woodrow Wilson won. That had to hurt.
Then Bill touched my elbow, and I snapped back to the present.
The Obamas and the Bidens were in front of us. I imagined President Obama riding over in the presidential limo with a man who had risen to prominence partly by lying about Barack's birthplace and accusing him of not being an American. At some point in the day's proceedings, Michelle and I shared a rueful look. It said, "Can you believe this?" Eight years before, on the bitterly cold day when Barack was sworn in, our heads were full of plans and possibilities. Today was just about putting on a game face and getting through it.
The President Elect finally arrived. I had known Donald Trump for years, but never imagined he'd be standing on the steps of the Capitol taking the oath of office as President of the United States. He was a fixture of the New York scene when I was a Senator—like a lot of big-shot real estate guys in the city, only more flamboyant and self-promoting. In 2005, he invited us to his wedding to Melania in Palm Beach, Florida. We weren't friends, so I assumed he wanted as much star power as he could get. Bill happened to be speaking in the area that weekend, so we decided to go. Why not? I thought it would be a fun, gaudy, over-the-top spectacle, and I was right. I attended the ceremony, then met Bill for the reception at Trump's Mar-a-Lago estate. We had our photo taken with the bride and groom and left.
The next year, Trump joined other prominent New Yorkers in a video spoof prepared for the Legislative Correspondents Association dinner in Albany, which is the state version of the more famous White House Correspondents' Association dinner. The idea was that the wax figure of me at the Madame Tussauds museum in Times Square had been stolen, so I had to stand in and pretend to be a statue while various famous people walked by and said things to me. New York Mayor Mike Bloomberg said I was doing a great job as Senator—then joked about running for President in 2008 as a self-funder. When Trump appeared, he said, "You look really great. Unbelievable. I've never seen anything like it. The hair is magnificent. The face is beautiful. You know, I really think you'd make a great President. Nobody could come close." The camera pulled back to reveal he wasn't talking to me after all but to his own wax statue. It was funny at the time.
When Trump declared his candidacy for real in 2015, I thought it was another joke, like a lot of people did. By then, he'd remade himself from tabloid scoundrel into right-wing crank, with his long, offensive, quixotic obsession with President Obama's birth certificate. He'd flirted with politics for decades, but it was hard to take him seriously. He reminded me of one of those old men ranting on about how the country was going to hell in a handbasket unless people started listening to him.
It was impossible to ignore Trump—the media gave him free wall-to-wall coverage. I thought it was important to call him out for his bigotry, which I did early and often, starting when he called Mexican immigrants rapists and drug dealers the day he announced his candidacy. But it wasn't until I saw him dominate a debate with a crowded field of talented Republican candidates—not with brilliant ideas or powerful arguments but with ugly attacks that drew gasps—that I realized he might be for real.
Now here he was, with his hand on the Bible, promising to preserve, protect, and defend the Constitution of the United States. The joke, it turned out, was on us.
It started to rain, and people around us fumbled with the thin plastic ponchos we'd been given. Backstage, I had urged Bill to wear his trench coat. The day was unusually warm, and Bill didn't think he needed it. Now he was glad he'd worn it—a small wifely victory on a torturous day. As awkward as the ponchos looked, they could have looked worse. I had heard that the first batch of white ponchos that arrived could have looked something like KKK hoods from a certain angle, and a sharp-eyed inaugural organizer quickly replaced them.
The new President's speech was dark and dystopian. I heard it as a howl straight from the white nationalist gut. Its most memorable line was about "American carnage," a startling phrase more suited to a slasher film than an inaugural address. Trump painted a picture of a bitter, broken country I didn't recognize.
I knew we still had real challenges, ones I had talked about endlessly on the campaign trail: income inequality and the increasing concentration of corporate power, continuing threats from terrorism and climate change, the rising cost of health care, the need to create more and better jobs in the face of accelerating automation. The American middle class really had gotten screwed. The financial crash of 2008–2009 cost them jobs and ripped away their security. It seemed like no one was ever held accountable. Americans across a broad spectrum felt alienated, from culturally traditional white voters unsettled by the pace of social change, to black men and women who felt as if the country didn't value their lives, to Dreamers and patriotic Muslim citizens who were made to feel like intruders in their own land.
Trump was great at rubbing salt in their wounds. But he was wrong about so much. There had been seventy-five straight months of job growth under President Obama, and incomes for the bottom 80 percent were finally starting to go up. Twenty million more people had health insurance thanks to the Affordable Care Act, the greatest legislative achievement of the outgoing administration. Crime was still at historic lows. Our military remained by far the most powerful in the world. These are knowable, verifiable facts. Trump stood up there in front of the world and said the exact opposite—just as he had throughout the campaign. He didn't seem to see or value any of the energy and optimism I saw when I traveled around the country.
Listening to Trump, it almost felt like there was no such thing as truth anymore. It still feels that way.
My predecessor in the Senate, Daniel Patrick Moynihan, used to say, "Everyone is entitled to his own opinion, but not his own facts." We can disagree about policies and values, but claiming that 2 + 2 = 5 and having millions of Americans swallow it is very different. When the most powerful person in our country says, "Don't believe your eyes, don't believe the experts, don't believe the numbers, just believe me," that rips a big hole in a free democratic society like ours. As Yale history professor Timothy Snyder writes in his book On Tyranny: Twenty Lessons from the Twentieth Century, "To abandon facts is to abandon freedom. If nothing is true, then no one can criticize power, because there is no basis upon which to do so. If nothing is true, then all is spectacle."
Attempting to define reality is a core feature of authoritarianism. This is what the Soviets did when they erased political dissidents from historical photos. This is what happens in George Orwell's classic novel Nineteen Eighty-Four, when a torturer holds up four fingers and delivers electric shocks until his prisoner sees five fingers as ordered. The goal is to make you question logic and reason and to sow mistrust toward exactly the people we need to rely on: our leaders, the press, experts who seek to guide public policy based on evidence, ourselves. For Trump, as with so much he does, it's about simple dominance.
This trend didn't start with Trump. Al Gore wrote a book called The Assault on Reason in 2007. In 2005, Stephen Colbert coined the word "truthiness," inspired by how Fox News was turning politics into an evidence-free zone of seething resentments. And the Republican politicians whom Fox propelled to power had done their part, too. Republican strategist Karl Rove famously dismissed critics who lived in "the reality-based community"—words intended as a slight—saying they failed to grasp that "we're an empire now, and when we act, we create our own reality."
But Trump has taken the war on truth to a whole new level. If he stood up tomorrow and declared that the Earth is flat, his counselor Kellyanne Conway just might go on Fox News and defend it as an "alternative fact," and too many people would believe it. Just look at what happened several weeks into his presidency when Trump falsely accused President Obama of having wiretapped him, a claim that was widely and quickly debunked. A subsequent poll found that 74 percent of Republicans nevertheless thought it was at least somewhat likely to be true.
Trump's inaugural address was aimed squarely at millions of Americans who felt insecure and frustrated, even hopeless, in a changing economy and society. A lot of people were looking for someone to blame. Too many saw the world in zero-sum terms, believing that gains made by fellow Americans they viewed as "other"—people of color, immigrants, women, LGBT people, Muslims—were not earned and must be coming at someone's expense. The economic pain and dislocation were real, and so was the psychic pain. It made for a toxic, combustible mix.
I hadn't been blind to the power of this anger. During the campaign, Bill and I both went back and reread The True Believer, Eric Hoffer's 1951 exploration of the psychology behind fanaticism and mass movements, and I shared it with my senior staff. On the campaign trail, I offered ideas that I believed would address many of the underlying causes of discontent and help make life better for all Americans. But I couldn't—and wouldn't—compete to stoke people's rage and resentment. I think that's dangerous. It helps leaders who want to take advantage of that rage to hurt people rather than help them. Besides, it's just not how I'm wired.
Maybe that's why Trump was now delivering the inaugural address and I was sitting in the crowd.
What would I have said if it were me up there? It would have been daunting to find the words to match the moment. I probably would have gone through a million drafts. My poor speechwriters would have been sprinting only steps ahead of me carrying the thumb drive with the final draft to the teleprompter operator. But I would have relished the chance to move beyond the rancor of the campaign, reach out to all Americans regardless of who they voted for, and offer a vision of national reconciliation, shared opportunity, and inclusive prosperity. It would have been an extraordinary honor to be the first woman to take the oath. I won't pretend I hadn't dreamt of that moment—for me, for my mother, for my daughter, her daughter, everyone's daughters—and for our sons.
Instead, the world was listening to the new President's undimmed fury. I remembered the late Maya Angelou reading one of her poems at Bill's first inauguration. "Do not be wedded forever to fear, yoked eternally to brutishness," she urged us. What would she say if she could hear this speech?
Then it was done, and he was our President.
"That was some weird shit," George W. reportedly said with characteristic Texas bluntness. I couldn't have agreed more.
We headed up the stairs to leave the platform and go back inside the Capitol, shaking hands along the way. I saw a man off to the side who I thought was Reince Priebus, head of the Republican National Committee and incoming White House Chief of Staff. As I passed by, we shook hands and exchanged small talk. Later I realized it hadn't been Priebus at all. It was Jason Chaffetz, the then–Utah Congressman and wannabe Javert who made endless political hay out of my emails and the 2012 tragedy in Benghazi, Libya. Later, Chaffetz posted a picture of our handshake with the caption "So pleased she is not the President. I thanked her for her service and wished her luck. The investigation continues." What a class act! I came this close to tweeting back, "To be honest, thought you were Reince."
The rest of the day was a blur of greeting old friends and trying to avoid eye contact with those people who'd said terrible things about me during the campaign.
I ran into Supreme Court Justice Ruth Bader Ginsburg, walking slowly but with steely determination. If I had won, she might have enjoyed a nice retirement. Now I hoped she'd stay on the bench as long as humanly possible.
At lunch in the Capitol, I sat at our assigned table and commiserated with Congresswoman Nancy Pelosi, the Democratic leader in the House of Representatives, who I think is one of the shrewdest, most effective politicians in Washington. She deserves enormous credit for marshalling the votes for the 2010 Affordable Care Act under nearly impossible circumstances and for standing up for what's right whether she's in the majority or the minority. Republicans have demonized her for years because they know she gets things done.
Senator John McCain of Arizona came over and gave me a hug. He seemed nearly as distraught as I was.
The niece of a top official in the incoming Trump administration came over to introduce herself and whisper in my ear that she had voted for me but was keeping it a secret.
Congressman Ryan Zinke, soon to be Trump's Interior Secretary, brought his wife over to say hello. This was somewhat surprising, considering that in 2014 he had called me the "Antichrist." Maybe he'd forgotten, because he didn't come equipped with any garlic or wooden stakes, or whatever one uses to ward off the Antichrist. But I hadn't forgotten. "You know, Congressman," I said, "I'm not actually the Antichrist." He was taken aback and mumbled something about not having meant it. One thing I've learned over the years is how easy it is for some people to say horrible things about me when I'm not around, but how hard it is for them to look me in the eye and say it to my face.
I talked with Tiffany Trump about her plans to attend law school. I kidded with Republican Senator John Cornyn about how I performed much better than expected in his state of Texas. In the President's remarks at lunch, when he was away from the glare of his angry supporters, Trump thanked Bill and me for coming. Then, finally, we could leave.
Little did I know that the first controversy of the new administration had already begun over the size of the crowd at the inauguration. As is its practice, the U.S. National Park Service quickly published photos to mark the occasion. This time the new President disputed the photographic evidence showing only a modest crowd and demanded that the Park Service go with the lie that the crowds were "huge." This flew in the face of what we could all see with our own eyes. I had the same view Trump did up there on the platform. Unlike him, I could compare it to what I had seen at inaugurals since 1993. I understood why he became so defensive. There really was a difference.
The episode was silly, but also an early warning: we were in a "brave new world."
* * *
* * *
If the inauguration on Friday was the worst of times, Saturday turned out to be the best of times.
I decided to stay at home in Chappaqua, New York, rather than attend the Women's March protesting the new President. It was another tough call. I wanted badly to join the crowds and chant my heart out. But I believed it was important for new voices to take the stage, especially on this day. There are so many exciting young women leaders ready to play bigger roles in our politics. The last thing I wanted was to be a distraction from the genuine outpouring of grassroots energy. If I showed up, nasty politics would unavoidably follow.
So I sat on my couch and watched in delight as the networks reported huge crowds in dozens of cities across the United States and around the world. Friends sent me excited reports of packed subway cars and streets overflowing with women and men of all ages. I scrolled through Twitter and sent out gratitude and good vibes.
The Women's March was the biggest single protest in American history. Hundreds of thousands of people gathered in cities like New York, Los Angeles, and Chicago. Thousands also turned out in places like Wyoming and Alaska. In Washington, the march dwarfed the crowd that had gathered to see Trump's inauguration the day before. And it was completely peaceful. Maybe that's what happens when you put women in charge.
It was a far cry from what happened when women first marched on Washington, the day before Woodrow Wilson's inauguration in 1913. Thousands of suffragettes trooped down Pennsylvania Avenue demanding the right to vote, including Alice Paul, Helen Keller, and Nellie Bly. Men lined the way, gawking, jeering, and eventually turning into an angry mob. The police did nothing, and scores of marchers were injured. The violence drew the nation's attention to the suffragette cause. The superintendent of police was fired. Congress held hearings. And seven years later, the Nineteenth Amendment to the Constitution was ratified, granting women the right to vote.
Nearly a century later, we'd made a lot of progress, but our new President was a painful reminder of how far we still had to go. That's why millions of women (and many supportive men) were pouring into the streets.
I will confess that the day was bittersweet. For years all over the world, I had seen women driving grassroots movements, assuming power for themselves and their communities, forcing warring armies to the peace table, rewriting the destinies of nations. Were we now seeing the stirrings of something similar in the streets of our own country? It was awe-inspiring, as I said on Twitter at the end of the day.
Yet I couldn't help but ask where those feelings of solidarity, outrage, and passion had been during the election.
Since November, more than two dozen women—of all ages, but mostly in their twenties—had approached me in restaurants, theaters, and stores to apologize for not voting or not doing more to help my campaign. I responded with forced smiles and tight nods. On one occasion, an older woman dragged her adult daughter by the arm to come talk to me and ordered her to apologize for not voting—which she did, head bowed in contrition. I wanted to stare right in her eyes and say, "You didn't vote? How could you not vote?! You abdicated your responsibility as a citizen at the worst possible time! And now you want me to make you feel better?" Of course, I didn't say any of that.
These people were looking for absolution that I just couldn't give. We all have to live with the consequences of our decisions.
There had been a lot of days since the election when I wasn't in a very forgiving mood toward anyone, including myself. I was—and still am—worried about our country. Something is wrong. How could sixty-two million people vote for someone they heard on tape bragging about repeated sexual assault? How could he attack women, immigrants, Muslims, Mexican Americans, prisoners of war, and people with disabilities—and, as a businessman, be accused of scamming countless small businesses, contractors, students, and seniors—and still be elected to the most important and powerful job in the world? How can we as a nation allow untold thousands of Americans to be disenfranchised by voter suppression laws? Why did the media decide to present the controversy over my emails as one of the most important political stories since the end of World War II? How did I let that happen? How did we?
For all my concerns, though, watching the Women's March, I couldn't help but be swept up in the joy of the moment and feel like the unmistakable vitality of American democracy was reasserting itself before our eyes. My Twitter feed filled up with photos of marchers holding funny, poignant, indignant signs:
"So Bad, Even Introverts Are Here."
"Ninety, Nasty, and Not Giving Up!"
"Science Is Not a Liberal Conspiracy."
One adorable little boy had this message around his neck: "I ♥ Naps but I Stay Woke."
I also saw young girls holding up quotes from my speeches over the years: "Women's Rights Are Human Rights." "I Am Powerful and Valuable." On a tough weekend, seeing those words lifted my spirits.
The people in the streets were sending a message to me and all of us: "Don't give up. This country is worth fighting for."
For the first time since the election, I felt hopeful.
Just keep going.
No feeling is final.
—Rainer Maria Rilke
## Grit and Gratitude
On November 9, it was cold and raining in New York City. Crowds on the sidewalks turned to face my car as we drove past. Some people were crying. Some raised their hands or fists in solidarity. There were little kids held aloft by their parents. This time, seeing them made my heart sink instead of soar.
My team had scrambled to find a hall for my concession speech. The soaring Jacob K. Javits Convention Center atrium where we had hoped to hold a victory party wasn't an option. At 3:30 A.M., after scouting a few locations, our advance staff walked into the lobby of the New Yorker Hotel in Midtown Manhattan, not far from where my family and I were staying. They asked the concierge to call and wake up the manager at home. At 4:30 A.M., they started to prepare one of the hotel's ballrooms for an event everyone had hoped would never happen. I learned later that the New Yorker was where Muhammad Ali recuperated after losing a bitterly fought fifteen-round heavyweight championship fight to rival Joe Frazier in 1971. "I never wanted to lose, never thought I would, but the thing that matters is how you lose," Ali said the following day. "I'm not crying. My friends should not cry." If we wrote it in a movie, no one would believe it.
That morning, Bill and I both wore purple. It was a nod to bipartisanship (blue plus red equals purple). The night before, I had hoped to thank the country wearing white—the color of the suffragettes—while standing on a stage cut into the shape of the United States under a vast glass ceiling. (We had really gone the distance on the symbolism.) Instead, the white suit stayed in the garment bag. Out came the gray and purple one I had intended to wear on my first trip to Washington as President Elect.
After I finished speaking, I hugged as many people in the ballroom as possible. There were lots of old friends and devoted campaign staffers, many of their faces wet with tears. I was dry-eyed and felt calm and clear. My job was to get through this morning, smile, be strong for everyone, and show America that life went on and our republic would endure. A life spent in the public eye has given me lots of practice at that. I wear my composure like a suit of armor, for better or worse. In some ways, it felt like I had been training for this latest feat of self-control for decades.
Still, every time I hugged another sobbing friend—or one stoically blinking back tears, which was almost worse—I had to fight back a wave of sadness that threatened to swallow me whole. At every step, I felt that I had let everyone down. Because I had.
Bill, Chelsea, and her husband, Marc, were by my side, as they had been throughout. So were Tim Kaine and his wife, Anne Holton, who were extraordinarily kind and strong under these wrenching circumstances. I chose Tim for my running mate out of a superb field of candidates because he had executive experience, a stellar record as mayor, governor, and senator, a well-deserved reputation for decency and good judgment, and he was fluent in Spanish from his time as a missionary. He would have been an effective partner and truth teller as my vice president. Also, I liked him a lot.
After delivering hugs and smiling so long and hard that my face ached, I asked my senior team to go back to our headquarters in Brooklyn and make sure everyone was okay. One final wave to the crowd, a final thank-you to Tim and Anne, a quick hug and kiss for Chelsea and Marc—who both knew everything I felt without me having to say a word—and Bill and I got into the backseat of a Secret Service van and were driven away.
I could finally let my smile drain away. We were mostly quiet. Every few minutes, Bill would repeat what he had been saying all morning: "I'm so proud of you." To that he now added, "That was a great speech. History will remember it."
I loved him for saying it, but I didn't have much to say in return. I felt completely and totally depleted. And I knew things would feel worse before they started feeling better.
It takes about an hour to drive from Manhattan to our home in Chappaqua. We live at the end of a quiet street full of trees, and whatever stress I'm feeling usually vanishes whenever I turn up the cul-de-sac. I absolutely love our old house and am always happy to be home. It's cozy, colorful, full of art, and every surface is covered with photos of the people I love best in the world. That day, the sight of our front gate was pure relief to me. All I wanted to do was get inside, change into comfy clothes, and maybe not answer the phone ever again.
I'll confess that I don't remember much about the rest of that day. I put on yoga pants and a fleece almost immediately. Our two sweet dogs followed me from room to room, and at one point, I took them outside and just breathed the cold, rainy air. Every once in a while, I'd turn on the news but then turn it off almost immediately. The question blaring in my head was, "How did this happen?" Fortunately, I had the good sense to realize that diving into a campaign postmortem right then would be about the worst thing I could do to myself.
Losing is hard for everyone, but losing a race you thought you would win is devastating. I remember when Bill lost his reelection as Governor of Arkansas in 1980. He was so distraught at the outcome that I had to go to the hotel where the election night party was held to speak to his supporters on his behalf. For a good while afterward, he was so depressed that he practically couldn't get off the floor. That's not me. I keep going. I also stew and ruminate. I run through the tape over and over, identifying every mistake—especially those made by me. When I feel wronged, I get mad, and then I think about how to fight back.
On that first day, I just felt tired and empty. The reckoning was still to come.
At some point, we ate dinner. We FaceTimed with our grandchildren, two-year-old Charlotte and her baby brother, Aidan, born in June 2016. I was reassured to see their mom. I knew Chelsea was hurting for me, which in turn hurt to think about, but those kids are an instant mood boost for all of us. We quietly drank them in, that day and every day after.
Perhaps most importantly, after sleeping hardly at all the night before, I climbed into our bed midday for a nice, long nap. I also went to bed early that night and slept in the next morning. I could finally do that.
I avoided the phone and email that first day. I suspected, correctly, that I was receiving a virtual avalanche of messages, and I couldn't quite handle it—couldn't handle everyone's kindness and sorrow, their bewilderment and their theories for where and why we had fallen short. Eventually, I'd dive in. But for now, Bill and I kept the rest of the world out. I was grateful for the one-billionth time that I had a husband who was good company not just in happy times but sad ones as well.
* * *
* * *
I doubt that many people reading this will ever lose a presidential election. (Although maybe some have: hi Al, hi John, hi Mitt, hope you're well.) But we all face loss at some point. We all face profound disappointment. Here's what helped me during one of the lowest points in my life. Maybe it'll help you too.
After that first day of laying low, I started reaching out to people. I answered a ton of emails; I returned phone calls. It hurt. There's a reason people isolate themselves when they're suffering. It can be painful to talk about it, painful to hear the concern in our friends' voices. Plus, in my case, we were all suffering. Everyone was so upset—for me, for themselves, for America. Often, I ended up doing the comforting rather than being comforted. Still, it was good to connect. I knew isolation wasn't healthy and that I'd need my friends now more than ever. I knew that putting off those conversations would only make them harder to have later on. And I badly wanted to thank everyone who had helped my campaign and make sure they were holding up okay under these circumstances.
What helped most was when someone said, "This has made me even more committed to the fight." "I'm stepping up my donations." "I've already started volunteering." "I'm posting more on Facebook; I won't stay quiet anymore." And best of all: "I'm thinking about running for office myself."
A young woman named Hannah, one of my field organizers in Wisconsin, sent me this note a few days after my loss:
The past two days have been very difficult. But when I think about how I felt on Tuesday morning, when I cried for an hour because I thought we were about to elect our first woman President, I know we cannot give up. Even though these last days have been a different kind of crying, your poise and grace have inspired me to stay strong. I do know that even though we have all been knocked down by this, we will rise. And through the next few years, we will be stronger together and keep fighting for what is right. From one nasty woman to another, thank you.
Since I spent a lot of time worrying that my loss would permanently discourage the young people who worked for my campaign, learning that my defeat hadn't defeated them was a huge relief. It also roused me. If they could keep going, so could I. And maybe if I showed that I wasn't giving up, other people would take heart and keep fighting, too.
It was especially important to me that all the people who worked on my campaign knew how grateful and proud I was of them. They'd sacrificed a lot over the past two years, in some cases putting personal lives on hold, moving across the country, and working long hours for not that much money. They never stopped believing in me, each other, and the vision of the country we were working so hard to advance. Now many of them didn't know where their next paycheck would come from.
I did two things right away. First, I decided to write and sign letters to all 4,400 members of my campaign staff. Thankfully, Rob Russo, who has been managing my correspondence for years, agreed to oversee the whole project. I also made sure we were able to pay everyone through November 22 and provide health insurance through the end of the year.
On the Friday after the election, we threw a party at a Brooklyn hotel near our headquarters. Under the circumstances, it was surprisingly great. There was a fantastic band—some of the same musicians who played at Chelsea and Marc's wedding in 2010—and the dance floor was packed. It felt a little like an Irish wake: celebration amid the sadness. Let it never be said that the Hillary for America staff didn't stick together when it counted. To help matters, there was an open bar.
After everyone worked up a sweat, I took the microphone to say thank you. Everyone screamed "Thank you!" right back at me. Really, I couldn't have asked for a more good-natured, hardworking team. I told them how important it was that they not let this defeat discourage them from public service or from throwing themselves into future campaigns with as much heart and commitment as they had given to mine. I reminded them about the losing campaigns I'd worked on in my twenties, including Gene McCarthy in the 1968 Democratic primaries and George McGovern in 1972—and the beatings Democrats took until everything changed in '92. We had stuck it out. I was counting on them to keep going too.
I also said that I had brought a small gift for them. A women's advocacy group called UltraViolet had sent 1,200 red roses to my house earlier that day, and I had them packed up and brought them to the party. They lay in heaps near the exits. "Please take a few as you head home tonight," I told everyone. "Think about the hope they represent and the love and gratitude that so many people around the country feel for all of you."
It was an echo of an earlier moment. My team had spent Wednesday and Thursday packing up our campaign offices in Brooklyn, fueled by pizzas sent by well-wishers from all over the country. Our neighbors in the building had taped signs on the elevator doors that read, "Thank You for What You Did." As staffers carried their last boxes out of headquarters, they were greeted by a crowd of children and their parents. The kids had covered the sidewalk in chalk messages: "Girl Power!" "Stronger Together!" "Love Trumps Hate!" "Please Don't Give Up!" When bedraggled members of our team filed out for the last time, the children handed them flowers. One last act of kindness from a borough that had been good to us again and again.
* * *
* * *
Over the next few weeks, I dropped any pretense of good cheer. I was so upset and worried for the country. I knew the proper and respectable thing to do was to keep quiet and take it all with grace, but inside I was fuming. The commentator Peter Daou, who worked on my 2008 campaign, captured my feelings when he tweeted, "If Trump had won by 3 million votes, lost electoral college by 80K, and Russia had hacked RNC, Republicans would have shut down America." Nonetheless, I didn't go public with my feelings. I let them out in private. When I heard that Donald Trump settled a fraud suit against his Trump University for $25 million, I yelled at the television. When I read the news that he filled his team with Wall Street bankers after relentlessly accusing me of being their stooge, I nearly threw the remote control at the wall. And when I heard he installed Steve Bannon, a leading promoter of the "Alt-Right," which many have described as including white nationalists, as his chief strategist in the White House, it felt like a new low in a long line of lows.
The White House is sacred ground. Franklin D. Roosevelt hung a plaque over the fireplace in the State Dining Room inscribed with a line from a letter that John Adams sent to his wife on his second night living in the newly built White House: "I pray heaven to bestow the best of blessings on this house and all that shall hereafter inhabit it. May none but honest and wise men ever rule under this roof." I hope Adams would have been okay with a wise woman. I can't imagine what he would say if he could see who was walking those halls.
Letters started pouring in from people across the country, many so poignant that after reading a few, I had to put them away and go for a walk. A third-year law student from Massachusetts named Rauvin wrote about how she imagined that she and her female friends and classmates would look back on this time:
On Nov. 8, 2016, we felt a sense of devastation, powerlessness, and disappointment that we had never felt before. So we cried. And then we squared our shoulders, picked each other up, and got to work. We moved onward and onward, keeping in mind that we would never, ever allow ourselves to feel again as we did that day. And though our anger and disappointment fueled us, it did not consume us, make us cynical or cruel. It made us strong. And eventually, eventually one of us will crash through that highest, hardest glass ceiling. And it will be because of our hard work, determination, and resilience. But it will also be because of you. Just you wait.
In a postscript, she added: "If I may recommend some salves: time with friends and family, of course, but also the first season of Friday Night Lights, the new season of Gilmore Girls, the Hamilton cast album, Martha Stewart's mac and cheese, a good book, a glass of red wine." Good advice!
A woman named Holly from Maryland wrote with additional sensible guidance:
I hope you will sleep as late as you like and wear your sneakers all day. Get a massage and stand in the sun. Sleep in your own bed and take long walks with your husband. Giggle with your granddaughter and play patty-cake with your grandson. . . . Breathe. Think only about whether you want strawberries or blueberries with your breakfast, about which Dr. Seuss book to read to your grandchildren. Listen to the wind or Chopin.
My friend Debbie from Texas sent me a poem to cheer me up. Her father told her that a friend of his wrote it after they worked for Adlai Stevenson, a two-time presidential candidate, on one of his landslide defeats to Dwight Eisenhower in the 1950s. I have to admit, it made me chuckle:
The election is now over,
The result is now known.
The will of the people
Has clearly been shown.
Let's all get together;
Let bitterness pass.
I'll hug your Elephant;
And you kiss my Ass.
Pam from Colorado sent me a box of a thousand handmade origami cranes held together by strings. She explained that, in Japan, a thousand folded cranes are a powerful symbol of hope and that hanging them in your home is considered extremely lucky. I hung them on my porch. I'd take all the luck and hope I could get.
I tried hard to let go of the burden of putting on a happy face or reassuring everyone that I was totally fine. I knew I would be fine eventually, but for those early weeks and months, I wasn't fine at all. And while I didn't spill my guts to everyone who crossed my path, I did answer honestly when asked how I was doing. "It'll be okay," I'd say, "but right now it's really hard." If I was feeling defiant, I'd respond, "Bloody, but unbowed," a phrase from "Invictus," Nelson Mandela's favorite poem. If they wanted to commiserate over the latest reports from Washington, sometimes I'd confess about how mad it all made me. Other times I'd say, "I'm just not quite up for talking about this." Everyone understood.
I also let people do things for me. This doesn't come easily to me. But Chelsea pointed out, "Mom, people want to do something helpful—they want you to let them." So when a friend said she was sending a box full of her favorite books . . . and another said he was coming up for the weekend even if it was just to take a walk together . . . and another said she was taking me to see a play whether I wanted to go or not . . . I didn't protest or argue. For the first time in years, I didn't have to consult a complicated schedule. I could just say "Yes!" without a second thought.
I thought a lot about my mother. Part of me was glad she wasn't around to experience another bitter disappointment. My narrowly losing the Democratic nomination to Barack Obama in 2008 had been hard for her, although she tried never to let me see it. Mostly, I just missed her. I wanted to sit down with her, hold her hand, and share all my troubles.
Friends advised me on the power of Xanax and raved about their amazing therapists. Doctors told me they'd never prescribed so many antidepressants in their lives. But that wasn't for me. Never has been.
Instead, I did yoga with my instructor, Marianne Letizia, especially "breath work." If you've never done alternate nostril breathing, it's worth a try. Sit cross-legged with your left hand on your thigh and your right hand on your nose. Breathing deeply from your diaphragm, place your right thumb on your right nostril and your ring and little fingers on your left. Shut your eyes, and close off your right nostril, breathing slowly and deeply through your left. Now close both sides and hold your breath. Exhale through the right nostril. Then reverse it: inhale through the right, close it, and exhale through the left. The way it's been explained to me, this practice allows oxygen to activate both the right side of the brain, which is the source of your creativity and imagination, and the left side, which controls reason and logic. Breathe in and out, completing the cycle a few times. You will feel calmer and more focused. It may sound silly, but it works for me.
It wasn't all yoga and breathing: I also drank my share of chardonnay.
I spent time in nature. The day after my concession, Bill and I were in an arboretum near our home. It was the perfect time of year for traipsing—crisp but not freezing, with the smell of fall in the air. We were lost in thought when we met a young woman out hiking with her three-month-old daughter strapped to her back and her dog underfoot. She seemed a little embarrassed to stop and greet us, but she said she couldn't help herself—she needed to give me a hug. It turned out, I needed it too. Later that day, she posted a photo of us on Facebook, which quickly went viral. The "HRC in the Wild" meme was born.
Throughout November and December, Bill and I laced up our shoes and hit the trails again and again, slowly working through why I lost, what I could have done better, what in the world was going to happen to America now. We also spent a fair amount of time talking about what we'd have for dinner that night or what movie to watch next.
I took on projects. In August 2016, we had bought the house next door: a classic ranch we had always liked the looks of, with a backyard that connected to ours. The idea was to have plenty of room for Chelsea, Marc, their kids, our brothers and their families, and our friends. Plus, I was getting a little ahead of myself and thinking about how to accommodate the large team that travels with a President. Through September and October, we had been quietly remodeling, but with the campaign in high gear, there hadn't been much time to think about any of that. Now I had nothing but time on my hands. I spent hours going over plans with the contractor and my interior decorator and friend Rosemarie Howe: paint swatches, furniture, a swing set for the backyard. Over the fireplace, I hung a vintage suffragette banner that Marc had given me that declared "Votes for Women." In the family room, we put up a colorful painting of the balloon drop at the Democratic National Convention. Bill and I had both gotten a kick out of those balloons, Bill especially. A memory of happier times.
By Thanksgiving, the work on the house was done. That morning, I walked around making sure everything was perfect before our friends and family descended for dinner. At one point, I stood on the front porch and saw some people gathered down at the corner of our street around a bunch of colorful homemade "Thank You" signs stuck in the ground. Kids from the neighborhood had made them for me for Thanksgiving, covered in hearts and rainbows and American flags. It was one of many kind gestures—not just from friends and loved ones but also from complete strangers—that made that first month more bearable.
Every Thanksgiving, it's become our tradition since leaving the White House to host a bunch of Chelsea's friends who don't travel home for the holiday or who hail from other countries and want to experience an American Thanksgiving in all its glory. There are always twenty or thirty of us sitting around long folding tables decorated with leaves, pinecones, and votive candles—nothing too high blocking people's views, so conversation moves easily back and forth. We start our meal with grace by Bill and then go around the table so everyone can say what he or she is thankful for during the past year. When it was my turn, I said I was grateful for the honor of running for President and for my family and friends who supported me.
Back in our old house, I organized every closet in a blitz of focused energy that sent our dogs scurrying from every room I entered. I called friends and insisted they take a pair of shoes they'd once said they liked or a blouse I suspected would fit just right. I have often been that pushy friend, so most of them knew to expect it. I also organized jumbled heaps of photos into albums, threw out stacks of old magazines and disintegrating newspaper clippings, and sorted through probably a million business cards that people had handed me over the years. With every gleaming drawer and every object placed in its correct, appointed spot, I felt satisfied that I had made my world just a little more orderly.
Some of my friends pushed me to go on vacation, and we did get away with Chelsea, Marc, and the grandkids for a few days to the Mohonk Mountain House, a favorite spot of mine in upstate New York. But after twenty months of nonstop travel for the campaign—on top of four years of globe-trotting as Secretary of State—I just wanted to sit in my quiet house and be still.
I tried to lose myself in books. Our house is packed with them, and we keep adding more. Like my mother, I love mystery novels and can plow through one in a single sitting. Some of my recent favorites are by Louise Penny, Jacqueline Winspear, Donna Leon, and Charles Todd. I finished reading Elena Ferrante's four Neapolitan novels and relished the story they tell about friendship among women. Our shelves are weighed down with volumes about history and politics, especially biographies of Presidents, but in those first few months, they held no interest for me whatsoever. I went back to things that have given me joy or solace in the past, such as Maya Angelou's poetry:
You may write me down in history
With your bitter, twisted lies,
You may trod me in the very dirt
But still, like dust, I'll rise. . . .
You may shoot me with your words,
You may cut me with your eyes,
You may kill me with your hatefulness,
But still, like air, I'll rise.
On raw December days, with my heart still aching, those words helped. Saying them out loud made me feel strong. I thought of Maya and her rich, powerful voice. She wouldn't have been bowed by this, not one inch.
I went to Broadway shows. There's nothing like a play to make you forget your troubles for a few hours. In my experience, even a mediocre play can transport you. And show tunes are the best soundtrack for tough times. You think you're sad? Let's hear what Fantine from Les Misérables has to say about that!
By far my favorite New York City performance was way off Broadway: Charlotte's dance recital. It's enchanting to watch a bunch of squirming, giggling two-year-olds trying to dance in unison. Some are intensely focused (that would be my granddaughter), some are trying to talk to their parents in the audience, and one girl just sat down and took off her shoes in the middle of everything. It was lovely mayhem. As I watched Charlotte and her friends laugh and fall down and get up again, I felt a twinge of something I couldn't quite place. Then I realized what it was: relief. I had been ready to completely devote the next four or eight years to serving my country. But that would have come with a cost. I would have missed a lot of dance recitals and bedtime stories and trips to the playground. Now I had those back. That's more than a silver lining. That's the mother lode.
Back at home, I caught up on TV shows Bill had been saving. We raced through old episodes of The Good Wife, Madam Secretary, Blue Bloods, and NCIS: Los Angeles, which Bill insists is the best of the franchise. I also finally saw the last season of Downton Abbey. That show always reminds me of the night I spent in Buckingham Palace in 2011 during President Obama's state visit, in a room just down the hall from the balcony where the Queen waves to the crowds. It was like stepping into a fairy tale.
On the Saturday after the election, I turned on Saturday Night Live and watched Kate McKinnon open the show with her impression of me one more time. She sat at a grand piano and played "Hallelujah," the hauntingly beautiful song by Leonard Cohen, who had died a few days before. As she sang, it seemed like she was fighting back tears. Listening, so was I.
I did my best, it wasn't much,
I couldn't feel, so I tried to touch
I've told the truth, I didn't come to fool you
And even though it all went wrong
I'll stand before the lord of song
With nothing on my tongue but hallelujah.
At the end, Kate-as-Hillary turned to the camera and said, "I'm not giving up and neither should you."
* * *
* * *
I prayed a lot. I can almost see the cynics rolling their eyes. But pray I did, as fervently as I can remember ever doing. Novelist Anne Lamott once wrote that the three essential prayers she knows are "Help," "Thanks," "Wow." You can guess which one I reached for last fall. I prayed for help to put the sadness and disappointment of my defeat behind me; to stay hopeful and openhearted rather than becoming cynical and bitter; and to find a new purpose and start a new chapter, so that the rest of my life wouldn't be spent like Miss Havisham from Charles Dickens's Great Expectations, rattling around my house obsessing over what might have been.
I prayed that my worst fears about Donald Trump wouldn't be realized, and that people's lives and America's future would be made better, not worse, during his presidency. I'm still praying on that one, and I can use all the backup you can muster.
I also prayed for wisdom. I had help from Bill Shillady, the United Methodist minister who co-officiated at Chelsea and Marc's marriage and led the memorial services for my mother. During the campaign, he sent me devotionals every day. On November 9, he sent me a commentary that originally appeared in a blog by Pastor Matt Deuel. I read it many times before the week was out. This passage in particular really moved me:
It is Friday, but Sunday is coming.
This is not the devotional I had hoped to write. This is not the devotional you wish to receive this day.
While Good Friday may be the starkest representation of a Friday that we have, life is filled with a lot of Fridays.
For the disciples and Christ's followers in the first century, Good Friday represented the day that everything fell apart. All was lost. And even though Jesus told his followers that three days later the temple would be restored . . . they betrayed, denied, mourned, fled, and hid. They did just about everything but feel good about Friday and their circumstances.
You are experiencing a Friday. But Sunday is coming! Death will be shattered. Hope will be restored. But first, we must live through the darkness and seeming hopelessness of Friday.
I called Reverend Bill, and we talked for a long time.
I reread one of my favorite books, The Return of the Prodigal Son by the Dutch priest Henri Nouwen. It's something I've gone back to repeatedly during difficult times in my life. You may know the parable about the younger of two sons who strays and sins but finally comes home. He's welcomed lovingly by his father but resented by his older brother, who had stayed behind and served his father honorably while the younger brother did whatever he wanted. Maybe it's because I'm the oldest in our family and something of a Girl Scout, but I've always identified with the older brother in the parable. How grating it must have been to see his wayward sibling welcomed back as if nothing had happened. It must have felt as if all his years of hard work and dutiful care meant nothing at all. But the father says to the older brother, "Have I not taken good care of you? Have you not been close to me? Have you not been at my side learning and working?" Those things are their own reward.
It's a story about unconditional love—the love of a father, and also the Father, who is always ready to love us, no matter how often we stumble and fall. It makes me think of my dad, a flinty, tight-lipped man who nevertheless always made sure I knew what I meant to him. "I won't always like what you do," he'd tell me, "but I will always love you." As a kid, I would come up with elaborate hypotheses to test him. "What if I robbed a store or murdered somebody? Would you still love me then?" He'd say, "Absolutely! I'd be disappointed and sad, but I will always love you." Once or twice last November, I thought to myself, "Well, Dad, what if I lose an election I should have won and let an unqualified bully become President of the United States? Would you still love me then?" Unconditional love is the greatest gift he gave me, and I've tried to give it to Chelsea and now to Charlotte and Aidan.
Nouwen sees another lesson in the parable of the Prodigal Son: a lesson about gratitude. "I can choose to be grateful even when my emotions and feelings are still steeped in hurt and resentment," he writes. "I can choose to speak about goodness and beauty even when my inner eye still looks for someone to accuse or something to call ugly. I can choose to listen to the voices that forgive and to look at the faces that smile even while I still hear words of revenge and see grimaces of hatred."
It's up to us to make the choice to be grateful even when things aren't going well. Nouwen calls that the "discipline of gratitude." To me, it means not just being grateful for the good things, because that's easy, but also to be grateful for the hard things too. To be grateful even for our flaws, because in the end, they make us stronger by giving us a chance to reach beyond our grasp.
My task was to be grateful for the humbling experience of losing the presidential election. Humility can be such a painful virtue. In the Bible, Saint Paul reminds us that we all see through a glass darkly because of our humbling limitations. That's why faith—the assurance of things hoped for and the conviction of things unseen—requires a leap. It's because of our limitations and imperfections that we must reach out beyond ourselves, to God and to one another.
As the days went by, November turned into December, and that horrible, no good, very bad time came to a close, I began to rediscover my gratitude. I felt the good effects of all that walking and sleep; I was getting calmer and stronger. I found myself thinking of new projects I'd like to take on. I started accepting invitations to events that spoke to my heart: a Planned Parenthood dinner, the Women in the World summit and the Vital Voices gala celebrating women leaders and activists from around the world, and gatherings with students at Harvard, Wellesley, and Georgetown. Those rooms were full of purposeful energy. I soaked it all up and found myself thinking more about the future than the past.
Do what you feel in your heart to be right—for you'll be criticized anyway. You'll be "damned if you do and damned if you don't."
—Eleanor Roosevelt
## Competition
For us, there is only the trying. The rest is not our business.
—T. S. Eliot
## Get Caught Trying
I ran for President because I thought I'd be good at the job. I thought that of all the people who might run, I had the most relevant experience, meaningful accomplishments, and ambitious but achievable proposals, as well as the temperament to get things done in Washington.
America was doing better than any other major country, but there was still too much inequality and too little economic growth. Our diversity was an advantage, spurring creativity and vitality, but rapid social and economic change alienated people who thought too much was happening too fast and felt left out. Our position in the world was strong, but we had to cope with a combustible mix of terrorism, globalization, and the advances in technology that fueled them both.
I believed that my experiences in the White House, Senate, and State Department equipped me to take on these challenges. I was as prepared as anyone could be. I had ideas that would make our country stronger and life better for millions of Americans.
In short, I thought I'd be a damn good President.
Still, I never stopped getting asked, "Why do you want to be President? Why? But, really—why?" The implication was that there must be something else going on, some dark ambition and craving for power. Nobody psychoanalyzed Marco Rubio, Ted Cruz, or Bernie Sanders about why they ran. It was just accepted as normal. But for me, it was regarded as inevitable—people assumed I'd run no matter what—yet somehow abnormal, demanding a profound explanation.
After the election, I thought a lot about this. Maybe it's because I'm a woman, and we're not used to women running for President. Maybe it's because my style of leadership didn't fit the times. Maybe it's because I never explained myself as bluntly as this.
So let me start from the beginning and tell you how and why I made the decision to run.
* * *
* * *
"You might lose," Bill told me. "I know," I said. "I might lose."
The problems started with history. It was exceedingly difficult for either party to hold on to the White House for more than eight years in a row. In the modern era, it had happened only once, when George H. W. Bush succeeded Ronald Reagan in 1989. No nonincumbent Democrat had run successfully to succeed another two-termer since Vice President Martin Van Buren won in 1836, succeeding Andrew Jackson.
There was still a lot of pent-up anger and resentment left over from the financial crash of 2008–2009, and while that had happened on the Republicans' watch, Democrats had presided over a recovery that had been too slow.
There also was "Clinton fatigue" to consider. Pundits were already complaining that the election would be an exhausting contest between two familiar dynasties: the Clintons and the Bushes.
Then there was the matter of my gender. No woman had ever won the nomination of a major party in the history of our country, let alone the presidency. It's easy to lose sight of how momentous that is, but when you stop to consider what it means and the possible reasons behind it, it's profoundly sobering.
It was a chilly day in autumn 2014, and Bill and I had been having the same conversation for months now. Should I run for President for a second time? Lots of talented people were ready to jump on board with my campaign if I ran. The press and most of the political class assumed I was already running. Some of them were so convinced by the caricature of me as a power-hungry woman that they couldn't imagine me doing anything else. I, on the other hand, could imagine lots of different paths for myself.
I already knew how it felt to lose. Until you experience it, it's hard to comprehend the ache in your gut when you see things going wrong and can't figure out how to fix them; the sharp blow when the results finally come in; the disappointment written on the faces of your friends and supporters. Political campaigns are massive enterprises with thousands of people working together toward a common goal, but in the end, it's intensely personal, even lonely. It's just your name on the ballot. You're embraced or repudiated all by yourself.
The race against Barack Obama in 2008 was close and hard-fought. By the end, he led in the all-important delegate count, but our popular vote totals were less than one-tenth of a percent apart. That made it all the more painful to accept defeat and muster up the good cheer to campaign vigorously for him. The saving grace was the respect I had for Barack and my belief that he would be a good President who would do everything he could to advance the values we both shared. That made it a lot easier.
Did I want to put myself through a grueling race all over again?
My life after leaving politics had turned out to be pretty great. I had joined Bill and Chelsea as a new board member of the Clinton Foundation, which Bill had turned into a major global philanthropy after leaving office. This allowed me to pursue my own passions and have an impact without all the bureaucracy and petty squabbles of Washington. I admired what Bill had built, and I loved that Chelsea had decided to bring her knowledge of public health and her private sector experience to the foundation to improve its management, transparency, and performance after a period of rapid growth.
At the 2002 International AIDS Conference in Barcelona, Bill had a conversation with Nelson Mandela about the urgent need to lower the price of HIV/AIDS drugs in Africa and across the world. Bill figured he was well positioned to help, so he began negotiating agreements with drugmakers and governments to lower medicine prices dramatically and to raise the money to pay for it. It worked. More than 11.5 million people in more than seventy countries now have access to cheaper HIV/AIDS treatment. Right now, out of everyone being kept alive by these drugs in developing countries around the world, more than half the adults and 75 percent of the children are benefiting from the Clinton Foundation's work.
After recovering from heart-bypass surgery in 2004, Bill joined with the American Heart Association to start the Alliance for a Healthier Generation, which has helped more than twenty million students in more than thirty-five thousand American schools enjoy healthier food and more physical activity. The Alliance made agreements with major beverage companies to reduce calories in drinks available in schools by 90 percent, and also partnered with Michelle Obama's Let's Move! initiative.
The foundation is also fighting the opioid epidemic in the United States; helping more than 150,000 small farmers in Africa increase their incomes; and bringing clean energy to island nations in the Caribbean and Pacific.
In 2005, Bill started the Clinton Global Initiative, a new model of philanthropy for the twenty-first century that brought together leaders from business, government, and the nonprofit sector to make concrete commitments for action on everything from distributing clean water, to improving energy efficiency, to providing hearing aids to deaf children. The annual conferences highlighted the most exciting commitments and their results. No one could just show up and talk; you had to actually do something. After twelve years, CGI members, and their affiliates in CGI America and CGI International, had made more than 3,600 commitments, which have improved the lives of more than 435 million people in more than 180 countries.
Among CGI's greatest hits were sending 500 tons of medical supplies and equipment to West Africa for those fighting the Ebola epidemic, and helping raise $500 million to support small businesses, farms, schools, and health care in Haiti. In the United States, at no expense to taxpayers, CGI helped launch an amazing partnership led by the Carnegie Corporation of New York to meet President Obama's goal of 100,000 new STEM (science, technology, engineering, and mathematics) teachers. And it supported the creation of America's largest private infrastructure fund—$16.5 billion invested by public employee pension funds, led by the American Federation of Teachers (AFT) and North America's Building Trades Unions (NABTU)—which has created 100,000 jobs and provided skills training to a quarter-million workers every year.
When I joined the foundation in 2013, I teamed up with Melinda Gates and the Gates Foundation to launch an initiative called No Ceilings: The Full Participation Project to advance rights and opportunities for women and girls around the world. I also created a program called Too Small to Fail to encourage reading, talking, and singing to infants and toddlers to help their brains develop and build vocabulary. And Chelsea and I started a network of leading wildlife conservation organizations to protect the endangered African elephants from poachers. None of these programs had to poll well or fit on a bumper sticker. They just had to make a positive, measurable difference in the world. After years in the political trenches, that was both refreshing and rewarding.
I knew from experience that if I ran for President again, everything Bill and I had ever touched would be subject to scrutiny and attack—including the foundation. That was a concern, but I never imagined that this widely respected global charity would be as savagely smeared and attacked as it was. For years, the foundation and CGI had been supported by Republicans and Democrats alike. Independent philanthropy watchdogs CharityWatch, GuideStar, and Charity Navigator gave the Clinton Foundation top marks for reducing overhead and having a measurable positive impact. CharityWatch gave it an A, Charity Navigator gave it four stars, and GuideStar rated it platinum. But none of that stopped brutal partisan attacks from raining down during the campaign.
I have written about the foundation at some length here because a recent analysis published in the Columbia Journalism Review showed that during the campaign there was twice as much written about the Clinton Foundation as there was on any of the Trump scandals, and nearly all of it was negative. That gets to me. As Daniel Borochoff, the founder of CharityWatch, put it, "If Hillary Clinton wasn't running for President, the Clinton Foundation would be seen as one of the great humanitarian charities of our generation." I believe that's exactly what it is and what it will continue to be, and I was proud to be a part of it.
Beyond my work with the foundation, I also spent time in 2013 and 2014 writing a book called Hard Choices about my experiences as Secretary of State. The book was long—more than six hundred pages about foreign policy!—but I still had more stories left on the cutting room floor and a lot more things I wanted to say. If I didn't run for President, there could be more books to write. Maybe I could teach and spend time with students.
What's more, like many former government officials, I found that organizations and companies wanted me to come talk to them about my experiences and share my thoughts on the world—and they'd pay me a pretty penny to do it. I continued giving many speeches without pay, but I liked that there was a way for me to earn a very good living without working for any one company or sitting on any boards. It was also a chance to meet interesting people.
I spoke to audiences from a wide range of fields: travel agents and auto dealers, doctors and tech entrepreneurs, grocers and summer camp counselors. I also spoke to bankers. Usually I told stories from my time as Secretary of State and answered questions about global hot spots. I must have recounted the behind-the-scenes story of the raid that brought Osama bin Laden to justice at least a hundred times. Sometimes I talked about the importance of creating more opportunities for women, both around the world and in corporate America. I rarely got partisan. What I had to say was interesting to my audiences, but it wasn't especially newsworthy. Many of the organizations wanted the speeches to be private, and I respected that: they were paying for a unique experience. That allowed me to be candid about my impressions of world leaders who might have been offended if they heard. (I'm talking about you, Vladimir.)
Later, my opponents spun wild tales about what terrible things I must have said behind closed doors and how as President I would be forever in the pocket of the shadowy bankers who had paid my speaking fees. I should have seen that coming. Given my record of independence in the Senate—especially my early warnings about the mortgage crisis, my votes against the Bush tax cuts, and my positions in favor of financial regulation, including closing the tax loophole for hedge funds known as carried interest—this didn't seem to be a credible attack. I didn't think many Americans would believe that I'd sell a lifetime of principle and advocacy for any price. When you know why you're doing something and you know there's nothing more to it and certainly nothing sinister, it's easy to assume that others will see it the same way. That was a mistake. Just because many former government officials have been paid large fees to give speeches, I shouldn't have assumed it would be okay for me to do it. Especially after the financial crisis of 2008–2009, I should have realized it would be bad "optics" and stayed away from anything having to do with Wall Street. I didn't. That's on me.
This is one of the mistakes I made that you'll read about in this book. I've tried to give an honest accounting of when I got it wrong, where I fell short, and what I wish I could go back and do differently. This isn't easy or fun. My mistakes burn me up inside. But as one of my favorite poets, Mary Oliver, says, while our mistakes make us want to cry, the world doesn't need more of that.
The truth is, everyone's flawed. That's the nature of human beings. But our mistakes alone shouldn't define us. We should be judged by the totality of our work and life. Many problems don't have either/or answers, and a good decision today may not look as good ten or twenty years later through the lens of new conditions. When you're in politics, this gets more complicated. We all want—and the political press demands—a "story line," which tends to cast people as either saints or sinners. You're either revered or reviled. And there's no juicier political story than the saint who gets unmasked as a sinner. A two-dimensional cartoon is easier to digest than a fully formed person.
For a candidate, a leader, or anyone, really, the question is not "Are you flawed?" It's "What do you do about your flaws?" Do you learn from your mistakes so you can do and be better in the future? Or do you reject the hard work of self-improvement and instead tear others down so you can assert they're as bad or worse than you are?
I've always tried to do the former. And, by and large, so has our country, with our long march toward a more perfect union.
But Donald Trump does the latter. Instead of admitting mistakes, he lashes out, demeans, and insults others—often projecting by accusing others of doing what he himself has done or is about to do. So if he knows that the Donald J. Trump Foundation is little more than a personal piggy bank, he'll turn around and accuse, with no evidence, the well-respected Clinton Foundation of being corrupt. There's a method to this madness. For Trump, if everyone's down in the mud with him, then he's no dirtier than anyone else. He doesn't have to do better if everyone else does worse. I think that's why he seems to relish humiliating people around him. And it's why he must have been delighted when Marco Rubio tried to match him in slinging crude personal insults during the primaries. Of course, it hurt Rubio much more than Trump. As Bill likes to say, never wrestle a pig in the mud. They have cloven hooves, which give them superior traction, and they love getting dirty. Sadly, Trump's strategy works. When people start believing that all politicians are liars and crooks, the truly corrupt escape scrutiny, and cynicism grows.
But I'm getting ahead of myself. Back to 2014, and deciding to run for President.
We've talked about my work at the foundation, my book, and my speeches, but by far the best part about my life after government—and probably the most compelling reason not to run—was being a grandmother. I loved it even more than I'd expected. Bill and I found ourselves looking for any excuse to drive down to Manhattan so we could drop by Chelsea and Marc's and see little Charlotte, who was born that September. We became the world's most enthusiastic babysitters, book readers, and playmates. We were doubly blessed when Aidan arrived in June 2016.
Running for President again would mean putting all this—my wonderful new life—on hold and climbing back on the high wire of national politics. I wasn't sure I was ready to do that.
* * *
* * *
My family was incredibly supportive. If I wanted to run, they would be there for me 100 percent. Chelsea had campaigned relentlessly in 2008, becoming a superb surrogate and sounding board for me. Bill knows more than almost anyone alive about what it takes to be President. He was convinced I was the best person for the job and strenuously denied that this was just a husband's love talking.
Still, the obstacles were daunting. Yes, I had left the State Department with some of the highest approval ratings of anyone in public life—one poll from the Wall Street Journal and NBC News in January 2013 put me at 69 percent. I was also the most admired woman in the world, according to the annual Gallup poll. Ah, the good old days.
But I knew that my high approval rating was partly because Republicans had been willing to work with me when I was Secretary and praised my service. They had trained their fire on President Obama and largely left me alone. Also, the press corps covering me in those years genuinely cared about the work of diplomacy and the issues I dealt with, which meant the news coverage of my work was substantive and, for the most part, accurate. I knew it would be different if I ran for President again. And as Bill said—and history supported—the country's perennial desire for change would make it hard for any Democrat to win, especially one like me who was closely tied to the current administration.
In 2014, President Obama's approval rating was stuck in the low 40s. Despite the administration's best efforts, the economic recovery was still anemic, with wages and real incomes stagnating for most Americans. The administration had botched the rollout of the new health care marketplaces, a centerpiece of the President's signature legislative accomplishment, the Affordable Care Act. A new terrorist group, ISIS, was seizing territory in Iraq and Syria and beheading civilians live on the internet. There was even a terrifying Ebola epidemic in Africa that many Americans worried would jump to the United States. Thankfully, the Obama administration reacted swiftly to shore up our public health defenses and support Ebola response efforts in West Africa. Despite the facts, conservative partisans warned breathlessly—and with zero evidence—that ISIS terrorists would sneak across our southern border and bring Ebola with them. It was a right-wing conspiracy theory trifecta.
In the run-up to the 2014 midterms, Bill and I both campaigned hard across the country for endangered Democratic incumbents and competitive challengers. Late at night, we'd compare notes about the anger, resentment, and cynicism we were seeing, and the vicious Republican attacks fueling it.
For years, GOP leaders had stoked the public's fears and disappointments. They were willing to sabotage the government in order to block President Obama's agenda. For them, dysfunction wasn't a bug, it was a feature. They knew that the worse Washington looked, the more voters would reject the idea that government could ever be an effective force for progress. They could stop most good things from happening and then be rewarded because nothing good was happening. When something good did happen, such as expanding health care, they would focus on tearing it down, rather than making it better. With many of their voters getting their news from partisan sources, they had found a way to be consistently rewarded for creating the gridlock voters say they hate.
The success of this strategy was becoming evident. In 2014, in Georgia and North Carolina, I campaigned for two smart, talented, independent-minded candidates who should have had a good chance to win: Michelle Nunn and Senator Kay Hagan. Both races were tight up until the end. But days before the election, a savvy Georgia political observer confided to me that he'd seen private polling that showed Nunn and other Democrats cratering. Republicans were using fears about ISIS and Ebola to scare people and raise questions about whether a Democrat, especially a woman, could really be tough enough on national security.
In several states, Republicans ran an ad mixing images of Ebola responders in hazmat suits with photos of President Obama playing golf. It's ironic to remember that now, with Donald Trump spending about 20 percent of his new presidency at his own luxury golf clubs. I sometimes wonder: If you add together his time spent on golf, Twitter, and cable news, what's left?
Bill told me about a particularly troubling conversation he had with an old friend who lived up in the Ozarks of northern Arkansas. He had become an endangered species in Arkansas—a still-loyal, progressive Democrat. Bill called and asked our friend if he thought two-term Senator Mark Pryor could be reelected. Mark was a moderate Democrat with a golden name. (His father, David, was an Arkansas legend, having served as Congressman, Governor, and Senator.) Mark had voted for Obamacare because he believed everyone deserved the high-quality health care he received when he suffered from cancer as a young man. Our friend said he didn't know, and he and Bill agreed the best way to find out was to visit a certain country store deep in the Ozarks where a couple hundred people regularly came out of the woods to buy food and talk politics.
When our friend got back, he called Bill and told him what the store owner had said: "You know, I always supported Clinton, and I like Mark Pryor a lot. He's a good man and fair to everyone. But we're going to give Congress to the Republicans." The store owner was no fool. He knew the Republicans wouldn't do anything for him and his neighbors. But he thought the Democrats hadn't done anything, either. "And at least the Republicans won't do anything to us," he said. "The Democrats want to take away my gun and make me go to a gay wedding."
Sure enough, Mark lost big on Election Day to Tom Cotton, one of the most right-wing members of Congress. It wasn't that voters were turning away from the policies Mark and other Democrats had championed—in fact, in the same election, they passed an increase in the state's minimum wage. But the politics of cultural identity and resentment were overwhelming evidence, reason, and personal experience. It seemed like "Brexit" had come to America even before the vote in the United Kingdom, and it didn't bode well for 2016. Our party might have won the popular vote in five of the past six presidential elections, but the political landscape for the 2016 race was shaping up to be extremely challenging.
As if all this wasn't enough to worry about, there was also the simple, inescapable fact that I was turning sixty-eight years old. If I ran and won, I would be the oldest President since Reagan. I suspected there'd be waves of rumor-mongering about my health—and everything else in my life. It would be invasive, crass, and insidious. But contrary to persistent rumors made up and spread by the right-wing media, my health was excellent. I had recovered fully from the concussion I suffered in late 2012. And the whole world could see I had no trouble keeping up a punishing travel schedule. I admired the likes of Diana Nyad, who at the age of sixty-four became the first person to swim from Cuba to Florida without a shark cage. When she finally emerged back on dry land, she offered three pieces of advice: Never ever give up. You're never too old to chase your dreams. And even if something looks like a solitary sport, it's a team effort. Words to live by!
Still, is this how I wanted to spend my time? Did I really want to put myself back in front of the firing squad of national politics for years on end, first in the campaign and then, hopefully, in the White House? Some of my dearest friends—including my longtime advisors and former chiefs of staff in the White House and the State Department, Maggie Williams and Cheryl Mills—told me I would be crazy to do it. Plenty of other people in my position had passed up the chance to run: everyone from General Colin Powell, to Mike Bloomberg, to New York Governor Mario Cuomo, who came so close to running, he had an airplane waiting on the tarmac to take him to New Hampshire when he finally decided "no."
* * *
* * *
So why did I do it?
I did it because when you clear away all the petty and not-so-petty reasons not to run—all the headaches, all the obstacles—what was left was something too important to pass up. It was a chance to do the most good I would ever be able to do. In just one day at the White House, you can get more done for more people than in months anywhere else. We had to build an economy that worked for everyone and an inclusive society that respected everyone. We had to take on serious national security threats. These were issues already on my mind all the time, and they would all require a strong, qualified President. I knew I would make the most of every minute. Once I started thinking about it that way, I couldn't stop.
As it happened, the person who gave me the chance to serve as Secretary of State would once again play a decisive role.
A month after I left the State Department in 2013, Barack and Michelle invited Bill and me to join them for a private dinner in the White House residence. The four of us talked about our kids and the experience of raising them in the fishbowl of the White House. We discussed life after the Oval Office. Barack and Michelle mused about maybe one day moving to New York, just as we had done. That prospect still felt very far away. We all had high hopes for Barack's second term. There was a lot of unfinished business, both at home and around the world. We ended up staying for hours, talking late into the night. If (back in the heated days of 2008) any of us could have gotten a glimpse of that evening, we wouldn't have believed it.
Over the next year or so, the President and I kept in regular touch. He invited me back for lunch that summer, and the two of us sat out on the terrace outside the Oval Office eating jambalaya. I think he was just a tiny bit jealous of my newfound freedom, which was a good reminder of how all-consuming the job is. We had lunch again the following spring. Some of the time the President and I talked about work, especially the foreign policy challenges he was facing in the second term. But gradually, as 2013 turned into 2014, our conversations turned more frequently to politics.
President Obama knew the challenges facing Democrats. He never took his reelection for granted, and while it was a resounding win in 2012 (the legitimately resounding kind), he knew that his legacy depended to a large degree on a Democratic victory in 2016. He made it clear that he believed that I was our party's best chance to hold the White House and keep our progress going, and he wanted me to move quickly to prepare to run. I knew President Obama thought the world of his Vice President, Joe Biden, and was close to some other potential candidates, so his vote of confidence meant a great deal to me. We had our differences in both style and substance, but overwhelmingly we shared the same values and policy goals. We both saw ourselves as pragmatic progressives trying to move the country forward in the face of implacable opposition from a Republican Party that had been taken over by the radical-conservative Tea Party fringe and was in thrall to its billionaire backers. I shared the President's sense of urgency about how much was at stake in 2016, but I still wasn't entirely sold that running was the right decision for me.
As I had found when he insisted that I become Secretary of State and literally wouldn't take no for an answer, President Obama is a persuasive and persistent advocate. In the summer of 2013, David Plouffe, Obama's former campaign manager who engineered my defeat in 2008, offered to provide any help and advice he could as I planned my next steps after leaving the State Department. I invited him over to my house in Washington, and quickly saw why the President had leaned on him so much. He really knew his stuff. We met again in September 2014, when he visited my house once more to give me a presentation about what it would take to build a winning presidential campaign. He spoke in detail about strategy, data, personnel, and timing. I listened carefully, determined that if I did jump into the race, I would avoid the mistakes that had dogged me the last time. Plouffe emphasized that time was of the essence, as hard as that was to believe more than two years before the election. In fact, he said I was late already and urged me to get started. He was right.
For me, political campaigns have always been something to get through in order to be able to govern, which is the real prize. I'm not the most natural politician. I'm a lot better than I'm usually given credit for, but it's true that I've always been more comfortable talking about others rather than myself. That made me an effective political spouse, surrogate, and officeholder, but I had to adjust when I became a candidate myself. At the beginning, I had to actively try to use the word I more. Luckily, I love meeting people, listening, learning, building relationships, working on policy, and trying to help solve problems. I would have loved to meet all 320 million Americans one at a time. But that's not how campaigns work.
In the end, I came back to the part that's most important to me. We Methodists are taught to "do all the good you can." I knew that if I ran and won, I could do a world of good and help an awful lot of people.
Does that make me ambitious? I guess it does. But not in the sinister way that people often mean it. I did not want to be President because I want power for power's sake. I wanted power to do what I could to help solve problems and prepare the country for the future. It's audacious for anyone to believe he or she should be President, but I did.
I started calling policy experts, reading thick binders of memos, and making lists of problems that needed more thought. I got excited thinking about all the ways we could make the economy stronger and fairer, improve health care and expand coverage, make college more affordable and job training programs more effective, and tackle big challenges, such as climate change and terrorism. It was honestly a lot of fun.
I talked with John Podesta, a longtime friend who had been Bill's Chief of Staff in the White House and was also a top advisor to President Obama. If I was going to do this again, I would need John's help. He promised that if I ran, he'd leave the White House and become chairman of my campaign. He thought we could put together a fantastic team very quickly. An energetic grassroots group called Ready for Hillary was already drumming up support. All of that was very reassuring.
I thought back to what made me run for Senate the first time. It was the late 1990s and Democrats in New York were urging me to run, but I kept turning them down. No First Lady had ever done anything like that before. And I hadn't run for office since I'd been student government president at Wellesley College.
One day I visited a school in New York with the tennis star Billie Jean King for an event promoting an HBO special about women in sports. Hanging above our heads was a big banner proclaiming the title of the film, Dare to Compete. Before my speech, the seventeen-year-old captain of the high school basketball team introduced me. Her name was Sofia Totti. As we shook hands, she bent down and whispered in my ear, "Dare to compete, Mrs. Clinton. Dare to compete." Something just clicked. For years, I had been telling young women to step up, participate, go for what you believe in. How could I not be willing to do the same? Fifteen years later, I was asking myself the same question.
There wasn't one dramatic moment where I declared, "I'm doing it!" Bill and I closed out 2014 with a trip to the beautiful home of our friends Oscar and Annette de la Renta in the Dominican Republic. We swam, ate good food, played cards, and thought about the future. By the time we got back, I was ready to run.
The most compelling argument is the hardest to say out loud: I was convinced that both Bill and Barack were right when they said I would be a better President than anyone else out there.
I also thought I'd win. I knew that Republicans had moved much further from the vital center of American politics than Democrats had, as nonpartisan political scientists have documented. But I still believed that the United States was a pretty sensible country. Previous generations faced much worse crises than anything we've seen, from the Civil War to the Great Depression, from World War II to the Cold War, and they responded by electing wise and talented leaders. Only rarely have Americans gotten carried away by extremes or enthralled by ideology, and never for long. Both major political parties, despite the madness of their respective nominating processes, nearly always managed to weed out the most extreme candidates. Before 2016, we'd never elected a President who flagrantly refused to abide by the basic standards of democracy and decency. If I was the best-qualified candidate, had good ideas about the future, held my own on the trail and in the debates, and demonstrated a capacity to get things done with both Republicans and Democrats, it was reasonable to believe I could get elected and be able to govern effectively.
That's why I ran.
There are things I regret about the 2016 campaign, but the decision to run isn't one of them.
I started this chapter with some lines from T. S. Eliot's poem "East Coker" that I've always loved:
There is only the fight to recover what has been lost
And found and lost again and again: and now, under conditions
That seem unpropitious. But perhaps neither gain nor loss.
For us, there is only the trying. The rest is not our business.
When I first read that, as a teenager in Park Ridge, Illinois, it struck a chord somewhere deep inside, maybe in that place where dim ancestral memories of indomitable Welsh and English coal miners hid alongside half-understood stories from my mother's childhood of privation and abandonment. "There is only the trying."
I went back to that poem a few years later, in 1969, when my classmates at Wellesley asked me to speak at our graduation. Many of us were feeling dismayed and disillusioned by the Vietnam War and the racial injustice in America, the assassinations of Dr. Martin Luther King Jr. and Robert F. Kennedy, and our seeming inability to change our country's course. My paraphrasing gave Eliot's elegant English verse a Midwestern makeover: "There's only the trying," I told my classmates, "again and again and again; to win again what we've lost before."
In the nearly fifty years since, it's become a mantra for me and our family that, win or lose, it's important to "get caught trying." Whether you're trying to win an election or pass a piece of legislation that will help millions of people, build a friendship or save a marriage, you're never guaranteed success. But you are bound to try. Again and again and again.
I want to be thoroughly used up when I die, for the harder I work, the more I live. Life is no "brief candle" to me. It is a sort of splendid torch which I have got hold of for the moment; and I want to make it burn as brightly as possible before handing it on to future generations.
—George Bernard Shaw
## Getting Started
You could say my campaign for President began with a snappy internet video filmed in April 2015 outside my home in Chappaqua. Or you could point to my formal announcement speech that June on Roosevelt Island in New York. But I think it started with something a lot more ordinary: a Chipotle burrito bowl.
If you're wondering what I'm talking about, you probably don't spend much time in the carnival fun house of cable and internet news. It was April 13, 2015, in Maumee, Ohio. Chipotle was a pit stop on my road trip from New York to Iowa, home of the first-in-the-nation caucus. It was a purposefully low-key trip. No press, no crowds. Just me, a few staff, and Secret Service agents. We bundled into an oversized black van I call "Scooby" because it reminds me of the Scooby-Doo Mystery Machine (our van has less shaggy psychedelic charm, but we love it just the same), and set out on our thousand-mile journey. I had a stack of memos to read and a long list of calls to make. I had also googled every NPR station from Westchester to Des Moines—all set for a long drive.
In Maumee, we pulled into the parking lot of a strip mall off the highway for lunch. I ordered a chicken burrito bowl with a side of guacamole. Nick Merrill, my traveling press secretary, made fun of me for eating it out of the little cup with a spoon, bypassing the chips. Nobody in the restaurant thought it was remarkable that I was there. In fact, nobody recognized me. Bliss!
But when members of the press found out, they reacted like a UFO had landed in Ohio and an extraterrestrial had wandered into a Chipotle. CNN ran grainy footage from the restaurant's security camera, which made it look a little like we were robbing a bank. The New York Times did an analysis that concluded my meal was healthier than the average Chipotle order, with fewer calories, saturated fat, and sodium. (Good "get" for the Times; they really ate CNN's lunch on that one.) The whole thing felt silly. To paraphrase an old saying, sometimes a burrito bowl is just a burrito bowl.
* * *
* * *
Soon I was back in Iowa, the state that handed me a humbling third-place finish in 2008. Like the road trip, I wanted this first visit to be no-frills. I would do more listening than talking, just as I had at the start of my first Senate campaign in New York. My new state director, Matt Paul, who knew Iowa inside and out after years of working for Governor Tom Vilsack and Senator Tom Harkin, agreed. Iowans wanted to get to know their candidates, not just listen to them give speeches. That's exactly what I wanted, too.
When Donald Trump started his campaign, he seemed confident that he already had all the answers. He had no ideological core apart from his towering self-regard, which blotted out all hope of learning or growing. As a result, he had no need to listen to anyone but himself.
I approached things differently. After four years traveling the world as Secretary of State, I wanted to reconnect with the problems that were keeping American families up at night and hear directly about their hopes for the future. I had a core set of ideas and principles but wanted to hear from voters to inform new plans to match what was really going on in their lives and in the country.
One of the first people I met in New Hampshire, another early contest state, provided a case in point. Pam was a grandmother in her fifties with gray hair and the air of someone who carries a lot of responsibility on her shoulders. She was an employee of a 111-year-old family-run furniture business I visited in Keene. We were talking about how to help small businesses grow, but Pam had a different challenge on her mind. Her daughter had gotten hooked on pain medication after giving birth to a baby boy, which led to a long struggle with drug addiction. Eventually Child and Family Services started calling Pam, warning that her grandson could end up in foster care. So she and her husband, John, took the child in, and Pam found herself back in the role of primary caretaker she thought she had finished years before.
Pam wasn't the complaining type. This was a labor of love, and she was glad to pick up the slack, especially now that her daughter was in treatment. But she was worried. A lot of families in town were facing similar struggles. In New Hampshire, more people were dying from drug overdoses than from car crashes. The number of people seeking treatment for heroin addiction had soared 90 percent over the past decade. For prescription drugs, the number was up 500 percent.
I knew a little about this. At the time, Bill and I were friends with three families who had lost young adult children to opioids. (Sadly, that number has now grown to five.) One was a charismatic young man who worked at the State Department while he was in law school. A friend of his offered some pills, he took them, went to sleep that night, and never woke up. Others took drugs after drinking, and their hearts stopped. After these tragedies, the Clinton Foundation partnered with Adapt Pharma to make available free doses of the opioid antidote naloxone (Narcan), which can save lives by helping prevent overdoses, to every high school and college in the United States.
On that first visit to New Hampshire, in a coffee shop in downtown Keene, a retired doctor leaned in and asked, "What can you do about the opioid and heroin epidemic?" It was chilling to hear that word, epidemic, but it was the right one. In 2015, more than thirty-three thousand people died from overdosing on opioids. If you add to that the number from 2014, it's more Americans than were killed in the entire Vietnam War. Resources for treatment couldn't come close to keeping up. Parents liquidated their savings to pay for their kids' treatment. Some called the police about their own children because they had tried everything else.
Yet despite all this, substance abuse wasn't getting much national attention, either in Washington or in the national media. I didn't think about it as a campaign issue until I started hearing stories like Pam's in Iowa and New Hampshire.
I called my policy team together and told them we had to get working right away on a strategy. My advisors fanned out. We held town hall meetings and heard more stories. In one session in New Hampshire, a substance abuse counselor asked anyone who had been impacted by the epidemic to raise his or her hand. Nearly every hand in the room went up. A woman in treatment told me, "We're not bad people trying to get good. We're sick people trying to get well."
To help her and millions of others do that, we came up with a plan to expand access to treatment, improve training for doctors and pharmacists prescribing prescription drugs, reform the criminal justice system so more nonviolent drug offenders end up in rehab instead of prison, and make sure every first responder in America carries naloxone, which is close to a miracle drug.
This became a model for how my campaign operated in those early months. People told me story after story about the challenges their families faced: student debt, the high cost of prescription drugs and insurance premiums, and wages too low to support a middle-class life. I'd use those conversations to guide the policies already being hammered out back in our Brooklyn headquarters. I wanted my policy shop to be bold, innovative, industrious, and, most importantly, responsive to people's real-life needs. Jake Sullivan, my director of policy planning at the State Department; Ann O'Leary, a longtime advisor of mine who shared my passion for children and health care policy; and Maya Harris, a veteran civil rights advocate, built and led a great team.
You can compare this to how Trump operated. When the opioid epidemic finally started getting news attention, he jumped on it as a way of making people believe that America was falling apart. But once he became President, he turned his back on everyone who needed help by seeking to cut money for treatment.
The press often seemed bored by the roundtables where these conversations happened. Critics dismissed them as staged or carefully controlled. But I wasn't bored. I wanted to talk with people, not at them. I also learned a lot. To me, this was a big part of what running for President was supposed to be.
* * *
* * *
Over the long months that I had weighed running a second time, I thought a lot about what kind of campaign I'd want. I certainly wanted one different from the one I ran during my 2008 primary loss to Barack Obama. I studied what he did right and I did wrong. There was more to learn after 2012, when the President put together another strong campaign that helped him win reelection over Mitt Romney by a healthy margin despite a lackluster economy. His operations were two of the best ever. I paid attention.
My low-profile first trip to Iowa reflected some of the lessons that I kept in mind as I started to put my own organization in place. In 2008, I had been criticized for arriving in Iowa like a queen, holding big rallies and acting like victory was inevitable. I never thought that was a fair description of me or our campaign; we believed I could prevail in a crowded and talented field, but we certainly didn't take Iowa for granted. In fact, we recognized that it wasn't an ideal first contest for me and spent a fair amount of 2007 trying to figure out how to make the best of it. Still, the criticism stuck, and I took it seriously. This time I was determined to run like an underdog and avoid any whiff of entitlement.
I also wanted to build on the best parts of my 2008 effort, especially the fighting spirit of our campaigns in Ohio and Pennsylvania, where I succeeded in forming a bond with working-class voters who felt invisible in George W. Bush's America. I had dedicated my victory in the Ohio primary to everyone "who's ever been counted out but refused to be knocked out, for everyone who has stumbled but stood right back up, and for everyone who works hard and never gives up." I wanted to bring that spirit to the 2016 campaign, along with the best lessons of Obama's victories.
We sought to set the right tone with my announcement video. It showed a series of Americans talking excitedly about new challenges they were taking on: two brothers starting a small business, a mom getting her daughter ready for the first day of kindergarten, a college student applying for her first job, a couple getting married. Then I appeared briefly to say that I was running for President to help Americans get ahead and stay ahead, and that I was going to work hard to earn every vote. This campaign wasn't going to be about me and my ambitions. It would be about you and yours.
There were other lessons to put into action. In 2008, the Obama campaign had been way ahead of us in using advanced data analytics to model the electorate, target voters, and test messages. It focused relentlessly on grassroots organizing and winning the delegates who would actually decide the nomination. It also built a "no drama" campaign organization that largely avoided damaging infighting and leaks.
John Podesta and I talked with President Obama and David Plouffe about how to construct a team that could replicate these successes. Plouffe was a big fan of Robby Mook, whom I ultimately chose as campaign manager. Robby had impressed David by helping me win against the odds—and against him—in Nevada, Ohio, and Indiana in 2008. In all three states, he put together aggressive field programs and competed hard for every vote. Then he went on to manage my friend Terry McAuliffe's successful longshot campaign for Governor of Virginia. Robby was on a roll—young but, like Plouffe, highly disciplined and levelheaded, with a passion for data and a talent for organizing.
Huma Abedin, my trusted and valued advisor for years, would be campaign vice chair. President Obama praised his pollsters Joel Benenson and John Anzalone and focus group expert David Binder, so I hired all three, as well as a veteran of the Obama data analytics team, Elan Kriegel. Navin Nayak came on board to coordinate all these different elements of opinion research. Here's how to keep it all straight: pollsters call up a random sample of people and ask their opinions about candidates and issues; focus groups gather a handful of people together in a room for an in-depth discussion that can last several hours; and data analytics teams make a lot of survey calls, crunch huge amounts of additional demographic, consumer, and polling data, and feed it all into complex models that try to predict how people will vote. These are all staples of modern campaigns.
To help guide messaging and create ads, I hired Jim Margolis, a respected Obama veteran, and Mandy Grunwald, who had been with me and Bill since our first national campaign in 1992. They worked with Oren Shur, my director of paid media, and several talented and creative ad agencies. I thought Jim's and Mandy's partnership would represent the best of both worlds. That's what I was going for with all my hiring decisions: mix the best available talent from the Obama campaigns with top-notch pros I already knew. The latter category included Dennis Cheng, who had raised hundreds of millions of dollars for my 2006 Senate reelection campaign and 2008 presidential campaign, and later helped build up the Clinton Foundation endowment; Minyon Moore, one of the most experienced political operatives in Democratic politics and a veteran of my husband's White House; and Jose Villarreal, a business leader who had worked with me at State and came on board to serve as my campaign treasurer.
As I built my team, I was focused on two tricky areas: how to strike the right balance with President Obama and his White House, and—drumroll for emphasis—how to improve my relationship with the press.
The challenge of striking a balance with President Obama wasn't personal at all. After four years in his Cabinet, we liked and trusted each other. There aren't many people in the world who know what it's like to run for President or live in the White House, but we had that in common, and it gave us a special bond. When he finally passed health care reform, something I had fought for long and hard, I was overjoyed and gave him a big hug before a meeting in the White House Situation Room. After his rough first presidential debate with Mitt Romney in 2012, I tried to cheer him up with a photoshopped image of Big Bird strapped to Mitt's family car. (Romney had promised to slash funding for PBS, and also famously took road trips with his dog on the roof of his car.)
"Please take a look at the image below, smile, and then keep that smile near at hand," I told the President.
"We'll get this done," he replied. "Just hold the world together five more weeks for me."
Now that we had switched places, and I was the candidate and he was the cheerleader, the challenge for me was navigating the tension between continuity and change. On the one hand, I believed deeply in what he had accomplished as President and desperately wanted to make sure a Republican wouldn't be able to undo it all. We might have areas of disagreement, such as on Syria, trade, and how to deal with an aggressive Russia, but by and large, I would defend his record, try to build on his accomplishments, and listen to his advice. He would call from time to time and share his thoughts on the race. "Don't try to be hip, you're a grandma," he'd tease. "Just be yourself and keep doing what you're doing." I was proud to have Barack's support, and nearly every day told audiences around the country that he didn't get the credit he deserved for putting our country back together after the worst financial crisis since the Great Depression.
At the same time, there were big problems that still needed fixing in America, and part of my job as candidate was to make it clear that I saw them and was ready to take them on. Inevitably, that meant pointing out areas where the Obama administration's efforts had fallen short, even if the main culprit was Republican obstruction.
It was a fine line to walk, as it would have been for Vice President Biden or anyone who had served in the Obama administration. If I failed to strike the right balance, I ran the risk of either seeming disloyal or being cast as the candidate of the status quo, both of which would be damaging.
In one of the first meetings of our new team, in a conference room on the twenty-ninth floor of a Midtown Manhattan office building, Joel Benenson presented the results of his early opinion research. He said Americans had two main "pain points" that would likely shape their views of the election: economic pressure and political gridlock. The economy was definitely in better shape than it had been after the financial crisis, but incomes hadn't begun to rise for most families, so people still felt like their progress was fragile and could be ripped away at any moment. And they had come to view dysfunction in Washington as a big part of the problem. They were right. I had seen that dysfunction firsthand and knew how hard it would be to break through it—although I think it's fair to say I underestimated how my opponents would wrongly accuse me of being responsible for a broken system. I had a record of success working with Republicans over the years. I had plans for aggressive campaign finance reform, which would remove some of the profit motive behind the gridlock. And I believed we had a strong shot at making progress. The problem remained: how to find a compelling way to talk about the pain Americans felt and their dissatisfaction with how things were going in the country, without reinforcing Republican criticisms of the Obama administration, which would be self-defeating and just plain wrong.
Joel said I was starting from a strong place. Fifty-five percent of voters in the battleground states had a favorable view of me, compared with just 41 percent with an unfavorable view. Voters liked that I had worked for Obama after losing to him in 2008. They thought it showed loyalty and patriotism. They also thought I had done a good job as Secretary of State, and most believed I was ready to be President. But even though I'd been in the public eye for decades, they knew little about what I had actually done, much less why I had done it. This presented both a challenge and an opportunity. Despite having near-universal name recognition, I would have to reintroduce myself—not as an extension of Bill Clinton or Barack Obama but as an independent leader with my own story, values, and vision.
There were also some warning signs to worry about. While my approval ratings were high, just 44 percent of voters said they trusted me to be their voice in Washington. That told us that some people respected me but weren't sure I was in it for them. I was determined to change that perception. The reason I had gotten into public service was to make life better for children and families, and now it was my job to make sure people understood that.
There was something else we needed to do: avoid repeating past problems with the political press corps. Over the years, my relationship with the political press had become a vicious cycle. The more they went after me, the more guarded I became, which only made them criticize me more. I knew that if I wanted 2016 to be different, I was going to have to try to change the dynamic and establish a more open and constructive give-and-take. There was some precedent. As a Senator, I got along surprisingly well with the rough-and-tumble journalists of New York. And I grew downright fond of the State Department press corps, which consisted largely of journalists who had written about foreign policy for years. We talked easily, went out together on the road, toured Angkor Wat in Cambodia, dined in a Bedouin tent in Saudi Arabia, danced in South Africa, and had adventures all over the globe. For the most part, they covered me fairly, and when I felt they didn't, they were open to my criticism. Now I would try to establish a similar rapport with the political reporters covering the campaign. I knew they were under constant pressure to write stories that would drive clicks and retweets, and that negative stories sell. So I was skeptical. But it was worth a shot.
To help me do it, I hired Jennifer Palmieri, a savvy professional with strong press relationships. Jennifer had worked for John Podesta in the Clinton White House and at the Democratic think tank the Center for American Progress. Most recently, she had been President Obama's Communications Director in the White House. The President loved Jennifer, and so did I. I asked Kristina Schake, a former top aide to Michelle Obama, and later Christina Reynolds, who had worked on the John Edwards and Obama campaigns, to be her deputies. They were joined by national press secretary Brian Fallon, a graduate of the acclaimed Chuck Schumer school of communications and a former spokesman for the Department of Justice, and Karen Finney, the former MSNBC host who had first worked for me in the White House. When Jennifer, Kristina, and I sat down together for the first time, I let two decades' worth of frustrations with the press pour out. Buckle up, I said, this is going to be a rough ride. But I was ready to try whatever they recommended to get off on a better foot this time.
With my senior team coming together, we got to work building an organization that could go the distance. Presidential campaigns are like start-ups on steroids. You have to raise an enormous amount of money very quickly, hire a huge staff, deploy them across the country, and build a sophisticated data operation largely from scratch. As a candidate, you have to manage all that while maintaining a grueling campaign schedule that keeps you hundreds or thousands of miles from headquarters nearly every day.
In 2008, I had a good, hardworking team. But I allowed internal rivalries to fester and didn't establish a clear chain of command until it was too late. Still, we came so close to winning. I vowed that this time we would do things differently.
I was determined to have the best data, the most field organizers, the biggest fund-raising network, and the deepest political relationships. I was thrilled that Beth Jones, a talented manager working at the White House, agreed to be campaign chief operating officer. To lead our organizing and outreach efforts, I turned to three political pros: Marlon Marshall, Brynne Craig, and Amanda Renteria. I also hired experienced organizers to run the key early states. In addition to Matt Paul in Iowa, there was Mike Vlacich, who helped reelect my friend Senator Jeanne Shaheen in New Hampshire and led my efforts to beat Trump there in November; Emmy Ruiz, who helped lead us to victory in the Nevada caucus before moving to Colorado for the general and helping us win there, too; and Clay Middleton, a longtime aide to Congressman Jim Clyburn, who helped us win a landslide victory in the South Carolina primary.
To infuse the campaign with a spirit of innovation, we got advice from Eric Schmidt, the former CEO of Google, and other top tech leaders, and hired engineers from Silicon Valley. Stephanie Hannon, an experienced engineer, became the first woman to serve as chief technology officer on a major presidential campaign. I hired one of President Obama's former aides, Teddy Goff, to handle all things digital, along with my longtime advisor Katie Dowd and Jenna Lowenstein from EMILY's List. They had a tough job on their hands with a less-than-tech-savvy candidate, but I promised to be a good sport about every Facebook chat, tweetstorm, and Snapchat interview they recommended.
To make sure we built the most diverse team ever assembled by a presidential campaign, I brought in Bernard Coleman as the first-ever chief diversity officer, made sure women were half the staff, and hired hundreds of people of color, including for senior leadership roles.
We put our headquarters in Brooklyn and the office soon teemed with idealistic, sleep-deprived twentysomethings. It felt like a cross between a tech start-up and a college dorm. I've been a part of a lot of campaigns going all the way back to 1968, and this was the most collegial and collaborative I've ever seen.
So how did it go?
Well, we didn't win.
But I can say with zero equivocation that my team made me enormously proud. They built a fantastic organization in the early states and helped me win the Iowa caucus, despite tough demographics, as well as the Nevada caucus and the South Carolina primary. In the general election, they recruited fifty thousand more volunteers than the 2012 Obama campaign did and contacted voters five million more times. My team absorbed one gut punch after another and never gave up, never turned on one another, and never stopped believing in our cause. That doesn't mean there weren't disagreements and debates over a wide range of questions. Of course there were—it was a campaign, for heaven's sake. But even on the night of our landslide defeat in the New Hampshire primary or during the worst days of the email controversy, nobody buckled.
And have I mentioned that we went on to win the national popular vote by nearly three million?
It was a terrific group of people. And I'm not just talking about the senior leadership. All the young men and women crowded around desks at headquarters in Brooklyn, working impossible hours . . . all the field organizers who were the heart and soul of the campaign . . . all the advance staff who lived out of suitcases for two years, organizing and staging events across the country . . . volunteers of every age and background—more Americans volunteered more time for the 2016 campaign than for any campaign in U.S. history. My team was full of dedicated people who left families and friends to move someplace new, knock on doors, make phone calls, recruit volunteers, and persuade voters. They worked intensely while juggling relationships, welcoming newborn babies, and handling other family obligations. Two of my young communications aides, Jesse Ferguson and Tyrone Gayle, kept working through difficult cancer treatments, never losing their devotion to the campaign or their senses of humor.
Some of my favorite moments out on the trail were when a volunteer would come up to me as I shook hands on a rope line after a rally. They'd whisper in my ear about what a great job our local organizer was doing or how welcoming our staff was to people who wanted to help and how their enthusiasm was infectious. That always made my day. The fact that so many of these young people have decided to stay in politics and keep up the fight despite our loss makes me very happy and proud.
Having said all that, of course the campaign didn't go as planned. I ended up falling into many of the pitfalls I had worried about and tried to avoid from the start. Some of that was my own doing, but a lot of it was due to forces beyond my control.
Despite my intention to run like a scrappy challenger, I became the inevitable front-runner before I shook my first hand or gave my first speech, just by virtue of sky-high expectations.
The controversy over my emails quickly cast a shadow over our efforts and threw us into a defensive crouch from which we never fully recovered. You can read plenty more about that later in this book, but suffice it to say that one boneheaded mistake turned into a campaign-defining and -destroying scandal, thanks to a toxic mix of partisan opportunism, interagency turf battles, a rash FBI director, my own inability to explain the whole mess in a way people could understand, and media coverage that by its very volume told the voters this was by far the most important issue of the campaign. Most people couldn't explain what it was really all about or how the allegations that I was a threat to national security squared with the support I had from respected military and civilian national security experts, including Republicans and Independents, but they understandably came away with the impression I had done a big, bad thing.
One result was that, right away, I was back in my usual adversarial relationship with the press, clamming up and trying to avoid "Gotcha!" interviews at a time when I needed to be reintroducing myself to the country. I watched my approval numbers drop and my disapproval and distrust numbers rise, as my message about all the things I wanted to do as President was blocked or overwhelmed.
There were other disappointments as well. In 2008, critics had slammed me for not being accessible to voters and avoiding traditional grip-and-grin campaigning. This time they went the other way and ridiculed my intimate listening sessions. "Where are the rallies? Why can't she draw a crowd?" they'd ask. That "enthusiasm" question never really went away, even when we drew large crowds.
Other than Iowa and Nevada, where we built extensive organizations, I struggled in caucuses just as I had the last time. By their structure and rules, caucuses favor the most committed activists who are willing to spend long hours waiting to be counted. That gave the advantage to the insurgent left-wing candidacy of Bernie Sanders. My advantage came in primaries, which have secret ballots and all-day voting, like a typical election, and much higher turnout. The difference was most clear in Washington State, which held both a caucus and a primary. Bernie won the caucus in March, and I won the primary in May, in which three times as many people voted. Unfortunately, most of the delegates were awarded based on the caucus.
Ultimately, none of this mattered much after I built up a large delegate lead in March. What did matter, and had a lasting impact, was that Bernie's presence in the race meant that I had less space and credibility to run the kind of feisty progressive campaign that had helped me win Ohio and Pennsylvania in 2008.
One piece of advice that President Obama gave me throughout the campaign was that we needed more message discipline, and he was right. In 1992, Bill relied on James Carville and Paul Begala to help him shape his winning message, and they made sure that everyone in the campaign—including the candidate—stuck to it day after day after day. In 2016, my campaign was blessed with many brilliant strategists, and they helped me develop a message, Stronger Together, that reflected my values and vision and a clear contrast with Trump. It may not have been catchy enough to break through the wall of negative coverage about emails—maybe nothing could—but it was the case I wanted to make. And when voters got a chance to hear from me directly, at the convention and in the debates, polls showed they liked what they heard.
It's true, though, that we struggled to stay on message. My advisors had to deal with a candidate—me—who often wanted something new to say, as opposed to just repeating the same stump speech over and over. In addition, more than in any race I can remember, we were constantly buffeted by events: from the email controversy, to WikiLeaks, to mass shootings and terrorist attacks. There was no such thing as a "normal day," and the press didn't cover "normal" campaign speeches. What they were interested in was a steady diet of conflict and scandal. As a result, when it came to driving a consistent message, we were fighting an uphill battle.
Add all this together, and I think you get a picture of a campaign that had both great strengths and real weaknesses—just like every campaign in history. There are important lessons to learn from what we got right and what we got wrong. But I totally reject the notion that it was an unusually flawed or dysfunctional campaign. That's just wrong. My team battled serious headwinds to win the popular vote, and if not for the dramatic intervention of the FBI director in the final days, I believe that in spite of everything, we would have won the White House. I've been criticized harshly by political pundits for saying that, and even some of my supporters have said they agree with me but I shouldn't say it. If you feel this way, I hope you'll keep going and give my response a fair reading.
* * *
* * *
Since the election, I've asked myself many times if I learned the wrong lessons from 2008. Was I fighting the previous war when I should have been focused on how much our politics had changed?
Much has been made about my campaign's supposed overreliance on Obama-style big data, at the expense of more traditional political gut instinct and trusting folks on the ground. This is another criticism I reject. It's true that some of our models were off—just like everyone else's, including the media, the Trump campaign, everyone—probably because some Trump supporters refused to talk to pollsters or weren't honest about their preferences or because people changed their minds. It's also true that, like any large organization, we could have done a better job listening to the anecdotal feedback we were getting from folks on the ground. It's not like we didn't try. My team was constantly in touch with local leaders, and I had trusted friends reporting back to me from all over the country, including a big group of Arkansans—the Arkansas Travelers—who fanned out in nearly every state. I believe they helped us win the razor-close Missouri primary, and they were a constant source of information and perspective for me. But every precinct leader and party chair in the country wants more attention and resources. Sometimes they're right, sometimes they're wrong. You can't make those decisions blind. You have to be guided by the best data available. This isn't an either/or choice. You need both data and good old-fashioned political instinct. I'm convinced that the answer for Democrats going forward is not to abandon data but to obtain better data, use it more effectively, question every assumption, and keep adapting. And we need to listen carefully to what people are telling you and try to assess that too.
Still, in terms of fighting the previous war, I think it's fair to say that I didn't realize how quickly the ground was shifting under all our feet. This was the first election where the Supreme Court's disastrous 2010 Citizens United decision allowing unlimited political donations was in full force but the Voting Rights Act of 1965 wasn't because of another terrible decision by the court in 2013. I was running a traditional presidential campaign with carefully thought-out policies and painstakingly built coalitions, while Trump was running a reality TV show that expertly and relentlessly stoked Americans' anger and resentment. I was giving speeches laying out how to solve the country's problems. He was ranting on Twitter. Democrats were playing by the rules and trying too hard not to offend the political press. Republicans were chucking the rule book out the window and working the refs as hard as they could. I may have won millions more votes, but he's the one sitting in the Oval Office.
* * *
* * *
Both the promise and the perils of my campaign came together on a warm and brilliantly sunny June day in 2015, when I formally announced my candidacy in a speech to thousands of supporters on Roosevelt Island in New York's East River. Now the event seems almost like a quaint throwback to an earlier era of politics—a time when policies and polish were assets, not liabilities. Nonetheless, that hopeful, joyous day on Roosevelt Island will always rank as one of my favorites.
For weeks before the speech, I went back and forth with my team about what to say and how to say it. I've never been very adept at summing up my entire life story, worldview, and agenda in pithy sound bites. I was also acutely aware that, as the first woman to be a credible candidate for President, I looked and sounded different than any presidential candidate in our country's history. I had no precedent to follow, and voters had no historical frame of reference to draw upon. It was exhilarating to enter uncharted territory. But uncharted, by definition, means uncertain. If I felt that way, I was sure that a lot of voters would feel even more wary about it.
I also knew that despite being the first woman to have a serious chance at the White House, I was unlikely to be seen as a transformative, revolutionary figure. I had been on the national stage too long for that, and my temperament was too even-keeled. Instead, I hoped that my candidacy—and if things worked out, my presidency—would be viewed as the next chapter in the long progressive struggle to make the country fairer, freer, and stronger, and to beat back a seriously scary right-wing agenda. This framing took me directly into the politically dangerous territory of seeking a so-called third term after Obama and being seen as the candidate of continuity instead of change, but it was honest. And I thought placing my candidacy in the grand tradition of my progressive forebears would help voters accept and embrace the unprecedented nature of my campaign.
So when Huma suggested launching the campaign on Roosevelt Island, named after Franklin Delano, I knew it was the right choice. I'm something of a Roosevelt buff. First on the list will always be Eleanor. She was a crusading First Lady and progressive activist who never stopped speaking her mind and didn't give a damn what people thought. I return to her aphorisms again and again: "If I feel depressed, I go to work." "A woman is like a teabag: you never know how strong she is until she's in hot water." There was a minor Washington tempest back in the 1990s when a newspaper claimed I was having séances in the White House to commune directly with Eleanor's spirit. (I wasn't, though it would have been nice to talk to her now and then.)
I'm also fascinated by Eleanor's husband, Franklin, and her uncle Teddy. I was riveted by Ken Burns's seven-part documentary about all three Roosevelts that aired on PBS in 2014. I was particularly struck by the parallels between what Teddy faced as President in the early years of the twentieth century, as the industrial revolution upended American society, and what we faced in the early years of the twenty-first century. In both eras, disruptive technological change, massive income inequality, and excessive corporate power created a social and political crisis. Teddy responded by breaking up powerful monopolies, passing laws to protect working people, and safeguarding the environment. He may have been a Republican, but he put the capital P in Progressive. He was also a shrewd politician who managed to fend off the demands of angry populists on his left, who wanted to go even further toward Socialism, and conservatives on his right, who would have let the robber barons amass even more wealth and power.
Teddy found the right balance and called it the "Square Deal." I loved that phrase, and the more I thought about the challenges facing America in the years following the financial crisis of 2008–2009, the more I felt that what we needed was another Square Deal. We needed to regain our balance, take on the forces that had crashed our economy, and protect hardworking families shortchanged by automation, globalization, and inequality. We needed the political skill to restrain unchecked greed while defusing the most destructive impulses of resurgent populism.
On tough days out on the road, when reading the news felt like getting your teeth kicked in, I'd remember what Teddy said about those of us who climb into the arena. "It is not the critic who counts," he said, but the competitor "who strives valiantly; who errs, who comes short again and again, because there is no effort without error and shortcoming; but who does actually strive to do the deeds . . . who at the best knows in the end the triumph of high achievement, and who at the worst, if he fails, at least fails while daring greatly."
I also was inspired by Franklin Roosevelt's New Deal program of the 1930s, which saved capitalism from itself following the Great Depression, and by his vision of a humane, progressive, internationalist America. Four Freedoms Park, at the tree-lined tip of Roosevelt Island, commemorates the universal freedoms FDR proclaimed during World War II: freedom of speech and worship, freedom from want and fear. It's a picturesque spot with a striking view of the New York skyline. Announcing my candidacy there felt right.
The final few days were a flurry of marking up drafts and rewriting lines with Dan Schwerin, my longtime speechwriter, who had been with me since the Senate. As the campaign went on, he would be joined by Megan Rooney, a wonderful writer who spent four years traveling the world with me at State and then went to the White House to write for President Obama. Despite our best efforts, when the morning of June 13 dawned, I was still not quite satisfied. I turned to the bottom of page 4, the key moment in the speech, when I was supposed to say, "That's why I'm running for President." What followed, "to make our economy work for you and for every American," was true and important. It was the result of deliberation and debate with my senior advisors, culminating a few days before around the table in my dining room in Washington. I had put down a draft in frustration, declared myself finished with all the slogans and sound bites, and said that I was really running for President to make the economy work for everyone, and why didn't we just say that and be done with it?
But something was missing—emotional lift, a sense that we were setting out on a common mission to secure our shared destiny. I remembered a note that Dan and I had received a few days earlier from Jim Kennedy, a great friend who has a deft way with words. He reflected on a line from Roosevelt's "Four Freedoms" speech: "Our strength is our unity of purpose." America is a family, Jim noted, and we should have one another's backs. In that moment, I had no idea that the election would turn into a contest between the divisiveness of Donald Trump and my vision of an America that's "stronger together." But it felt right to call for shared purpose, to remind Americans that there is much more that unites us than divides us.
I picked up my ballpoint pen and, playing off Jim's language, wrote, "We Americans may differ, bicker, stumble, and fall; but we are at our best when we pick each other up, when we have each other's back. Like any family, our American family is strongest when we cherish what we have in common and fight back against those who would drive us apart."
A few hours later, I was standing at the podium in the blinding June sun, looking out at the excited faces of cheering supporters. I saw little kids perched on their parents' shoulders. Friends smiled up at me from the front row. Bill, Chelsea, and Marc were glowing with pride and love. The stage was shaped like our campaign logo: a big blue H with a red arrow cutting across the middle. All around it, a sea of people clapped, hollered, and waved American flags.
I allowed myself a moment to think, "This is really happening. I am going to run for President, and I am going to win." Then I started to speak. It was hard to read the teleprompter with the sun in my eyes, but I knew the words well by this point. It was a long speech, full of policies and insights developed over the previous months of listening to people such as Pam in New Hampshire. That's not everyone's cup of tea. But I thought it was the kind of speech a candidate for the most important job in the world ought to give: serious, substantive, honest about the challenges ahead, and hopeful about our ability to meet them.
I told a couple jokes. "I may not be the youngest candidate in this race," I said, "but I will be the youngest woman President in the history of the United States." Little did I know that, in fact, I would end up being the youngest candidate, running against septuagenarians Bernie Sanders and Donald Trump.
I was pleased with how the speech was received. The journalist Jon Allen, who has followed me over the years, declared, "Clinton pretty much nailed the vision thing." Jared Bernstein, Joe Biden's former top economic advisor, smartly described it as a "reconnection agenda" (I loved that) that aimed to "reunite economic growth with the prosperity of middle- and low-income families."
But it was E. J. Dionne, one of my favorite political commentators, who had the most thought-provoking—and, in retrospect, haunting—reaction. "Hillary Clinton is making a bet and issuing a challenge. The bet is that voters will pay more attention to what she can do for them than to what her opponents will say about her," E. J. wrote. "The challenge is to her Republican adversaries: Can they go beyond low-tax, antigovernment bromides to make credible counteroffers to the nurses, truckers, factory workers, and food servers whom Clinton made the heroes of her Roosevelt Island narrative about grace under pressure?"
We know now that I lost that bet—not because a Republican came along and made a more credible counteroffer to middle-class voters but because Donald Trump did something else: appeal to the ugliest impulses of our national character. He also made false promises about being on the side of working people. As Michael Bloomberg later said at the Democratic National Convention, "I'm a New Yorker, and I know a con when I see one." Me too.
As I would often do in big moments over the course of the campaign, I closed the speech by talking about my mother, Dorothy, who had passed away in 2011. She lived to be ninety-two years old, and I often thought about all the progress she witnessed over the course of her long life—progress won because generations of Americans kept fighting for what they knew to be right. "I wish my mother could have been with us longer," I said. "I wish she could have seen Chelsea become a mother herself. I wish she could have met Charlotte. I wish she could have seen the America we're going to build together." I looked out at the crowd and up at the New York skyline across the water, smiled, and said, "An America where a father can tell his daughter, yes, you can be anything you want to be—even President of the United States."
Time is the coin of your life. You spend it.
Do not allow others to spend it for you.
—Carl Sandburg
## A Day in the Life
A presidential campaign is a marathon run at the pace of a sprint. Every day, every hour, every moment counts. But there are so many days—nearly six hundred, in the case of the 2015–2016 campaign—that you have to be careful not to burn out before hitting the finish line.
President Obama drilled this point home when I was getting ready to run. He reminded me that when we faced off in 2008, we would often end up staying at the same hotel in Iowa or New Hampshire. He said his team would be finished with dinner and getting ready to call it a night when we finally got there, completely spent. By the time he woke up the next morning, we'd be long gone. In short, he thought we overdid it. "Hillary," he said, "you've got to pace yourself this time. Work smart, not just hard." Whenever we saw each other, he'd say it again, and he'd tell John and Huma to remind me.
I tried to follow his advice. After all, he won twice. My approach came down to two words: routine and joy. At the beginning, I put some routines in place to keep my traveling team and me as healthy and productive as possible through one of the hardest things any of us would ever do. And we all tried our best to savor every moment that came our way—to find joy and meaning in the daily grind of campaigning. Not a day went by when we didn't.
Since the election, my life and routine have changed greatly. But I still treasure many moments from that long and sometimes strange trip. Many mental snapshots that I took along the way are in this chapter. So are a lot of details about a typical day on the trail: what I ate, who did my hair and makeup, what my mornings were like.
It may seem strange, but I get asked about these things constantly. Philippe Reines, my longtime advisor, who played Trump in our debate prep sessions, has my favorite explanation why. He calls it the "Panda Principle." Pandas just live their lives. They eat bamboo. They play with their kids. But for some reason, people love watching pandas, hoping for something—anything—to happen. When that one baby panda sneezed, the video became a viral sensation.
Under Philippe's theory, I'm like a panda. A lot of people just want to see how I live. And I do love spending time with my family and getting some sun, just like a panda—and while I'm not into bamboo, I like to eat.
I get it. We want to know our leaders, and part of that is hearing about Ronald Reagan's jelly bean habit and Madeleine Albright's pin collection.
In that spirit, if you've ever wondered what a day in the life of a presidential candidate is like—or if you've ever asked yourself, "Does Hillary Clinton just . . . eat lunch, like a normal person?"—this is for you.
* * *
* * *
Six A.M.: I wake up, sometimes hitting the snooze button to steal a few more minutes. Snoozing leaves you more tired—there are studies on this—but in that moment, it seems like such a great idea.
As often as we can, we arrange my schedule so I can sleep in my own bed in Chappaqua. Many nights, that isn't possible, and I wake up in a hotel room somewhere. That's okay; I can sleep anywhere. It's not unusual for me to sleep through a bumpy plane landing. But waking up at home is the best.
Bill and I bought our home in 1999 because we loved the bedroom. It's one and a half stories high with a vaulted ceiling and windows on three sides. When we first saw it as prospective home buyers, Bill said that we would always wake up happy here, with the light streaming in and the view of the garden around us. He was right.
There's a colorful portrait of Chelsea in her late teens on one wall of our bedroom, and photos of family and friends scattered everywhere. We loved the wallpaper in our bedroom in the White House—yellow with pastel flowers—so I tracked it down for this bedroom too. There are stacks of books on our bedside tables that we are reading or hoping to read soon. For years, we've been keeping careful track of everything we read. Plus, Bill being Bill, he has a rating system. The best books get three stars.
After waking up, I check my email and read my morning devotional from Reverend Bill Shillady, which is usually waiting in my inbox. I spend a few minutes in contemplation, organizing my thoughts and setting my priorities for the day.
Then it's time for breakfast. When I'm home, I head downstairs. On the road, I order room service. It's hard to plan exactly what or when I'll be eating over the course of the day, since we're always on the go, so breakfast is key. Usually I opt for scrambled egg whites with vegetables. When they're around, I add fresh jalapeños. Otherwise, it's salsa and hot sauce. I'm a black coffee and strong black tea person, and I drink a huge glass of water in the morning and keep drinking water all day long, since I fly a lot, which can be dehydrating.
Over breakfast, I start reading the stack of press clips and briefing papers that have arrived overnight from my staff. If I'm home, Oscar Flores, a Navy veteran who had worked in the White House and is now our residence manager, prints it all out for me. I also take another look at the day's schedule, which is a logistical masterpiece. My team—Lona Valmoro, my invaluable scheduler since my Senate days, who also worked with me at the State Department; Alex Hornbrook, director of scheduling, who previously did the same job for Vice President Biden; and Jason Chung, director of advance—are miracle workers. They juggle dates and places with grace and create flawless events out of thin air. It isn't unusual to call them from the plane as we are landing at night to say, "We need to completely redo tomorrow's schedule to add one more state and two more events." Their answer is always "No problem."
If Bill's in town, he's probably still asleep. He's a night owl; I'm an early bird. But sometimes he'll get up with me, and we'll read the papers (we get four: the New York Times, the New York Daily News, the New York Post, and the Journal News, our local paper) and drink our coffee and talk about what we have going on that day. It's probably a lot like what's happening at that moment in our neighbors' houses, except in our case, one of us is running for President and the other one used to be President.
I try to find time for yoga or a strength and cardio workout. At home, I work out in an old red barn out back that we've converted into a gym and an office for Bill, with space in the converted hayloft for the Secret Service. I'm no match for Ruth Bader Ginsburg, however, who pumps iron and does planks and push-ups two days a week. Her regimen is daunting; mine is more forgiving. But if she can find the time and energy to exercise regularly, so can I (and you!). When I'm on the road, I have a mini exercise routine I've now done in hotel rooms across America.
Then there's hair and makeup. Long ago in a galaxy far, far away, having my hair and makeup done was a special treat every now and again. But having to do it every single day takes the fun out of it.
Luckily, I have a glam squad that makes it easy. Two hairdressers have taken great care of me in New York for years: John Barrett, whose full-service salon is in Manhattan, and Santa Nikkels, whose cozy salon is just a few minutes from my house in Chappaqua. They're both terrific—though a lot of people were baffled to discover, after my emails were made public, that I had regular "appointments with Santa."
When I'm in New York and need help with my makeup, I see Melissa Silver (recommended to me by Vogue's Anna Wintour after she saw me at an event and knew I needed help).
On the campaign trail, I have a traveling team: Isabelle Goetz and Barbara Lacy. Isabelle is French and full of positivity; she doesn't walk so much as bop. She's been doing my hair on and off since the mid-1990s, which means we've been together through a lot of hairstyles. Barbara, like Isabelle, is perpetually cheerful. In addition to doing my makeup on the campaign, she does makeup for movies and TV shows such as Veep. I, of course, don't want to be compared with Selina Meyer in any way, shape, or form, but there's no denying, Julia Louis-Dreyfus looks fantastic.
While they get me ready, I'm usually on the phone or reading my briefings for the day. That hour is valuable, so I occasionally schedule calls with staff to discuss electoral strategy or a new policy. They usually don't mind speaking over the blow dryer. Isabelle and Barbara do their best to work around me until they tell me they need me to be still, s'il vous plaît.
At the beginning of the campaign, Isabelle and Barbara got me ready for the day once a week or so, as well as for big events such as debates. I tried to take care of my own hair and makeup the rest of the time. But photos don't lie, and since I looked better when they were with me, it became an everyday thing. When they travel with me, Isabelle and Barbara are always nearby, ready to touch me up before interviews or debates. Every time our plane lands, Isabelle rushes forward with hairspray, and Barbara spritzes my face with a vaporizer full of mineral water. "The air on planes is so dry!" she laments. Then she spritzes everyone else in the vicinity, including, at times, the Secret Service.
I appreciate their talents and like how they make me look. But I've never gotten used to how much effort it takes just to be a woman in the public eye. I once calculated how many hours I spent having my hair and makeup done during the campaign. It came to about six hundred hours, or twenty-five days! I was so shocked, I checked the math twice.
I'm not jealous of my male colleagues often, but I am when it comes to how they can just shower, shave, put on a suit, and be ready to go. The few times I've gone out in public without makeup, it's made the news. So I sigh and keep getting back in that chair, and dream of a future in which women in the public eye don't need to wear makeup if they don't want to and no one cares either way.
After hair and makeup, it's time to get dressed. When I ran for Senate in 2000 and President in 2008, I basically had a uniform: a simple pantsuit, often black, with a colorful shell underneath. I did this because I like pantsuits. They make me feel professional and ready to go. Plus, they helped me avoid the peril of being photographed up my skirt while sitting on a stage or climbing stairs, both of which happened to me as First Lady. (After that, I took a cue from one of my childhood heroes, Nancy Drew, who would often do her detective work in sensible trousers. "I'm glad I wore pants!" she said in The Clue of the Tapping Heels after hoisting herself up on the rafters of a building in pursuit of a rare cat.) I also thought it would be good to do what male politicians do and wear more or less the same thing every day. As a woman running for President, I liked the visual cue that I was different from the men but also familiar. A uniform was also an antidistraction technique: since there wasn't much to say or report on what I wore, maybe people would focus on what I was saying instead.
In 2016, I wanted to dress the same as I did when I wasn't running for President and not overthink it. I was lucky to have something few others do: relationships with American designers who helped me find outfits I could wear from place to place, in all climates. Ralph Lauren's team made the white suit I wore to accept the nomination and the red, white, and blue suits I wore to debate Trump three times. More than a dozen American designers made T-shirts to support my campaign and even held an event during New York Fashion Week to show them off.
Some people like my clothes and some people don't. It goes with the territory. You can't please everybody, so you may as well wear what works for you. That's my theory, anyway.
When I leave for several days on the road, I try to be superorganized, but inevitably I overpack. I throw in more outfits than I need, just in case the weather changes or something spills on me or an eager fan leaves makeup on my shoulder after an exuberant hug. Huma, someone who knows a thing or two about being stylish while working twenty-hour days, tries to advise me. She's the one who will tell me I have on two different earrings, which happened a few times. I also overdo it on reading material; for a while, I filled an entire rolling suitcase with briefing memos and policy papers. Oscar helps me load everything into the cars. Sometimes Bill, marveling at all the stuff I'm bringing, asks, "Are you running away from home?"
When the cars are loaded, the husband is hugged, and the dogs are cuddled, we're off.
We fly in and out of the Westchester County Airport, just a short drive from our house. I make a policy of trying not to be "wheels up" before 8:30 A.M. on the nights I sleep at home. Everyone on my team has at least an hour's drive home after we land in Westchester, and we often land late. An 8:30 A.M. start time means everyone gets at least some sleep.
For the primaries and the beginning of the general election, my traveling team was small. It consisted of Huma; Nick Merrill; trip director Connolly Keigher; Sierra Kos, Julie Zuckerbrod, and Barbara Kinney, who videotaped and photographed life on the trail; and my Secret Service detail, which was usually two agents, sometimes three. A rotating cast of additional staff joined depending on what was happening that day: speechwriters, members of the policy team, state organizers. By the end of the campaign, the team was much bigger and so was the plane.
A note about the Secret Service. Bill and I have been under Secret Service protection since 1992, as soon as he secured the Democratic nomination for President. It took some getting used to, but after twenty-five years, it feels normal—and to their great credit, the agents bend over backward to be as unobtrusive as possible. They are somehow both low-key and ferociously vigilant. The agents are with us at our home all day every day. When I leave the house to do something casual around town—like go to the market or take a walk—agents come with me. They hang back and give me space to do whatever I'm doing. Sometimes I forget that they're there, which is exactly what they want. I'm grateful for the relationships we've built with many of these dedicated men and women over the years. We've also gotten to spend time with their spouses and children at the holiday party Bill and I host for our agents and their families every year, and I've met some of their extended families out on the campaign trail, too.
When Bill and I travel, whether into Manhattan to see a play or all the way to Nevada for campaign events, the Secret Service kicks into higher gear. They coordinate ahead of time to make sure they know the details of every place we'll visit: all the entrances and exits, the fastest traffic routes, and, just in case, backup routes and the nearest hospitals. They organize the motorcade, run background checks, and work with local police at every stop. It's an enormous undertaking, and they do it seamlessly.
The only part of this I have a hard time with is the size of the motorcade. I understand why it's necessary, but it drives me crazy to see people sitting in traffic that I've caused. This feels especially problematic when I'm campaigning—shutting down highways seemed like the quickest way to make people resent me, which was the exact opposite of what I wanted to do. So I always ask the lead agent to avoid using lights and sirens whenever possible. I'm also embarrassed to admit that I do a fair amount of backseat driving. That's pretty rich coming from someone who hasn't driven a car regularly in twenty-five years. Luckily, the agents are too polite to tell me to put a sock in it.
On a typical day on the trail, after leaving the house, our motorcade of two or three cars pulls up right to the plane on the tarmac. Door-to-door service is both a security must and an extremely nice perk. For the primaries and the beginning of the general, we flew in planes with nine or ten seats. The traveling press had a plane of their own, which took extra coordination. Eventually we chartered a Boeing 737 for the general election—big enough for all of us, with "Stronger Together" painted on the side and H logos on the tip of each wing.
The plane was our home away from home for months. For the most part, it served us well. Of course, there were occasional hiccups. One day we were in Little Rock and had to get to Dallas. The plane had a mechanical issue, so they sent another one. While we were waiting on the tarmac, my staff got off the plane to stretch their legs. I decided to close my eyes after a grueling few days. I woke up a few hours later and asked, "Are we there already?" In fact, we hadn't moved. At a certain point in a long campaign, all sense of time and space disappears.
Over the course of the campaign, we were joined by a number of flight attendants. They were all excellent, but my favorite was Elizabeth Rivalsi. She's a trained nutritionist and made fresh, delicious food for us in her kitchen in Queens, which she then packed into containers and brought on the plane: salmon salad, chicken tenders made with almond flour, poblano pepper soup. Her surprise smash hit was brownies made out of chickpea flour. She also had a big basket full of snacks that she regularly replenished with different items. It was a little adventure every time we boarded and checked out the stash. I have a weakness for Pepperidge Farm Goldfish crackers and was delighted to find out that 55 goldfish were only 150 calories—not bad! One time, Liz brought something I hadn't tried before: Flavor Blasted Goldfish. We passed around the bag and discussed whether it was better than the original. Some of my staff thought yes, which was incorrect.
As you can tell, we took eating seriously. Someone once asked what we talked about on long flights. "Food!" we chorused. It's funny how much you look forward to the next meal when you're living out of a suitcase. In 2008, we often relied on junk food to see us through; I remember a lot of pizza with sliced jalapeños delivered right to the plane. This time I was determined that we would all be healthier. I asked friends for good on-the-go snack recommendations. A few days later, shipments of canned salmon, as well as Quest and Kind protein bars, arrived at my house, which we lugged onto the plane in canvas totes. When the Quest bars got cold, they were too hard to eat, so we sat on them for a few minutes to warm them up, with as much dignity as one can muster at such a moment.
I also splurge every now and again on burgers and fries and enjoy every bite.
Several of us put hot sauce on everything. I've been a fan since 1992, when I became convinced it boosted my immune system, as research now shows that it does. We were always on the lookout for new concoctions. One favorite is called Ninja Squirrel Sriracha. Julie the videographer came back from vacation in Belize with four little bottles of the best hot sauce any of us have ever had: Marie Sharp's. We immediately loved the red habanero pepper flavor the most. Everyone quietly jockeyed for that bottle, then handed it over sheepishly when confronted. Eventually we realized we could just order more, and peace returned.
Then there was the food we eat all over the country. We had a few favorite spots: a Middle Eastern takeout place in Detroit; a Cuban restaurant by the airport in Miami; lattes made with honey and lavender from a bakery in Des Moines. At the Iowa State Fair, in the 100-degree August heat, I drank about a gallon of lemonade. Nick handed me a pork chop on a stick, which I devoured. When we got back to the plane, I told him, "I want you to know that I did not eat that pork chop on a stick because it is politically necessary. I ate that pork chop on a stick because it was delicious." He nodded wordlessly and kept eating his own state fair discovery: red velvet funnel cake.
One hot night in Omaha, Nebraska, I was consumed with the desire for an ice cream bar—the simple kind, just vanilla ice cream with a chocolate shell. Connolly called an advance staffer, who kindly picked some up from the drugstore and met us at the plane on our way out of town. We said thank you and devoured them before they could melt.
One of my favorite places to eat and drink is the Hotel at Kirkwood Center in Cedar Rapids, Iowa. It's run by hospitality and culinary students from Kirkwood Community College, and they do a great job. On one of our first visits, I ordered a vodka martini with olives, as cold as they could make it. Cecile Richards, the indomitable leader of Planned Parenthood and a Texan, was with me, and she insisted I try it with Tito's Handmade Vodka, the pride of Austin. It was a great drink. After that, whenever we stay at Kirkwood, the waiter sends over an ice-cold Tito's martini with olives, without me even having to order it.
We take birthdays and holidays seriously on the road. We put up decorations on board for Halloween and Christmas, and there's always a supply of birthday cakes on hand. We can't light candles—no fire allowed on the plane—so we tell the birthday boy or girl to pretend that they're lit and make a wish. We even found an iPhone app that simulates a lighter, to take the game further, which we also used to "light" the menorah we had on board during Hanukkah.
I am famously hard to surprise on my birthday, but for 2016, my team managed to sneak a cake into my hotel suite in Miami and gather silently in the living room while I was on the phone in the bedroom. When I walked out, they both startled and delighted me with an enthusiastic rendition of "Happy Birthday" and a chocolate cake with turquoise frosting. Since it was still early in the morning, we brought the cake with us on the plane to eat later. The night before, we had all celebrated together with an Adele concert. Perfect.
My team and I lived a lot of life together during our year and a half on the road. Families changed. Babies were born. Beloved friends and family passed away. Some people got engaged; some got separated. We raised a glass when Lorella Praeli, our director of Latino outreach, took the oath to become an American citizen. Several of us traveled to New Haven, Connecticut, a few weeks after the campaign began to hit the dance floor at Jake Sullivan's wedding to Maggie Goodlander. We were often away from home, under the gun, pushing ourselves as hard as we could to win. As a result, we relied on one another. We came to know one another's habits and preferences. We'd often gather in my room in the evenings to order room service and talk about that day's news coverage or go over the next day's schedule. We watched the Olympics together, and the Republican debates. Both inspired yelling, though of different kinds.
We could be impatient with one another—frustrated, exhausted, demoralized—but we also made one another laugh, broke hard news gently, kept our wits about us, and always stayed focused on the road ahead.
It was grueling. Sometimes it wasn't fun at all. But it was also wonderful.
* * *
* * *
Every day on the trail was packed with events: rallies, roundtables, interviews, fund-raisers, OTRs ("off-the-records," or unannounced visits to shops, parks, libraries, schools, hospitals—really anywhere).
When we landed in a city, we'd jump from event to event. Sometimes our "drive time" would stretch to an hour or more. To make the most of it, we would schedule radio interviews back to back. I'd also FaceTime with Charlotte, who was now old enough to kind of have a conversation with me. I'd cheer as she spun around in her tutu. We'd sing songs together. Then I'd blow kisses, hang up, and head off to another event.
Rallies are a whole other world. It's thrilling to hear a crowd cheer for you. It's thrilling to hear them cheer for your ideas. But I'll admit that no matter how many times I've stood before large crowds, it's always a little daunting. Our rallies were diverse, boisterous, and happy—the kind of place you could bring your hundred-year-old mother or your one-year-old son. I loved seeing all the homemade posters kids would wave while smiling ear to ear. One of the best things about our campaign logo (the H with the → arrow) was that anyone can draw it, even little kids. We wanted children to spread out poster boards on their kitchen tables, grab markers and glitter pens, and go to town. They sent a lot of homemade H art to our campaign headquarters. We covered the walls with it.
For the music at our rallies, we chose a lot of empowering women artists—Sara Bareilles, Andra Day, Jennifer Lopez, Katy Perry, and Rachel Platten—as well as songs from Marc Anthony, Stevie Wonder, Pharrell Williams, and John Legend and the Roots. We loved to see our crowds singing along to the music. To this day, I can't hear "Fight Song," "Roar," or "Rise Up" without getting emotional.
Some people came to our rallies again and again. I got to know a few of them. A woman named Janelle came with her husband and daughter to a rally in Iowa headlined by Katy Perry, the first of many she did for me. Janelle had a homemade sign: "Thirteenth Chemo Yesterday. Three More. Hear Me Roar!" She was in the process of fighting breast cancer. I was with Bill, and we walked over to introduce ourselves. We had a nice long talk. Over the next eleven months, I saw her many times. She'd visit me on the trail, update me on her health, and her daughter would tell me how second grade was going. Janelle kept promising me that she'd see me at my inauguration. I kept telling her I'd hold her to it and she'd better be there. For my second debate against Trump in Saint Louis, I invited her to come as my guest.
My staff would bring groups of people backstage to meet me before I spoke, and those brief conversations were often very meaningful. I met a lot of women in their eighties and nineties who said how excited they were to finally vote for a woman for President. Many dressed up in pantsuits and pearls for the occasion. I imagined myself in thirty years, putting on nice clothes and going to hear my candidate speak. One, Ruline Steininger, even caucused for me in Iowa when she was 102 years old. She made it very clear that she was going to be around to vote for me on Election Day, and she was.
At an event at a large arena in New Hampshire, I stepped into a side room before going out to speak and met a group of public school employees. One of them, a man named Keith, who worked in a school library, told me his story. Keith was his mother's caregiver. She had Alzheimer's disease. He couldn't afford adult day care or a home health aide, so he had to bring his mom with him to work every day. That stopped me in my tracks. He got a little choked up talking to me, and I got a little choked up hearing it. I thanked him for sharing his story. Later, I told my policy staff, who were already working on plans for Alzheimer's research and elder care, to think even bigger.
On the rope lines at rallies, I encountered a feature of modern campaigning that has become far more prevalent since 2008: the selfie. There is no stopping the selfie. This is now how we mark a moment together. And to be clear, if you see me in the world and want a selfie and I'm not on the phone or racing to get somewhere, I'll be glad to take one with you. But I think selfies come at a cost. Let's talk instead! Do you have something to share? I want to hear it (provided it's not deeply insulting—I have limits). I'd love to know your name and where you're from and how things are going with you. That feels real to me. A selfie is so impersonal—although it does give your wrist a break from autographs, now obsolete.
Roundtable events were special. As I mentioned earlier, they gave me a chance to hear directly from people in a setting in which they felt comfortable. Sometimes those conversations were searing. I met a ten-year-old girl in Las Vegas who took a deep breath and described in a trembling voice how terrified she was of her parents being deported because they were undocumented. Everyone in that room wanted to give her a hug, but I was the lucky one. She came over and sat on my lap as I said what I'd say to Chelsea whenever she was anxious as a little girl: Don't you worry. Let me do the worrying for you. And also, you are very brave.
We tried to make time for OTRs, seeing local sights and dropping by local businesses, whenever we could. If we were running late, these would be the first to fall off the schedule—all the more reason not to announce them, so no one would be disappointed if we couldn't make it. My personal preference for an OTR was anywhere that sold kids' toys, clothes, or books. I would load up on gear for my grandchildren and the new babies of friends and staffers. I also picked up little presents for Bill on the road: ties, shirts, cuff links, a watch. He loves nothing more than to get something neat from a craftsman somewhere in America. It's just about his favorite thing.
For me, fund-raisers were a little more complicated than other campaign events. Even after all these years, it's hard for me to ask for other people's money. It's hard to ask someone to host an event for you in their home or business. But until the day comes that campaign finance reform is signed into law and upheld by the Supreme Court, if you want to run a viable national campaign, there's no way around it: you're going to have to do some serious fund-raising, online, by phone, by mail, and in person. I reject the idea that it's impossible to do it while maintaining your integrity and independence. Bernie Sanders attacked me for raising money from people who worked in finance. But I reminded him that President Obama had raised more money from Wall Street than anyone in history, and that didn't stop him from imposing tough new rules to curb risk and prevent future financial crashes. I would have done the same, and my donors knew it.
I was grateful to everyone who gave money to our campaign or helped raise it. We tried hard to use every penny wisely. The campaign staff will attest that Robby Mook in particular was downright stingy about travel expenses and office supplies. Snack budget? Absolutely not. Buy your own chips. Your own hotel room? Not a chance. Find a roommate. And while you're at it, take the bus instead of the train. We were all in this together: our fund-raising team working around the clock; our national campaign staff living and working on a tight budget; me, flying around the country going to fund-raisers; and our donors, opening their wallets to show their solidarity and support. Our campaign had more than three million donors. The average donation was under $100. And ours was the first campaign in history for which the majority of donors were women. That meant a lot to all of us.
Sometimes we just needed to have some fun. One beautiful summer evening, Jimmy and Jane Buffett hosted a concert for us at their home in the Hamptons on Long Island. I was the first presidential candidate Jimmy ever endorsed, and he wanted to do something special for me. So he, Jon Bon Jovi, and Paul McCartney played a set in a tent full of twinkly lights, and everyone danced on the lawn under the stars. It was magical.
But my favorite events were with kids. They'd sit cross-legged in front of me on the floor, or join me on a couch or drape themselves over chairs, and I'd answer their questions. "What's your favorite part about running for President?" Meeting kids like you. "Who's your favorite President?" With lots of love to Bill and President Obama, it's Abraham Lincoln. "What are you going to do to protect the planet?" Reduce our carbon footprint, invest in clean energy, protect wildlife, and fight pollution. The children listened with great seriousness and asked follow-ups. They were my kind of crowd. They also sometimes told me what was worrying them: for instance, the death of a pet or a grandparent's illness. Many kids asked what I would do about bullying, which made me want to become President even more. I had an initiative called Better Than Bullying ready to go.
I had a lot of respect for the press corps who traveled with us. For the most part, it was comprised of "embeds"—journalists permanently "embedded" with us from the beginning of the campaign till the end. That meant they got to know us and we got to know them. A lot of the embeds were journalists in their late twenties and early thirties, which made this assignment a big opportunity for them. They worked as long and hard as we did. Some veteran reporters also joined us for stretches. Network anchors and big-time columnists would parachute in for interviews and a taste of the road, but they never stayed long.
The traveling press corps asked tough questions. They were hungry. I had to admire that. With rare exceptions, they were also very professional. I can't say we were completely comfortable with one another, though. As I write elsewhere in this book, I tend to treat journalists with caution, and I often feel like they focus too much on the wrong things. I understand that political coverage has to be about the horse race, but it's become almost entirely about that and not about the issues that matter most to our country and to people's lives. That's something that has gotten increasingly worse over the years. That's not entirely the press's fault: the way we consume news has changed, which makes getting clicks all important, which in turn encourages sensationalism. Still, they're responsible for their part.
Having said that, I respected them. Once in a while, we'd go out for drinks or dinner as a group and have a wide-ranging, off-the-record talk. I'd bring Halloween candy and birthday cake back to their cabin on the plane. They'd sometimes roll oranges with questions written in Sharpie up the aisle and try to reach my seat all the way in front. Sometimes on night flights, we'd put on music and open the wine and beer. When any of them were sick or dealing with family problems—that happens during a long campaign—I'd ask Nick to keep me updated. Some of the journalists also started dating one another—that also happens during a long campaign—and since nothing makes me happier than playing matchmaker, I was always eager for the scoop. I also was delighted that many of the journalists assigned to our campaign were women. During the 1972 presidential campaign, the reporters who traveled with the candidates were called the boys on the bus. By 2016, it was the girls on the plane.
* * *
* * *
A lot of days and nights on the trail can blur into one another. You'd be surprised how many times we had to ask each other, "Were we in Florida or North Carolina yesterday?" It wasn't out of the ordinary for two people to answer at once, but with different states. But some days stood out, for better or worse.
One of the best days ever was November 2, 2016: game seven of the World Series, the night the Chicago Cubs made history. We were in Arizona for one of our final rallies. It was a big one: more than twenty-five thousand people came out. Before I went onstage, I asked for an update on the game. It was the top of the sixth inning. The Cubs led the Cleveland Indians 5–3. Gulp.
Like everyone in Cubs Nation, I had been following the playoffs and the series with all my fingers crossed. I started watching Cubs games with my dad when I was a little girl, sitting on his lap or on the floor near his chair in the den. We'd cheer and groan, and at the end of the season, we'd say, "Next year, we'll win the Series!" (To assuage my disappointment, I also became a Yankees fan. It didn't feel disloyal, because they were in the other league.)
Some people on my staff were fans, too—no one more than Connolly, who, like me, grew up outside Chicago. She carried a huge W flag with her on the road, and every time the Cubs won, putting them one step closer to their first world championship in 108 years, she draped it on the bulkhead of the plane or wore it like a cape. Whenever we could, we watched the games together, holding our breath.
That night in Arizona, when the rally was over, the first thing I asked was "Who won?" No one yet. The score was 6–6 in the ninth inning. We had a fifteen-minute drive back to the hotel. But that meant maybe missing the end of the game. We couldn't risk it. Instead, Philippe, who was traveling with us for the final stretch, pulled it up on his iPad, and we all stood around him to watch, standing on a section of grass in the parking lot. Capricia Marshall, one of my close friends and the former Chief of Protocol at the State Department, was there too. She's from Cleveland and is a big Indians fan, so she did some trash-talking.
Following an anxiety-inducing rain delay, the game went into extra innings. We stayed put in the parking lot. When Chicago recorded the final out in the bottom of the tenth to edge the Indians 8–7, Connolly was the happiest I've ever seen her. I reached for that W flag, and we stretched it out between us and took a million photos. Then we drove back to the hotel, ordered a bunch of food to my hotel suite, and watched the highlight reel—especially reliever Mike Montgomery's game-winning save, which he pulled off with a giant smile on his face, like he had all the confidence in the world that he was about to make our dreams come true.
A much less fun day was September 11, 2016, the day I was sick at the National September 11 Memorial Museum. It means a lot to me to commemorate that solemn day, so missing this event wasn't an option. But I felt awful. I'd been fighting a cough from what I thought was allergies for at least a month and saw my internist, Dr. Lisa Bardack, on September 9. She told me the cough was actually pneumonia, and I should take a few days off. I said I couldn't. She gave me strong antibiotics, and I went on with my schedule, including filming Between Two Ferns with comic Zach Galifianakis that afternoon. The next day, I stuck to a scheduled debate prep session. On Sunday, when I got to the memorial, the sun was beaming down. My head ached. You know the rest.
In a funny twist, when I arrived, one of the first people I saw was Senator Chuck Schumer, my friend and former colleague. "Hillary!" he said. "How are you? I just had pneumonia!" At this point, the fact that I had pneumonia wasn't public, so this was totally out of the blue. The difference between us was that Chuck didn't have to go out in public as a candidate when he was under the weather. He told me he had followed his doctor's orders and stayed home for a week. Looking back, I should have done the same. Instead, I ended up having to parade in front of the cameras after leaving my daughter's apartment—where I had gone to rest—to reassure the world that I was fine.
Luckily, most of my memories of being in New York during the campaign were a lot better.
I raced all over the city for the New York primary, hitting all five boroughs. I played dominoes in Harlem, drank boba tea in Queens, spoke at historic Snug Harbor on Staten Island, ate cheesecake at Junior's in Brooklyn, rode the subway in the Bronx (struggling with the MetroCard reader like a typical commuter), and had ice cream at a shop called Mikey Likes It on the Lower East Side. As I tucked into my ice cream, an English reporter who was part of the traveling press corps that day shouted, "How many calories are in that?" All of us, including the rest of the press, booed in response, me louder than anyone. In the end, we won the New York primary by 16 points.
I went on Saturday Night Live and taped that episode of Funny or Die's Between Two Ferns, which was surely one of the more surreal experiences of my life. It's an odd thing to be a politician on a comedy show. Your job isn't to be funny—you're not, especially compared with the actual comedians, so don't even try. Your job is to be the straight guy. That's pretty easy, especially for me, whose life is basically taking whatever's thrown my way. The most important thing is to be game. Luckily, I'm game for a lot. SNL asked me to play a character named Val the Bartender, who would pour drinks for Kate McKinnon, who played me. "Would you sing 'Lean On Me' together?" they asked. I said yes, even though I have a terrible singing voice. (For a couple weeks after, people would shout, "Hey, Val!" at me on the trail.) On Between Two Ferns, when Zach Galifianakis asked me, "I'm going to sneak up on you in a gorilla mask, is that cool?" I said sure. Why not? You only live once.
I marched in the 2016 New York City Pride Parade. Back in the day, in 2000, I was the first First Lady in history to march in a Pride parade. This time we had a big contingent from Hillary for America marching together behind a "Love Trumps Hate" banner. The New York City crowds cheered for us with gusto.
Most importantly, Bill and I welcomed the arrival of our grandson, Aidan, on June 18, 2016, at Lenox Hill Hospital on the Upper East Side of Manhattan. It was a sunny day with hardly a cloud in the sky—a prediction, perhaps, of his personality. He is the happiest little boy.
It's hard to ask more of a city than that.
* * *
* * *
There's one more group of days I want to describe, because they're unlike any other: debate prep.
It's the debate prep team's job to put me through my paces so I'm not hearing anything for the first time during the actual debate. My team, led by Ron Klain, Karen Dunn, and Jake, helped me prepare for all twelve debates. Ron is a lawyer and veteran political strategist who served in the Clinton and Obama White Houses. Karen, also a lawyer, worked for me in the Senate and later for President Obama. And Jake, who knew every word of every one of our policies, was a champion debater in college and grad school. All three had helped prepare President Obama for his debates as well. They worked with two indefatigable campaign staffers, Sara Solow and Kristina Costa, to produce thick briefing binders for me, covering hundreds of topics. As a lifelong fan of school supplies, I fussed over the tabs and dividers and armed myself with a bouquet of highlighters in every color. I spent evenings studying in hotel rooms across America and at my kitchen table. By the end, I knew my opponents' positions inside and out—in some cases, better than they did.
We held most of our debate prep sessions at the Doral Arrowwood, a hotel near my home in Westchester County. We were joined by more people from my team: campaign consultants Joel Benenson, Mandy Grunwald, and Jim Margolis; Tony Carrk, our head of research and an Obama debate-prep veteran; and Bob Barnett, who had helped prepare Democratic candidates for debates since Walter Mondale. We would gather at noon and work late into the evening. We'd practice specific exchanges, fine-tune answers, and try to plan out dramatic "moments" that would help shape the coverage of the debate, although often the most important clashes are the hardest to predict. The hotel would supply us with a smorgasbord that they'd replenish throughout the day—sandwiches, salads, fruit, bagels, and chicken soup. They also had a freezer full of Oreo ice cream bars that we kept emptying and they kept refilling. Anytime you looked around the room, you'd see someone holding one or the stick and wrapper on the table in front of them.
Debate prep helped me get ready emotionally for some of the most consequential moments of the campaign. A presidential debate is theater. It's a boxing match. It's high-stakes surgery. Pick your metaphor. One wrong move—one roll of the eyes or slip of the tongue—can spell defeat. In debate prep, I practiced keeping my cool while my staff fired hard questions at me. They'd misrepresent my record. They'd impugn my character. Sometimes I'd snap back and feel better for getting it off my chest. I'd think to myself, "Now that I've done that here, I don't have to do it on live TV." It worked.
I remember becoming frustrated with my team's advice at one point. I couldn't quite understand how they were recommending I handle a potentially contentious exchange with Bernie. Finally, I said to Jake, who had been peppering me with questions and grimacing at my answers, "Just show me! You do it!" So he became me, and I took on the role of attack dog against myself. It was a truly surreal experience. Finally, he mock-pleaded for mercy: "You're right, you're right, do it your way."
Then there was Philippe-as-Trump. That was a sight to see. The first time I walked into the room for a prep session with him, he was already at the podium, staring at the distant wall and refusing to make eye contact with me. "Oh God, he's ready to be obnoxious," I said. None of us had any idea.
Philippe took his character study very seriously, including the physicality. Trump looms and lurks on a debate stage, so Philippe did too, always hanging out on the edge of my peripheral vision. He wore a suit like Trump's (a little baggy), a tie like Trump's (way too long), and actual Trump-brand cuff links and a Trump-brand watch he found on eBay. He wore three-and-a-half-inch shoe heighteners, flailed his arms like Trump, shrugged and mugged like Trump. I didn't know whether to applaud or fire him.
The weeks that Philippe spent studying tapes of Trump in the Republican debates paid off. He knew how Trump's mind worked: how a question about Social Security would take Trump on a twisted journey into government waste, undocumented immigrants, and terrorism, always terrorism. He would say the craziest things—which I know Philippe is capable of doing all on his own, but he made clear to us from that first day that 90 percent of what he'd say was straight from the horse's mouth, with the remaining 10 percent being his best guess as to what Trump would say. I never knew which was which. In the end, Trump hardly said a thing in any of the three debates that I was hearing for the first time.
It quickly became evident that normal debate prep wouldn't work this time. Trump wouldn't answer any question directly. He was rarely linear in his thinking or speaking. He digressed into nonsense and then digressed even more. There was no point in refuting his arguments like it was a normal debate—it was almost impossible to identify what his arguments even were, especially since they changed minute to minute. Winning, we realized, would mean hitting hard (since he couldn't bear it), staying cool (since he often resorted to viciousness when cornered), throwing his own words back at him (since he couldn't stand hearing them), and making my own arguments with clarity and precision (since he couldn't do the same for himself).
At our last practice before the first debate, I walked in to find Philippe-as-Trump and Ron-as-me practicing the opening handshake. They were half joking, but Philippe had raised the issue that, unlike two men debating who just meet in the middle and shake hands, there was a question of whether Trump would try to hug or—dare I say it—kiss me. Not out of affinity or chivalry, but rather to create a moment where he would tower over me, making it clear he was a guy and I was a girl. Fair enough, I said, let's practice. Philippe came at me with his arms outstretched. I tried to stiff-arm him and get away. It ended with him literally chasing me across the room, putting me in a bear hug, and kissing the back of my head. What can I say? We were committed. If you haven't seen it, it's worth pulling up on YouTube.
It stopped being funny when we saw the Access Hollywood tape. I was not going to shake that man's hand. When we came onstage in the actual debate, I think my body language made it pretty clear he should stay away. And he did. But throughout that debate, which was town-hall style—meaning we weren't confined to standing at podiums and could walk around the stage—Trump stalked and lurked. Philippe had done the same thing during prep.
Several times a session—and we had twenty-one of them in the general—just as he had warned, Philippe-as-Trump would say something so outlandish, none of us could quite believe it. Then he'd tell us it was almost verbatim from a Trump rally, interview, or primary debate. One day Philippe-as-Trump started complaining about how the "Mike guy" screwed up and the "Mike guy" shouldn't get paid. We were totally confused but kept going. When the ninety-minute session was over, I asked, "Who is Mike?" It turns out he was saying "mic guy." Philippe explained that, on two occasions, Trump had blamed the microphone for bad audio and said the contractor shouldn't get paid. After his dismal performance in the first debate, Trump really did say it was because his mic had been sabotaged. Philippe had called it.
In the end, thanks to our practice sessions, I felt that deep sense of confidence that comes with rigorous preparation. Like accepting the nomination, these debates were a first for me. The pressure you feel when you're about to walk onstage is almost unbearable—almost, but not quite. You bear it by working hard to get ready. You bear it by having good people by your side. You bear it by not just hoping but knowing you can handle a lot, because you already have.
At least, that's what always worked for me.
* * *
* * *
No matter how I spent the day or where in the country I happened to be, I always called Bill before falling asleep. We'd catch each other up on the latest news about the election or what was happening with our family and friends. Sometimes we vented frustrations about how the campaign was going. Then we'd take a moment to figure out when we'd see each other next, and say good night. I'd fall asleep feeling calmer and wake up in the morning with new energy and a list of new ideas to pursue. Even on the hardest days, those conversations kept me grounded and at peace.
It is hard to be a woman.
You must think like a man,
Act like a lady,
Look like a young girl,
And work like a horse.
—A sign that hangs in my house
## Sisterhood
Above all, be the heroine of your life, not the victim.
—Nora Ephron
## On Being a Woman in Politics
In these pages, I put to paper years' worth of frustration about the tightrope that I and other women have had to walk in order to participate in American politics. I have a lot to say—I could fill an entire book—and not all of it is upbeat or even-tempered. But there is joy and pride to be found in this chapter, too. My experiences as a woman in politics have been complex and disappointing at times, but ultimately rewarding beyond measure.
* * *
* * *
In politics, the personal narrative is vital.
My husband had a powerful story to tell: he lived for a while on a farm with no indoor plumbing, his father died before he was born, he stopped his stepfather from beating his mother, he became the first in his family to go to college.
Barack Obama had a powerful story to tell: he was raised by his teenage mom and grandparents, his father was Kenyan, he spent part of his childhood living in Indonesia and grew up to become a community organizer and law professor whose story could have been written only in America.
Few people would say that my story was quite so dazzling.
I grew up in a white middle-class family in Park Ridge, a suburb of Chicago. My dad served during World War II and left every morning for his small business in the city along with all the other fathers in our neighborhood heading to their jobs. My mom stayed at home to take care of my brothers, Hugh and Tony, and me, like all the mothers in our neighborhood. And my life looked like the lives of all the girls I knew. We attended excellent public or parochial schools, where first-rate teachers had high expectations for us. I went to our local Methodist church for Sunday services and youth activities all week long. I was a Brownie, then a Girl Scout. I got my first summer job when I was thirteen, working at a park three mornings a week. My hangouts were everyone's hangouts: the public library, the local movie theater, swimming pools, skating rinks. My family watched TV together at night. When the Beatles performed for the first time on The Ed Sullivan Show in 1964, my friends and I gathered together around the screen, alternately silently captivated and shrieking with glee.
It's a story that many would consider perfectly ordinary. Don't get me wrong: I loved my childhood, and every year that passes, I appreciate more how hard my parents worked to give it to me. But my story—or at least how I've always told it—was never the kind of narrative that made everyone sit up and take notice. We yearn for that showstopping tale—that one-sentence pitch that captures something magical about America; that hooks you and won't let go. Mine wasn't it.
Yet there is another story of my life; one that I believe is as inspiring as any other. I wish I had claimed it more publicly and told it more proudly. It's the story of a revolution.
I was born right when everything was changing for women. Families were changing. Jobs were changing. Laws were changing. Views about women that had governed our lives for millennia were changing—finally! I came along at just the right moment, like a surfer catching the perfect wave. Everything I am, everything I've done, so much of what I stand for flows from that happy accident of fate.
The fact that the women's movement happened alongside the civil rights movement—indeed, was entwined with it in many ways, compelling America to reckon with entrenched notions of human value and opening doors of opportunity that had previously been sealed shut to millions—made it that much more thrilling and meaningful.
I know that for a lot of people, including a lot of women, the movement for women's equality exists largely in the past. They're wrong about that. It's still happening, still as urgent and vital as ever.
And it was and is the story of my life—mine and millions of other women's. We share it. We wrote it together. We're still writing it. And even though this sounds like bragging and bragging isn't something women are supposed to do, I haven't just been a participant in this revolution. I've helped lead it.
I was one of just 27 women out of 235 students in my class at Yale Law School. The first woman partner at the oldest law firm in Arkansas. The first woman to chair the national board of the Legal Services Corporation. The person who declared on the world stage that "human rights are women's rights and women's rights are human rights." The first First Lady to be elected to public office. The first woman Senator from New York. In fact, for a few weeks, I was both. By a quirk of the calendar, I was sworn in before Bill left office.
And I was the first woman to be nominated for President by a major political party and win the national popular vote.
I never figured out how to tell this story right. Partly that's because I'm not great at talking about myself. Also, I didn't want people to see me as the "woman candidate," which I find limiting, but rather as the best candidate whose experience as a woman in a male-dominated culture made her sharper, tougher, and more competent. That's a hard distinction to draw, and I wasn't confident that I had the dexterity to pull it off.
But the biggest reason I shied away from embracing this narrative is that storytelling requires a receptive audience, and I've never felt like the American electorate was receptive to this one. I wish so badly we were a country where a candidate who said, "My story is the story of a life shaped by and devoted to the movement for women's liberation" would be cheered, not jeered. But that's not who we are. Not yet.
Maybe it's because we take this story for granted—yeah, yeah, the women's movement happened, why are we still talking about it? Maybe it's too female. Maybe it's at once too big (a sweeping historical shift) and too small (just another middle-class Midwestern girl finding her way in the world).
But I do think it's special.
It's not a typical political narrative, but it's mine.
* * *
* * *
This has to be said: sexism and misogyny played a role in the 2016 presidential election. Exhibit A is that the flagrantly sexist candidate won. A whole lot of people listened to the tape of him bragging about sexually assaulting women, shrugged, and said, "He still gets my vote."
But Donald Trump didn't invent sexism, and its impact on our politics goes far beyond this one election. It's like a planet that astronomers haven't precisely located yet but know exists because they can see its impact on other planets' orbits and gravities. Sexism exerts its pull on our politics and our society every day, in ways both subtle and crystal clear.
A note here on terminology. Others might have a different view, but here's how I see the distinction between sexism and misogyny. When a husband tells his wife, "I can't quite explain why and I don't even like admitting this, but I don't want you to make more money than me, so please don't take that amazing job offer," that's sexism. He could still love her deeply and be a great partner in countless ways. But he holds tight to an idea that even he knows isn't fair about how successful a woman is allowed to be. Sexism is all the big and little ways that society draws a box around women and says, "You stay in there." Don't complain because nice girls don't do that. Don't try to be something women shouldn't be. Don't wear that, don't go there, don't think that, don't earn too much. It's not right somehow, we can't explain why, stop asking.
We can all buy into sexism from time to time, often without even noticing it. Most of us try to keep an eye out for those moments and avoid them or, when we do misstep, apologize and do better next time.
Misogyny is something darker. It's rage. Disgust. Hatred. It's what happens when a woman turns down a guy at a bar and he switches from charming to scary. Or when a woman gets a job that a man wanted and instead of shaking her hand and wishing her well, he calls her a bitch and vows to do everything he can to make sure she fails.
Both sexism and misogyny are endemic in America. If you need convincing, just look at the YouTube comments or Twitter replies when a woman dares to voice a political opinion or even just share an anecdote from her own lived experience. People hiding in the shadows step forward just far enough to rip her apart.
Sexism in particular can be so pervasive, we stop seeing it. It reminds me of the opening anecdote from author David Foster Wallace's 2005 commencement speech at Kenyon College. Two young fish are swimming along. They meet an older fish swimming the other way, who nods at them and says, "Morning, boys, how's the water?" The two young fish swim on for a bit, until one looks at the other and asks, "What's water?"
"In other words," Wallace said, "the most obvious realities are often the ones that are the hardest to see and talk about."
I'd say that sums up the problem of recognizing sexism—especially when it comes to politics—quite nicely.
* * *
* * *
It's not easy to be a woman in politics. That's an understatement. It can be excruciating, humiliating. The moment a woman steps forward and says, "I'm running for office," it begins: the analysis of her face, her body, her voice, her demeanor; the diminishment of her stature, her ideas, her accomplishments, her integrity. It can be unbelievably cruel.
I hesitate to write this, because I know that women who should run for office might read it and say "no thanks," and I passionately believe that the only way we're going to get sexism out of politics is by getting more women into politics.
Still, I can't think of a single woman in politics who doesn't have stories to tell. Not one.
For the record, it hurts to be torn apart. It may seem like it doesn't bother me to be called terrible names or have my looks mocked viciously, but it does. I'm used to it—I've grown what Eleanor Roosevelt said women in politics need: a skin as thick as a rhinoceros hide. Plus, I've always had a healthy self-esteem, thanks no doubt to my parents, who never once told me that I had to worry about being prettier or thinner. To them, I was great exactly how I was. I don't know what magic they performed to make that stick in my head all these years—I wish I did, so that parents everywhere could learn the trick. All I know is, I've been far less plagued by self-doubt than a lot of women I know.
And yet . . . it hurts to be torn apart.
It didn't start with running for office. When I got glasses in the fourth grade—way smaller than the Coke-bottle ones I wore later in life—I was dubbed "four-eyes." It wasn't the most original taunt, but it stung. In junior high, a few unkind schoolmates noticed the lack of ankles on my sturdy legs and did their best to embarrass me. I did talk to my mom about that one. She told me to ignore it, to rise above, to be better. That advice prepared me well for a barrage of insults later on.
At college, I was spared some of the hostility many young women face because I went to Wellesley. Being at a women's college offered me the freedom to take risks, make mistakes, and even fail without making me question my fundamental worth. It also gave me opportunities to lead that I wouldn't have had at a coed college at that time. But once I left Wellesley, things changed.
When my friend and I went to take the law school admissions test in 1968, we were among the only women in the room. We were waiting for the test to start when a group of young men started harassing us. "You don't need to be here." "Why don't you go home and get married?" One said, "If you take my spot at law school, I'll get drafted, and I'll go to Vietnam, and I'll die." It was intense and personal. I just kept my eyes down, hoping the proctor would come to start the test, trying hard not to let them rattle me.
There was a professor at Harvard Law School who looked at me—a bright and eager college senior, recently offered admission—and said, "We don't need any more women at Harvard." That's part of why I went to Yale.
When I started out as an attorney, I would take cases in small rural courthouses in Arkansas, and people would come to watch the "lady lawyer"—it was such a novelty. You could hear them commenting from the gallery on what I was wearing and how my hair looked. One time in the early 1980s, I was trying a case in Batesville, Arkansas, and in the middle of the trial, in walked six men in full camouflage. They came in and sat right behind the lawyers and just stared hard at me. As any woman who's experienced that kind of staring knows, it was truly unnerving. Afterward the bailiff explained that it was deer season and these hunters had come into town from their camp for supplies. When they heard that a woman was trying a case in court, they had to see it for themselves.
I thought of that a few years later, when a woman doctor came to Arkansas from California to be an expert witness in a trial for my firm. She had short, spiky hair. My boss, the lead attorney on the case, told her to go buy a wig. Otherwise, he said, the jurors wouldn't be able to hear what she had to say. They'd be too focused on how she didn't look like a "normal" woman. I remember how taken aback she was at this request. I would have been too, not so long before, but by then I wasn't. That saddened me. I'd become used to a narrower set of expectations.
Once Bill entered politics, the spotlight on me was glaring and often unkind. I've written about this before but it's worth saying again: one of the reasons he lost the Governor's race in 1980 was because I still went by my maiden name. Let that sink in for a moment and please imagine how it felt. I was naïve. I didn't think anyone would care. Maybe people would even respect what it said about our marriage: that I wanted to preserve my pre-Bill identity, that I was proud of my parents and wanted to honor them, that Bill supported my choices. When he lost, and I heard over and over that my name—my name!—had played a part, I was heartsick that I might have inadvertently hurt my husband and let down his team. And I questioned whether there was room in public life for women like me, who might appear slightly unconventional but still had so much to offer.
So I added "Clinton" to Hillary Rodham. I asked my friends for hair, makeup, and clothing advice. That's never come easily to me, and until then, I didn't care. But if wearing contact lenses or changing my wardrobe would make people feel more comfortable around me, I'd try it.
Later, when Bill was running for President for the first time, I stumbled again. I now had the right name, wore makeup, styled my hair. But I hadn't tamed my tongue. One of Bill's opponents in the primary attacked my job at a Little Rock law firm as a way of going after Bill. This really got under my skin. "I suppose I could have stayed home and baked cookies and had teas," I told the press in exasperation, "but what I decided to do was pursue my profession." That did it. Suddenly I was in the middle of a full-blown political firestorm, with self-righteous moralists saying I had insulted American mothers. As someone who believes in supporting mothers, fathers, and families of all kinds, this hurt. And once again, I feared that my pursuit of my individual dreams—in this case, my career, which meant so much to me—would end up hurting my husband.
None of these experiences made me retreat from my beliefs. But I've never really been naïve again. Not much surprises me anymore. Throughout the 2016 campaign, my staff would come to me wide-eyed. "You'll never believe what Trump said today. It was vile." I always believed it. Not just because of who Trump is but because of who we can be at our worst. We've seen it too many times to be surprised.
* * *
* * *
In my experience, the balancing act women in politics have to master is challenging at every level, but it gets worse the higher you rise. If we're too tough, we're unlikable. If we're too soft, we're not cut out for the big leagues. If we work too hard, we're neglecting our families. If we put family first, we're not serious about the work. If we have a career but no children, there's something wrong with us, and vice versa. If we want to compete for a higher office, we're too ambitious. Can't we just be happy with what we have? Can't we leave the higher rungs on the ladder for men?
Think how often you've heard these words used about women who lead: angry, strident, feisty, difficult, irritable, bossy, brassy, emotional, abrasive, high-maintenance, ambitious (a word that I think of as neutral, even admirable, but clearly isn't for a lot of people).
The linguist George Lakoff both identified this problem and embodied it when he said about Senator Elizabeth Warren, "Elizabeth has a problem. She is shrill, and there is a prejudice against shrill women." How about we stop criticizing how she speaks—which is just fine, by the way—and start paying attention to what she has to say about families and the economy?
We're also called divisive, untrustworthy, unlikable, and inauthentic. Those words ring powerfully for me. As the campaign went on, polls showed that a significant number of Americans questioned my authenticity and trustworthiness. A lot of people said they just didn't like me. I write that matter-of-factly, but believe me, it's devastating.
Some of this is a direct result of my actions: I've made mistakes, been defensive about them, stubbornly resisted apologizing. But so have most men in politics. (In fact, one of them just became President with a strategy of "never apologize when you're wrong, just attack harder.")
I've been called divisive more times than I can count, and for the life of me, I can't understand why. Politics is a divisive business, it's true, and our country has gotten more polarized with every passing year. But what specifically did I do that was so unacceptable? Run for office? Lots of men do. Work on health care, one of the most contentious issues in America? Same. Cast votes as a Senator? So did my ninety-nine colleagues. When it comes to some of my most controversial actions—like my vote giving President Bush the authority to go to war in Iraq—I was far from alone. That doesn't make it right, but it also doesn't explain the venom targeted at me specifically. Why am I seen as such a divisive figure and, say, Joe Biden and John Kerry aren't? They've run for President. They've served at high levels of government. They've cast votes of all kinds, including some they regret, just like me. What makes me such a lightning rod for fury?
I'm really asking. I'm at a loss.
I know some of the distrust people feel toward me is because they've watched as I've been sucked into partisan investigations over the years—Whitewater, Travelgate, emails—each one carried out at significant taxpayer expense, each amounting to exactly nothing, but all of them leaving a mark on my reputation nearly impossible to erase.
But I think there's another explanation for the skepticism I've faced in public life. I think it's partly because I'm a woman.
Hear me out.
Historically, women haven't been the ones writing the laws or leading the armies and navies. We're not the ones up there behind the podium, rallying crowds, uniting the country. It's men who lead. It's men who speak. It's men who represent us to the world and even to ourselves.
That's been the case for so long that it has infiltrated our deepest thoughts. I suspect that for many of us—more than we might think—it feels somehow off to picture a woman President sitting in the Oval Office or the Situation Room. It's discordant to tune into a political rally and hear a woman's voice booming ("screaming," "screeching") forth. Even the simple act of a woman standing up and speaking to a crowd is relatively new. Think about it: we know of only a handful of speeches by women before the latter half of the twentieth century, and those tend to be by women in extreme and desperate situations. Joan of Arc said a lot of interesting things before they burned her at the stake.
Meanwhile, when a woman lands a political punch—and not even a particularly hard one—it's not read as the normal sparring that men do all the time in politics. It makes her a "nasty woman." A lot of women have had that spat in their faces (and worse) for saying not that much at all. God forbid two women have a disagreement in public. Then it's a catfight.
In short, it's not customary to have women lead or even to engage in the rough-and-tumble of politics. It's not normal—not yet. So when it happens, it often doesn't feel quite right. That may sound vague, but it's potent. People cast their votes based on feelings like that all the time.
I think this question of "rightness" is connected to another powerful but undefinable force in politics: authenticity. I've been asked over and over again by reporters and skeptical voters, "Who are you really?" It's kind of a funny question when you think about it. I'm . . . Hillary. You've seen me in the papers and on your screens for more than twenty-five years. I'll bet you know more about my private life than you do about some of your closest friends. You've read my emails, for heaven's sake. What more do you need? What could I do to be "more real"? Dance on a table? Swear a blue streak? Break down sobbing? That's not me. And if I had done any of those things, what would have happened? I'd have been ripped to pieces.
Again, I wonder what it is about me that mystifies people, when there are so many men in politics who are far less known, scrutinized, interviewed, photographed, and tested. Yet they're asked so much less frequently to open up, reveal themselves, prove that they're real.
Some of this has to do with my composure. People say I'm guarded, and they have a point. I think before I speak. I don't just blurt out whatever comes to mind. It's a combination of my natural inclination, plus my training as a lawyer, plus decades in the public eye where every word I say is scrutinized. But why is this a bad thing? Don't we want our Senators and Secretaries of State—and especially our Presidents—to speak thoughtfully, to respect the impact of our words?
President Obama is just as controlled as I am, maybe even more so. He speaks with a great deal of care; takes his time, weighs his words. This is generally and correctly taken as evidence of his intellectual heft and rigor. He's a serious person talking about serious things. So am I. And yet, for me, it's often experienced as a negative.
Even some fair-minded people who want to like me feel that there's something too controlled about how I speak. Often, it's just about finding the right words. And impulsive doesn't mean the same thing as truthful. Just look at Donald Trump.
Still, there's no denying that my cautiousness has had the effect of making some people feel like they weren't getting the unvarnished me, which in turn prompted the question "What is she hiding?" This frustrated me to no end, and I never figured out how to solve it. I'm not sure there was a solution.
It's another variant on the impossible balancing act. If we're too composed, we're cold or fake. But if we say what we think without caution, we get slammed for it. Can you blame us for feeling like we can't win, no matter what we do?
Consider another emotional act: crying. I can think of many male politicians who have teared up from time to time. Some have been mocked for it; Senator Ed Muskie's political career was all but scuttled by his tears in the 1972 New Hampshire primary, even though it may have just been snow blowing in his eyes. But many men have been treated with compassion and even admiration for their displays of emotion. Ronald Reagan, George H. W. Bush, Bob Dole, my husband, George W. Bush, Barack Obama—they've all welled up at moments of high sentiment. That makes sense because they are humans, and sometimes humans cry.
But when a woman cries, it can be viewed far less charitably. I remember what happened to Pat Schroeder, the talented and hilarious Congresswoman from Colorado who considered running for President in 1987. She ultimately decided against it, and when she held a press conference to announce that, she cried for about three seconds. Today, when you type "Pat Schroeder" into Google, the very first suggestion is "Pat Schroeder crying." Twenty years later, she was still receiving hate mail because of it—mostly from women who felt like she let them down.
I had my own famed tearful moment, just before the New Hampshire primary in 2008. I didn't even cry, not really. I was talking about how tough running for office can be (because it can be very tough), and my eyes glistened for a moment and my voice quavered for about one sentence. That was it. It became the biggest news story in America. It will, no doubt, merit a line in my obituary someday: "Her eyes once watered on camera."
Interestingly, many would say that my tears turned out to be a good thing for me. Dozens if not hundreds of pundits have commented about how that moment "humanized" me. Maybe that's true. If so, I'm both fine with that and a little beleaguered at the reminder that, yet again, I—a human—required "humanizing" at all.
Still, some sought to capitalize on my perceived vulnerability in the press and on the campaign trail. When he was asked about my tears, former Democratic Senator John Edwards of North Carolina, who was still in the presidential race at the time, jumped at the chance to call me weak. "I think what we need in a Commander in Chief is strength and resolve," he said. "Presidential campaigns are a tough business, but being President of the United States is also a very tough business. And the President of the United States is faced with very, very difficult challenges every single day and difficult judgments every single day. What I know is that I'm prepared for that." Shortly after, he dropped out.
In any case, this whole topic of "being real" can feel very silly. I wish we could just dismiss it and go about our business, whoever we are, without worrying about whether we are satisfying some indefinable standard of realness. As the Nigerian author Chimamanda Ngozi Adichie writes, "It's not your job to be likable. It's your job to be yourself."
Yet the issues of authenticity and likability had an impact on the most consequential election of our lifetimes, and it will have an impact on future ones. So there's something extremely serious going on here, too—especially since crude, abusive, fact-free rhetoric was characterized as authentic in 2016.
I've tried to adjust. After hearing repeatedly that some people didn't like my voice, I enlisted the help of a linguistic expert. He said I needed to focus on my deep breathing and try to keep something happy and peaceful in mind when I went onstage. That way, when the crowd got energized and started shouting—as crowds at rallies tend to do—I could resist doing the normal thing, which is to shout back. Men get to shout back to their heart's content but not women. Okay, I told this expert, I'm game to try. But out of curiosity, can you give me an example of a woman in public life who has pulled this off successfully—who has met the energy of a crowd while keeping her voice soft and low? He could not.
I'm not sure how to solve all this. My gender is my gender. My voice is my voice. To quote Secretary of Labor Frances Perkins, the first woman to serve in the U.S. Cabinet, under FDR, "The accusation that I'm a woman is incontrovertible." Other women will run for President, and they will be women, and they will have women's voices. Maybe that will be less unusual by then. Maybe my campaign will have helped make it that way, and other women will have an easier time. I hope so.
Near the start of my campaign, I met with my friend Sheryl Sandberg, the chief operating officer of Facebook, who has thought about these issues a great deal. She told me that if there was one thing she wanted everyone to know from her book Lean In: Women, Work, and the Will to Lead, it's this: the data show that for men, likability and professional success are correlated. The more successful a man is, the more people like him. With women, it's the exact opposite. The more professionally successful we are, the less people like us. Hearing it put that simply, with data behind it, felt like a lightbulb turning on. Here was proof of something so many women have felt intuitively throughout our lives.
Sheryl shared another insight: that women are seen favorably when they advocate for others, but unfavorably when they advocate for themselves. For example, there's virtually no downside to asking for a raise if you're a man. You'll either get it or you won't, but either way, you won't be penalized for trying. A woman who does the same is more likely to pay a price. Even if she gets a salary bump, she'll lose a measure of goodwill. The exception is when a woman asks for a raise on someone else's behalf. Then she's seen as generous and a team player. This, too, resonated with me. People like me when I'm in a supporting role: campaigning for my husband, serving as a member of President Obama's Cabinet. It's okay for me to be a fierce advocate in those capacities. But when I stand up and say, "Now I'd like a chance to lead," everything changes.
You have a steep mountain to climb, Sheryl warned that day. "They will have no empathy for you."
* * *
* * *
It's not easy for any woman in politics, but I think it's safe to say that I got a whole other level of vitriol flung my way. Crowds at Trump rallies called for my imprisonment more times than I can count. They shouted, "Guilty! Guilty!" like the religious zealots in Game of Thrones chanting "Shame! Shame!" while Cersei Lannister walked back to the Red Keep. As Susan Bordo, a Pulitzer Prize–nominated gender studies professor, put it in her book The Destruction of Hillary Clinton, "It was almost medieval." Mary Beard, the Classics professor at the University of Cambridge, observed that this venom harkened back to an even earlier time. One popular image among Trump supporters, found on everything from T-shirts to coffee mugs, depicted Trump holding up my severed head, like Perseus from ancient Greek mythology, lifting high the head of Medusa.
What in the world was this? I've been in politics for a long time, but I was taken aback by the flood of hatred that seemed only to grow as we got closer to Election Day. I had left the State Department one of the most admired public servants in America. Now people seemed to think I was evil. Not just "not my cup of tea" but evil. It was flabbergasting and frightening.
Was this all because I'm a woman? No. But I believe it was motivation for some of those chanters and some of that bile.
Later I read an interview with Margaret Atwood, the prescient author of The Handmaid's Tale, which put the campaign into yet another historical light. "You can find websites that say Hillary was actually a Satanist with demonic powers," she said. "It's so seventeenth century that you can hardly believe it." The Puritan witch hunts may be long over, but something fanatical about unruly women still lurks in our national subconscious.
That doesn't just affect me and other candidates. It affects our supporters. Nearly four million people joined a Facebook group supporting my campaign, fittingly called Pantsuit Nation. It was a secret group. It had to be. Otherwise its members were exposing themselves to vicious sexist online harassment, from both the right and the left.
You can hardly open a newspaper these days without reading another grim story: female engineers reporting blatant harassment in Silicon Valley; women entrepreneurs making pitches to investment firms and being propositioned in response; a new study finding that women are given a harder time than men in job interviews; another finding that women are penalized when they decline to reveal their salary history, while men end up making more when they do the same.
That's why it's so maddening that the basic fact that sexism is alive and well should still be up for debate. I can't count the number of times that good-hearted men who should know better dismiss the notion that sexism and outright misogyny are still potent forces in our national life. "But things have changed," they say, as Donald Trump brags about groping women and a few weeks later wins the presidency, as his rally-goers chant "Trump that bitch," as the White House proudly releases photos of old white men gleefully deciding which health services to take away from women.
And on that fundamental question of whether it would be good to see a woman—any woman, not just me—become President, the electorate is deeply, depressingly divided. A 2014 Pew Research Center poll found that 69 percent of Democratic women and 46 percent of Democratic men (not terrible, but you can do better than that, Democratic men!) said they hoped to see a female President in their lifetime, but only 20 percent of Republican women and only 16 percent of Republican men did. In 2008, researchers found that more than a quarter of the population expressed anger or upset feelings at the mere thought of a female President. And after the 2016 election, the Diane D. Blair Center of Southern Politics and Society at the University of Arkansas put out a report on the impact of sexism on the race. Researchers asked people to respond to five statements that reflect sexist thinking, including "Feminists are seeking for women to have more power than men" and "Discrimination against women is no longer a problem in the United States." In results that surprised no one, more than a third of respondents gave answers that were sexist. Trump voters were more sexist than Clinton voters. Republicans were far more sexist than Democrats. And not just men; women were quite sexist, too.
On that note, beginning even before I ran, political commentators wondered whether I'd inspire an unbeatable wave of women to come out and vote for me, in the same way President Obama inspired record-breaking black turnout. I hoped I would, of course, but I had my doubts. Gender hasn't proven to be the motivating force for women voters that some hope it might be. If it were, we'd probably have had a woman president or two by now, don't you think? In the end, I won an overwhelming majority of the votes of black women (94 percent) and Latino women (68 percent), and I won women overall by a safe margin (54 percent). But I failed to win a majority of white women, although I did better with them than Obama did in 2012.
So yes, things have changed. Some things are a lot better. But many are still bad. And they are connected—the bad is the backlash to the good. Women's advancement has set into motion vast changes that inspire intense feelings of all kinds. Some of us are exhilarated. Others feel a whole lot of rage.
* * *
* * *
The good news—and there is good news—is that there's another side to all of this. It can also be deeply rewarding to be a woman in politics. You know that just by being in the room, you're making government more representative of the people. You're bringing a vital perspective that would otherwise go unheard. That always made me stand up a little straighter. It's why I love the song "The Room Where It Happens" from Lin-Manuel Miranda's brilliant musical Hamilton:
No one really knows how the game is played
The art of the trade
How the sausage gets made
We just assume that it happens
But no one else is in the room where it happens.
It felt really good to be in rooms where things happen—the Oval Office, the Senate chamber—as an advocate for issues that mattered to me: education, equal pay, health care, women's rights. Maybe those issues would have been close to my heart even if I were a man, but maybe not. Life naturally pushed me in their direction. A young mom interested in policy often ends up working on kids' issues. A First Lady is often involved with women's issues. That was okay with me. Some might have found it limiting, but I consider these real-life issues that affect us all.
Later, I moved into different realms: working to rebuild New York after 9/11 as a hometown Senator, supporting our troops and caring for our wounded warriors and all our vets as a member of the Senate Armed Services Committee, keeping our country and world safe as U.S. Secretary of State. I moved into different rooms: the Situation Room, foreign ministries, the United Nations. And I found that the decades of work I had done on women and families served me well in all those places, because it meant that I understood the intricacies of people's lives. I knew how governments could help or hurt families. I knew how to marshal resources and support to the people who needed them most. It turned out that my work on so-called women's and children's issues prepared me well for nearly everything else I've ever done.
I also believe the fact that I'm a woman is one reason why so many people open up to me about the details of their lives and families. They tell me about their children's medical diagnoses, their caregiving of aging parents, troubles in their marriages and family's finances, painful experiences with sexual harassment and discrimination. Warmhearted male politicians also receive these confessionals, but from what I can see, women hear them more often. Maybe it's easier to cry in front of us. Maybe it feels like talking to a girlfriend. All I know is that a lot of people have grabbed my hand and told me their worries and dreams, and that's been a unique privilege.
* * *
* * *
There's another thing that women confide in me about, and that's stories of their reproductive health. No essay about women in politics could be complete without talking about this. It is such a central part of women's lives: whether we become mothers and at what age and under what circumstances. Reproductive health in all its complexity—pregnancy, fertility, birth control, miscarriage, abortion, labor, birth—can comprise some of the most joyful and terrifying moments we will ever experience. But a lot of the time, we process these moments in silence. These stories go unspoken, even among women. Then I meet women at rallies or dinners or fund-raisers, or just taking a walk, and they take a deep breath and let it all out.
At this moment in America, more than forty-four years since Roe v. Wade, women's access to birth control and abortion is still under constant threat. I saw the effect of this in the 2016 election. Reproductive health was rarely mentioned in any of the primary debates, and when it was mentioned, it was often because I brought it up. I was dismayed when Bernie Sanders dismissed Planned Parenthood as just another part of "the establishment" when they endorsed me over him. Few organizations are as intimately connected to the day-to-day lives of Americans from all classes and backgrounds as Planned Parenthood, and few are under more persistent attack. I'm not sure what's "establishment" about that, and I don't know why someone running to be the Democratic nominee for President would say so.
After the election, Bernie suggested that Democrats should be open to nominating and supporting candidates who are anti-choice. Other topics, such as economic justice, are sacrosanct, but apparently women's health is not. I don't mean to criticize only Bernie here—a lot of progressives join him in thinking that reproductive rights are negotiable. And to be clear, I believe there's room in our party for a wide range of personal views on abortion. I've been working for a quarter century with Democrats and Republicans alike to reduce the number of abortions, in part by expanding access to birth control and family planning, and we've made progress. And I picked as my running mate Tim Kaine, a Democrat personally opposed to abortion because of his Catholic faith but supportive of women's rights as a matter of law and policy.
But when personal views on abortion become public actions—votes on legislation or judges or funding that erode women's rights—that's a different matter. We have to remain a big tent, but a big tent is only as strong as the poles that hold it up. Reproductive rights is central to women's rights and women's health, and it's one of the most important tent poles we've got. And remember: it's a constitutional right as defined in Roe v. Wade.
There's overwhelming evidence about what happens when these rights are denied. Texas has defunded Planned Parenthood and refused to expand Medicaid, and maternal mortality doubled between 2010 and 2014. That's the worst in the nation, and it's higher than the rate in many developing countries. Six hundred women have died in Texas—not from abortions, but from trying to give birth. The number of Texas teenagers having abortions actually increased when support for family planning was cut. In one county, Gregg, it went up 191 percent between 2012 and 2014.
Ultimately, I'm pro-choice, pro-family, and pro-faith because I believe that our ability to decide whether and when to become mothers is intrinsic to our liberty. When government gets involved in this intimate realm—whether in places like China, which forced women to have abortions, or in Communist Romania, which forced women to bear children—it is horrific. I've visited hospitals in countries where poor women have no access to safe and legal abortion. I've seen what happens when desperate women take matters into their own hands.
As I see it, this issue comes down to the question: Who decides? We can debate the morality of abortion forever—and I have spent many hours engaged in such debates and surely will spend many more—but at the end of the day, who decides whether a woman gets or stays pregnant? A Congressman who has never met her? A judge who has spoken with her for maybe a few minutes? Or should the woman be able to make this momentous decision about her life, her body, her future, for herself?
Someone's got to decide. I say let women decide.
* * *
* * *
I'm not sure what we call our current era of feminism—I've lost count of which wave we're in. But there's a lot that feels new. There are all these new words. Mansplaining. The second I heard it, I thought, "Yes! We needed a word for that!" Intersectionality: an academic term for that vital idea that feminism must engage race and class. Revenge porn Trolls. Modern twists on ancient harms.
While we're defining things, let's take a moment for feminism: "the advocacy of women's rights on the basis of the political, economic, and social equality of the sexes." Not domination. Not oppression. Equality. Or as the English writer and philosopher Mary Wollstonecraft put it 225 years ago, "I do not wish women to have power over men, but over themselves."
Then there's emotional labor. Now, that's a good one. It describes all the unpaid, uncounted, often unseen work that people—overwhelmingly women—perform to keep their families and workplaces humming along. Organizing office birthday parties. Arranging the kids' summer camp. Coordinating visits with in-laws. Helping the new employee feel welcome and included. The list is endless: all the little details without which life would devolve into chaos and misery. Not all women take on these tasks, and that's fine, and some men do, and I salute them—but it's largely women's work. Finally, someone thought to name it.
In my marriage, I've definitely been the one to perform the bulk of the emotional labor. I'm the one who schedules family visits, vacations, and dinners with friends. Bill has many positive qualities, but managing the logistical details of a household is not one of them. Of course, our situation is unique. For years, he was a Governor, then the President. He wasn't going to be the parent keeping track of the SAT registration deadline, although he always knew exactly what Chelsea was studying in school. We've also been privileged, since moving into the Governor's mansion years ago, to have people helping ensure that we're well fed and taken care of. Neither of us has had to make an emergency run to the store to pick up milk in decades. Still, even our privileged lives require a lot of small but vital actions and decisions to keep rolling along, and I'm the one who tends to handle them.
That labor extends to my friendships. In March 2017, a few of my close girlfriends came to New York for the weekend. A new friend joined us and asked, "How do you all know each other?" That led to my friends going around the table explaining in great detail how I have lovingly interfered in their lives over the years. "When I got sick, Hillary hounded me until I went to her doctor and called me immediately after for a full report." "That's nothing! When my little girl cut her face, Hillary insisted I get a plastic surgeon and then called back ten minutes later with the best one in Washington on the phone." They knew me well.
It happens at work, too. I make sure everyone has eaten, that my staff is wearing sunscreen if we're at an event in the baking sun. When reporters who traveled abroad with us got sick or injured, I made sure they had ginger ale and crackers and would send the State Department doctor to their room with Cipro and antinausea drugs.
None of this is unusual. I've seen women CEOs serve coffee at meetings, women heads of state walk tissues over to a sneezing staffer. It's also not new. It was women like Dr. Dorothy Height who did a lot of the unglamorous work of the civil rights movement, recruiting volunteers and organizing workshops and coordinating sit-ins and freedom rides. It is women who do a lot of the daily knitting in Congress, identifying problems, bringing together stakeholders, building effective coalitions. It's often women who handle constituent outreach, answering phones and responding to letters and emails. And in my experience, a lot of women make those calls and write those letters to Congress. We're not just the designated worriers in our families; we're also the designated worriers for our country.
I think all this may help explain why women leaders around the world tend to rise higher in parliamentary systems, rather than presidential ones like ours. Prime ministers are chosen by their colleagues—people they've worked with day in and day out, who've seen firsthand their talents and competence. It's a system designed to reward women's skill at building relationships, which requires emotional labor.
Presidential systems aren't like that. They reward different talents: speaking to large crowds, looking commanding on camera, dominating in debates, galvanizing mass movements, and in America, raising a billion dollars. You've got to give it to Trump—he's hateful, but it's hard to look away from him. He uses his size to project power: he looms over the podium, gets in interviewers' faces, glowers, threatens to punch people. I watched a video of one of our debates with the sound off and discovered that, between his theatrical arm waving and face making and his sheer size and aggressiveness, I watched him a lot more than I watched me. I'm guessing a lot of voters did the same thing. I also suspect that if a woman was as aggressive or melodramatic as he is, she'd be laughed or booed off the stage. In the end, even though I was judged to have won all three of our debates, his supporters awarded him points for his hypermasculine, aggressive behavior.
As for me, when it comes to politics, my style can be viewed as female. I've always focused on listening over speaking. I like town hall meetings because I get to hear from people and ask follow-up questions to my heart's content. I prefer one-on-one or small group conversations to big speeches and finding common ground over battling it out.
When I was a Senator, I spent a lot of time getting to know my colleagues, including gruff Republicans who wanted nothing to do with me at first. In 2000, Trent Lott, the Republican Leader, wistfully wondered if lightning would strike and I wouldn't take the oath of office. By 2016, he was telling people I was a very capable lady who did a good job—and he told my husband that I had done more to help the victims of Hurricane Katrina than anyone outside the Gulf Coast. A number of other conservative Republicans also came to like me when I was their colleague in the Senate, helping them pass bills, refilling their coffee cups in the Senate Dining Room, or sitting beside them in the Senate's private prayer meeting. One ultraconservative Senator came to see me to apologize for having hated me and saying terrible things about me over the years. He asked, "Mrs. Clinton, will you forgive me?" I know that might sound incredible now, but it's true. I told him that of course I would.
Dramatic spiritual conversions aside, emotional labor isn't particularly thrilling as far as the political media or some of the electorate is concerned. I've been dinged for being too interested in the details of policy (boring!), too practical (not inspiring!), too willing to compromise (sellout!), too focused on smaller, achievable steps rather than sweeping changes that have little to no chance of ever coming true (establishment candidate!).
But just as a household falls apart without emotional labor, so does politics grind to a halt if no one is actually listening to one another or reading the briefings or making plans that have a chance of working. I guess that might be considered boring. I don't find it boring, but you might. But here's the thing: someone has to do it.
In my experience, a lot of the time, it's women. A lot of the time, it's dismissed as not that important. And I don't think that's a coincidence.
* * *
* * *
"This is not okay," I thought.
It was the second presidential debate, and Donald Trump was looming behind me. Two days before, the world heard him brag about groping women. Now we were on a small stage, and no matter where I walked, he followed me closely, staring at me, making faces. It was incredibly uncomfortable. He was literally breathing down my neck. My skin crawled.
It was one of those moments where you wish you could hit Pause and ask everyone watching, "Well? What would you do?"
Do you stay calm, keep smiling, and carry on as if he weren't repeatedly invading your space?
Or do you turn, look him in the eye, and say loudly and clearly, "Back up, you creep, get away from me, I know you love to intimidate women but you can't intimidate me, so back up."
I chose option A. I kept my cool, aided by a lifetime of dealing with difficult men trying to throw me off. I did, however, grip the microphone extra hard.
I wonder, though, whether I should have chosen option B. It certainly would have been better TV. Maybe I have overlearned the lesson of staying calm—biting my tongue, digging my fingernails into a clenched fist, smiling all the while, determined to present a composed face to the world.
Of course, had I told Trump off, he surely would have capitalized on it gleefully. A lot of people recoil from an angry woman, or even just a direct one. Look at what happened to Elizabeth Warren, silenced in the Senate chamber for reading a letter from Coretta Scott King because it was critical of Jeff Sessions, a male Senator, during his confirmation hearing for Attorney General. (Moments later, Jeff Merkley, a male Senator, was allowed to read the letter. Funny how that worked.) Senator Kamala Harris was derided as "hysterical" for her entirely coolheaded and professional questioning of Jeff Sessions (him again) during a Senate hearing. As one writer put it, she was being "Hillary'd." Arianna Huffington was recently interrupted in a meeting of the Uber board of directors when she was making a point about—of all things—how important it was to increase the number of women on the board! And the man who talked over her did so to say that increasing women would only mean more talking! You can't make this up.
In other words, this isn't something that only happens to me. Not even close.
It also doesn't just happen to women on the Democratic side of politics. Trump made fun of Carly Fiorina's face because she competed against him for President. He lashed out against Megyn Kelly and Mika Brzezinski in gross, physical terms because they challenged him. Maybe that's why Nicolle Wallace, White House Communications Director for George W. Bush, has warned that the Republican Party is in danger of being "permanently associated with misogyny" if leaders don't stand up to Trump's treatment of women.
This hearkens back to a powerful ad we ran during the campaign called "Mirrors." It shows adolescent girls looking tentatively at themselves in the mirror—tucking their hair behind their ears, evaluating their profile, trying to decide if they are okay-looking, like so many girls do when they see themselves. Over their images, we ran a tape of cruel things Trump has said on the record about women over the years: "She's a slob." "She ate like a pig." "I'd look her right in that fat, ugly face of hers." Was this the voice we wanted in our daughters' heads? Our granddaughters'? Our nieces'? Or our sons' or grandsons' or nephews' heads for that matter? They deserve better than the toxic masculinity Trump embodies.
Well, he's in their heads now. His voice resounds far and wide.
Now it's on all of us to make sure his ugly words don't damage our girls—and boys—forever.
* * *
* * *
Two days before the debate, my team and I had finished a grueling morning debate prep session. We had taken a break for lunch. The television was on in the room, with no volume. Then a commentator came on to warn viewers that they were about to hear something vulgar. Boy, was that true.
I don't have a lot to say about the Access Hollywood tape that hasn't been said. I will just note that Donald Trump is gleefully describing committing sexual assault. That got somewhat lost in the shock of it all. Too many people focused on his boorishness—such a crude man, so vulgar. True. But even if he were the height of elegance and graciousness, it wouldn't make it okay that he's describing sexual assault.
For many, hearing the Donald Trump tape was literally sickening. As for me, it made me sad—for women and girls, for men and boys, for all of us. It was . . . horrible, just horrible. It still is. And it always will be, because that tape is never going away. It's part of our history now.
To divert attention from his own ugliness, Trump brought to our second debate three women who had accused my husband of bad acts decades ago, plus a woman whose accused rapist I had been ordered by a judge to represent back in Arkansas. It was an awful stunt.
I don't know what the Trump campaign was hoping to accomplish other than the obvious: dredge up old allegations that had been litigated years before, divert attention from the Access Hollywood tape, throw me off my game, and distract voters from the election's unbelievably high stakes. He wasn't trying to make a stand for these women. He was just using them.
This was a presidential debate. That's a big deal. We were supposed to talk about issues that mattered to people's lives. Instead, Trump used this moment to get back in his comfort zone. He loves to humiliate women, loves to talk about how disgusting we are. He was hoping to rattle me. I was determined not to give him that satisfaction.
Before I stepped onstage, Ron Klain said to me, "He's trying to get in your head." I said, "Ya think?" Then I went out there and won the debate.
* * *
* * *
Something I wish every man across America understood is how much fear accompanies women throughout our lives. So many of us have been threatened or harmed. So many of us have helped friends recover from a traumatic incident. It's difficult to convey what all this violence does to us. It adds up in our hearts and our nervous systems.
A few years ago, the hashtag #yesallwomen was trending for a while. It spoke to me, like it did to so many others. In college and law school, we had a million defensive habits: hold your keys like a weapon when you're out alone at night, walk one another home no matter what. Many women I know have been groped, grabbed, or worse. It even happens to members of Congress. Senator Kirsten Gillibrand has written frankly about how Congressmen have leered at her and grabbed her waist in the congressional gym.
I'm very lucky that nothing too bad ever happened to me. One time in college, I went on a blind date with a young man who wouldn't take repeated nos for an answer, and I had to slap him to get him away from me. But he did back off, and I went to bed that night shaken but not traumatized. And when I was twenty-nine, working for Jimmy Carter's presidential campaign in Indiana, I had dinner one night with a group of older men who were in charge of the Democratic Party's get-out-the-vote operation in the state. I had been pestering them for a while for information about their Election Day plans, and they were annoyed with me. I started explaining once again what I needed to know from them and why. Suddenly one of the men reached across the table, grabbed me by my turtleneck, and yanked me toward him. He hissed in my face, "Just shut up." I froze, then managed to pull his hand from my neck, tell him to never touch me again, and walk out of the room on shaking legs. The whole incident probably lasted thirty seconds. I'll never forget it.
Yet that's nothing compared to the violence that millions of women and girls across our country endure on a regular basis.
About four months before Donald Trump's Access Hollywood tape was released, a very different message went viral. An unnamed woman known as Emily Doe who had been sexually assaulted while unconscious wrote a letter about her ordeal and read it in court to her attacker, a Stanford athlete. A friend forwarded the letter to me. I read it once, then immediately went back to the beginning and read it again. I hope I can meet the author someday and tell her how brave I think she is.
"To girls everywhere," she wrote, "I am with you . . .
On nights when you feel alone, I am with you. When people doubt you or dismiss you, I am with you. I fought every day for you. So never stop fighting, I believe you. As the author Anne Lamott once wrote, "Lighthouses don't go running all over an island looking for boats to save; they just stand there shining." Although I can't save every boat, I hope that by speaking today, you absorbed a small amount of light, a small knowing that you can't be silenced, a small satisfaction that justice was served, a small assurance that we are getting somewhere, and a big, big knowing that you are important, unquestionably, you are untouchable, you are beautiful, you are to be valued, respected, undeniably, every minute of every day, you are powerful, and nobody can take that away from you.
Early on the morning of November 9, when it came time to decide on what I'd say in my concession speech, I remembered those words. Inspired by them, I wrote these:
"To all the little girls who are watching this, never doubt that you are valuable and powerful and deserving of every chance and opportunity in the world to pursue and achieve your own dreams."
Wherever she is, I hope Emily Doe knows how much her words and her strength meant to so many.
* * *
* * *
There's yet another side to the matter of women in politics. It's not just that politics can be rewarding for those women who choose to enter it. In the long run, it also makes our politics better for everyone. I believe this as strongly as I believe anything. We need our politics to resemble our people. When the people who run our cities, states, and country overwhelmingly look a certain way (say, white and male) and overwhelmingly have a shared background (wealthy, privileged) we end up with laws and policies that don't come close to addressing the realities of Americans' lives. And since that's a basic requirement of government, it's a pretty big thing to get wrong.
In other words, representation matters.
Is representation everything? Of course not. Just because I'm a woman, it doesn't mean I'd be a good President for women. (I would have been, but not only because of my gender.)
But it does matter, and often in concrete ways. I remember when I was pregnant with Chelsea, working at the Rose Law Firm in Little Rock, and repeatedly went to my superiors to ask about their maternity leave policy. They avoided the question until there was no longer any way to avoid it, then stammered that they didn't have a policy. "No woman who's worked here has ever come back after having a baby." So I wrote my own. I was a new partner and had the power to do that. But what about more junior lawyers or support staff? Would they have been expected to come in a few days after giving birth, or not come back to work at all? It took a woman in the room to notice a huge hole in the firm's policies and care enough to fix it.
Representation matters in less visible but no less valuable ways, too. I remember being riveted as a little girl whenever a woman appeared in our history lessons: Abigail Adams, Sojourner Truth, Ida Tarbell, Amelia Earhart. Even if it just amounted to a sentence in a dusty book—and often that's all they got—it thrilled me. The great men in our history books thrilled me too, but it meant something different, something quietly momentous, to learn that a woman had done something important. It opened the world up a little more. It made me dream a little bigger. I remember coming home from school and opening Life magazine to read about Margaret Chase Smith, the gutsy Republican Senator from Maine who stood up to Joe McCarthy. Years later, when I became First Lady, I wrote her a fan letter.
As a young woman, I was moved and inspired watching Barbara Jordan speak out eloquently for the rule of law on the House Judiciary Committee during the Watergate hearings; Geraldine Ferraro stand onstage as the vice presidential candidate for my party; Barbara Mikulski shake up the U.S. Senate; Dianne Feinstein take on the NRA; and Shirley Chisholm run for President. What hadn't felt possible suddenly was.
When Chelsea was a little girl, I saw the power of representation through a new lens. I watched her leaf through the pages of her children's books, searching intently for the girl characters. Now little girls have a new group of fictional heroines to look up to, including Wonder Woman and General Leia (she got a promotion from Princess). Slowly but surely, Hollywood is moving in the right direction.
That's why it meant so much to me to see all the little girls and young women at my campaign rallies and all the moms and dads pointing and saying, "Look. You see? She's running for President. You're smart like she is. You're tough like she is. You can be President. You can be anything you want to be."
After the election, I received a letter from a medical student named Kristin in Dearborn, Michigan. She wrote,
I saw you speak for the first time as a small girl. My mom took me, and helped me up to stand on a fence and held me by the back of my overalls because I kept trying to wave to you and cheer you on. I was so ecstatic to hear such a smart woman speak, and I've never looked back. You never let that version of me down. I read your history as I got older, and then I got to see more speeches and read your writings. You never let down the older versions of me either.
To this day, even knowing how things turned out, the memories of all those proud and excited girls—and the thought of the women they will become—means more to me than I can express.
I know that there are some reading this who will sneer. Representation! It's so soft, so wimpy, so liberal. Well, if you can't imagine why it would matter for many of us to see a woman elected President—and that it wouldn't matter only to women, just like the election of Barack Obama made people of all races, not just African Americans, feel proud and inspired—I'd simply urge you to accept that it matters to many of your fellow Americans, even if it doesn't to you.
I wish so badly that I had been able to take the oath of office and achieve that milestone for women. Still, there were many feminist moments in this election we shouldn't forget. I will always remember Bill's speech at the 2016 Democratic National Convention. At one point, he uttered the memorable words, "On February 27, 1980, fifteen minutes after I got home from the National Governors Association conference in Washington, Hillary's water broke." Watching from our home in New York, I had to laugh. That was the first time that had ever been said about a presidential nominee. I thought it was about time.
* * *
* * *
There's another moment I want to note that a lot of people missed when it happened but which I will never forget.
A few days before election night 2016, Beyoncé and Jay-Z performed at a rally for me in Cleveland. Beyoncé took the microphone. "I want my daughter to grow up seeing a woman lead our country and know that her possibilities are limitless," she said. "We have to think about the future of our daughters, our sons, and vote for someone who cares for them as much as we do. And that is why I'm with her."
And then, that infamous 1992 quote appeared in giant block letters on a huge screen behind her. "I suppose I could have stayed home and baked cookies and had teas, but what I decided to do was pursue my profession."
Something that had been controversial was being reclaimed as a message of independence and strength—just like I had meant it to be all those years ago!—right before my eyes.
Thanks, Beyoncé.
* * *
* * *
Will we ever have a woman President? We will.
I hope I'll be around to vote for her—assuming I agree with her agenda. She'll have to earn my vote based on her qualifications and ideas, just like anyone else.
When that day comes, I believe that my two presidential campaigns will have helped pave the way for her. We did not win, but we made the sight of a woman nominee more familiar. We brought the possibility of a woman president closer. We helped bring into the mainstream the idea of a woman leader for our country. That's a big deal, and everyone who played a role in making that happen should feel deeply proud. This was worth it. I will never think otherwise. This fight was worth it.
That's why I am heartened that a wave of women across America have expressed more willingness to run for office after this election, not less. I'll admit, I was worried that it would go the other way. And I will always do my part to encourage more women to run and to send the message to little girls, teenagers, and young women that their dreams and ambitions are worth chasing.
Over the years, I've hired and promoted a lot of young women and young men. Much of the time, this is how it went:
ME: I'd like you to take on a bigger role.
YOUNG MAN: I'm thrilled. I'll do a great job. I won't let you down.
YOUNG WOMAN: Are you sure I'm ready? I'm not sure. Maybe in a year?
These reactions aren't innate. Men aren't naturally more confident than women. We tell them to believe in themselves, and we tell women to doubt themselves. We tell them this in a million ways, starting when they're young.
We've got to do better. Every single one of us.
What would happen if one woman told the truth about her life?
The world would split open.
—Muriel Rukeyser
## Motherhood, Wifehood, Daughterhood, Sisterhood
I don't know what it's like for other women, but growing up, I didn't think that much about my gender except when it was front and center. Like in eighth grade, when I wrote to NASA to say that I dreamt of becoming an astronaut, and someone there wrote back: Sorry, little girl, we don't accept women into the space program. Or when the boy who beat me in a student government race in high school told me I was really stupid if I thought a girl could be elected President of the school. Or when I heard from Wellesley College: I was in. On these occasions, I felt my gender powerfully. But most of the time, I was just a kid, a student, a reader, a fan, a friend. The fact that I was female was secondary; sometimes it practically slipped my mind. Other women may have had different experiences, but that's how it was for me.
My parents made that possible. They treated my brothers, Hugh and Tony, and me like three individual kids, with three individual personalities, instead of putting me in a box marked "female" and them in a box marked "male." They never admonished me for "not acting like a girl" when I played baseball with the boys. They stressed the importance of education, because they didn't want their daughter to feel constrained by tired ideas of what women should do with our lives. They wanted more for me than that.
Later in life, I started to see myself differently when I took on roles that felt deeply and powerfully womanly: wife, daughter to aging parents, girlfriend, and most of all, mother and grandmother. These identities transformed me yet somehow also felt like the truest expressions of myself. They felt both like pulling on a new garment and shedding my skin.
I don't talk a lot about these pieces of my life. They feel private. They are private. But they're also universal experiences, and I believe in the value of women sharing our stories with one another. It's how we support each other through our private struggles and how we find the strength to build the best possible lives for ourselves.
These roles haven't been easy or painless. Sometimes they've been very painful indeed. But they have been worth it. My goodness, have they been worth it.
Years rolled on again, and Wendy had a daughter. This ought not to be written in ink but in a golden splash.
—J. M. Barrie
On the final night of the Democratic National Convention in July, my daughter introduced me to the nation. I was backstage, ready to walk onstage the instant she was done. At least, I was supposed to be ready. But I couldn't pull myself away from the television, where her face filled the screen. Hearing her talk, I was grateful for waterproof mascara. The fact that my poised, beautiful daughter was also standing up there as Charlotte and Aidan's mother—she had given birth to her son only five weeks earlier—made this even more special.
During a burst of applause near the end of her remarks, Jim Margolis, who was keeping his eye on the clock, yelled to me, "We've gotta go!" But Chelsea wasn't done, and I didn't want to miss any of it. Finally, Jim yelled, "Now we've really gotta go!" I snapped to attention, and we raced down the hall and up the stairs in the dark. I stepped out onstage in the nick of time.
From the moment she was born, Chelsea has captivated me. I suspect a lot of parents know what I mean. My child has me hooked. That night was no different. She looked so happy recounting stories of growing up. It's always interesting to me to hear her perspective of her childhood. You try so many things as a parent. I remember how hours after she was born, Bill walked around the hospital room with tiny Chelsea in his arms, explaining everything to her. We didn't want to waste a moment.
Here's what Chelsea talked about at the DNC: Our weekly trips to the library and church. Lazy afternoons outside lying on the grass and spotting shapes in the clouds. Playing a game of her invention, Which Dinosaur Is the Friendliest? She says I warned her not to be fooled, that even seemingly friendly dinosaurs were still dinosaurs. That sounds like me: wasting no opportunity to impart some practical advice, even in absurd circumstances.
She talked about her favorite books that we read to her and those she later read by herself and told us all about, like the science fantasy A Wrinkle in Time.
Mostly Chelsea talked about me always being there and how she always knew how much we loved and valued her. I cannot express the happiness it brings to hear my daughter say that. This was my number one priority every day of her childhood: making sure she knew that nothing was more important than her. I worried about this, because Bill and I were extremely busy people. We worked long hours, we traveled frequently, and the phone in our house rang constantly, often with urgent news. It wouldn't be unexpected for a little girl growing up surrounded by all that to feel overlooked. Over the years, I've met politicians' kids who say, "I was pretty lonely. I had to compete with the whole world for my parents' attention." That was the worry that kept me up at night when Chelsea was young. I couldn't bear the thought.
One way we handled that was by not excluding her from our work. We talked about issues and politics with her starting from a young age. In her speech at the Democratic National Convention, she described how hard it was to see me lose the fight for health care reform in 1994, when she was fourteen. She was there to comfort me and help provide diversions, like watching Pride and Prejudice together.
For me, becoming a mother was the fulfillment of a long-held dream. I love children—love just sitting with them and being silly, love bringing smiles to their sweet faces. If you're ever looking for me at a party, you're likely to find me wherever the kids are. Before I even met my husband and thought about starting a family, I was a lawyer and advocate for children. When Bill and I learned that we were going to be parents, we were ecstatic. We jumped around our kitchen like we were kids ourselves.
Getting pregnant was not easy for me, but pregnancy itself was blessedly uneventful. Chelsea arrived three weeks early. I was gigantic and more than ready to meet my little one. Neither Bill nor I cared a bit whether the baby was a boy or girl. But when the doctor said, "It's a girl!" I felt so happy, it was like a sunburst beaming out of my chest. A girl!
I hadn't realized how much I wanted a daughter until she arrived. She was a wish so secret, I didn't even know that I had wished it. Then she was here, and I knew: she was what I always wanted.
If we'd had a son, I'm sure I would have been just as over the moon. I would have realized at once that I had always wanted a son—a sweet little boy to raise into a strong and caring man.
But that's not what happened. We had a daughter. And not just any daughter but someone who brought such joy and love into our lives. It felt like fate. It was the greatest thing that ever happened to me by a mile.
There's just something about daughters. From the very beginning, I felt a rush of wisdom that I wanted to impart to her about womanhood: how to be brave, how to build real confidence and fake it when you have to, how to respect yourself without taking yourself too seriously, how to love yourself or at least try to and never stop trying, how to love others generously and courageously, how to be strong but gentle, how to decide whose opinion to value and whose to disregard quietly, how to believe in yourself even when others don't. Some of these lessons were hard-won for me. I wanted badly to save my daughter the trouble. Maybe Chelsea could skip all that and arrive more quickly at a place of self-assurance.
My desire to be the best mother in the world didn't translate into knowledge about how to do it. At first, I was pretty inept. In those early days, she wouldn't stop crying. I was nearly frantic. Finally, I sat down and tried my best to make eye contact with this squirming infant. "Chelsea," I said firmly, "this is new for both of us. I've never been a mother before. You've never been a baby. We're just going to have to help each other do the best we can." Those weren't magic words that stopped her wailing, but they helped, if for no other reason than that they reminded me I was completely new at this and should be gentle with myself.
Over the years, I've met so many frazzled new mothers who can't figure out how to soothe their babies or get them to nurse or sleep, and I see in their eyes that same discombobulation I felt in those early days of Chelsea's life. It reminds me all over again how having a newborn is like every switch in your body being flicked on simultaneously. Your brain becomes a one-track mind—is the baby okay, is the baby hungry, is the baby sleeping, is the baby breathing—playing on an endless loop. If you're a new mother reading this, sleep-deprived and semicoherent, maybe wearing a tattered sweatshirt and dreaming of your next shower, please know that so many of us have been right where you are. You're doing great. It'll get easier, so just hang in there. And maybe ask your partner or mom or friend to take over for a few hours so you can have that shower and get some sleep.
Chelsea was born in 1980, a time when opportunities for women were greater than ever before in human history. She wouldn't face some of the closed doors I had. Bill and I were determined that our daughter was never going to hear "Girls can't do that." Not if we could help it.
What I couldn't know back then, holding this tiny baby in my arms, is how much she would teach me about courage, confidence, and grace. Chelsea has an inner strength that amazes me. She is smart, thoughtful, observant, and even under stress or attack, conducts herself with poise and self-possession. She is gifted at friendship, always eager to meet new people but also comfortable with solitude. She trusts her mind and feeds it constantly. She stands up for what she believes. She is one of the toughest people I know, but her toughness is quiet and deliberate, easy to underestimate. That makes her even more formidable. Her smile is full of real joy.
Bill and I had a hand in all of this, I'm sure. But Chelsea has been Chelsea from the very start. I think most parents find that their children are more formed when they arrive than we expect. It's like Kahlil Gibran wrote in The Prophet: "Your children are not your children. They come through you but not from you. You may give them your love but not your thoughts, for they have their own thoughts. You may strive to be like them, but seek not to make them like you, for life goes not backward, nor tarries with yesterday."
Like all moms, I wanted to protect Chelsea from illness and injury, bullies, disappointments, and a dangerous world. I also had a different set of threats in mind, which are particular to the daughters of public figures. She grew up on the front page of newspapers. She was attacked by right-wing personalities on the radio and mocked on television when she was just thirteen years old—it still makes my blood boil. There were plenty of nights when I wondered if we had made a terrible mistake by subjecting her to this life. I worried not just that she'd feel self-conscious but also that she'd become too practiced in the art of putting on a happy face for the cameras. I wanted her to have a rich interior life: to be sincere and spontaneous; to own her feelings, not stifle them. In short, I wanted her to be a real person with her own identity and interests.
The only way I knew how to do that was to make her life as normal as possible. Chelsea had chores at the White House. If she wanted a new book or game, she had to save her allowance to buy it. When she was bratty—to her credit, an extremely rare occurrence—she was chastised and sometimes punished. Our go-to was no TV or phone privileges for a week.
But there's a limit to how much you can make life normal for the President's daughter. So we also decided to embrace and celebrate the incredible opportunities that her unusual childhood and adolescence afforded. She went on visits overseas with us: touring the Forbidden City in China, riding an elephant in Nepal, having conversations with Nelson Mandela. She even found herself at fourteen discussing One Hundred Years of Solitude with Gabriel García Márquez. Since she had always been interested in science and health, Bill made a point of introducing her to just about every scientist and doctor who visited the White House. She relished these conversations and experiences. "This is so cool!" she said the first time we saw Camp David, on her first flight on Air Force One, when she came along as I led the U.S. delegation to the 1994 Winter Olympics in Norway. I watched her—the questions she asked, her excited reflections on everything we saw and experienced—and was delighted. She never grew bored or acted entitled. She knew how special it all was.
Perhaps most important to me, Chelsea never needed to be reminded to thank everyone who made our lives both extraordinary and ordinary: the White House staff, her teachers, her Secret Service detail, her friends' parents. She treated them all the exact same way—even heads of state. Her gratitude toward the people in her life ran deep. It led to many "proud mom" moments for me, as the kids would say.
Over the years, I worried about Chelsea less and less, as it became clear I didn't have to. I also learned from her more and more. In stressful moments, she's the calmest person in the room. She also seizes every chance to be silly with her friends and, now, her kids. These are the actions of someone who understands that life will throw a lot of challenges your way, and you should build up your inner resources of peace and happiness whenever you can.
And as was particularly evident in the 2016 campaign, she's intrepid. Chelsea traveled far and wide campaigning for me, and she did it with Aidan, whom she was still nursing. It's like that line from the late Ann Richards, the Governor of Texas: "Ginger Rogers did everything Fred Astaire did, just backward and in high heels." Chelsea did everything an energetic campaign surrogate would do, just with a tiny baby attached to her and all the gear that he required.
She'd call me from the road to tell me everything that she was seeing and hearing. "I'm not sure we're breaking through," she said, both during the primary and the general. "It feels really hard to get the facts out." Her time on the 2016 campaign trail started with a bang. On her very first day, when she politely raised questions about Bernie's health care plan—she has a master's degree in public health and a doctorate in international relations with a focus on public health institutions, so she knows what she's talking about—she got absolutely hammered for it.
I remember our conversation on the phone that night. Chelsea was frustrated with herself that her words didn't match what she knew or felt. (I can empathize!) She left some people with the impression that she thought Bernie wanted to get rid of all health care—an absurd notion and of course not what she meant or said. She felt awful—awful that she had left a false impression about anything, with anyone, and especially because it was related to something that she understands and cares about deeply. I wished I could give her a big hug. Instead, we talked it out.
Our conversation might seem a little different from the average mother-daughter talk, but underneath, it's a lot like anyone's. We started in problem-solving mode. We reviewed the policy and how better to talk about the differences between Bernie's plan and mine. Chelsea had been right on the specifics that day: at that stage in the campaign, Bernie's health care plan called for starting over to get to single payer, which is what she said. But we both knew that wasn't going to matter at this point. We returned to the basics: why my plan to improve the Affordable Care Act and add a public option was the right one to get to universal coverage. As you can tell, Chelsea and I are thought partners on this topic in particular, and her approach to thinking through problems and solutions is a lot like mine. (We recently shared a smile and a sigh when we heard Bernie called for improving the Affordable Care Act immediately by embracing the approach that I proposed as a candidate: a public option in fifty states and lowering the Medicare age to fifty-five.)
We gave ourselves a few minutes to vent about all the hate that at times seemed visceral toward me, our family, and all women stepping out. Then we switched gears and put the frustrating day behind us. We laughed about a photo of Charlotte at ballet class that Marc had sent us. We talked about how glad we were that Chelsea's low-level nausea seemed to have passed. (She was a few months pregnant.) And we said our I-love-yous and hung up, knowing that tomorrow would be another opportunity to make our case and grateful that we had each other's backs.
Every day, I was humbled by her fierce support of me. As a candidate, I was glad to have her in my corner, working diligently to explain important issues and why she believed so deeply in my plans—and me. And as her mom, I was and am so proud that she continues to rise above the attacks hurled at her every single day.
More than anyone else, it was Chelsea who helped me to see that my stance on same-sex marriage was incompatible with my values and the work I had done in the Senate and at the State Department to protect the rights of LGBT people. She impressed upon me that I had to endorse marriage equality if I was truly committed to equal human dignity, and as soon as I left the State Department, I did. Later, when I received the endorsement of the Human Rights Campaign, I thought of her. And it was Chelsea who told me about the Zika virus long before it was in the newspapers. "This is going to be a huge problem," she said, and she was right. We're still not doing enough.
When Charlotte was born, I felt the joy that comes with seeing your child take the great reservoir of love she has and enlarge it to include her own children, along with a true partner of her own. Marc is a great dad, and together they are fantastic parents. Sometimes Chelsea and I do a dance that I expect is familiar to a lot of new moms and grandmothers out there: I'll go to put the baby down for a nap or feed the toddler a snack, and Chelsea will swoop in. "Mom, that's not the way I do that." She can recite the latest American Academy of Pediatrics guidelines on sleep, infant feeding, and screen time, and I get to enjoy the special pleasure that comes from being a grandparent and knowing you don't have to worry about the baby, because your child is handling the worrying. You can just focus on being the most loving and helpful grandparent you can be.
Chelsea has been by my side at every difficult moment since she arrived on this planet, and I've leaned on her more than I ever thought I would. Late on election night, when it was clear I had lost, she was sitting next to me, looking at me with a face full of love, sending all her considerable strength and grace toward me as hard as she could. As always, she helped see me through the darkness.
* * *
* * *
I was confident that Bill would be great at parenting. His father died before Bill was born; he knew how lucky he was to have this chance that his own father never had. Still, a lot of men are thrilled to be dads but not so thrilled about all the work that a child requires. The writer Katha Pollitt has observed how even the most egalitarian relationships can contort under the strain of child rearing, and all of a sudden the mom is expected to do everything, while the dad pitches in here and there. She calls it becoming "gender Republicans"—a nifty phrase, if perhaps a little unfair to all the feminist Republicans out there, who really do exist.
I knew that I had enough energy and devotion for two, if it turned out that Bill wasn't a co-equal in the child-raising department. But I really hoped that wouldn't happen. Our marriage had always been a true partnership. Though he was Governor and then President—jobs that would seem to "beat" a lot of others, if you were the kind of person who ranked jobs like that—my career was important to me, too. So was my time and, more broadly, my identity. I couldn't wait to become a mother, but I didn't want to lose everything else about myself in the becoming. I was counting on my husband not just to respect that but also to join me in guarding against it.
So it was a wonderful thing when Chelsea arrived, and Bill dove into parenting with characteristic gusto. We arrived at the hospital with Bill clutching the materials from the Lamaze classes we had attended together. When it turned out that Chelsea was breech, he fought to be in the operating room with me and hold my hand during the C-section. Being Governor came in handy when he asked to be the first father ever permitted by that hospital to do so. After we brought her home, he handled countless midnight feedings and diaper changes. We took turns making sure the parade of family and friends who wanted to spend time with Chelsea were looked after. As our daughter grew up, we both read her good-night stories. We both got to know her teachers and coaches. Even when Bill became President, he rearranged his schedule as much as he could to have dinner with us nearly every night that he was in Washington. And when he was somewhere else in the world, he'd call Chelsea to talk about her day and go over her homework with her.
Every year, our daughter adored her father more and more. As she entered adolescence, I wondered if that would change at all. I remembered how my own dad and I grew somewhat distant from each other once I became a teenager. I provoked him with a lot of fiery political arguments. He was at a loss to navigate the occasionally stormy seas of teenage girlhood. Would that happen with Chelsea and Bill? As it turned out, no. He lived for their debates; the fiercer the better. He didn't leave me to deal with the "girl stuff": heartache, self-esteem, safety. He was right there with us.
Did I handle more of the family responsibilities, especially while Bill was President? Of course. He was President. This was something we'd talked through before he ran, and I was more than up for it.
But I never felt like I was alone in the work of raising our wonderful daughter. And I know a lot of wives of busy men who would say otherwise. Bill wanted to be a great President, but that wouldn't have mattered to him if he wasn't also a great dad.
Every time I see my husband and daughter laugh over some private joke that only they know . . . every time I overhear a conversation between them, two lightning-quick minds testing each other . . . every time I see him look at her with total love and devotion . . . I'm reminded again that I chose exactly the right person to have a family with.
I don't want to be married just to be married. I can't think of anything lonelier than spending the rest of my life with someone I can't talk to, or worse, someone I can't be silent with.
—Mary Ann Shaffer and Annie Barrows
My marriage to Bill Clinton was the most consequential decision of my life. I said no the first two times he asked me. But the third time, I said yes. And I'd do it again.
I hesitated to say yes because I wasn't quite prepared for marriage. I hadn't figured out what I wanted my future to be yet. And I knew that by marrying Bill, I would be running straight into a future far more momentous than any other I'd likely know. He was the most intense, brilliant, charismatic person I had ever met. He dreamt big. I, on the other hand, was practical and cautious. I knew that marrying him would be like hitching a ride on a comet. It took me a little while to get brave enough to take the leap.
We've been married since 1975. We've had many, many more happy days than sad or angry ones. We met in the library at Yale Law School one evening and started chatting, and all these years later, that conversation is still going strong. There's no one I want to talk to more than him.
I know some people wonder why we're still together. I heard it again in the 2016 campaign: that "we must have an arrangement" (we do, it's called a marriage); that I helped him become President and then stayed so he could help me become President (no); that we lead completely separate lives, and it's just a marriage on paper now (he is reading this over my shoulder in our kitchen with our dogs underfoot, and in a minute he will reorganize our bookshelves for the millionth time, which means I will not be able to find any of my books, and once I learn the new system, he'll just redo it again, but I don't mind because he really loves to organize those bookshelves).
I don't believe our marriage is anyone's business. Public people should be allowed to have private lives, too.
But I know that a lot of people are genuinely interested. Maybe you're flat-out perplexed. Maybe you want to know how this works because you are married and would like it to last forty years or longer, and you're looking for perspective. I certainly can't fault you on that.
I don't want to delve into all the details, because I really do want to hold on to what's left of my privacy as much as I can.
But I will say this:
Bill has been an extraordinary father to our beloved daughter and an exuberant, hands-on grandfather to our two grandchildren. I look at Chelsea and Charlotte and Aidan and I think, "We did this." That's a big deal.
He has been my partner in life and my greatest champion since the moment we met. He never once asked me to put my career on hold for his. He never once suggested that maybe I shouldn't compete for anything—in work or politics—because it would interfere with his life or ambitions. There were stretches of time in which my husband's job was unquestionably more important than mine, and he still didn't play that card. I have never felt like anything but an equal.
His late mother, Virginia, deserves much of the credit. She worked hard as a nurse anesthetist, held strong opinions, and had an unmatched zest for life. As a result, Bill is completely unbothered by having an ambitious, opinionated, occasionally pushy wife. In fact, he loves me for it.
Long before I thought of running for public office, he was saying, "You should do it. You'd be great at it. I'd love to vote for you." He helped me believe in this bigger version of myself.
Bill was a devoted son-in-law and always made my parents feel welcome in our home. Toward the end of my mother's life, when I wanted her to move into our house in Washington, he said yes without hesitation. Though I expected nothing less, this meant the world to me.
I know so many women who are married to men who—though they have their good qualities—can be sullen, moody, irritated at small requests, and generally disappointed with everyone and everything. Bill Clinton is the opposite. He has a temper, but he's never mean. And he's funny, friendly, unflappable in the face of mishaps and inconveniences, and easily delighted by the world—remember those balloons at the convention? He is fabulous company.
We've certainly had dark days in our marriage. You know all about them—and please consider for a moment what it would be like for the whole world to know about the worst moments in your relationship. There were times that I was deeply unsure about whether our marriage could or should survive. But on those days, I asked myself the questions that mattered most to me: Do I still love him? And can I still be in this marriage without becoming unrecognizable to myself—twisted by anger, resentment, or remoteness? The answers were always yes. So I kept going.
On our first date, we went to the Yale University Art Gallery to see a Mark Rothko exhibit. The building was closed, but Bill talked our way in. We had the building entirely to ourselves. When I think about that afternoon—seeing the art, hearing the stillness all around us, giddy about this person whom I had just met but somehow knew would change my life—it still feels magical, and I feel happy and lucky all over again.
I still think he's one of the most handsome men I've ever known.
I'm proud of him: proud of his vast intellect, his big heart, the contributions he has made to the world.
I love him with my whole heart.
That's more than enough to build a life on.
I looked up at the blue sky, feeling, in fact, a burst of energy, but mostly feeling my mother's presence, remembering why it was that I'd thought I could hike this trail.
—Cheryl Strayed
I've met a lot of strong people in my life but no one stronger than my mother.
People say that about their mothers all the time. But consider the life of Dorothy Howell.
Starting when she was three or four, her parents would leave her alone all day in their fifth-floor walk-up in Chicago. When she got hungry, she had to bundle herself up, walk down all those stairs, go to a nearby restaurant, produce a meal voucher, eat, and then walk all the way home. Alone.
At age eight, she was put on a train headed to California. Her parents were getting divorced, so they sent her and her three-year-old sister to live with their paternal grandparents. The little girls made the journey by themselves—no adults. It took four days.
Her grandmother wore long black Victorian dresses. Her grandfather hardly said a word. Their rules were incredibly strict. When my mother dared to go trick-or-treating one Halloween, the punishment was confinement to her bedroom for a full year, coming out only to go to school.
By the time she was fourteen, my mother couldn't take it anymore. She found a job as a housekeeper for a local family. She looked after the children in exchange for a place to live. She had one blouse and skirt that she washed every night. But the family was kind to her—finally, a little kindness. They encouraged her to keep going to high school.
When Mom graduated from high school, she moved back to Chicago because her mother sent her a letter suggesting that maybe they could be a family again. Despite everything, she missed her mom and wanted badly to be reunited. But when she got there, her mother made it clear that what she really wanted was a housekeeper. Something broke in my mom's heart forever. Still, she was a good daughter, and we dutifully visited my grandmother a few times a year.
Mom moved into a small apartment, found an office job, and met my dad, Hugh Rodham. They married in 1942 and after World War II had me, followed by my two brothers. We lived in a house in the suburbs. Mom, a homemaker, was a blur of constant energy, cooking, cleaning, hanging laundry, doing dishes, helping us with our homework, and sewing clothes for me. When I was in high school, she made me a dress—white with a print of red roses—that I thought was the prettiest I'd ever seen. She loved us intensely and worked hard to make our childhoods meaningful and fun. We played lots of games, read lots of books, went on lots of meandering walks, and talked about everything under the sun.
Back in the day, kids and their parents didn't consider each other friends. That's not how it worked. They were the parents. We were the kids.
But when I look back, there was no question that she was my best friend.
Even as a little girl, I saw how strong she was. She was so competent. When Mom said something, you knew that she meant it. When she told me to stand up for myself with a neighborhood bully, I did. She was so determined that some of her determination rubbed off on me.
She was not a huge personality. She didn't pound her fists on the table or yell like my dad did—that's not how she made her presence known. But she knew what she believed. She lived her values. She would do anything for us, and we would do anything for her. All of that made her powerful.
When I got older, the full extent of her loveless, lonely childhood hit me. I wondered if I could have survived such an ordeal with my spirit and dignity intact. She knew that she was worthy of love and decent treatment, even though the world told her otherwise for a long time. How did she hold on to that self-respect in the face of all that disregard? The most important people in her life told her she was nothing. How did she know that wasn't true? I marveled at the mental strength it must have taken to keep believing that a better day was coming, that she would find her place, that hard work would see her through, that her life had meaning despite how unfair fate had been to her.
When I became a mother myself and discovered how much patience and resilience it requires, I saw my mother's strength in a new way. She was raised with such neglect, to the extent that she was raised at all. How did she learn how to give my brothers and me such a loving and secure childhood? We talked about this. She said she carefully observed every family she ever met, including that family she worked for as a fourteen-year-old all those years ago. She paid attention to how the parents spoke to each other and to their kids. She saw that gentle firmness was possible and that families could actually laugh together, and not just sit in stony silence. Mostly, she figured it out on her own. It wasn't hard for her, she said. She loved us and was so happy to be around us, it was easy to show it.
But I know other people whose parents had cruel childhoods and who internalized that cruelty and dished it out to their own kids later. That's how abuse gets passed on through the generations. That's probably what happened with my grandmother, in fact. My mom single-handedly stopped that cycle dead in its tracks.
In my experience, as people get older, either they start looking after their parents or their parents keep looking after them. My parents kept looking after me. When they visited, they fussed over me: Did I need a sweater? Was I hungry? I'm generally the one who looks after everyone else, so it was very sweet and rather amusing to have the roles reversed.
We were close. After Bill became Governor of Arkansas in 1979, my parents moved to Little Rock. Dad was retired, and they were ready for a new chapter to unfold, preferably as near to their beloved baby granddaughter as possible.
Dad died just a few months after Bill became President. I begged Mom to come live with us in the White House, but it wasn't surprising that she said no thank you. She was too independent for that. She did come visit us for weeks at a time, staying in a bedroom on the third floor. She even traveled a few times with Bill, Chelsea, and me on foreign trips.
After I became a Senator and we left the White House, Mom moved close by, to an apartment building in Northwest Washington, D.C. She loved walking around town; going to museums and the zoo (they're free in Washington!); having dinner with Bill and me a few nights a week; and seeing a lot of my brother Tony, who lives in Virginia just outside Washington with his wife, Megan, and my nephews Zach and Simon and niece Fiona.
A few years later, I asked again, and she finally agreed to come live with Bill and me, because it was getting too hard for her to live on her own. Mom had some heart problems, which meant that unpacking groceries or folding laundry could leave her breathless. She who was always in ceaseless motion now moved gingerly, and she worried about injuring herself.
I was glad that Mom agreed to live with us without my having to fight her on it, but I was ready to fight her on it. Her independence was important, but so were her health and safety. When she still lived alone, there were times I'd be at work in the Senate and realize that I hadn't heard from her all day and panic a little. Had she fallen? Was she okay? At our house, there were always people around. If Mom moved in, we wouldn't have to worry as much anymore.
Except it wasn't as easy as that. We discovered something many parents and children find out late in life: that the balance between them is different once the child is grown and the parent is aging. Mom didn't want to be mothered; she still wanted to mother. I didn't want to encroach on her independence and dignity—the thought horrified me—but I also wanted to be straightforward with her about what I thought she could and couldn't do anymore. No more walking down the basement steps alone; they were too steep, she could fall. She did it anyway. She bristled at any restriction and largely ignored my suggestions. Any time I felt impatient, I reminded myself that I would be just as stubborn as she was.
There was one major fact that kept the balance steady between us: I still needed my mother. I needed her shoulder to lean on; I needed her wisdom and advice. I used to come home from a long day in the Senate—or, in 2007 and 2008, from a day on the campaign trail—and slide in next to her at our kitchen table and let all my frustrations and worries tumble out. Mostly, she just listened. When she gave advice, it always came down to the same basic idea: you know the right thing to do. Do what's right.
Mom lived with us for five years, and I treasured every day. The whole family did. Our home was a busy place thanks to her. Grandson Zach came by after school to see her all the time. Tony and Megan brought Fiona and Simon over frequently or took Mom back to their home for the weekend. She relished her time with them. She talked to my brother Hugh, who lived in Florida, every single day. Same with Chelsea—not a day went by without a phone call, and every week, Chelsea and Marc came to see her. She enchanted all our friends. Several of Chelsea's male friends adopted Mom as their honorary grandmother and would stop in to check on her and stay for dinner, debating the finer points of philosophy or The Sopranos. She was good company: quick-witted and well read. The day she died at ninety-two, she was halfway through The Mind's Eye by Oliver Sacks.
We were so lucky to have her with us for so long. Many of my friends had lost their mothers by then, but here was mine, greeting me every morning and night with a sweet smile and a pat on the hand. I never missed a chance to tell her that I loved her. On a lot of nights, I made the choice to put aside my briefing books for an hour or two so we could watch something on TV (she adored Dancing with the Stars) or have a late dinner together. Briefing books could wait. This time with Mom was precious. I would have given anything to have that kind of time with my dad; I wasn't going to let this opportunity pass me by.
I was grateful for her long, full life, grateful for every moment we shared, grateful that I had the means to care for her the way I did, and grateful for the deep love she shared with Chelsea and the wise advice she gave her. I can't count the number of people across the country I've met who would love nothing more than to have their aging parents living comfortably at home with them. But they can't afford it, or they don't have the room. We had the room. We could afford it. I feel extraordinarily lucky for that. We didn't leave anything unsaid between us. I feel lucky for that, too.
After Mom died, even though I was Secretary of State, I felt just like a little girl again, missing my mother.
Isn't it funny how that happens.
A British publication once offered a prize for the best definition of a friend. Among the thousands of answers received were: "One who multiplies joys, divides grief, and whose honesty is inviolable." And "One who understands our silence." The winning definition read: "A friend is the one who comes in when the whole world has gone out."
—Bits and Pieces magazine
Every single one of these experiences—the joys and struggles of marriage, motherhood, and daughterhood—I have shared with my friends.
My friends are everything to me. Some have been by my side since I was five; I'm still friends with Ernie, who walked with me to kindergarten the first day. They've seen me at my worst, and I've seen them at theirs. We've been through it all: divorces, remarriages, births of children, deaths of parents and spouses. Some of my closest friends have passed away, and I miss them every single day, which makes me value the friends who are still with me even more. We've sat at each other's hospital bedsides. We've danced at our children's weddings. We've drunk good wine and eaten good food, gossiped and hiked and read books together. We have, in short, been an indivisible team.
Some of these friends are men, and some are women. And I want to take a moment to celebrate my male friends, who have been in my corner over the years come hell or high water. There are some out there who say women and men can't really be friends. I can't understand that. I don't know what I'd do without the men who challenge me, encourage me, hold me to account, and make me laugh so hard I can't breathe.
But my girlfriends . . . my girlfriends are something else entirely.
In my experience, there's a special strength at the heart of friendships between women. We get real with each other. We talk about raw and painful things. We admit to each other insecurities and fears that we sometimes don't admit even to ourselves.
Here's an example: I loved motherhood passionately. But there were days when it felt—there's no other way to say this—very, very boring. I would read the same children's book twenty times in a row and feel myself become duller. My colleagues were doing interesting, challenging work, and I was at home singing "Itsy Bitsy Spider" for the millionth time. I wondered if I was a monster for feeling this way, so I asked my friends. Their verdict: nope, just a normal mom.
When I struggled to get pregnant, I talked to my girlfriends. When Bill and I had trouble in our marriage, I talked to my girlfriends. When I lost the 2016 election, I talked to my girlfriends in a particularly open way about how it felt to fail. I have never hesitated to be honest with them, even if what I had to say was gloomy or blunt. They know who I am deep inside, so I'm never scared of losing their good opinion. There are a lot of people for whom I put on a happy face, but not my friends.
It's bewildering to me when female friendships are depicted in movies or on TV as catty or undermining. I'm sure there are relationships like that, but in my experience, they're not the norm. Friendships between women provide solace and understanding in a world that can be really hard on us. The pressure to be a perfect wife, mother, and daughter can be unbearable. What a relief it is to find people you can share it all with and be reassured that you're doing just fine.
If you're unconvinced that friends are worth it, consider the data. (Here is where my friends would say, "Of course Hillary has data.") Studies show that when seniors interact on a regular basis with friends, they have fewer problems with memory and depression, greater physical mobility, and are more likely to get regular checkups. Now that I'm officially in the senior category, I'm holding on even more tightly to my friends. They're literally keeping me strong.
Making friends in adulthood can be hard for anybody. For Bill and me, there are added complications. Do we let people into our lives who we don't know very well? What if they just want to get to know us in order to have a good story to tell? We've been burned by people who've done that. It's not fun to feel used.
Then there's the risk that people face when they become our friends. If you go out to dinner with me, your picture might be in the paper. You might be hounded by trolls online. You might lose friends who detest me because of my politics. You might even need to hire a lawyer. I almost want to offer a disclaimer to new friends: these side effects may occur.
It's for reasons like these that a lot of well-known public figures don't really make new friends. They close the circle. It's understandable. And yet I try to keep making new friends. Just in the past year, I've become close to a few new people, including a mystery writer I've been reading for years who is now my pen pal. For me, it's worth the risk. I get so much from my friendships: I learn so much, I laugh so much. And it feels really good to build my community, to feel connected to an ever-larger web of people from different backgrounds and different chapters of my life. I don't want to spend time just with politicians. Who in the world wants that?
I have spent so much of my life in the public eye, keeping a tight hold on what I say and how I react to things, that it is such a relief to have friends with whom I can be vulnerable and unedited. I don't just enjoy that, I need it. It keeps me sane.
It comes down to this for me: I don't want to live a narrow life. I want to a live a big, expansive one. I think of the poet Mary Oliver's question about what each of us plans to do with our one wild, precious life. To me, that answer includes staying open to new friends—hearing their stories and sharing mine in turn.
There's a special group of women I've met over the years I want to mention: other First Ladies, women Senators, and Secretaries of State. I wouldn't say we're intimates, but we know and understand one another in a way few others do. We know what it's like to see our husbands attacked and our marriages questioned relentlessly and have to explain that to our children. We know what it's like to be outnumbered in a vastly male-dominated field and to stay dignified and cheerful despite being patronized or talked over on a daily basis. It doesn't matter what political party we belong to. We're connected in a deeper way.
It reminds me of what Sandra Day O'Connor, who for a long time was the only woman on the Supreme Court, said when Ruth Bader Ginsburg joined her there: "The minute Justice Ginsburg came to the court, we were nine justices. It wasn't seven and then the women. We became nine. And it was a great relief to me."
The women who have walked the paths I've walked have been a relief to me, too. And I hope I've been the same to them.
I don't believe any of us gets through life alone. Finding meaning and happiness takes a village. My friends have been my village. I wouldn't have it any other way.
To console does not mean to take away the pain but rather to be there and say, "You are not alone, I am with you. Together we can carry the burden. Don't be afraid. I am here." That is consolation. We all need to give it as well as to receive it.
—Henri Nouwen
## Turning Mourning into a Movement
They radiated strength. They were proud women who had seen a lot, cried a lot, and prayed a lot. I walked around the room, introducing myself one by one to the dozen mothers who had come from all over the country. I listened to their stories and took in their quiet, fierce dignity.
It was November 2015. We were in the homey Sweet Maple Cafe on Chicago's West Side. Each of the mothers around the table had lost children to gun violence or in encounters with police officers. They had come to talk about what happened to their kids and to see if I would do something about it—or if I was just another politician after their votes.
Later, some of these mothers would form a traveling sisterhood: the Mothers of the Movement. They told their stories in churches and community centers and onstage at the Democratic National Convention. Their courage, their generosity of spirit, their refusal to give up—all of it inspired and motivated me.
Thanks in part to the Mothers' example, I ended up speaking frequently and forcefully throughout the campaign about gun violence, racial justice, police reform, and mass incarceration. These are complicated issues, substantively and politically, but listening to the Mothers' stories and watching the steady drumbeat of mass shootings and deadly police incidents that continued throughout 2015 and 2016 convinced me that they were too important to ignore. So I made criminal justice reform a priority with my very first policy speech, stressing the need for communities to respect the police who protect them and for the police to respect the people they serve. I also criticized the powerful National Rifle Association for its extreme opposition to commonsense gun safety measures. Going after the NRA is dangerous for candidates, but I felt compelled to speak out on behalf of the dead and injured victims of gun homicides, accidents, and suicides. If I had won, we could have made progress toward keeping guns out of the hands of criminals and domestic abusers and making sure fewer parents have to bury their children the way the Mothers of the Movement did. My profound disappointment that I couldn't deliver that outcome will never go away.
The Mothers' stories, and the stories of others who lost loved ones to gun violence, deserve to be told and heard. We've got to keep saying their names. In that first meeting in Chicago, there was no press and no audience—just us. I was accompanied by my senior policy advisor Maya Harris and director of African American Outreach LaDavia Drane.
Sybrina Fulton, whose unarmed seventeen-year-old son Trayvon Martin was shot and killed outside a convenience store near Orlando, Florida, in 2012, kicked things off. "We're just regular moms," she said. "We don't want to be community activists, we don't want to be the mothers of senseless gun violence, we don't want to be in this position—we were forced into this position. None of us would have signed up for this."
Trayvon was killed while wearing a hooded sweatshirt and taking a walk to buy some Skittles candy at the corner store. Jordan Davis was shot in Jacksonville, Florida, while listening to music in a car that a white man thought was too loud and too "thug." Twelve-year-old Tamir Rice was playing in a Cleveland park with a toy gun when he was shot by a police officer. Eric Garner was choked to death by an officer after selling loose cigarettes on a Staten Island street. Some of the stories were about criminal gun violence; others, excessive force by police officers. These issues require different policy solutions and different political responses. But the common theme that ran through all the stories was race. And the anguish all these mothers felt was the same—anguish that no mother, no parent, should have to bear.
Jordan's mother, Lucia McBath, remembers comforting her son after they heard about Trayvon's murder on the news. Jordan didn't know Trayvon. They lived in different parts of Florida. But the news hit him hard. "Mom, how did this happen to Trayvon? He wasn't doing anything wrong," he asked. Lucia didn't have a good answer. Nine months later, Jordan was dead as well. Now Travyon's and Jordan's moms were sitting at the same table.
"We lay in bed, and on our bad nights, our dark nights, we stare at the ceiling and cry," Gwen Carr told me. She's the mother of Eric Garner. "We replay in our heads over and over what happened to our children."
Hadiya Pendleton was a fifteen-year-old honor student when she was randomly shot in a Chicago park. Just a week before, she had performed with her high school band at President Obama's second inauguration in Washington. "There are no words for what we go through every day just waking up," her mother, Cleo, told me. "I didn't have a voice after Hadiya passed. For like three or four days, the only thing I could do was open my eyes and scream, literally at the top of my lungs."
My throat tightened as I listened to the Mothers tell these stories, watching them remain composed despite the shattering pain behind their words. The writer Elizabeth Stone says that having a child is like deciding to have your heart go walking around outside your body. The thought of something happening to your kid is unimaginable to any parent. These mothers had lived that nightmare.
They also faced different, deeper fears that I never had to think about. My daughter and grandchildren are white. They won't know what it's like to be watched with suspicion when they play in the park or enter a store. People won't lock their car doors when they walk by. Police officers won't pull them over for driving in the "wrong" neighborhood. Gangs aren't likely to settle their feuds on the streets where they walk to school.
"As people of color, we feel the greatest impact of this injustice, of this inhumane treatment," Gwen Carr said. "Some people say that we're racist because we say 'Black lives matter.' We know that all lives matter, but we need people to understand that black lives matter also. So treat us as such. Don't just treat us like common animals. We're not. We're American citizens, and we deserve fair treatment."
Treating everyone with care and respect is especially important for the men and women charged with keeping us all safe. I feel strongly about this: the vast majority of police officers are honorable, brave public servants who put their lives on the line every day to protect others. As a Senator, I spent years fighting for first responders who served at Ground Zero and later suffered lasting health effects. They paid a terrible price for serving the rest of us. I also have the unique experience of being guarded around the clock for more than twenty-five years by highly trained men and women committed to take a bullet for me if a threat ever came. If that doesn't teach you to respect the courage and professionalism of law enforcement, nothing will. The officers I've known have been proud of their integrity, disgusted by the use of excessive force, and eager to find new and better ways to do their jobs. Every time a police officer falls in the line of duty—something that happens with sickening frequency—it's a reminder of how much we owe them and their families.
Throughout the campaign, I had many meetings and discussions with law enforcement members to hear their views about what we could do better. In August 2016 I met with a group of retired and current police chiefs from across the country, including Bill Bratton from New York, Charlie Beck from Los Angeles, and Chuck Ramsey from Philadelphia. They stressed the importance of building relationships between their officers and the communities they serve. They also stressed that part of what we owe our officers is honesty and a willingness to confront hard truths.
One hard truth we all have to face is that we all have implicit biases. I have them, you have them, and police officers have them: deeply ingrained thoughts that can lead us to think "Gun!" when a black man reaches for his wallet. Acknowledging this during the campaign may have cost me the support of some police officers and organizations, who seemed to think my concern for dead children and other victims showed a presumption of wrongdoing by police. That stung. But I was grateful for the support of other law enforcement officers who wanted to rebuild bonds of trust that would make them and all of us safe and who thought I was the best candidate to make that happen. Dallas Sheriff Lupe Valdez said at the Democratic National Convention, "We put on our badges every day to serve and protect, not to hate and discriminate." She and other officers believe, as I do, that we can work together to improve policing without vilifying the men and women who put their lives on the line to do it.
As a candidate, I worked with civil rights advocates and law enforcement leaders to develop solutions that would help, from body cameras to new training guidelines for de-escalating tense situations. I also spoke often about the importance of trying harder to walk in one another's shoes. That means police officers and all of us doing everything we can to understand the effects of systemic racism that young black and Latino men and women face every day, and how they are made to feel like their lives are disposable. It also means imagining what it's like to be a police officer, kissing his or her kids and spouse good-bye every day and heading off to do a dangerous but necessary job.
This kind of empathy is hard to come by. The divisions in our country run deep. As Maria Hamilton said to me, "It's been like that for five hundred years, Hillary. People just haven't been talking about it." Her unarmed son Dontre was killed in 2014, shot more than a dozen times by a police officer in Milwaukee after a scuffle in a public park, where he had fallen asleep on a bench. Her words were a reminder that for these mothers and generations of black parents before them, the killing and mistreatment of young black men and women was tragic but not shocking. This has been the reality of life in America for a long time. But we can't accept it as our inevitable future.
Maria's words pointed to the complex relationship between race and gun violence. It is not a coincidence that it is the leading cause of death for young black men, outstripping the next nine causes of death combined. That is the result of decades of policy choices, neglect, underinvestment, gangs and thugs, and adversarial policing in communities of color. That said, it's a mistake to think that gun violence is a problem just for black people or poor people or only in cities. Gun violence touches every class, color, and community, with thirty-three thousand people dying from guns each year—an average of ninety a day. That's a particularly devastating fact because gun violence is largely preventable. Other developed nations don't have this problem. They have commonsense laws to keep guns out of the hands of dangerous people. Those laws work. They save lives. The United States has made a cruel choice as a country not to take simple steps that would help prevent—or at least lessen—this epidemic.
The Mothers know this all too well. Consider the story of Annette Nance-Holt. She worked hard to rise through the ranks of the Chicago Fire Department, becoming a battalion chief. She and her ex-husband, Ron, a Chicago police commander, did everything they could to give their son, Blair, a safe, comfortable, middle-class life. They taught him to be generous and humble, and to feel grateful for all he had. By the time he was sixteen, Blair was a kind, hardworking, music-loving high school student on the honor roll. He was planning to go to college to study business, the first step to accomplishing his dream of being in the music industry.
Even though Annette and Ron devoted their lives to keeping their city safe, in the end, they couldn't protect their beloved child. One day in 2007, Blair was riding a public bus from school to his grandparents' store, where he sometimes helped out. A young gang member opened fire on a group of teenagers, aiming for someone in a rival gang. A friend sitting next to Blair jumped up to run to the back of the bus, but Blair pushed her back into the seat. He saved her life, but was killed himself.
All the mothers around the table with me that day in Chicago had stories like that. And they each had decided to do whatever she could to protect other children from suffering the fate of their own. They were focused intensely on curbing gun violence, reforming policing, and ensuring accountability for these deaths. Sybrina Fulton founded the Trayvon Martin Foundation to support families and to advocate for gun safety reforms. Geneva Reed-Veal, whose twenty-eight-year-old daughter, Sandra Bland, died after being jailed for a minor traffic violation, redoubled her community work through her church. All of the mothers were discovering that their stories and moral authority could make them powerful public advocates. As Cleo Pendleton put it, "When I found my voice, I couldn't shut up."
But progress was far too slow. They were understandably frustrated by how hard it was to even get a hearing from local authorities and the U.S. Justice Department, let alone action. Too many of them had been brushed off or insulted, and even attacked in the media. Sybrina and her ex-husband had to listen to their son's killer tell the press they "didn't raise their son right" and later make a small fortune auctioning off the gun that killed Trayvon.
"We need better laws," Gwen Carr told me. "If there's a crime, there should be accountability, whether you wear blue jeans, a blue business suit, or a blue uniform. We need accountability across the board, and we're not getting that."
The others agreed, and they clearly weren't sure I'd turn out to be any different from the other politicians who'd already let them down. Still, they had accepted my invitation to this meeting in Chicago and were generous with sharing their stories. Now they were waiting to see what I'd do.
Lezley McSpadden was direct with me. Her eighteen-year-old son, Michael Brown, was shot and killed in 2014 by a police officer in Ferguson, Missouri. "Are we going to see change?" Lezley asked. "Once again we're around a table, we're pouring our hearts out, we're getting emotional, we tell you what we feel—but are we going to see any change? Are we going to see some action?"
* * *
* * *
The politics of guns have been toxic for a long time. Despite the fact that, according to a June 2017 Quinnipiac University poll, 94 percent of Americans support comprehensive background checks for gun sales, including 92 percent of gun owners, many politicians have shied away from taking on the NRA. The vocal minority of voters against gun safety laws have historically been more organized, better funded, and more willing to be single-issue voters.
In the 1990s, my husband fought hard to pass both a ten-year ban on assault weapons and the Brady Bill, which, for the first time, required background checks on many gun purchases at federally licensed firearms dealers. In the years since, that law has blocked more than two million purchases by convicted felons, domestic abusers, and fugitives. The NRA funded an intense backlash to the new safety measures and helped defeat a lot of Democratic members of Congress in the disastrous 1994 midterm elections. Then, in 2000, the NRA helped beat Al Gore.
After these searing political experiences, it became conventional wisdom that it was safer for Democrats to say nothing at all about guns and hope the NRA stayed away.
I never agreed with this approach. I thought it was wrong on the policy and wrong on the politics. I've always hated gun violence on a gut level and was proud that Bill's administration had taken on the NRA and won. My commitment to stopping senseless gun violence deepened after going to Littleton, Colorado, in 1999. Bill and I visited with grieving family members of teenagers killed in the Columbine High School massacre. We huddled together over coffee cups and memorial books in a local Catholic church. I had thought about those kids every day since I'd heard the news a month earlier. I was especially moved by the story of seventeen-year-old Cassie Bernall. Press accounts at the time said that one of the student-killers asked her if she believed in God. After Cassie said yes, he shot her. When I met Cassie's mother, Misty, I gave her a big hug and asked her to tell me about her daughter. We sat down together and started looking at photos. Some of the Columbine families talked to Bill and me about what more could be done to keep other schools and families safe from gun violence. I believed we needed new measures that would go even further than what the Clinton administration had accomplished.
Later, as a Senator, I represented rural upstate New York as well as the cities. I understood and appreciated the perspective of law-abiding gun owners wary of any new regulations. I remembered my father teaching me to shoot in rural Pennsylvania, where we spent summers when I was growing up. I also lived in Arkansas for many years and went on a memorable December duck hunting expedition with some friends in the 1980s. I'll never forget standing hip deep in freezing water, waiting for the sun to rise, trying to stave off hypothermia. I did manage to shoot a duck, but when I got home, Chelsea, who had just watched Bambi, was outraged by the news that I'd shot "some poor little duck's mommy or daddy."
These experiences reinforced for me that, for many Americans, hunting and gun ownership are ingrained in the culture. Many see them as links to our frontier past and to the age-old American ethic of self-reliance. For a lot of people, being able to own a gun is a matter of fundamental freedom and self-defense. It's also a source of security and confidence in a chaotic world. I understand all that. It's why this issue is so emotionally charged. For people on both sides of the debate, it's intensely personal.
In all my political campaigns, I've done my best to strike a fair balance between standing up for commonsense gun safety measures and showing respect for responsible gun owners. I've always said that I recognize the Second Amendment and have never proposed banning all guns.
Yet, even before I got into the 2016 race, NRA chief Wayne LaPierre promised his organization would "fight with everything we've got" to stop me from becoming President. He warned that if I won, it would mean "a permanent darkness of deceit and despair forced upon the American people." All he was missing was a tinfoil hat.
Wayne LaPierre helped make the NRA one of the most reactionary and dangerous organizations in America. Instead of being concerned with the interests of everyday gun owners, many of who support commonsense safety protections, the NRA has essentially become a wholly owned subsidiary of the powerful corporations that make and sell guns. Their bottom line and twisted ideology are all that matters to them, even if it costs thousands of American lives every year.
I had a healthy appreciation for the political damage the NRA could do. I'd seen it before and expected worse this time. But I also knew that a lot of swing voters, especially women, were as horrified by gun violence as I was, and were open to smart solutions that would keep their families and communities safer. So I shook off the threats and got to work.
My team and I collaborated with gun safety advocates such as the organization Moms Demand Action to develop new proposals for keeping guns out of the hands of domestic abusers and other violent criminals. I called for universal background checks, barring anyone on the terrorist no-fly list from buying a gun, and giving survivors and families the right to hold gun makers and sellers accountable. For example, I believed that families who lost children in the 2012 mass shooting at Sandy Hook Elementary School in Newtown, Connecticut, should be able to sue Remington Arms for marketing its AR-15 assault rifle to civilians. It infuriated me that a special law gave gun manufacturers immunity from such suits.
After the massacre of nine parishioners at Mother Emanuel Church in Charleston, South Carolina, in June 2015, my team focused on why the twenty-one-year-old white supremacist killer was able to buy a gun despite having an arrest record that should have been flagged by the required background check. We found that, under current law, if a background check is not completed after three days, a store is free to sell a gun with no questions asked. This is the result of an amendment the NRA designed and pushed through Congress during the debate over the Brady Bill in 1993. Experts say that more than fifty-five thousand gun sales that should have been blocked have been allowed to proceed because of what we started calling the "Charleston loophole." I made closing it and other gun loopholes a major part of my campaign.
* * *
* * *
Listening to the Mothers' stories in Chicago, I was more sure than ever that taking on the gun lobby was the right thing to do, whatever the cost. I told them about some of the reforms that my policy team had been working on, and asked them to stay in touch with us and not be shy about sending ideas and criticisms. I said how much hearing their stories meant to me and how determined I was to be their champion. I'm sure my words failed me, but it was hard to express how honored I felt by their willingness to open up so completely with me. "We're better than this, and we need to act like we are," I said.
As our meeting broke up, the Mothers started talking intensely among themselves. Soon they were taking photos and making plans. Many of them had never met before, but they were already bonding like sisters. I saw how powerful they were together. Later, when they decided to go on the road for my campaign, traveling around South Carolina and other early primary states to speak on my behalf, I was moved and grateful. The Mothers of the Movement were born.
Over the months that followed, I always looked forward to running into the Mothers out on the trail. On hard days, a hug or smile from them would give me an extra boost. And I made a point to be upbeat around them. I figured there was enough sadness in their lives, so the least I could do was to be cheerful with them.
But it wasn't easy. New tragedies kept unfolding. In July 2016 a black man named Philando Castile was shot seven times during a traffic stop in the Twin Cities, while his girlfriend Diamond Reynolds and her four-year-old daughter sat in the car. Later, video showed the little girl pleading with her mother to stay quiet so she wouldn't be killed as well. "I don't want you to get shooted," she said. "Okay, give me a kiss," Diamond responded. "I can keep you safe," her tiny daughter assured her, before starting to cry. Two weeks later, I met with the grieving family in Minnesota and heard about how beloved Castile was in the community, including at the magnet school in Saint Paul where he worked, and that he and Diamond had planned to get married.
That same month, five police officers were ambushed and killed by a sniper in Dallas while protecting a peaceful protest march. I was horrified by the news and quickly canceled an event I had been planning to do with Joe Biden in Scranton, Pennsylvania. It didn't feel right to go to a campaign rally on the day after such a tragedy. Instead, I went to a conference of ministers in Philadelphia and paid tribute to the fallen officers and offered prayers for their families. I called Mayor Mike Rawlings and offered my support. Dallas Police Chief David Brown urged Americans to stand with the brave men and women who risk their lives to keep the rest of us safe. "We don't feel much support most days. Let's not make today most days," he said. I agreed completely. Less than two weeks later, another three officers were ambushed and killed in Baton Rouge, Louisiana. And as I'm writing this, a New York City police officer, a mother of three, was gunned down in cold blood. This violence—against police, against young black men and women, against anyone—must stop.
Since the election, I've often thought about my time with the Mothers of the Movement. Whenever I've started to feel sorry for myself, I've tried to remember how these mothers persevered through infinitely harder circumstances. They're still doing everything they can to make our country a better place. If they can, so can I and so can we all.
I think about how I felt standing with them in a prayer circle, like we did at the Trayvon Martin Foundation's annual dinner in Florida. Eight of us leaning our heads together, clasping hands, looking downward in contemplation. One of the Mothers led us in prayer, her voice rising and falling as she thanked God for making all things possible.
I remember something Gwen Carr said on our visit to the Central Baptist Church in Columbia, South Carolina. In the first days after losing her son, Eric, she couldn't even get out of bed. But then, she said, "The Lord talked to me and told me, 'Are you going to lay here and die like your son, or are you going to get up and uplift his name?' " She realized in that moment that none of us can rest as long as there are others out there to be helped. She said, "I had to turn my sorrow into a strategy, my mourning into a movement."
* * *
* * *
Guns became a flash point in both the primaries and the general election. Bernie Sanders, who loved to talk about how "true progressives" never bow to political realities or powerful interests, had long bowed to the political reality of his rural state of Vermont and supported the NRA's key priorities, including voting against the Brady Bill five times in the 1990s. In 2005, he voted for that special immunity law that protects gun makers and sellers from being sued when their weapons are used in deadly attacks. The NRA said the Protection of Lawful Commerce in Arms Act was the most important gun-related legislation in more than twenty years. Then-Senator Barack Obama and I had voted against it. I couldn't believe Bernie continued to support the law ten years later when he ran for President.
I hammered him on the issue every chance I got. We had a revealing exchange in a town hall debate in March 2016. A man stepped up to the microphone to ask a question. His fourteen-year-old daughter had been shot in the head during a shooting spree outside a Cracker Barrel restaurant. After a few scary days on life support, she pulled through and ended up being the lone survivor of the attack. The father asked what we were going to do to address the epidemic of gun violence stalking our country.
"I am looking at your daughter, and I'm very grateful that she is laughing and she is on a road to recovery," I said. "But it never should have happened." I told him about some of the steps I wanted to take to keep families safe, including repealing the immunity protection for gun manufacturers. The moderator then asked Bernie his thoughts about a new lawsuit challenging that corporate immunity. To my surprise, the Senator doubled down. He argued passionately that people like me who talked about suing gun makers were really talking about "ending gun manufacturing in America." To him, the idea that a manufacturer could be held liable for what happens with its guns was tantamount to saying that "there should not be any guns in America." I couldn't have disagreed more strongly. No other industry in our country has the kind of protection he supported for gun manufacturers. And in every other situation, he was the loudest voice in the room calling for corporations to be held accountable for their actions. Why was this one issue so different? As I told the crowd, it was like he was reading straight from the NRA's talking points. After months of pressure from activists and victims' families, Bernie finally said he would reconsider his vote.
Bernie and I disagreed on guns, but the Republicans were far more extreme. Just days after terrorists shot and killed fourteen people and seriously injured twenty-two others at an office holiday party in San Bernardino, California, Senate Republicans blocked a bill to stop individuals on the no-fly list from buying guns and explosives. I thought it was a no-brainer that if you're too dangerous to get on a plane, you're too dangerous to buy a gun! But the Republicans refused to defy the NRA.
Then there was Donald Trump. From the start of the campaign, he did everything he could to ingratiate himself with the gun lobby, which may have been wary that a New York billionaire with a history of being sympathetic to gun control wouldn't be a natural ally. So he overcompensated. He promised to force schools to allow guns in classrooms and to overturn efforts President Obama made to strengthen the background check system. After the rampage at Umpqua Community College in Roseburg, Oregon, in which eight students and one professor were killed, Trump called the attack horrible but didn't seem to think anything could be done about it. "You're going to have these things happen," he said flippantly. After the June attack at the Pulse nightclub in Orlando that killed forty-nine young people, many of them LGBT people of color, Trump said it was "too bad" that people at the club "didn't have guns attached to their hips"—even though all the research and a growing body count prove that more guns mean more deaths.
Republicans liked to rile up their base with tales about how I was going to shred the Constitution and take away their guns. It didn't matter that I said the opposite as clearly as I could, including in my acceptance speech at the Democratic National Convention: "I'm not here to repeal the Second Amendment. I'm not here to take away your guns. I just don't want you to be shot by someone who shouldn't have a gun in the first place." I was used to being the gun lobby's favorite villain. But as he so often did, Trump took it to another level. In August 2016, he told a rally in North Carolina that if I were elected President, there'd be no way to stop me from appointing liberal justices to the Supreme Court. Well, he said, maybe the "Second Amendment people" might find a way to stop me. Many of us took that to mean: maybe someone would shoot me.
Trump's remark caused a stir in the press. I was particularly concerned that if a "Second Amendment person" came after me, he'd be coming after my security detail of Secret Service agents. His campaign tried to downplay the comment, but everyone heard the innuendo loud and clear. Later, there were reports that the Secret Service told Trump's team to get their candidate to knock it off.
As for the NRA, it kept its promise to do everything it could to stop me. All told, the gun lobby spent more than $30 million supporting Trump, more money than any other outside group and more than double what it spent to support Mitt Romney in 2012. About two-thirds of that money paid for more than ten thousand negative ads attacking me in battleground states. The organization didn't have the guts to take on my specific policy proposals—which were widely popular, even with a lot of gun owners. Instead, it went for fearmongering and demonizing. In one ad, a woman is alone in bed when a robber breaks into the house. "Don't let Hillary leave you protected with nothing but a phone," the narrator warns, suggesting falsely that I would have stopped law-abiding Americans from having a gun.
I'm sure that some of my fellow Democrats will look at this high-priced onslaught and conclude, as many have in the past, that standing up to the NRA just isn't worth it. Some may put gun safety on the chopping block alongside reproductive rights as "negotiable," so as not to distract from populist economics. Who knows—the same might happen to criminal justice reform and racial justice more broadly. That would be a terrible mistake. Democrats should not respond to my defeat by retreating from our strong commitments on these life-or-death issues. The vast majority of Americans agree that we need to do more on gun safety. This is a debate we can win if we keep at it.
* * *
* * *
As I met more survivors of gun violence and the families of victims, I was amazed at how many shared the Mothers of the Movement's conviction that they had to channel their private pain into public action.
One of the most powerful voices came from someone who had trouble speaking: former Arizona Congresswoman Gabby Giffords, who was shot in the head in 2011 while meeting with constituents in the parking lot of a Tucson supermarket. Before the shooting, Gabby was a rising political star: brilliant, magnetic, and effective. After the shooting, she had to persevere through intense physical therapy and relearn how to walk and talk. Nonetheless, she and her husband, the former astronaut and fighter pilot Captain Mark Kelly, became passionate advocates for gun safety. I loved campaigning with them and watching crowds fall in love with Gabby, just as I had. "Speaking is difficult for me," she would say, "but come January, I want to say these two words: Madam President."
Other advocates were less famous but no less courageous, including the families of Sandy Hook Elementary victims in Newtown, Connecticut. Every time I tried to talk about the massacre of little children that happened at that school in 2012, I started to choke up. I don't know how some of the grieving parents found the strength to share their experiences at campaign events, but I will always be grateful that they did.
Nicole Hockley joined me at a town hall meeting in New Hampshire. Her six-year-old son, Dylan, was shot to death despite a special education teacher's heroic efforts to shield him from the bullets. After the massacre, Nicole became the managing director of Sandy Hook Promise, an organization that has trained nearly two million people across the country to identify potentially violent behavior and intervene before there's a dangerous attack.
One of Nicole's partners at Sandy Hook Promise is Mark Barden. His seven-year-old son, Daniel, was killed that day. Mark remembers how, on the morning of the shooting, Daniel woke up early so that he and Mark could watch the sunrise together. And when it came time for his older brother, Jake, to go to school, Daniel ran down the driveway to give him a hug and kiss good-bye.
After the shooting, Mark and his wife, Jackie, were the ones who sued Remington Arms, the company that makes the military-grade weapon the killer used in the attack. They argued that Remington should be held responsible for selling and marketing military weapons to civilians. (The case has been dismissed and is now on appeal.)
Then there's Nelba Márquez-Greene, who spoke with me at an event in Hartford, Connecticut. She lost her six-year-old daughter, Ana, at Sandy Hook. The night before the shooting, she and her husband took Ana and Isaiah, Ana's younger brother, out for a family dinner at the Cheesecake Factory. They splurged and ordered two rounds of dessert. Isaiah, also a Sandy Hook student, heard the shots that killed his sister from a nearby classroom. The family buried Ana two days before Christmas, her unopened gifts sitting under the tree.
Nelba, a therapist for troubled youth, now runs the Ana Grace Project, which trains teachers and schools how to reduce social isolation and create safe and welcoming communities for students. At the start of the school year following the shooting, Nelba wrote an open letter to the teachers in their district. "When you Google 'hero,' there should be a picture of a principal, a school lunch worker, a custodian, a reading specialist, a teacher, or a bus monitor," she wrote. "Real heroes don't wear capes. They work in America's schools."
One of those heroes was Dawn Hochsprung, the principal of Sandy Hook Elementary. When Dawn heard the gun shots, she raced into the hallway. She saw the gunman and lunged at him to knock the weapon out of his hands. She died trying to protect her students.
During the campaign, I met Dawn's grown daughter, Erica Smegielski. When she died, Dawn had been helping Erica plan her summer wedding. Erica couldn't imagine walking down the aisle without her mom. But slowly she pieced her life back together and managed to have a joyous wedding celebration. Then Erica went to work at Everytown for Gun Safety, Mike Bloomberg's organization that advocates for commonsense gun laws. Erica threw herself into my campaign, speaking all over the country and telling her story in a powerful television ad. She once told me that I reminded her of Dawn. It's a compliment I'll never forget.
As hard as the politics of guns are, and as divided as the country feels, we've got to do better. The NRA can spend all it wants. Donald Trump can pal around with Alex Jones, the conspiracy theorist who has called the Sandy Hook massacre a hoax. What a despicable lie. They're on the wrong side of justice, history, basic human decency. And it's because of the Sandy Hook parents, the Mothers of the Movement, Gabby and Mark, and so many other incredibly brave survivors and family members that I know in my heart that one day we will stem the tide and save lives.
I think about something I heard Erica say during the campaign. She was explaining how she picked herself up after the loss of her mother and decided to devote her life to gun safety. "What if everyone who faced tough odds said, 'It's hard, so I'm going to walk away'?" she asked. "That's not the type of world I want to live in."
Me neither, Erica.
I love people who harness themselves, an ox to a heavy cart,
who pull like water buffalo, with massive patience,
who strain in the mud and the muck to move things forward,
who do what has to be done, again and again.
—Marge Piercy
## Idealism and Realism
Service is the rent we pay for living.
It is the very purpose of life, and not something you do in your spare time.
—Marian Wright Edelman
## Change Makers
One of the most persistent challenges I faced as a candidate was being perceived as a defender of the status quo, while my opponents in the primaries and the general election seized the sought-after mantle of "change." The same thing happened to me in 2008. I never could figure out how to shake it.
Change might be the most powerful word in American politics. It's also one of the hardest to define. In 1992 and 2008, change meant electing dynamic young leaders who promised hope and renewal. In 2016, it meant handing a lit match to a pyromaniac.
The yearning for change springs from deep in the character of our restless, questing, constantly-reinventing-itself country. That's part of what makes America great. But we don't always spend enough time thinking about what it takes to actually make the change we seek. Change is hard. That's one reason we're sometimes taken in by leaders who make it sound easy but don't have any idea how to get anything done. Too often we fail to think big enough or act fast enough and let opportunities for change slip away. Or we don't have the patience to see things through.
I've been thinking about what it means to be a change maker for most of my life. My journey took me from student-activist to citizen-advocate to politician–policy maker. Along the way, I never stopped searching for the right balance of idealism and realism. Sometimes I had to make painful compromises. But I've also had the great privilege of meeting people whose lives were healthier, freer, and fuller because of my work. Today, despite losing in 2016, I am more convinced than ever that driving progress in a big, raucous democracy like ours requires a mix of principle and pragmatism—plus a whole lot of persistence.
Nobody did more to help me understand this than Marian Wright Edelman, the founder of the Children's Defense Fund and my first boss. When I met her in the spring of 1970, her accomplishments were already stunning. She was the first black woman to pass the bar exam in Mississippi, after having graduated from Yale Law School in 1963. She became a civil rights lawyer for the NAACP in Jackson and established a Head Start program for poor kids who desperately needed it. Marian worked with Dr. King and opened Bobby Kennedy's eyes to the reality of poverty in America by taking him to tiny shacks in the Mississippi Delta and introducing him to children so hungry they were nearly catatonic.
Marian showed me what it takes to make real and lasting change. She gave me my start as an activist, held me to account as I grew into a national leader, and was there for me when things fell apart as a candidate.
* * *
* * *
I was in my early twenties when I met Marian, but I'd already spent a lot of time trying to figure out how to be an effective activist.
My parents—especially my mother—raised me and my brothers in the Methodist tradition of "faith in action." At church, we were taught to be "doers of the word, not hearers only." That meant stepping outside the pews, rolling up our sleeves, and doing "all the good you can, for all the people you can, in all the ways you can, as long as ever you can." That credo, attributed to the founder of Methodism, John Wesley, inspired generations of Methodists to volunteer in hospitals, schools, and slums. For me, growing up in a comfortable middle-class suburb, it provided a sense of purpose and direction, pointing me toward a life of public service.
My activist faith was sharpened by the social upheavals of the 1960s and 1970s. In college and law school, my friends and I spent many long nights debating the morality and efficacy of civil disobedience, dodging the draft, and other forms of resistance. What would it take to end an unjust war in Vietnam, expand civil rights and women's rights, and combat poverty and injustice? Should our goal be reform or revolution? Consensus or conflict? Should we protest or participate?
The "Left," of which we considered ourselves a part, was divided. Radicals talked about revolution and believed conflict was the only way to drive change. Not surprisingly, I agreed more with the liberals who argued that the system had to be reformed from the inside. Partly it was a question of temperament—I'm a pragmatist by both nature and nurture—but I was also watching and learning as events swirled around me.
At Wellesley, I tried to find ways to push the college toward more progressive positions through negotiation rather than disruption. I ran for student government president in 1968 because I thought I could do a good job convincing college administrators to make changes that students wanted. My platform included adding students to faculty committees, recruiting more students and faculty of color, opening up the curriculum, and easing curfews and other social restrictions. I won and spent the next year trying to translate the demands of restive students into measurable change on campus.
That summer, I was in Chicago's Grant Park when antiwar protests outside the Democratic National Convention turned into a melee that shocked the nation. My longtime close friend Betsy Ebeling and I narrowly missed being hit by a rock thrown by someone in the crowd behind us. Mayor Richard Daley's police force was clearly more to blame for the violence than the kids in the park were. But the whole scene left me worried that the antiwar movement was causing a backlash that would help elect Richard Nixon and prolong the war. It was a terrifying, infuriating, exhilarating, and confusing time to be a young activist in America.
In May 1970, just a few days after four unarmed college student protesters were shot and killed by National Guardsmen on the campus of Kent State University in Ohio, I spoke to the fiftieth anniversary convention of the League of Women Voters in Washington. The civic organization had invited me after my Wellesley graduation speech made national news the previous year. I wore a black armband in memory of the students who had been killed at Kent State. In my remarks, I tried to explain the tension so many young activists were feeling, wavering "back and forth between thinking that talk at this point was useless, and believing somehow that we had to continue using words." This was a time when eighteen-year-old kids could be drafted to fight a war they believed was wrong but didn't yet have the right to vote. Many of my peers were beside themselves with anger and despair. They had given up hope that progress was possible, at least through traditional means.
I had read an article in the Washington Post about League of Women Voters members holding a vigil on the steps of the Capitol to protest Nixon's recent invasion of Cambodia. Nixon had promised to end the war and now seemed to be escalating it instead. I believed invading Cambodia was both immoral and illegal. But I knew not everyone in the audience wanted to hear this. That vigil at the Capitol was controversial, even internally. One member from Connecticut who had not participated was quoted by the Post as saying she didn't believe in protests and was afraid the vigil would tar the league's reputation. I thought that was absurd and said so. "Not to stand up and protest today against the forces of death is to be counted among them," I said, using the kind of hypercharged language that was common back then, at least for student activists. "People—living, breathing, caring human beings—who have never been involved before must be now. The luxury of long-range deliberation and verbiage-laden analysis must be forgone in favor of action."
Despite the hot (and verbiage-laden!) rhetoric, my idea of action wasn't terribly radical. I urged league members to use their economic power—"Do you know what kind of activities the corporations that you invest in are engaged in? How much longer can we let corporations run us?"—and to help antiwar activists use the political system more effectively. I felt passionately that nobody could sit on the sidelines in a time of such upheaval.
Considering everything that was going on, my friends and I sometimes wondered whether going to Yale Law School was a morally defensible choice or if we were selling out. A few of our classmates were indeed there just to open the door to a big paycheck and the chance to defend corporations that exploited workers and consumers. But for many of us, our legal education was arming us with a powerful new weapon as activists. The law could seem arid and abstract in our classrooms and textbooks, but we cheered for crusading lawyers across the country who were driving change by challenging injustices in court. When I started volunteering at the New Haven Legal Services Clinic, I saw firsthand how the law could improve or harm lives. I still believed there was a place for protests—and I moderated a mass meeting at Yale where students voted for a campus strike after the Kent State shootings, in part because the male students couldn't agree which of them should take charge—but more and more, I was coming to see how the system could be changed through hard work and reform.
All this crystalized for me when I went to work for Marian at the Children's Defense Fund. She sent me to her home state of South Carolina to gather evidence for a lawsuit seeking to end the practice of incarcerating teenagers in jails with adults. A civil rights lawyer lent me his car, and I drove all over the state going to courthouses, meeting with parents of thirteen-, fourteen-, or fifteen-year-old boys who were stuck in jail with grown men who had committed serious felonies. It was eye-opening and outrageous.
Next, I went undercover—really!—in Dothan, Alabama, to expose segregated schools that were trying to evade integration. Posing as the young wife of a businessman who had just been transferred to the area, I visited the all-white private school that had just opened in town and received tax-exempt status. When I started asking questions about the student body and curriculum, I was assured that no black students would be enrolled. Marian used the evidence that I and other activists gathered in the field to pressure the Nixon administration to crack down on these so-called segregated academies. It was thrilling work because it felt meaningful and real. After years spent studying social justice from a distance, I was finally doing something.
Another early job for Marian was going door-to-door in a working-class Portuguese neighborhood in New Bedford, Massachusetts, to figure out why so many families were keeping their children out of school. One answer was that, in those days, most schools couldn't accommodate children with disabilities, so those kids had no choice but to stay home. I'll never forget meeting one young girl in a wheelchair on the small back porch of her house. She told me how badly she wanted to go to school. But the wheelchair made it impossible. It seemed like it should be such a simple problem to solve.
This became a clarifying moment for me. I had been raised to believe in the power of reason, evidence, argument, and in the centrality of fairness and equality. As a campus liberal in the foment of the sixties, I took "consciousness raising" seriously. But talking about fairness alone wouldn't get a ramp built for this girl's wheelchair at the local public school. Raising public awareness would be necessary but not sufficient for changing school policies and hiring and training new staff to give students with disabilities an equal education. Instead of waiting for a revolution, the kind of change this girl needed was more likely to look like the sociologist Max Weber's description of politics: "a strong and slow boring of hard boards." I felt ready to do it.
Under Marian's leadership, we gathered data to document the scope of the problem. We wrote a report. We built a coalition of like-minded organizations. And we went to Washington to argue our case. It took until 1975, but the Children's Defense Fund's work eventually helped convince Congress to pass the Education for All Handicapped Children Act, requiring all public schools to make accommodations for students with disabilities.
This kind of work isn't glamorous. But my experience with CDF convinced me that this is how you make real change in America: step by step, year by year, sometimes even door by door. You need to stir up public opinion and put pressure on political leaders. You have to shift policies and resources. And you need to win elections. You need to change hearts and change laws.
Although I never imagined running for office myself, I came to see partisan politics as the most viable route in a democracy for achieving significant and lasting progress. Then, as now, plenty of progressive activists preferred to stand apart from party politics. Some saw both Democrats and Republicans as corrupt and compromised. Others were discouraged by repeated defeats. It was soul crushing to watch Democrats lose every single presidential election between 1968 and 1988 except one. But despite it all, I was attracted to politics. Even when I grew disillusioned, I knew that winning elections was the key that could unlock the change our country needed. So I stuffed envelopes for Gene McCarthy in New Hampshire, registered voters for George McGovern in Texas, set up field offices for Jimmy Carter in Indiana, and enthusiastically supported my husband's decision to run for office in Arkansas.
* * *
* * *
My identity as an advocate and activist remained important to me as I grew older. When I myself was lobbied and protested as a public official, it was a little like stepping through the looking glass. Whenever I grew frustrated, I'd remind myself how it felt to be on the other side of the table or out in the street with a sign and a megaphone. I'd been there. I knew that the activists giving me a hard time were doing their jobs, trying to drive progress and hold leaders accountable. That kind of pressure is not just important—it's mission-critical for a healthy democracy. As FDR supposedly told a group of civil rights leaders, "Okay, you've convinced me. Now make me do it."
Still, there was an inherent tension. Some activists and advocates saw their role as putting pressure on people in power, including allies, and they weren't interested in compromise. They didn't have to strike deals with Republicans or worry about winning elections. But I did. There are principles and values we should never compromise, but to be an effective leader in a democracy, you need flexible strategies and tactics, especially under difficult political conditions. I learned that the hard way during our battle for health care reform in the early nineties. Reluctance to compromise can bring about defeat. The forces opposed to change have it easier. They can just say no, again and again, and blame the other side when it doesn't happen. If you want to get something done, you have to find a way to get to yes.
So I've never had much respect for activists who are willing to sit out elections, waste their votes, or tear down well-meaning allies rather than engage constructively. Making the perfect the enemy of the good is shortsighted and counterproductive. And when someone on the left starts talking about how there's no difference between the two parties or that electing a right-wing Republican might somehow hasten "the revolution," it's just unfathomably wrong.
When I was Secretary of State, I met in Cairo with a group of young Egyptian activists who had helped organize the demonstrations in Tahrir Square that shocked the world by toppling President Hosni Mubarak in early 2011. They were intoxicated by the power of their protests but showed little interest in organizing political parties, drafting platforms, running candidates, or building coalitions. Politics wasn't for them, they said. I feared what that would mean for their future. I believed they were essentially handing the country over to the two most organized forces in Egypt: the Muslim Brotherhood and the military. In the years ahead, both fears proved correct.
I had similar conversations with some Black Lives Matter activists during the 2016 campaign. I respected how effectively their movement grabbed hold of the national debate. I welcomed it when activists such as Brittany Packnett and DeRay Mckesson pressed me on specific issues and engaged constructively with my team and me to make our platform better and stronger. And I was honored when they endorsed me for President. But I was concerned when other activists proved more interested in disruption and confrontation than in working together to change policies that perpetuate systemic racism.
This was on my mind during a memorable encounter with a few young activists in August 2015. They had driven up from Boston to attend one of my town hall meetings in Keene, New Hampshire. Well, attend is not quite the right word. Disrupt is more accurate. The town hall was focused on the growing problem of opioid abuse that was ravaging small towns across America, but the activists were determined to grab the spotlight for a different epidemic: the young black men and women being killed in encounters with police, as well as the broader systemic racism that devalued black lives and perpetuated inequities in education, housing, employment, and the justice system. In short: a cause worth fighting for.
They arrived too late to get into the town hall, but my staff suggested that we meet afterward so the activists could raise their concerns directly with me. Maybe we could even have a constructive back-and-forth. It started well enough. We were standing backstage in a small circle, which gave the discussion an intimate directness.
"What you're doing as activists and as people who are constantly raising these issues is really important," I said. "We can't get change unless there's constant pressure." Then I asked a question that I'd been wondering about for some time: how they planned to build on their early success. "We need a whole comprehensive plan. I am more than happy to work with you guys," I said.
But these activists didn't want to talk about developing a policy agenda. One was singularly focused on getting me to accept personal responsibility for having supported policies, especially the crime bill that my husband signed in 1994, which he claimed created a culture of mass incarceration. "You, Hillary Clinton, have been in no uncertain way, partially responsible for this. More than most," he declared.
I thought these activists were right that it was time for public officials—and all Americans, really—to stop tiptoeing around the brutal role that racism has played in our history and continues to play in our politics. But his view of the '94 crime bill was oversimplified beyond recognition.
The Violent Crime Control and Law Enforcement Act was passed during the crack epidemic that ravaged America's cities in the 1980s and early 1990s. It included important and positive provisions, such as the Violence Against Women Act and a ban on assault weapons. It set up special drug courts to keep first-time offenders out of prison, funded after-school and job opportunities for at-risk young people, and provided resources to hire and train more police officers. Unfortunately, the only way to pass the law was to also include measures that congressional Republicans demanded. They insisted on longer federal sentences for drug offenders. States that were already increasing penalties were emboldened. States that weren't doing so, started to. And all that led to higher rates of incarceration across the country. As chairman of the Senate Judiciary Committee, Joe Biden helped write the compromise legislation. Bernie Sanders voted for it. So did most congressional Democrats. It was also supported by many black leaders determined to stop the crime wave decimating their communities. As Yale Law School professor James Forman Jr. explains in his book Locking Up Our Own: Crime and Punishment in Black America, "African Americans have always viewed the protection of black lives as a civil rights issue, whether the threat comes from police officers or street criminals."
So, yes, the crime bill was flawed. It was a tough compromise. And it's fair to say, as Bill himself has done in the years since, that the negative consequences took a heavy toll, especially in poor and minority communities. "I signed a bill that made the problem worse," Bill said at a national conference of the NAACP in July 2015, referring to excessive incarceration. I agreed with him, which is why I was the first candidate to call for "an end to the era of mass incarceration" and proposed an aggressive agenda for criminal justice reform. It's painful now to think about how we're going backward on these issues under President Trump, with an Attorney General who favors longer sentences for drug offenders and less oversight of police departments, and who is hostile to civil rights and voting rights across the board.
So I understood the frustration of the Black Lives Matter activists, and I respected their conviction. I knew they spoke from a lifetime of being ignored and disrespected by authority figures. But I kept trying to steer the conversation back to the question of how to develop and advance a concrete agenda on racial justice.
"There has to be some positive vision and plan that you can move people toward," I said. "The consciousness raising, the advocacy, the passion, the youth of your movement is so critical. But now all I'm suggesting is—even for us sinners—find some common ground on agendas that can make a difference right here and now in people's lives."
We went round and round awhile longer on these questions, but it felt like we were talking past one another. I don't think any of us left the conversation very satisfied.
I took seriously the policies some of the Black Lives Matter activists later put forward to reform the criminal justice system and invest in communities of color. I asked Maya and our team to work closely with them. We incorporated the best of their ideas into our plans, along with input from civil rights organizations that had been in the trenches for decades. In October 2015, my friend Alexis Herman, the former Secretary of Labor, hosted a meeting in Washington for me with another group of activists. We had an engaging discussion about how to improve policing, build trust, and create a sense of security and opportunity in black neighborhoods. They spoke about feeling not only like outsiders in America but intruders—like someone no one wants, no one values. As one woman put it, "If you look like me, your life doesn't have worth." It was wrenching to hear a young American say that.
Finding the right balance between principle and pragmatism isn't easy. One example of how hard that was for me was the effort to reform welfare in the nineties—another tough compromise that remains controversial. Bill and I both believed that change was needed to help more people get the tools and support to transition from welfare to work, including assistance with health care and childcare. But Republicans in Congress were determined to rip up the social safety net. They wanted to slash funding and guarantees for welfare, Medicaid, school lunches, and food stamps; deny all benefits even to documented immigrants; and send children born out of wedlock to teen mothers to orphanages—all while offering little support to people who wanted to find work. It was cold-blooded. I encouraged Bill to veto the Republican plan, which he did. They passed it again with only minimal changes. So he vetoed it again. Then Congress passed a compromise plan. It was still flawed but on balance seemed like it would help more than it hurt.
It was a hard call. Bill and I lay awake at night talking it over. The new plan no longer block granted Medicaid and food stamps and instead put more money into them, along with childcare, housing, and transportation for people moving from welfare to work. We hoped Bill's administration would be able to fix some of the legislation's problems in a second term and keep pressing to do more to help Americans lift themselves out of poverty. Ultimately, he decided to accept the bad with the good and sign the legislation into law.
Two of the loudest voices opposing the compromise plan belonged to Marian Wright Edelman and her husband, Peter, who was an Assistant Secretary of Health and Human Services. Marian wrote an impassioned op-ed in the Washington Post calling this the "defining moral litmus test" of Bill's presidency. Peter resigned in protest. I respected Marian's and Peter's position—in fact, I expected no less from them—but it was painful to see one of the defining relationships of my life become strained.
There was never a full breach, and eventually we were drawn back together by the same shared passions that made us such close friends in the first place. Marian and I both threw ourselves into the fight to create the Children's Health Insurance Program, which emerged out of the ashes of the Clinton administration's failure to pass universal health care reform in 1993–1994. I learned a lot of lessons about what it takes to get things done in Congress, including how to work across the aisle and lean more effectively on outside allies like Marian. Those lessons paid off when CHIP became a bipartisan success story that continues to provide health care to millions of kids every year. Now Donald Trump proposes dismantling the program, which would be tragic.
In 1999, when I paid a visit to the Children's Defense Fund's farm in Tennessee for the dedication of a library in honor of the writer Langston Hughes, Marian and I went for a long walk around the grounds. It felt good to be back by her side. The next year, I watched with great pride as Bill awarded Marian the Presidential Medal of Freedom for her lifetime of advocacy.
Looking back, our disagreement over welfare reform was a testament to how deeply we both cared about policy—and to how different it is to be an advocate on the outside as opposed to a policy maker on the inside. What didn't change, though, and what ultimately brought us back together, was the passion we shared for children.
* * *
* * *
For me, it always comes back to children. The one core belief I've articulated more often and more fervently than any other in all my years in public life is that every child deserves the chance to live up to his or her God-given potential. I've said that line so many times, I've lost count. But the idea remains as powerful and motivating for me as ever. I continue to believe that a society should be judged by how we treat the most vulnerable among us, especially children, and that the measure of our success should be how many kids climb out of poverty, get a good education, and receive the love and support they deserve.
This has been a consistent through-line of my career, starting with my days with Marian at the Children's Defense Fund, and my work as a law student on early childhood development at the Yale Child Study Center and on child abuse at Yale–New Haven Hospital. Maybe it goes back even further, to the lessons I learned from my mother about her own painful childhood. She went out of her way to help girls in our town who were in trouble, in need, or just looking for a friend, because she believed that every child deserves a chance and a champion. I came to believe that too, and in every job I've ever held, I've tried to be that champion. It's a big part of why I ran for President and what I'd hoped to accomplish if I won.
I'm sure that in our hypercynical age, this sounds like just a lot of happy talk—the kind of thing politicians say when they're trying to show their softer side. After all, who doesn't love kids? Everybody professes to, even when their policies would actually hurt children. But I mean it. This is real for me.
Nothing makes me more furious than seeing kids get taken advantage of or mistreated—or not getting the opportunity, the support, the encouragement, and the security they need to succeed. You've already read about how hard it is for women in politics to express anger the way men do, and how I've struggled with the damned-if-you-do-damned-if-you-don't double bind that presents. But for me, there's always been an exception when it comes to children. I have zero patience for adults who hurt or neglect kids. My temper just boils over. That's what sparked many of the big battles I've taken on in my career.
For example, I fought so hard for health care reform in the nineties in part because of some children I met at a hospital in Cleveland. The kids all had preexisting conditions, so their families couldn't get insurance. One father of two little girls with cystic fibrosis told me the insurance company said, "Sorry, we don't insure burning houses." He pointed to his girls with tears in his eyes and said, "They called my little girls burning houses." His words nearly knocked the wind out of me. And the thought of those kids kept me going through every stumble and setback, until we finally convinced Congress to pass CHIP.
I had a similar experience early in 2016, when I read a story in the newspaper about the water crisis in Flint, Michigan. An alarming number of children were sick with lead poisoning, apparently because state authorities had failed to properly test or treat the water supply. I spent years as First Lady and as a Senator working to reduce the danger to kids from lead paint poisoning, which threatens the health of hundreds of thousands of young children across our country. But I'd never even heard of anything like what was happening in Flint.
The city used to be a thriving center for auto manufacturing, but, as vividly documented in Michael Moore's 1989 film Roger & Me, the city was slowly hollowed out by plant closings and job losses. By 2013, the median household income was less than $25,000, and more than 40 percent of residents, most of them black, lived in poverty. In 2013 and 2014, the city's emergency fiscal manager appointed by Michigan's Republican Governor came up with a plan to save a little money: instead of buying drinking water from Detroit's municipal system, as the city had long done, it would draw from the Flint River.
Almost immediately, families in town began to complain about the color, taste, and odor of the water, as well as rashes and other health concerns. Parents brought bottles of brown, smelly water to show officials. "This is what my baby is drinking," they said. "This is what she bathes in." They were ignored or given false assurances that the water was safe to drink. It was the cruelest kind of indifference. It turns out the Michigan Department of Environmental Quality never treated the river water with an anticorrosive agent that would have cost just $200 a day. That violation of federal law caused lead to leach from pipes into the city's water. Children under the age of five years old are the most vulnerable to lead poisoning, which can irreparably harm brain development and cause learning and behavioral problems. In Flint, thousands of kids may have been exposed, and the rate of lead poisoning diagnosed among children nearly doubled.
For two years or so, the state government hardly did anything about the problem. It wasn't until a group of outside doctors performed their own testing and exposed just how toxic the water was that the public health crisis became national news. When I heard about it in January 2016, I was appalled. I asked members of my team to go to Flint right away and see if they could learn more. I also called the Mayor, Karen Weaver, and asked, "What can I do to help?" She was eager for anything that would put a spotlight on Flint and pressure on the Governor to finally help fix things.
So that's exactly what I did. I raised a ruckus out on the campaign trail and on television, and called on the Governor to declare a state of emergency, which would trigger federal aid. Within a few hours, he did. That just made me more determined to keep banging the drum. At the end of the next Democratic primary debate, the moderator, Lester Holt, asked, "Is there anything that you really wanted to say tonight that you haven't gotten a chance to say?" I jumped at the opportunity to tell a national audience about what was happening in Flint.
"Every single American should be outraged," I said. "A city in the United States of America where the population which is poor in many ways and majority African American has been drinking and bathing in lead-contaminated water—and the Governor of that state acted as though he didn't really care." I was getting pretty worked up. "I'll tell you what," I continued, "if the kids in a rich suburb of Detroit had been drinking contaminated water and being bathed in it, there would've been action."
That comment may have made some people uncomfortable, but it's hard to deny that what happened in Flint never would have happened in an affluent community like Grosse Pointe. State authorities would have rushed to help, and resources would have poured in. By the same token, the schools in wealthy Bloomfield Hills are never going to look like the schools in Detroit, where children sit in classrooms infested with rodents and mold, with ceilings caving in and the heat barely functioning. All across the country, there are examples of poor communities and communities of color living with dangerous levels of toxic pollution—and it's always children who pay the biggest price.
After the debate, my campaign team was thrilled. Finally, they thought I was showing the kind of passion they believed voters wanted to see. For months, we had been losing the "outrage primary." Bernie was outraged about everything. He thundered on at every event about the sins of "the millionaires and billionaires." I was more focused on offering practical solutions that would address real problems and make life better for people. But now, in defense of those sick kids in Flint, I was the one full of righteous indignation.
A couple weeks later, I went to Flint to see what was happening for myself. It was even more heartbreaking than I imagined. Mayor Weaver and I sat down with a group of mothers in the pastor's office of the House of Prayer Missionary Baptist Church. I noticed that the church's water fountains were all marked "Out of Order," a small reminder of what this town had been living with for the past two years.
Then the mothers told me their stories. One shared that she'd been pregnant with twins when she had a reaction to the poisoned water. "It was so horrible," she said. First, she went to the emergency room with a rash. Then she had a miscarriage and needed a blood transfusion. It was emotionally devastating. What's more, it bothered her that every resident had to pay a hefty fee to use the water in the first place. Imagine, she said, "paying for poison."
"I have seizures now. That's something I didn't have before," another mom told me, fighting back tears. "Our lives have been just so damaged."
"Our conversations are not about birthdays anymore. They're not about swimming lessons," said a third mother. "They're about hospital visits and going to the ER."
One mom, Nakiya, introduced me to her adorable six-year-old son, Jaylon. He was scampering around us, taking pictures with a phone, smiling from ear to ear. Nakiya told me he'd been exposed to high levels of lead and was now having trouble in school. All I wanted to do was scoop Jaylon up in my arms, hold him tight, and promise that everything was going to be okay. Later, after speaking to the church congregation, I found Nakiya and Jaylon again. Barb Kinney, our campaign photographer, asked if he'd like to try out her fancy Nikon camera. Jaylon's eyes got big as flashbulbs, and he nodded his head. Soon he was snapping shots like a pro.
Before we left, I gave Jaylon a big hug. But I couldn't promise that everything would be okay or that the problems in Flint would go away anytime soon. In fact, I was worried that Republicans in Michigan and Washington still weren't taking the crisis seriously.
I wanted to do more to help. The people of Flint couldn't wait for the next election. They certainly couldn't wait for the Revolution. They needed change right away. "The Mayor said something that struck me," I told a few local leaders. "Rather than have people come in from the outside, let's hire people from the inside. Every church could be a dispensing station or an organizing hub." We made plans to keep in touch.
As soon as I got on the plane, I turned to Maya. I was burning with frustration over what I'd seen. "How could this have happened?" I fumed. "It's criminal! We've got to do something about it." Over the next several weeks, we worked with Mayor Weaver, local pastors, the community college, the NAACP, and others to line up support and funding for a new public-private partnership that hired unemployed young people to deliver clean water to families who needed it. Chelsea made two visits of her own and helped launch the Mayor's program. People from across the country also answered the call to help. Hundreds of union plumbers arrived to install water filters for free. Students at universities all over the Midwest raised funds for clean water deliveries. A kindergartner in New Hampshire, who lost his first tooth and received $5 from the tooth fairy, told his parents he wanted to donate it "so those little kids can have water." His mom was so proud, she sat down right away and wrote me a letter about it.
The situation in Flint is still dire. It's heartbreaking and outrageous. This is not something that should ever happen in America, period. It's lousy governance and shameful politics at their worst. It took until the end of 2016 for Congress to agree on a relief package. Most of the city's thirty thousand lead-based water pipes have yet to be replaced, forcing residents to continue to rely on bottled and boiled water. Five state officials, including the head of Michigan's health department, have been charged with involuntary manslaughter. Meanwhile, the schools are still inadequate, there aren't enough jobs, and too many children go to bed hungry.
This still infuriates me. But I do take some comfort in the compassion and generosity that many Americans showed when they learned about the crisis. One of the most rewarding parts of running for President was getting to see that spirit up close, in a million ways. For example, one day in September 2015, I held a town hall meeting in Exeter, New Hampshire. One of the residents who stood up to ask a question was a ninth-grade teacher, in the classroom for thirteen years, asking how we can help kids from low-income families find more opportunities for summer enrichment. Then a young woman stood up. She was just back from a year of working in a middle school in the Watts section of Los Angeles, through the AmeriCorps national service program. Next was someone who works with young survivors of commercial sexual exploitation and trafficking. Then a twenty-two-year veteran of the Navy with a son on active duty in the Marine Corps. One after another, these Americans asked me their questions, and each of them had his or her own extraordinary story of service and giving back to the community. That's part of what I love about America. Those people in Exeter, and everyone who lent a hand to help out in Flint, are examples of how real change happens. Progress comes from rolling up your sleeves and getting to work.
To me, Flint was so much more than something to rail about on the campaign trail, even if outrage is good politics. And in this case, it's possible that it wasn't good politics. I don't know if my advocacy for the heavily African American community of Flint alienated white voters in other parts of Michigan, but it certainly didn't seem to help, as I lost the state narrowly in both the primary and the general election. Either way, that's not what it was about for me. There were real live kids to help. Kids like Jaylon. And as I learned from Marian Wright Edelman nearly a half century ago, there's nothing more important than that.
* * *
* * *
Marian had one more lesson to teach me. In the dark days immediately following November 8, 2016, when all I wanted to do was curl up in bed and never leave the house again, Marian sent me a message. Come back to CDF, she said. The Children's Defense Fund was hosting a celebration in Washington for an inspiring group of kids who had beaten the odds, thriving despite poverty, violence, and abandonment. Before the election, Marian had asked me to deliver the keynote. Now she wanted me to know that it was even more important that I come.
It was hard to imagine giving a speech so soon after conceding the election. But if there was anyone who knew how to pick herself up, get back on her feet, and get back to work, it was Marian. She'd been doing it all her life and helping the rest of us do it too. For decades, I'd heard Marian say, "Service is the rent we pay for living." Well, I decided, you don't get to stop paying rent just because things don't go your way.
So there we were, on November 16, together again at the Children's Defense Fund. Marian stepped to the podium, and talked about our long partnership and all we'd done together to lift up children and families. Then she pointed to her two granddaughters sitting in the audience and said, "Because of all the paths she's paved for them, one day soon your daughter or my daughter or our granddaughters are going to sit in that Oval Office, and we can thank Hillary Rodham Clinton." I wanted to cry and curse and cheer all at the same time.
To leave the world a bit better, whether by a healthy child, a garden patch, or a redeemed social condition; to know even one life breathed easier because you lived. This is to have succeeded.
—attributed to Ralph Waldo Emerson
## Sweating the Details
"The decisions a Commander in Chief makes can have a profound and lasting impact on all Americans, but none more so than the brave men and women who serve, fight, and die for our country." That was Matt Lauer introducing NBC's "Commander in Chief Forum" from the deck of the aircraft carrier U.S.S. Intrepid on September 7, 2016. I was standing just offstage listening to his introduction, nodding my head.
Lauer promised the forum would be an opportunity to "talk about national security and the complex global issues that face our nation." That's exactly what I wanted. With Election Day just two months away, it was time to have a serious discussion about each candidate's qualifications to be President and how he or she would lead the country. This wouldn't be a formal debate with me and Donald Trump onstage at the same time. Instead, we'd each do our own thirty-minute session answering questions from Lauer and the audience. I was confident that with a real focus on substance and a clear contrast of our records, Americans would see that I was ready to be Commander in Chief, and Donald Trump was dangerously unprepared.
Plus, I happen to love talking about foreign policy. As Secretary of State, I got to do that pretty much nonstop for four years in 112 countries. But as a candidate for President, I was rarely asked about anything beyond domestic issues. One exception was during a campaign stop in Iowa, when a voter asked a question about the dangers of unexploded bombs from the Vietnam War left behind in Laos. It was so surprising, I nearly dropped the microphone.
Lauer and NBC were promoting this forum as a chance to finally get serious about foreign policy and national security. I was slightly surprised that Trump had agreed to it. He had been tripped up on easy questions about nuclear weapons (he said that more countries could have them, including Saudi Arabia), NATO (he called it obsolete), torture (he was for it), and prisoners of war (he said he prefers soldiers who don't get captured). He kept lying about opposing the Iraq War even after a recording emerged of him saying he supported it. And he had a penchant for saying absurd things such as "I know more about ISIS than the Generals do, believe me." Nobody believed him. In fact, more than a hundred senior national security officials from Republican administrations publicly denounced him. Many signed a letter warning that Trump "lacks the character, values, and experience" to be Commander in Chief. They wrote that he would be "the most reckless President in American history," and would "put at risk our country's national security and well-being."
Trump's campaign signed up for this forum nonetheless. They won a coin toss and chose to go second. So there I was, waiting in the wings for Lauer to call me out to the stage.
He began with a broad question about the most important characteristic that a Commander in Chief can possess. I used my answer to talk about steadiness, a quality that nobody ever associates with Donald Trump. Lauer cut in to say, "You're talking about judgment." That wasn't what I was talking about, exactly, but it was close enough. "Temperament and judgment, yes," I replied.
I've been around the block enough times to know that something bad was coming. Lauer had the look of someone proud of himself for having laid a clever trap.
"The word judgment has been used a lot around you, Secretary Clinton, over the last year and a half, and in particular concerning your use of your personal email and server to communicate while you were Secretary of State," Lauer said. "You've said it's a mistake. You said you made not the best choice. You were communicating on highly sensitive topics. Why wasn't it more than a mistake? Why wasn't it disqualifying, if you want to be Commander in Chief?"
It was disappointing but predictable that he had so quickly steered the supposedly high-minded "Commander in Chief Forum" to the subject of emails, months after the director of the FBI had announced there was no case and closed the investigation. I understood that every political reporter wanted his or her pound of flesh. But Lauer had already grilled me about emails in an interview back in April. I figured this must be about "balance." Many in the mainstream media bend over backward to avoid criticism from the right about being soft on Democrats. If Lauer intended to ask Trump tough questions, he had to make a show of grilling me, too.
Of course, that isn't balanced at all—because balanced doesn't mean strictly equal. It means reasonable. It means asking smart questions backed by solid reporting and making decisions about coverage that will help people get the information they need to make sound decisions. Picking the midpoint between two sides, no matter how extreme one of them is, isn't balanced—it's false equivalence. If Trump ripped the shirt off someone at a rally and a button fell off my jacket on the same day, the headline "Trump and Clinton Experience Wardrobe Malfunctions, Campaigns in Turmoil" might feel equal to some, but it wouldn't be balanced, and it definitely wouldn't be fair. Most important, the voters wouldn't learn anything that would help them decide who should be president.
The Lauer episode was a perfect example. I made a mistake with my emails. I apologized, I explained, I explained, and apologized some more. Yet here we were, after all these months, and after the FBI finished its work, at a forum supposed to be about the security of our country, and to balance the fact that Trump was going to have a hard time answering even the most straightforward questions, we were spending our time on emails.
After the election, a report from Professor Thomas Patterson at Harvard's Shorenstein Center on Media, Politics, and Public Policy explained how damaging the pursuit of false equivalency can be. "If everything and everyone are portrayed negatively, there's a leveling effect that opens the door to charlatans," it said. "The press historically has helped citizens recognize the difference between the earnest politician and the pretender. Today's news coverage blurs the distinction."
Here I was, facing the blurring in real time, with a charlatan waiting in the wings. But what could I do? I launched into my standard answer on the emails, the one I'd given a thousand times before: "It was a mistake to have a personal account. I would certainly not do it again. I make no excuses for it," and so forth. I also explained that, as the FBI had confirmed, none of the emails I sent or received was marked as classified.
Instead of moving on to any of a hundred urgent national security issues, from the civil war in Syria, to the Iranian nuclear agreement, to the threat from North Korea—the issues this forum was supposed to be about—Lauer stayed on emails. He asked four follow-ups. Meanwhile, the clock was ticking, and my thirty minutes to discuss serious foreign policy challenges were slipping away.
Finally, after learning absolutely nothing new or interesting, Lauer turned to a question from one of the veterans NBC had picked to be in the audience. He was a self-described Republican, a former Navy lieutenant who had served in the first Gulf War, and he promptly repeated the right-wing talking point about how my email use would have landed anyone else in prison. Then he asked how could he trust me as President "when you clearly corrupted our national security?"
Now I was ticked off. NBC knew exactly what it was doing here. The network was treating this like an episode of The Apprentice, in which Trump stars and ratings soar. Lauer had turned what should have been a serious discussion into a pointless ambush. What a waste of time.
When another veteran in the audience was finally allowed to ask about how to defeat ISIS, Lauer interrupted me before I began answering. "As briefly as you can," he admonished. Trump should have reported his performance as an in-kind contribution.
Later, there were rumors ginned up by fake news reports that I was so mad at him I stormed off stage, threw a tantrum, and shattered a water glass. While I didn't do any of that, I can't say I didn't fantasize about shaking some sense into Lauer while I was out there.
Now I wish I had pushed back hard on his question. I should have said, "You know, Matt, I was the one in the Situation Room advising the President to go after Osama bin Laden. I was with Leon Panetta and David Petraeus urging stronger action sooner in Syria. I worked to rebuild Lower Manhattan after 9/11 and provide health care to our first responders. I'm the one worried about Putin subverting our democracy. I started the negotiations with Iran to prevent a nuclear arms race in the Middle East. I'm the one national security experts trust with our country's future." And so much more. Here's another example where I remained polite, albeit exasperated, and played the political game as it used to be, not as it had become. That was a mistake.
Later, I watched Lauer soft-pedal Trump's interview. "What do you believe prepares you to make decisions that a Commander in Chief has to make?" he asked. Then he failed to call Trump out on his lies about Iraq. I was almost physically sick.
Thankfully, a lot of viewers reacted exactly the same way. The Washington Post published a stinging editorial:
Judging by the amount of time NBC's Matt Lauer spent pressing Hillary Clinton on her emails during Wednesday's national security presidential forum, one would think that her homebrew server was one of the most important issues facing the country this election. It is not. There are a thousand other substantive issues—from China's aggressive moves in the South China Sea to National Security Agency intelligence-gathering to military spending—that would have revealed more about what the candidates know and how they would govern. Instead, these did not even get mentioned in the first of five and a half precious prime-time hours the two candidates will share before Election Day, while emails took up a third of Ms. Clinton's time.
Criticism of Lauer and NBC poured in. New York Times columnist Nicholas Kristof called the forum "an embarrassment to journalism." Slate's Will Saletan described it as "one of the weakest, least incisive performances I've seen from a presidential forum moderator." And The Daily Show's Trevor Noah had my favorite take: "During World War II, on multiple occasions, kamikaze planes crashed into the Intrepid, and last night Matt Lauer continued that tradition," he said. "I don't know what the f— he was doing, and neither did he."
Sadly, though, millions of people watched. And in my view, the "Commander in Chief Forum" was representative of how many in the press covered the campaign as a whole. According again to Harvard's Shorenstein Center, discussion of public policy accounted for just 10 percent of all campaign news coverage in the general election. Nearly all the rest was taken up by obsessive coverage of controversies such as email. Health care, taxes, trade, immigration, national security—all of it crammed into just 10 percent of the press coverage. The Shorenstein Center found that not a single one of my many detailed policy plans received more than a blip of press coverage. "If she had a policy agenda, it was not apparent in the news," it concluded. "Her lengthy record of public service also received scant attention." None of Trump's scandals, from scamming students at Trump University, to stiffing small businesses in Atlantic City, to exploiting his foundation, to refusing to release his taxes as every presidential candidate since 1976 has done—and on and on—generated the kind of sustained, campaign-defining coverage that my emails did.
The decline of serious reporting on policy has been going on for a while, but it got much worse in 2016. In 2008, the major networks' nightly newscasts spent a total of 220 minutes on policy. In 2012, it was 114 minutes. In 2016, it was just 32 minutes. (That stat is from two weeks before the election, but it didn't change much in the final stretch.) By contrast, 100 minutes were spent covering my emails. In other words, the political press was telling voters that my emails were three times more important than all the other issues combined.
Maybe this bothers me so much because I'm an unapologetic policy wonk. It's true that I sweat the details, whether it's the precise level of lead in the drinking water in Flint, the number of mental health facilities in Iowa, the cost of specific prescription drugs, or how exactly the nuclear triad works. Those aren't just details if it's your kid or your aging parent whose life depends on it—or, when it comes to nukes, if all life on earth depends on it. Those details ought to be important to anyone seeking to lead our country.
* * *
* * *
I've always thought about policy in a very practical way. It's how we solve problems and make life better for people. I try to learn as much as I can about the challenges people face and then work with the smartest experts I can find to come up with solutions that are achievable, affordable, and will actually make a measurable difference. For the campaign, I hired a policy team with deep experience in government and relied on an extensive network of outside advisors drawn from academia, think tanks, and the private sector. The crew in Brooklyn proudly hung a sign above their desks that read "Wonks for the Win." They produced reams of position papers. Many included budget scores, substantive footnotes—the whole nine yards. It felt like a White House-in-waiting, which is exactly what I had in mind. I wanted to be able to hit the ground running, ready to sign executive orders and work with Congress to pass as much legislation as possible in my first hundred days in office. I also wanted voters to know exactly what they could expect from me as President, how it would affect their lives, and be able to hold me accountable for delivering.
Over the course of the 2016 race, I also came to better appreciate other ways of thinking about policy: as a window to a candidate's character and a tool for mobilization.
Joe Biden likes to say, "Don't tell me what you value. Show me your budget, and I'll tell you what you value." This is something I've always believed as well: that the policies you propose say a lot about your principles and priorities. You can evaluate a candidate's childcare plan based on how much it will cost, who it will help, and whether it has a chance of passing Congress. But you can also see it as a window into the candidate's heart: this is a person who cares about children and believes society has a responsibility to help care for the most vulnerable among us. The piece that perhaps I undervalued is that, from this perspective, the details of the plan may matter less than how it's framed and sold to the public—in other words, the optics of it. I cared about the optics, but not nearly as much as I cared about the merits of the plans themselves, and it showed.
Policy can also be a source of inspiration. I don't know how many Trump supporters really believed that he'd build a giant wall across the entire southern border and get Mexico to pay for it. But hearing him say it got them excited. You don't have to like the idea to see that it gave them something to talk to their friends about, tweet, and post on Facebook. It was a rallying call more than it was a credible policy proposal, but that didn't make it any less powerful—especially if voters weren't hearing me talk about immigration or any of their economic concerns because of overwhelming coverage of emails.
These different ways of thinking about policy helped shape both the primaries and the general election in 2016.
From the beginning, I expected a strong primary challenge from the left. It happens almost every time, and it was clear this time that there was a lot of populist energy waiting to find a champion. Anger at the financial industry had been building for years. The Occupy Wall Street movement had helped shine a light on the problem of income inequality. And after years of biting their tongues about the Obama administration's compromises, left-wing Democrats were ready to let loose.
Senator Elizabeth Warren was the name most often mentioned as a potential candidate, but I wasn't convinced she was going to jump in. After all, she had joined all the other Democratic women Senators in signing a letter urging me to run. I've long admired Elizabeth's passion and tenacity, especially her farsighted efforts to create the Consumer Financial Protection Bureau in 2011, which has now returned nearly $12 billion to more than twenty-nine million Americans ripped off by predatory lenders, credit card companies, and other corporate miscreants. So before I announced my candidacy, I invited her to my house in Washington to take her temperature and see if we might be able to work together. I think we both were a little wary, but we approached each other with good faith, good intentions, and open minds. I came away convinced that if Elizabeth believed her views and priorities would be included and respected in my campaign, she might become my champion rather than my challenger. In our meeting, we talked about some of the issues she cares about most, including student debt and financial reform. Knowing that Elizabeth believes "personnel is policy," I asked her to recommend experts whose advice I could seek. She gave me a list, and my team methodically worked through it, making sure our agenda was informed by the perspectives of people she trusted. Two friends we share in common—the political consultant Mandy Grunwald, who also worked for Elizabeth, and the former financial regulator Gary Gensler, who served as my campaign's chief financial officer—helped us stay connected. Later, Elizabeth was on my list of potential choices for Vice President.
Elizabeth never joined the race, but Bernie Sanders, the Democratic Socialist Senator from Vermont, did. Even though I understood that a lot of Democratic primary voters were looking for a left-wing alternative, I admit I didn't expect Bernie to catch on as much as he did. Nothing in my experience in American politics suggested that a Socialist from Vermont could mount a credible campaign for the White House. But Bernie proved to be a disciplined and effective politician. He tapped into powerful emotional currents in the electorate. And he was aided by the fact that the primaries began with the white, liberal bastions of Iowa and New Hampshire, his neighboring state. When a Des Moines Register poll in January 2016 found that 43 percent of likely Iowa Democratic caucusgoers identified as Socialists, I knew there could be trouble ahead.
Bernie and I had a spirited contest of ideas, which was invigorating, but I nonetheless found campaigning against him to be profoundly frustrating. He didn't seem to mind if his math didn't add up or if his plans had no prayer of passing Congress and becoming law. For Bernie, policy was about inspiring a mass movement and forcing a conversation about the Democratic Party's values and priorities. By that standard, I would say he succeeded. But it worried me. I've always believed that it's dangerous to make big promises if you have no idea how you're going to keep them. When you don't deliver, it will make people even more cynical about government.
No matter how bold and progressive my policy proposals were—and they were significantly bolder and more progressive than anything President Obama or I had proposed in 2008—Bernie would come out with something even bigger, loftier, and leftier, regardless of whether it was realistic or not. That left me to play the unenviable role of spoilsport schoolmarm, pointing out that there was no way Bernie could keep his promises or deliver real results.
Jake Sullivan, my top policy advisor, told me it reminded him of a scene from the 1998 movie There's Something About Mary. A deranged hitchhiker says he's come up with a brilliant plan. Instead of the famous "eight-minute abs" exercise routine, he's going to market "seven-minute abs." It's the same, just quicker. Then the driver, played by Ben Stiller, says, "Well, why not six-minute abs?" That's what it was like in policy debates with Bernie. We would propose a bold infrastructure investment plan or an ambitious new apprenticeship program for young people, and then Bernie would announce basically the same thing, but bigger. On issue after issue, it was like he kept proposing four-minute abs, or even no-minute abs. Magic abs!
Someone sent me a Facebook post that summed up the dynamic in which we were caught:
BERNIE: I think America should get a pony.
HILLARY: How will you pay for the pony? Where will the pony come from? How will you get Congress to agree to the pony?
BERNIE: Hillary thinks America doesn't deserve a pony.
BERNIE SUPPORTERS: Hillary hates ponies!
HILLARY: Actually, I love ponies.
BERNIE SUPPORTERS: She changed her position on ponies! #WhichHillary? #WitchHillary
HEADLINE: "Hillary Refuses to Give Every American a Pony"
DEBATE MODERATOR: Hillary, how do you feel when people say you lie about ponies?
WEBSITE HEADLINE: "Congressional Inquiry into Clinton's Pony Lies"
TWITTER TRENDING: #ponygate
Early in the race, in 2015, there was a day when Bernie and I both happened to be in the Amtrak passenger lounge at New York's Penn Station waiting for the train to D.C. We talked for a bit, and he said he hoped we could avoid personal attacks, including on our families. I know what that's like. I agreed and said I hoped we could keep our debates focused on substance.
Yet despite this pledge, as time went on, Bernie routinely portrayed me as a corrupt corporatist who couldn't be trusted. His clear implication was that because I accepted campaign donations from people on Wall Street—just as President Obama had done—I was "bought and paid for."
This attack was galling for many reasons, not least because Bernie and I agreed on the issue of campaign finance reform; the need to get dark money out of politics; and the urgency of preventing billionaires, powerful corporations, and special interests from buying elections. We both supported a constitutional amendment to overturn the disastrous Supreme Court decision in Citizens United that opened the floodgates to super PACs and secret money. I also proposed new measures to boost disclosure and transparency and to match small donor contributions, based on New York City's successful system, which would help level the playing field for everyday Americans.
Where Bernie and I differed was that he seemed to see the dysfunction of our politics almost solely as a problem of money, whereas I thought ideology and tribalism also played significant roles. Bernie talked as if 99 percent of Americans would back his agenda if only the lobbyists and super PACs disappeared. But that wouldn't turn small-government conservatives into Scandinavian Socialists or make religious fundamentalists embrace marriage equality and reproductive rights. I also was—and am—concerned about the Republican-led assault on voting rights, their efforts to gerrymander safe congressional districts, and the breakdown of comity in Congress. In addition to getting big money out of politics, I thought we had to wage and win the battle of ideas, while also reaching across the aisle more aggressively to hammer out compromises. That's how we can start to break down the gridlock and actually get things done again.
Because we agreed on so much, Bernie couldn't make an argument against me in this area on policy, so he had to resort to innuendo and impugning my character. Some of his supporters, the so-called Bernie Bros, took to harassing my supporters online. It got ugly and more than a little sexist. When I finally challenged Bernie during a debate to name a single time I changed a position or a vote because of a financial contribution, he couldn't come up with anything. Nonetheless, his attacks caused lasting damage, making it harder to unify progressives in the general election and paving the way for Trump's "Crooked Hillary" campaign.
I don't know if that bothered Bernie or not. He certainly shared my horror at the thought of Donald Trump becoming President, and I appreciated that he campaigned for me in the general election. But he isn't a Democrat—that's not a smear, that's what he says. He didn't get into the race to make sure a Democrat won the White House, he got in to disrupt the Democratic Party. He was right that Democrats needed to strengthen our focus on working families and that there's always a danger of spending too much time courting donors because of our insane campaign finance system. He also engaged a lot of young people in the political process for the first time, which is extremely important. But I think he was fundamentally wrong about the Democratic Party—the party that brought us Social Security under Roosevelt; Medicare and Medicaid under Johnson; peace between Israel and Egypt under Carter; broad-based prosperity and a balanced budget under Clinton; and rescued the auto industry, passed health care reform, and imposed tough new rules on Wall Street under Obama. I am proud to be a Democrat and I wish Bernie were, too.
Throughout the primaries, every time I wanted to hit back against Bernie's attacks, I was told to restrain myself. Noting that his plans didn't add up, that they would inevitably mean raising taxes on middle-class families, or that they were little more than a pipe dream—all of this could be used to reinforce his argument that I wasn't a true progressive. My team kept reminding me that we didn't want to alienate Bernie's supporters. President Obama urged me to grit my teeth and lay off Bernie as much as I could. I felt like I was in a straitjacket.
I eagerly looked forward to our first debate in October 2015. At last, that was a place where it would be appropriate to punch back. I held long prep sessions at my house to map out thrusts and parries with Jake, Ron Klain, Karen Dunn, and Bob Barnett, who played Bernie in our practice sessions.
I was determined to use this first debate with Bernie to go straight at the core differences between us. I wanted to debunk the false charge that I wasn't a true progressive and explain why I thought Socialism was wrong for America—and that those two propositions were in no way contradictory. It was beyond frustrating that Bernie acted as if he had a monopoly on political purity and that he had set himself up as the sole arbiter of what it meant to be progressive, despite giving short shrift to important issues such as immigration, reproductive rights, racial justice, and gun safety. I believed we could and should fight both for more equal economic opportunities and greater social justice. They go hand in hand, and it's wrong to sacrifice the latter in the name of the former.
As the date approached, the first debate took on added significance. Bernie was rising in the polls. Vice President Biden was considering jumping in the race. And I was set to testify before the Republican-created special congressional committee investigating the terrorist attacks in Benghazi. It seemed as if everything would come to a head during one week in October.
In the end, Biden bowed out. The Republicans swung at me and missed at the eleven-hour-long Benghazi hearing. And the debate went better than I could have hoped.
Beforehand, I was full of nerves but confident I had prepared as well as I possibly could and excited to finally stop biting my tongue and get in there and mix it up. I got my chance. Bernie and I clashed right out of the gate on Socialism and capitalism, whether Denmark should serve as a model for America, and what it means to be a progressive. "I love Denmark," I said (and I do), but we aren't Denmark. "We are the United States of America. It's our job to rein in the excesses of capitalism so that it doesn't run amok and doesn't cause the kind of inequities we're seeing in our economic system. But we would be making a grave mistake to turn our backs on what built the greatest middle class in the history of the world." My defense of the American system of free enterprise may not have helped me with those self-identified Socialists in Iowa, but what mattered to me in that moment was saying what I believed.
The moderator, CNN's Anderson Cooper, pressed me on whether I was really a progressive or just a squishy moderate or a shape-shifting opportunist. I explained that I had been consistent throughout my career in fighting for a set of core values and principles. "I'm a progressive," I said, "but I'm a progressive who likes to get things done." I thought that summed up my fundamental disagreement with Bernie fairly well.
Still, and this is important, Bernie deserves credit for understanding the political power of big, bold ideas. His call for single-payer health care, free college, and aggressive Wall Street reform inspired millions of Americans, especially young people. After I won the nomination, he and I collaborated on a plan to make college more affordable that combined the best elements of what we'd both proposed during the primaries. That kind of compromise is essential in politics if you want to get anything done. Then we worked together to write the most progressive Democratic platform in memory.
Bernie and I may have had different views about the role of policy—a road map for governing versus a tool for mobilization—but Donald Trump didn't care about policy at all. He seemed proud of his ignorance and didn't even pretend to come up with plans for how he'd build his wall, fix health care, bring back all the lost jobs in manufacturing and coal mining, and defeat ISIS. It was like he'd just wave a magic wand. He ridiculed me for taking the job seriously. "She's got people that sit in cubicles writing policy all day," he told Time magazine. "It's just a waste of paper." I kept waiting for reporters and voters to challenge him on his empty, deceitful promises. In previous elections, there was always a moment of reckoning when candidates had to show they were serious and their plans were credible. Not this time. Most of the press was too busy chasing ratings and scandals, and Trump was too slippery to be pinned down. He understood the needs and impulses of the political press well enough that if he gave them a new rabbit every day, they'd never catch any of them. So his reckoning never came.
Trump also refused to prepare for our debates. It showed. When we went head-to-head for the first time on September 26, 2016, at Long Island's Hofstra University, he wilted under questioning and nearly had a full-on meltdown. He tried to turn it around by attacking me for not showing up fumbling and incoherent like he did. I wasn't having it. Yeah, I did prepare, I said. "You know what else I prepared for? I prepared to be President."
Later, Chuck Todd of NBC's Meet the Press actually criticized me for being too prepared. I'm not sure how that's possible—can you be too prepared for something so important? Does Chuck ever show up for Meet the Press and just wing it? The fact that I was up against Donald Trump—perhaps the least prepared man in history, both for the debates and for the presidency—made the comment even more puzzling. Were they so enthralled by his rabbit-a-day strategy that insults, false charges, and fact-free assertions were now the best evidence of authenticity?
I thought about that exchange often as I watched Trump's first hundred days in office. I even allowed myself a little chuckle when he fumed, "Nobody knew health care could be so complicated." He also discovered that foreign policy is harder than it looks. The President of China had to explain the complexity of the North Korea challenge to him. "After listening for ten minutes, I realized it's not so easy," Trump said. Can you hear my palm slapping my forehead? Sometimes it seems like Trump didn't even want to be President at all. "This is more work than in my previous life," he told a reporter. "I thought it would be easier."
I can't help but think about how different my first hundred days would have been. A haunting line from the nineteenth-century poet John Greenleaf Whittier comes to mind: "For all sad words of tongue and pen, the saddest are these: 'It might have been.' "
Trump's first major initiative was the Muslim ban, which immediately ran into trouble in court. Mine would have been a jobs and infrastructure package funded by raising taxes on the wealthiest Americans. He failed to start building his great, beautiful wall paid for by Mexico. I would have pushed for comprehensive immigration reform with a path to citizenship. He appointed an Attorney General whose record on civil rights was so problematic, Coretta Scott King once warned that making him a judge would "irreparably damage" the work of her husband, Dr. Martin Luther King Jr. I would have worked across the aisle on bipartisan criminal justice reform—there was a real opportunity there for progress. He tried to repeal Obamacare and strip health care away from tens of millions of Americans. I would have gone after the drug companies to bring down prices and fought for a public option to get us even closer to affordable, truly universal health care. He alienated allies like German Chancellor Angela Merkel, while embracing dictators like Russia's Vladimir Putin. What would I have done? There's nothing I was looking forward to more than showing Putin that his efforts to influence our election and install a friendly puppet had failed. Our first face-to-face meeting would really have been something. I know he must be enjoying everything that's happened instead. But he hasn't had the last laugh yet.
* * *
* * *
Since the election, I've been thinking a lot about how we can do a better job of pushing policy back into our politics.
I have a new appreciation for the galvanizing power of big, simple ideas. I still think my health care and college plans were more achievable than Bernie's and that his were fraught with problems, but they were easier to explain and understand, and that counts for a lot. It's easy to ridicule ideas that "fit on a bumper sticker," but there's a reason campaigns use bumper stickers: they work.
Bernie proved again that it's important to set lofty goals that people can organize around and dream about, even if it takes generations to achieve them. That's what happened with universal health care. For a hundred years, Democrats campaigned on giving all Americans access to affordable, quality care. Bill and I tried to get it done in the 1990s, and we succeeded in creating CHIP, which provides coverage to millions of kids. It wasn't until Obama was swept into office with a supermajority in the Senate that we could finally pass the Affordable Care Act. Even then, the ACA was a hodgepodge of imperfect compromises. But that historic achievement was possible only because Democrats had kept universal health care as our North Star for decades.
There's a historical irony here: Bill's presidency is often associated with small-bore initiatives such as midnight basketball and school uniforms—the opposite of those big, transformative ideas that liberals dream about. But that view misses so much. I believe Bill's impact on our party and our country was profound and transformative. He reinvented a moribund party that had lost five of the previous six presidential elections, infusing it with new energy and ideas, and proving that Democrats could be pro-growth and pro-environment, pro-business and pro-labor, pro–public safety and pro–civil rights. He reversed trickle-down economics, balanced the federal budget, challenged Americans to embrace a new ethic of national service with AmeriCorps, and presided over two terms of peace and broadly shared prosperity.
The new Democratic Party he built went on to win the popular vote in six of the next seven elections between 1992 and 2016. He also inspired a generation of modernizing progressives in other Western democracies, especially Tony Blair's New Labour Party in the United Kingdom. In short, there was nothing small bore about the Clinton presidency.
I believe my presidency also would have been transformative because of the big ideas I proposed to build an economy that works for everyone, not just those at the top. Here are a few of them:
First, we need the biggest investment in good jobs since World War II. This should include a massive infrastructure program that repairs and modernizes America's roads, bridges, tunnels, ports, airports, and broadband networks; new incentives to attract and support manufacturing jobs in hard-hit communities from Coal Country to Indian country; debt-free college and improved training and apprenticeship programs to help people without college degrees get higher-paying jobs; support for small business by expanding access to capital and new markets and cutting taxes and red tape; a big push to expand clean energy production, including deploying half-a-billion solar panels in four years; and major investments in scientific research to create the jobs and industries of tomorrow.
Second, to make the economy fairer, we need new rules and incentives to make it easier for companies to raise wages and share profits with employees and harder for them to ship jobs overseas and bust unions. We have to make sure Wall Street can't wreck Main Street again, and get smarter and tougher on trade so American workers aren't caught in an unwinnable race against subsidized or state-owned industries, substandard labor conditions, or currency manipulation.
Third, we have to modernize workforce protections with a higher minimum wage, equal pay for women, paid family and medical leave, and affordable childcare. We should defend and improve the Affordable Care Act to reduce prices and expand coverage, including with a public option.
Fourth, we can pay for all of this with higher taxes on the top 1 percent of Americans who have reaped the lion's share of income and wealth gains since 2000. This would also help reduce inequality.
I could go on, but that gives you a flavor of some of the things I would have tried to get done as President. Unfortunately, despite the fact that I talked about these ideas endlessly, they never got much media attention, and most people never heard about any of them. I failed to convince the press that economics was more important than emails. But it was. Just as frustrating is the fact that I never managed to convince some skeptics that I really was in it to help working families. I thought that based on my years fighting for health care reform, my record in helping create jobs as a Senator, my efforts to raise the alarm before the financial crisis, and my early commitment to address the opioid epidemic, people would see me as a proven change maker and a fighter for children and families. Instead, I never quite shook the false perception that I was a defender of the status quo.
In my more introspective moments, I do recognize that my campaign in 2016 lacked the sense of urgency and passion that I remember from '92. Back then, we were on a mission to revitalize the Democratic Party and bring our country back from twelve years of trickle-down economics that exploded the deficit, hurt the middle class, and increased poverty. In 2016, we were seeking to build on eight years of progress. For a change-hungry electorate, it was a harder sell. More hopeful voters bought it; more pessimistic voters didn't.
Another lesson from this election, and from the Trump phenomenon in particular, is that traditional Republican ideology is bankrupt. For decades, the big debates in American politics were about the size and role of government. Democrats argued for a more active federal government and a stronger social safety net, while Republicans argued for a smaller government, lower taxes, and fewer regulations. The country seemed fairly evenly divided, or perhaps tilted slightly to the center-right. Then Trump came along and pulled back the curtain on what was really going on. We learned that many Republican voters didn't have any problem with big government, so long as it was big government for them. Perhaps this has always been true—you may recall the infamous sign at Tea Party rallies that read, with no hint of irony, "Keep Your Government Hands off My Medicare"—but Trump brought it out into the open. He promised to protect Social Security, Medicare, and Medicaid, while abandoning free trade and getting tough on bankers, in direct contradiction of Republican orthodoxy. Instead of paying a price for it, he swept away all his more traditional GOP rivals. Once in office, Trump abandoned most of his populist promises and largely hewed to the party line. But that shouldn't obscure the fact that many of his voters wanted to chuck the orthodoxy and preserve entitlements. The reality is that doctrinaire trickle-downers who control Congress wield enormous power without having any real constituency for their policies outside the Republican donor class. When Republicans were opposing Obama or attacking me, they could unite against a common enemy, but now that they're in power and people actually expect them to deliver results, we're seeing that there's little holding the Republican Party together.
The implications of all this are potentially profound. If Trump can't deliver for working families, Democrats have to, and be able to explain it. It may be hard for us to match his grandiose promises, because we still believe in arithmetic, but we can offer real results. We still believe in trade, but we've got to be clearer about how we'd be tougher on countries trying to take advantage of American workers, and how we'd provide more funding up front for people hurt by foreign competition. We still believe in immigration, but we have to make a better case that if done right it will help all working people.
Democrats should reevaluate a lot of our assumptions about which policies are politically viable. These trends make universal programs even more appealing than we previously thought. I mean programs like Social Security and Medicare, which benefit every American, as opposed to Medicaid, food stamps, and other initiatives targeted to the poor. Targeted programs may be more efficient and progressive, and that's why during the primaries I criticized Bernie's "free college for all" plan as providing wasteful taxpayer-funded giveaways to rich kids. But it's precisely because they don't benefit everyone that targeted programs are so easily stigmatized and demagogued. We've seen this with the Affordable Care Act. For years, it was attacked as a new subsidy for poor people of color. A lot of working-class whites didn't think it benefited them at all, especially if they lived in states where Republican leaders refused to expand Medicaid. In white-majority states where Medicaid was expanded, such as Arkansas and Kentucky, the beneficiaries were overwhelmingly white working families. But many voted for Trump anyway, betting he would take health care away from "others" and let them keep theirs. It was only when many Americans realized that repealing the ACA would take away universal protections they had come to enjoy, especially regarding preexisting conditions, that the law became popular. Medicaid's expansion has made it more popular, too.
The conclusion I reach from this is that Democrats should redouble our efforts to develop bold, creative ideas that offer broad-based benefits for the whole country.
Before I ran for President, I read a book called With Liberty and Dividends for All: How to Save Our Middle Class When Jobs Don't Pay Enough, by Peter Barnes, which explored the idea of creating a new fund that would use revenue from shared national resources to pay a dividend to every citizen, much like how the Alaska Permanent Fund distributes the state's oil royalties every year. Shared national resources include oil and gas extracted from public lands and the public airwaves used by broadcasters and mobile phone companies, but that gets you only so far. If you view the nation's financial system as a shared resource, then you can start raising real money from things like a financial transactions tax. Same with the air we breathe and carbon pricing. Once you capitalize the fund, you can provide every American with a modest basic income every year. Besides cash in people's pockets, it would also be a way of making every American feel more connected to our country and to one another—part of something bigger than ourselves.
I was fascinated by this idea, as was my husband, and we spent weeks working with our policy team to see if it could be viable enough to include in my campaign. We would call it "Alaska for America." Unfortunately, we couldn't make the numbers work. To provide a meaningful dividend each year to every citizen, you'd have to raise enormous sums of money, and that would either mean a lot of new taxes or cannibalizing other important programs. We decided it was exciting but not realistic, and left it on the shelf. That was the responsible decision. I wonder now whether we should have thrown caution to the wind and embraced "Alaska for America" as a long-term goal and figured out the details later.
Interestingly, some Republican elder statesmen such as former U.S. Treasury Secretaries James Baker and Hank Paulson recently proposed a nationwide carbon dividend program that would tax fossil fuel use and refund all the money directly to every American. They think it's a reasonable conservative response to the problems of climate change and income inequality, and a good alternative to government regulation. Under such a plan, working families with small carbon footprints could end up with a big boost in their incomes. We looked at this for the campaign as well, but couldn't make the math work without imposing new costs on upper-middle-class families, which I had pledged not to do. Still, it's tantalizing. A conservative government in Sweden created a similar program in 1991, and within a decade, it had reduced greenhouse gas emissions and expanded the economy by 50 percent, because so many Swedes used their tax rebates to increase energy efficiency, thus creating new jobs, increasing productivity, and lowering their electric bills.
We need to be thinking outside the box because the challenges we face are only getting bigger and more complex. Climate change is one example. Another is the long-term effects of automation and artificial intelligence, both on employment and national security. Bear with me here, because I have a lot to say about this. Over the past few years, I've had a series of alarming conversations with leading technologists in Silicon Valley who warn that this could be the first great technological revolution that ends up displacing more jobs than it creates. The impact of trade on our manufacturing industry received a lot more attention during the campaign, but many economists say that advances in technology actually have displaced far more jobs than trade in recent decades.
For instance, between 1962 and 2005, about four hundred thousand steelworker jobs disappeared. Competition from steel made in China and other countries was part of the problem. But technological innovation and automation were the bigger culprits. They allowed manufacturers to produce the same amount of steel with fewer and fewer workers, at lower costs.
The same story has been replicated across many industries, and it isn't slowing down anytime soon. The arrival of self-driving cars could displace millions of truckers and taxi drivers. Some economists estimate that automation could put a third of all American men aged twenty-five to fifty-four out of work by 2050. Even if we manage to create new industries and new categories of jobs to replace those we've lost, the speed and breadth of the changes we're facing will be destabilizing for millions of people.
I'm not suggesting that we should try to stop the march of technology. That would cause more problems than it solves. But we do need to make sure it's working more for us than against us. If we can figure that out, including how to talk about it in a way that Americans will understand and support, that will be both good policy and good politics.
There's another angle to consider as well. Technologists like Elon Musk, Sam Altman, and Bill Gates, and physicists like Stephen Hawking have warned that artificial intelligence could one day pose an existential security threat. Musk has called it "the greatest risk we face as a civilization." Think about it: Have you ever seen a movie where the machines start thinking for themselves that ends well? Every time I went out to Silicon Valley during the campaign, I came home more alarmed about this. My staff lived in fear that I'd start talking about "the rise of the robots" in some Iowa town hall. Maybe I should have. In any case, policy makers need to keep up with technology as it races ahead, instead of always playing catch-up.
Across the board, we should be unafraid to kick the tires on transformative ideas. Like taxing net worth instead of annual income, which would make our system fairer, reduce inequality, and provide the resources to make the major investments our country needs. Or a national service initiative much broader than anything we have now, perhaps even universal. We should totally reimagine our training and workforce development system so that employers and unions are true partners, and people who don't go to college can find a good job and enjoy a middle-class life. We need to completely rethink how Americans receive benefits such as retirement and health care so that they're universal, automatic, and portable. As you probably can tell by now, I love talking about this stuff. The point is, we have to think big and think different.
No matter what I do in the years ahead, I'll be chasing down new policy ideas that I think could make a difference. Not every election will be so filled with venom, misinformation, resentments, and outside interference as this one was. Solutions are going to matter again in politics. Democrats must be ready when that day comes.
Well-behaved women seldom make history.
—Laurel Thatcher Ulrich
## Making History
"I just want to show you this," said David Muir, the young ABC News anchor, as he walked me to the window. "This is the crowd that's waiting for you."
It was late on Tuesday, June 7, 2016, the day of the final Democratic primaries. Muir and I were on the second floor of the Brooklyn Navy Yard, in a small room crowded with cameras, hot lights, and a TV crew making final arrangements for our interview. The window looked out onto a cavernous hangar that was packed with thousands of cheering people waving American flags and stomping their feet. In the middle stood an empty stage.
"Oh my gosh," I said, clasping my hands to my heart. "Look at that!"
"It's eight years ago to the day that you conceded. And tonight you will go out there for a very different reason," Muir said.
I thought back to that painful day in 2008 when I stood in front of a much more somber crowd in the National Building Museum in Washington, and thanked my supporters for putting eighteen million cracks in the highest, hardest glass ceiling. Now here I was, closer than ever to shattering that ceiling once and for all.
"Is it sinking in?" he asked.
"This is sinking it in, I can tell you that," I said, pointing to the crowd below. "It's an overwhelming feeling, David, really."
* * *
* * *
It had been a difficult week. Heck, it had been a difficult year. The primaries had gone on longer and been far more bruising than anyone expected. The delegate math hadn't been in question since March, but Bernie had hung on to the bitter end, drawing blood wherever he could along the way. I somewhat understood why he did it; after all, I stayed in the race for as long as I could in 2008. But that race was much closer, and I endorsed Barack right after the last primary. On this day in New York, Bernie was still more than a month away from endorsing me.
I spent the previous days campaigning like crazy in California. Even if I had the nomination locked up, I wanted to win California. I wanted to close out the primaries with a burst of enthusiasm and head toward our convention in Philadelphia with the wind at my back. The polls looked good, but I was anxious. Too many times in this campaign I had felt like Charlie Brown with the football. There had been the squeaker in Iowa and surprise losses in Michigan and Indiana. This time I wasn't going to leave anything to chance.
That Monday, I had raced all over Southern California, holding rallies, doing local TV and radio interviews, and trying to encourage as many of my supporters as possible to get out and vote. A little after 5:00 p.m., as we were driving to yet another rally at Long Beach City College, my phone started buzzing. The Associated Press had just sent out a breaking news alert. Its reporters had been canvassing superdelegates, the party leaders who join delegates selected in primaries and caucuses in choosing the nominee at the convention. According to the AP's latest count, I had just hit the magic number of delegates needed to win. "Hillary Clinton Becomes the Democratic Party's Presumptive Presidential Nominee," it declared. I had to read it twice to believe it.
You might think this was good news. I'd won! But that's not how I felt at all. I was focused entirely on the next day's California primary, along with the contests in Montana, New Mexico, North Dakota, New Jersey, and South Dakota. This news could very well depress turnout among my supporters. And I wanted to be able to walk out onstage Tuesday night and declare victory, not have it announced in an out-of-the-blue tweet from the Associated Press the day before. I told Huma and Greg Hale, an Arkansas farmer and event-production-and-visuals wizard whom I've known since he was four years old, that I imagined a sea of people waving small American flags as the backdrop, and they teased me about doing my own advance work. But I had been waiting for this moment for months, and I wanted it to be perfect.
We arrived at the college in Long Beach, and I went into a makeshift greenroom. It was part of a locker room and felt like a cage. I was annoyed and not sure what to say. What was the best way to acknowledge the news in my rally speech without making too big a deal of it? I wanted to just pretend it hadn't happened, but that didn't seem like a viable option. Nick, who with Huma was on the phone with the rest of the team in Brooklyn, suggested a formulation. "Why not say we're on the brink of a historic moment?" That would have to do, I grumbled.
I also was unsatisfied with the draft for the victory speech I was supposed to deliver on Tuesday night. It didn't feel right: too small, too political, not worthy of the moment. I felt the weight of expectations and history pressing down on me.
If the primaries were over, and I was the presumptive nominee, that meant I was now all that stood between Donald Trump and the White House. It would just be me and him, one-on-one, with stakes that couldn't possibly be higher. Everyone would be counting on me. We absolutely had to win.
On top of all that, I was about to become the first woman ever nominated by a major party for President of the United States. That goal has been so elusive for so long. Now it was about to be real.
I'd been thinking about all the women who had marched, rallied, picketed, went to jail, and endured ridicule, harassment, and violence so that one day someone like me could come along and run for President. I thought about the brave women and men who gathered in Seneca Falls, New York, in 1848 for the first great conference on women's rights. Frederick Douglass, the African American social reformer and abolitionist, was there. He described his fellow participants as "few in numbers, moderate in resources, and very little known in the world. The most we had to connect us was a firm commitment that we were in the right and a firm faith that the right must ultimately prevail."
Sixty-eight "ladies" and thirty-two "gentlemen" signed the Declaration of Sentiments, which asserted boldly, "We hold these truths to be self-evident that all men and women are created equal." All men and women. The backlash was fierce. The Seneca Falls 100 were called dangerous fanatics. They were also dismissed as batty old maids—I'm not sure how one can be both, but apparently these activists were. One newspaper declared, "These rights for women would bring a monstrous injury to all mankind." But those brave suffragettes never lost faith.
What could I say on Tuesday night that would be worthy of that legacy and the hope that millions were now investing in me?
For a long time, the campaign had been trying to figure out the best way to talk about the historic nature of my candidacy. There were brainstorming sessions in Brooklyn, as well as polls and focus groups. Many of our core supporters were very excited by the idea of finally breaking the glass ceiling. Celebrating that could help keep people energized and motivated in the general election. But some younger women didn't see what the big deal was. And many undecided women in battleground states didn't want to hear about it at all. Some were afraid that by leaning into the fact that I was a woman, my campaign would end up turning away men—a disheartening but all-too-real possibility. So that wasn't much help.
I was torn. I wanted to be judged on what I did, not on what I represented or what people projected onto me. But I understood how much this breakthrough would mean to the country, especially to girls and boys who would see that there are no limits on what women can achieve. I wanted to honor that significance. I just didn't know the best way to do it.
* * *
* * *
I carried all that uncertainty with me back from California, all the way to David Muir's interview room in the Brooklyn Navy Yard on Tuesday night. Results were starting to come in. I won the New Jersey primary. Bernie won the North Dakota caucus. The big prize, California, was still out there, but all signs pointed to another victory. Bill and I had worked hard on my speech, but I still felt unsettled. Maybe it was about not being ready to accept "yes" for an answer. I had worked so hard to get to this moment, and now that it had arrived, I wasn't quite sure what to do with myself.
Then Muir walked me over to the window, and I looked out at that crowd—at thousands of people who'd worked their hearts out, resisted the negativity of a divisive primary and relentlessly harsh press coverage, and poured their dreams into my campaign. We'd had big crowds before, but this felt different. It was something more than the enthusiasm I saw on the trail. It was a pulsing energy, an outpouring of love and hope and joy. For a moment, I was overwhelmed—and then calm. This was right. I was ready.
After the interview, I went downstairs to where my husband was sitting with the speechwriters going over final tweaks to the draft. I read it over one more time and felt good. Just as they were racing off to load the speech into the teleprompter, I said I had one more thing to add: "I'm going to talk about Seneca Falls. Just put a placeholder in brackets and I'll take care of it."
I took a deep breath. I didn't want the emotion of the moment to get to me in the middle of my speech. I said a little prayer and then headed for the stage. At the last moment, Huma grabbed my arm and whispered, "Don't forget to take a minute to savor this." It was good advice. The roar when I stepped out was deafening. I felt a surge of pride, gratitude, and pure happiness. I stood at the podium, my arms outstretched, taking it all in.
"Tonight's victory is not about one person," I said. "It belongs to generations of women and men who struggled and sacrificed and made this moment possible."
Like in my campaign launch speech on Roosevelt Island, I took the opportunity to talk about my mother. When I thought about the sweep of history, I thought about her. Her birthday had just passed a few days earlier. She was born on June 4, 1919—the exact same day that Congress passed the Nineteenth Amendment to the Constitution, finally granting women the right to vote.
"I really wish my mother could be here tonight," I told the crowd in Brooklyn. I had practiced this part several times, and each time, I teared up. "I wish she could see what a wonderful mother Chelsea has become, and could meet our beautiful granddaughter, Charlotte." I swallowed hard. "And, of course, I wish she could see her daughter become the Democratic Party's nominee for President of the United States."
* * *
* * *
A month and a half later, I was preparing to formally accept the nomination at the Democratic National Convention in Philadelphia. The Republicans had just finished their convention in Cleveland. Trump had given a dark and megalomaniacal speech in which he described a badly broken American and then declared, "I alone can fix it." I wasn't sure how voters were going to react to that, but I thought it went against America's can-do spirit that says, "We'll fix it together." His speech, like his entire candidacy, was about stoking and manipulating people's ugliest emotions. He wanted Americans to fear one another and the future.
Other Republicans did their best Trump imitations at the GOP convention. New Jersey Governor Chris Christie, a former prosecutor, led the crowd through a mock indictment of me for various supposed crimes. The crowd shouted its verdict: "Guilty!" The irony, apparently lost on Christie but nobody else, was that the investigation into my emails was over, but the investigation into the closing of the George Washington Bridge as an act of political retribution was ongoing and would eventually cause two of Christie's allies to be sentenced to prison.
It was sad to watch the Republican Party go from Reagan's "Morning in America" to Trump's "Midnight in America." The dystopian, disorganized mess in Cleveland got panned by the press and offered us the chance to provide a clear contrast when Democrats gathered in Philadelphia on July 25.
Bill, Chelsea, my senior team, and nearly every Democratic leader in the country were there. I wasn't. The tradition is that the nominee does not arrive until the end. So I was home alone in Chappaqua, watching television and working on my acceptance speech. It was a little lonely, but I enjoyed the rare moment to myself after so many hectic months on the campaign trail.
Michelle Obama stole the show on the first night with her graceful, fiercely personal speech. Just as she had done for eight years, she represented our best selves as Americans and reminded us that "When they go low, we go high." Senator Cory Booker, whom I had also considered as a potential Vice President, gave a rousing and heartfelt speech. Riffing off one of the most powerful lines from the Declaration of Independence, he urged Americans to follow the example of our Founders and "pledge to each other our lives, our fortunes, and our sacred honor."
On the second day, the convention got down to business with formal nominations and then a roll call vote by state. Since the outcome is rarely in doubt, this can be a somewhat tedious affair. But when you're the one getting nominated, it feels like high drama.
In 2008, I had surprised the convention by appearing on the floor with the New York delegation in the middle of the roll call. I moved to suspend the vote and nominate Barack Obama by acclamation. Up at the podium, Nancy Pelosi asked if there was a second for my motion, and the whole arena roared its approval.
This time we expected a full roll call. When it was Illinois's turn, my best friend from growing up, Betsy Ebeling, stepped to the microphone and announced ninety-eight votes for me. "On this historic, wonderful day, in honor of Dorothy and Hugh's daughter and my sweet friend—I know you're watching—this one's for you, Hill." Back in Chappaqua, I couldn't stop smiling.
Slowly, state by state, the tallies grew, and I got closer and closer to a majority of delegates. Then, a little after 6:30 P.M., South Dakota put me over the top, and my supporters in the hall broke into sustained jubilation. There were still more states to go, so the roll call went on. Finally, we came to Vermont, which had asked to go last. Bernie came forward and, in an echo of eight years before, said, "I move that Hillary Clinton be selected as the nominee of the Democratic Party for President of the United States." The place erupted.
The long primary was over. The final delegate count was 2,842 for me and 1,865 for Bernie. I know it couldn't have been easy for him to make that statement on the floor, and I appreciated it.
That evening, the actor Elizabeth Banks emceed a joyful and moving series of testimonials from people who had gotten to know me over the years—people who let me into their lives, and became a part of mine.
There was Anastasia Somoza, whom I met when she was just nine years old. Anastasia was born with cerebral palsy, and became a passionate advocate for people with disabilities. She worked on my first campaign for Senate, interned in my office, and became a lifelong friend.
Jelani Freeman, another former intern in my Senate office, lived in six different foster homes between the ages of eight and eighteen. Many kids in that situation never graduate from high school. Jelani got a master's degree and a law degree. He said that I encouraged him to persevere and rise as high as he could. The real story was that he was the one who encouraged me. His example inspired me to keep up my advocacy for children, especially kids in foster care.
Ryan Moore also spoke. When I first met him, Ryan was seven years old and wearing a full body brace that must have weighed forty pounds. He was born with a rare form of dwarfism that kept him in a wheelchair, but it didn't dim his unbeatable smile and sense of humor. I met Ryan's family at a health reform conference in 1994 and learned about their battles with the insurance company to pay for his costly surgeries and treatments. Their story—and Ryan's tenacity—kept me going through all the ups and downs of our battle for health care reform.
Then there was Lauren Manning, who was gravely injured on 9/11. More than 82 percent of her body was badly burned, giving her a less than 20 percent chance of survival. But she fought her way back and reclaimed her life. Lauren and her husband, Greg, became vocal advocates on behalf of other 9/11 families. I did everything I could as a Senator to be a champion for them, as well as for the first responders who got sick from their time at Ground Zero.
I found it very moving to listen to these friends tell their stories, just as it had been to see Betsy during the roll call. It was like an episode of that old television program This Is Your Life. I was flooded with memories and pride in everything we'd accomplished together.
But none of that prepared me for what Bill had to say when it was his turn to speak.
He looked great up there at the podium, with his distinguished shock of white hair and dignified bearing. "Back where he belongs," I thought. Four years before, he had masterfully laid out the case for reelecting Barack Obama. This time he left the economic statistics behind and spoke from the heart.
"In the spring of 1971, I met a girl," he began. I knew right away that this was going to be different. In fact, I don't think there's ever been a major political speech like it. Bill talked about how we met and fell in love. "We've been walking and talking and laughing together ever since," he said, "and we've done it in good times and bad, through joy and heartbreak." He took the American people by the hand and walked them down the path of our lives together, with love, humor, and wisdom. He shared private little moments, like the day we dropped Chelsea off at college for the first time. "There I was in a trance just staring out the window trying not to cry," Bill recalled, "and there was Hillary on her hands and knees desperately looking for one more drawer to put that liner paper in."
Sitting by myself in the home we'd made together, surrounded by the mementos of our life and love, I felt like my heart was bursting. "I married my best friend," Bill said. It was like hearing a love letter read out loud on national television.
As soon as the speech wrapped up, I jumped in our van and raced over to a country inn down the road, where a large group of friends and neighbors had gathered. I was positively beaming when I walked in. What a night!
A camera crew was waiting, ready to connect me directly to the arena in Philadelphia. An adorable six-year-old girl named Remie came over and gave me a hug. We were both wearing red, and I complemented her dress as she smiled bashfully. With Remie by my side, I was ready to speak to the convention and the country.
Onstage in Philadelphia, the giant video screen above the arena began flashing the pictures of every previous U.S. President, one white man after another, until finally Barack Obama. Then the screen appeared to shatter into a million pieces, and there I was, live from Crabtree's Kittle House Restaurant and Inn in Chappaqua. On the convention floor, people held up red and blue placard signs that said, "History."
I thanked the convention for the incredible honor they'd given me. "And if there are any little girls out there who stayed up late to watch," I said, as the camera pulled back to show little Remie and our other friends crowded behind me, "let me just say, I may become the first woman President, but one of you is next."
I hugged and thanked everyone I could find. I didn't want to leave, didn't want the night to end. Later, I heard that social media was buzzing with parents posting pictures of their daughters who had indeed stayed up late to watch, while others shared photos of mothers and grandmothers who hadn't lived to see this day. A writer named Charles Finch tweeted, "There are days when you believe the arc of history thing." That's exactly how it felt: like all of us together were bending the arc of history just a little bit further toward justice.
* * *
* * *
The next day, I sneaked into Philadelphia so I could make a surprise appearance with President Obama after his speech. He was masterful, of course, and incredibly generous. He talked about what it takes to sit behind the desk in the Oval Office and make life-and-death decisions that affect the whole world, and how I'd been there with him, helping make those hard choices. He looked up at where Bill was sitting and said with a smile, "There has never been a man or a woman—not me, not Bill, nobody—more qualified." Bill loved it and jumped to his feet and applauded. When Barack finished, I popped out from backstage and gave him a big hug.
Then, on the final day of the convention, it was time for me to give the most important speech of my life. In some ways, this was easier than that night at the Brooklyn Navy Yard. I was ready to be the party's standard-bearer in the battle to come, and I was confident in the vision I wanted to share with the country. I would argue that Americans are always "stronger together," and that if we worked together, we could rise together. We could live up to our country's motto, e pluribus unum: "out of many, we are one." Trump, by contrast, would tear us apart.
We had settled on Stronger Together as our theme for the general election after a lot of thought and discussion. Remarkably, three separate brainstorming processes all led to the same answer. My team in Brooklyn had started with three basic contrasts we wanted to draw with Trump. He was risky and unqualified, but I was steady and ready to deliver results on Day One. He was a fraud who was in it only for himself, but I was in it for children and families and would make our economy work for everyone, not just those at the top. He was divisive, while I would work to bring the country together. The challenge was to find a way to marry all three together in a memorable slogan that reflected my values and record. Stronger Together did that better than anything else we could think of.
While the team in Brooklyn worked on this, I asked Roy Spence to spend some time thinking outside the box about campaign themes and messages. Roy is an old friend from the McGovern campaign who started a large ad agency in Austin, Texas. When Jake Sullivan and Dan Schwerin, my director of speechwriting, got on the phone with Roy to exchange notes, they were shocked to hear him propose exactly the same phrase the team in Brooklyn had come up with: Stronger Together. Our top political consultants, Joel Benenson, Mandy Grunwald, and Jim Margolis, also reached the same conclusion independently. Considering how rarely all these smart people agreed on anything, we took it as a sign. Stronger Together it would be.
By the time I got to our convention, I felt even better about this decision. Trump's "I Alone Can Fix It" speech in Cleveland had provided the perfect foil. The history surrounding us in Philadelphia offered further inspiration. Independence Hall was just a few blocks from our hotel. It was there, 240 years before, that representatives from thirteen unruly colonies transformed themselves into a single, unified nation. It wasn't easy. Some of the colonists wanted to stick with the King. Some wanted to stick it to the King and go their own way. They had different backgrounds, interests, and aspirations. Somehow they began listening to one another and compromising, and eventually found common purpose. They realized they'd be stronger together than they ever could be on their own.
On Thursday, the last day of the convention, Bill and I sat around the dining room table in our suite at the Logan Hotel, going over a draft of my speech, trying to get it just right. I tried not to think about how many millions of people would be watching and how enormous the stakes would be. Instead, I focused on trying to make my argument as clear and compelling as possible. If I did a good job, and the country saw me without all the usual nonsense getting in the way, the rest would take care of itself. Suddenly, with a squeal of delight, our granddaughter, Charlotte, burst into the room and ran over to us. I put down the draft and chased after her, finally scooping her up in my arms and giving her a kiss. Any tension I'd been feeling drained away in a flash. There was nowhere else in the world I wanted to be other than right there, holding my granddaughter.
After a few more hours of tweaking and practicing, I put on another suffragette-white pantsuit and got ready to head to the arena. The television was still on, and just before I walked out the door, I saw Khizr and Ghazala Khan come to the podium. I had first heard about the Khans the previous December, when an intern on my speechwriting team came across the story of their son, Humayun, a heroic captain in the U.S. military who was killed protecting his unit in Iraq. I talked about Captain Khan in a speech in Minneapolis about counterterrorism and the importance of working with American Muslims, not demonizing them. My team followed up with the family and invited them to share their experiences at the convention.
None of us were prepared for how powerful it would be. Mr. Khan solemnly offered to lend Donald Trump his copy of the Constitution that he kept in his pocket. It instantly became one of the most iconic moments of the whole election. Like millions of others, I was transfixed. Watching Mr. and Mrs. Khan up there, still grieving, incredibly dignified, patriotic to the core, filled me with a rush of pride and confidence in our party and our country.
Then I had to hurry to the arena. We had NPR on the whole way so I didn't miss a minute.
I watched backstage as Chelsea gave a perfect introduction that brought me to tears.
"My parents raised me to know how lucky I was that I never had to worry about food on the table," she said. "I never had to worry about a good school to go to. That I never had to worry about a safe neighborhood to play in. And they taught me to care about what happens in our world and to do whatever I could to change what frustrated me, what felt wrong. They taught me that's the responsibility that comes with being smiled on by fate."
"I know my kids are a little young," she continued, "but I'm already trying to instill those same values in them."
Chelsea finished her remarks and introduced a film about my life by Shonda Rhimes. I love how Shonda makes tough, smart female characters come alive on television, and I was hoping she could do the same for me. Boy, did she deliver. Her film was funny, poignant, just perfect. When it was over, Chelsea came back on and welcomed me—"my mother, my hero"—to the stage. There was a deafening roar.
Looking out into that arena full of cheers and banners and music, with thousands of excited people and millions more at home, was one of the proudest and most overwhelming moments of my life.
"Standing here as my mother's daughter, and my daughter's mother, I'm so happy this day has come," I said. "Happy for grandmothers and little girls and everyone in between. Happy for boys and men, too—because when any barrier falls in America, for anyone, it clears the way for everyone. When there are no ceilings, the sky's the limit."
* * *
* * *
Even after everything that's happened, I still believe that.
I still believe that, as I've said many times, advancing the rights and opportunities of women and girls is the unfinished business of the twenty-first century. That includes one day succeeding where I failed and electing a woman as President of the United States.
On November 8 and the days that followed, hundreds of women visited the grave of the great suffragette leader Susan B. Anthony in Rochester, New York. They covered her headstone with "I Voted" stickers. People did the same to the statue in Seneca Falls commemorating the spot by the river where Amelia Bloomer first introduced Anthony to Elizabeth Cady Stanton, sparking the partnership at the heart of the suffragette movement.
A lot of women shared stories like this one, which I received from a woman named Marcia in California:
My mother is 92, in hospice care, and quite frail. A couple weeks ago, my sister and I helped her vote, completing her mail-in ballot. For President? "Hillary, of course," she told us. We cheered! In a soft, weak voice, she whispered, "I did it. I did. I did." This will be her last vote. And, because I live some distance from her, it may be the last time I see her in this life. I will always cherish the memory of her voting for a woman for President for the first time in her life.
In my concession speech, I said, "We have still not shattered that highest and hardest glass ceiling, but some day someone will—and hopefully sooner than we might think right now." History is funny that way. Things that seem far off and impossible have a way of turning out to be nearer and more possible than we ever imagined.
Of the sixty-eight women who signed the Declaration of Sentiments in 1848, only one lived to see the Nineteenth Amendment ratified. Her name was Charlotte Woodward, and she thanked God for the progress she had witnessed in her lifetime.
In 1848, Charlotte was a nineteen-year-old glove maker living in the small town of Waterloo, New York. She would sit and sew for hours every day, working for meager wages with no hope of ever getting an education or owning property. Charlotte knew that if she married, she, any children she might have, and all her worldly possessions would belong to her husband. She would never be a full and equal citizen, never vote, certainly never run for office. One hot summer day, Charlotte heard about a women's rights conference in a nearby town. She ran from house to house, sharing the news. Some of her friends were as excited as she was. Others were amused or dismissive. A few agreed to go with her to see it for themselves. They left early on the morning of July 19 in a wagon drawn by farm horses. At first, the road was empty, and they wondered if no one else was coming. At the next crossroads, there were wagons and carriages, and then more appeared, all headed to Wesleyan Chapel in Seneca Falls. Charlotte and her friends joined the procession, heading toward a future they could only dream of.
Charlotte Woodward was more than ninety years old when she finally gained the right to vote, but she got there. My mother had just been born and lived long enough to vote for her daughter to be President.
I plan to live long enough to see a woman win.
To know oneself is, above all, to know what one lacks.
It is to measure oneself against Truth, and not the other way around.
—Flannery O'Connor
## Frustration
Too long a sacrifice can make a stone of the heart.
—William Butler Yeats
## Country Roads
"We're going to put a lot of coal miners and coal companies out of business." Stripped of their context, my words sounded heartless. Republican operatives made sure the clip was replayed virtually nonstop on Facebook feeds, local radio and television coverage, and campaign ads across Appalachia for months.
I made this unfortunate comment about coal miners at a town hall in Columbus just two days before the Ohio primary. You say millions of words in a campaign and you do your best to be clear and accurate. Sometimes it just comes out wrong. It wasn't the first time that happened during the 2016 election, and it wouldn't be the last. But it is the one I regret most. The point I had wanted to make was the exact opposite of how it came out.
The context is important. The moderator asked how I would win support from working-class whites who normally vote Republican. Good question! I had a lot to say about that. I was looking right at my friend, Congressman Tim Ryan, who represents communities in southeastern Ohio suffering from job losses in coal mines and steel plants. I wanted to speak to their concerns and share my ideas for bringing new opportunities to the region. Unfortunately, a few of my words came out in the worst possible way:
Instead of dividing people the way Donald Trump does, let's reunite around policies that will bring jobs and opportunities to all these underserved poor communities. So, for example, I'm the only candidate who has a policy about how to bring economic opportunity using clean renewable energy as the key into Coal Country. Because we're going to put a lot of coal miners and coal companies out of business, right Tim? And we're going to make it clear that we don't want to forget those people. Those people labored in those mines for generations, losing their health, often losing their lives to turn on our lights and power our factories. Now we've got to move away from coal and all the other fossil fuels, but I don't want to move away from the people who did the best they could to produce the energy that we relied on.
If you listened to the full answer and not just that one garbled sentence pulled out of it, my meaning comes through reasonably well. Coal employment had been going down in Appalachia for decades, stemming from changes in mining technology, competition from lower-sulfur Wyoming coal, and cheaper and cleaner natural gas and renewable energy, and a drop in the global demand for coal. I was intensely concerned about the impact on families and communities that had depended on coal jobs for generations. That's why I had proposed a comprehensive $30 billion plan to help revitalize and diversify the region's economy. But most people never heard that. They heard a snippet that gave the impression that I was looking forward to hurting miners and their families.
If you were already primed to believe the worst about me, here was confirmation.
I felt absolutely sick about the whole thing. I clarified and apologized and pointed to my detailed plan to invest in coal communities. But the damage was done.
For many people, coal miners were symbols of something larger: a vision of a hardworking, God-fearing, flag-waving, blue-collar white America that felt like it was slipping away. If I didn't respect coal miners, the implication was that I didn't respect working-class people generally or at least not working-class white men in small towns and red states. And with the clip of my comments playing on a loop on Fox News, there was basically nothing I could say to make people think otherwise.
The backlash was infuriating for many reasons. For one, there was the double standard. Donald Trump hardly went a single day on the campaign trail without saying something offensive or garbling a thought. He received criticism, but it rarely stuck (with a couple of big exceptions). Many in the press and political chattering class marveled at how Teflon-coated Trump seemed to be, ignoring their own role in making him so. I got none of this leeway. Even the smallest slipup was turned into a major event. Yet at the same time, I was routinely criticized for being too cautious and careful with my words. It was an unwinnable dynamic.
But the coal-mining gaffe felt terrible in ways that went beyond my normal frustrations over double standards. This wasn't some dumb comment about an unimportant issue. I genuinely cared a lot about struggling working-class families in fading small towns. I cared a lot about coal communities in particular. Not for political reasons—I knew I wasn't going to win a lot of votes in places like West Virginia—but for personal ones.
I lived in Arkansas for years and fell in love with Ozark mountain towns a lot like those across Appalachia. In fact, coal had been mined in Arkansas for decades, and Bill and I knew retired miners suffering from black lung disease. As an attorney, he had represented more than a hundred of them, trying to help them get the benefits they deserved. When I got to the Senate, I worked with Senator Robert Byrd of West Virginia to do what I could to support legislation to protect the safety and pensions of coal miners.
I also represented once-prosperous industrial cities in upstate New York where factories had closed and jobs dried up, just like in southeastern Ohio and western Pennsylvania. I respected the defiant pride that so many who lived there felt for their hometowns and understood the mistrust they felt toward outsiders swooping in with grand pronouncements about their lives and futures. I found that by listening, building coalitions, and helping people to help themselves, we could start turning things around and create new opportunities for businesses and jobs. I worked with eBay to help small businesses in rural upstate communities get online and reach new customers. My office connected chefs and restaurant owners from Manhattan with farmers and winemakers in the Hudson Valley and the Finger Lakes in an effort to expand sales. And we worked with upstate universities to bring in new research grants that could help them become hubs for job-creating industries such as biotech and clean energy. I loved that work because it produced results and made people's lives better.
Appearing to dismiss the men and women of Coal Country—or any Americans working hard against the odds to build better lives for themselves and their families—wasn't something I could just shrug off. This really bothered me, and I wanted badly to do something about it.
* * *
* * *
It's worth pausing for a moment to be clear about the bigger picture. Terms like "working class" and "blue collar" get thrown around a lot and can mean different things to different people. Generally, when academics and political analysts talk about the working class, they mean people without a college degree. But frequently people use the term in a broader way. How much money people make, the kinds of jobs they do, the communities they live in, and a basic sensibility or set of values all get wrapped up together in our image of what it means to be working class. And there's often a tendency to equate working class with white and rural. How we think and talk about this has big implications for our politics.
I came of age in an era when Republicans won election after election by peeling off formerly Democratic white working-class voters. Bill ran for President in 1992 determined to prove that Democrats could compete in blue-collar suburbs and rural small towns without giving up our values. By focusing on the economy, delivering results, and crafting compromises that defused hot-button issues such as crime and welfare, he became the first Democrat since World War II to win two full terms.
By 2016, the country was more diverse, more urban, and more college-educated, with working-class whites making up a shrinking portion of the electorate. Barack Obama had written a new playbook about how to win the Presidency by mobilizing younger, more diverse voters. My campaign strategy was built on that playbook. But I still wanted to help those small towns that Bill had won twenty-four years before and the Rust Belt communities like those I had represented in the Senate. Even before the campaign began, I was focused on the shocking numbers of poor white women and men who were dying younger than their parents because of smoking, substance abuse, and suicide—what's been called an epidemic of despair. This decline in life expectancy was unprecedented in the modern history of our country. It's the kind of thing that happened in Russia after the disintegration of the Soviet Union.
Back in 2013 and 2014, I started talking about McDowell County, West Virginia, where more than one-third of the residents lived in poverty and only half had a high school degree. Jobs were scarce, and drug use was rampant. McDowell County was one of the poorest communities in the country, but lots of other small towns and rural areas were also dealing with stagnant wages and disappearing jobs. Social networks that provided support and structure in previous generations were weaker than ever, with schools failing, labor unions shrinking, jobs leaving, church attendance declining, trust in government falling, and families becoming more fractured. People trying to build a future in these hard-hit communities didn't face just ceilings on their aspirations. It was as if the floor had collapsed beneath them, too.
What could be done to help? I pointed to an ambitious effort in McDowell County led by the American Federation of Teachers under president Randi Weingarten and nearly a hundred partners from the local community, government, business, labor, nonprofits, and foundations. They recognized that the problems McDowell faced with its schools, jobs, housing, infrastructure, and public health were all connected, so they had to work on all of them at the same time, with new investments, fresh thinking, and lots of hard work. Their public-private partnership, named Reconnecting McDowell, had no guarantee of success, but I thought the effort was exciting. After a few years, it showed real results: the high school graduation rate increased from about 72 percent to nearly 90 percent, while dropout rates and teen pregnancy declined. The schools were wired with broadband, homes were connected with fiber, and every middle school student received a laptop.
But even the best philanthropic effort was unlikely to turn the tide across Appalachia unless it was backed up by strong, effective policies at both the state and federal levels—something that Republicans in Congress and state legislatures never supported.
Appalachian coal mining jobs had been in a long decline, but between 2011 and 2016, the bottom fell out. Nationwide, coal production fell by 27 percent. Nearly sixty thousand coal miners and contractors lost their jobs, 40 percent of them in Kentucky and West Virginia alone. Big coal companies such as Peabody Energy, Arch Coal, and Alpha Natural Resources went bankrupt, threatening the pensions of thousands of retired miners.
This was a crisis that demanded a serious response. There was a tension between the urgent imperative to reduce America's dependence on fossil fuels, especially coal, that were the main cause of climate change and the need to help the communities whose livelihoods had long depended on producing those fuels. I believed it was possible and imperative to do both. As I would say later in that ill-fated town hall, we had to move away from coal, but we couldn't move away from the hardworking people who kept America's lights on and our factories churning for generations.
When I launched my campaign for President in June 2015, I specifically mentioned Coal Country and the need to help distressed communities make the transition to a more sustainable economic future. It was a call I'd repeat in nearly every speech I gave, all over the country.
I also got to work developing the detailed plan to invest $30 billion in revitalizing coal communities that I mentioned earlier. Consulting with national experts and local leaders, my team came up with great ideas for new incentives to attract jobs and industries to Appalachia, improving infrastructure and broadband internet, training programs that would lead to real jobs instead of worthless certificates, and more support for schools and students. We also worked with the United Mine Workers of America union on steps to hold the coal companies accountable and guarantee health care and a secure retirement for miners and their families. I spoke out publicly when the union said it would be helpful, and I exerted pressure behind the scenes when needed. In the end, Peabody Energy, one of the biggest coal companies, agreed to extend benefits for more than twelve thousand retired miners and their families. If I had won the election, I would have used the full power of the federal government to do even more.
No other candidate came close to this level of attention to the real challenges facing coal communities. On the left, Bernie Sanders advocated for leaving all fossil fuels in the ground, including coal. On the right, Donald Trump made promises about reopening mines but offered zero credible ideas for how he'd reverse decades of decline and job loss. So it was frustrating and painful that thanks in large part to my one unfortunate comment and opposition in West Virginia to President Obama's executive order mandating a reduction in carbon dioxide emissions, both of those candidates were far more popular in the state than I was.
* * *
* * *
A few weeks after my "gaffe," I went to Appalachia to apologize directly to people I had offended. I knew it was unlikely to change the outcome of the upcoming West Virginia primary or the general election in November, but I wanted to show my respect. I wanted to make it clear that I would be a President for all Americans, not just the ones who voted for me.
Prominent Democrats in West Virginia suggested I fly in and out of Charleston and make a speech in front of a friendly audience. My team on the ground liked that—it would take the least amount of time away from my packed campaign schedule and would mean a warmer reception than I was likely to receive in more rural parts of the state. But that wasn't what I had in mind. I wanted to go deep into the southern coalfields to communities facing the biggest challenges, where Trump was most popular and my coal-miner gaffe was getting the most attention. As one of my advisors put it, that would be like Trump holding a rally in downtown Berkeley, California. That's pretty much what I was going for.
We designed a trip that would take me from eastern Kentucky to southern West Virginia to southeastern Ohio, concluding with an economic policy speech in Athens, Ohio, with my friend Senator Sherrod Brown, who was also on my list of potential choices for Vice President.
We started in Ashland, Kentucky, where I met with a dozen steelworkers who'd lost their jobs when the factory where they'd worked for decades closed. I also talked with men who worked on the railroads and watched as the decline of coal and steel production led to reductions in rail service, which in turn cost more jobs and further isolated the region.
I had known going into the campaign that many communities still hadn't recovered from the Great Recession, and a lot of working-class Americans were hurting and frustrated. Unemployment was down and the economy was growing, but most people hadn't had a raise in fifteen years. The average family income was $4,000 less than when my husband left office in 2001. I knew this backward and forward.
When I got out there and heard the deep despair, those numbers became ever more real. I listened to people talk about how worried they were about their kids' futures. A lot of men were embarrassed that they depended on disability checks to pay the bills and that the jobs they could find didn't pay enough to support a real middle-class life. They were furious that after all they'd done to power our economy, fight our wars, and pay their taxes, no one in Washington seemed to care, much less be trying to do anything about it.
Usually when I meet people who are frustrated and angry, my instinctive response is to talk about how we can fix things. That's why I spent so much time and energy coming up with new policies to create jobs and raise wages. But in 2016 a lot of people didn't really want to hear about plans and policies. They wanted a candidate to be as angry as they were, and they wanted someone to blame. For too many, it was primarily a resentment election. That didn't come naturally to me. I get angry about injustice and inequality, abuse of power, lying, and bullying. But I've always thought it's better for leaders to offer solutions instead of just more anger. That's certainly what I want from my leaders. Unfortunately, when the resentment level is through the roof your answers may never get a hearing from the people you want to help most.
We left Kentucky and crossed into West Virginia. Just as I remembered from 2008, there was very spotty cell phone coverage as we drove into the Mountain State. That drove the traveling team nuts, but I was thinking more about the bigger problem of how the lack of connectivity hamstrung businesses and schools and held back economic development. Nearly 40 percent of people in rural America don't have access to broadband, and research shows those communities have lower incomes and higher unemployment. That's a solvable problem, and one I was eager to take on.
I thought back to how much I loved campaigning in West Virginia during the 2008 primary, when I won the state by 40 points. My favorite memory was celebrating Mother's Day with my mom and daughter in the small town of Grafton, West Virginia, where the holiday was invented a hundred years earlier. It was one of the last Mother's Days I ever had with my mom, and it was a great one.
We drove into Mingo County, arguably Ground Zero for the coal crisis. In 2011 there had been more than 1,400 miners in the county. By 2016, there were just 438. Our destination was the town of Williamson, home to a promising public-private partnership similar to Reconnecting McDowell that was trying desperately to marshal the resources and the political will needed to expand and diversify the local economy, as well as improve public health.
After about three hours, we arrived at the Williamson Health and Wellness Center. It was drizzling, but outside on the street was a crowd of several hundred angry protestors chanting "We want Trump!" and "Go home Hillary!" Many held up signs about the so-called war on coal. One woman explained to a reporter why she was supporting Trump: "We're tired of all the darn handouts; nobody takes care of us." Another had painted her hands red to look like blood and kept yelling about Benghazi. Standing with them was Don Blankenship, the multimillionaire former CEO of a large coal company who was convicted for conspiring to violate mine safety regulations after the Upper Big Branch mine explosion killed twenty-nine workers in 2010. He was due to report to prison just days later, but he made time to come protest me first.
I knew I wouldn't get a warm welcome in West Virginia. That was the point of my visit, after all. But this level of anger took me aback. This wasn't just about my comments in one town hall. This was something deeper.
* * *
* * *
Since the election, I've spent a lot of time thinking about why I failed to connect with more working-class whites. Many commentators talk as if my poor showing with that group was a new problem that stemmed mostly from my own weaknesses and Trump's unique populist appeal. They point to the white voters who switched from Obama to Trump as evidence. West Virginia, a heavily white working-class state, tells a different story. From Franklin Roosevelt's election in 1932 to Bill's reelection in 1996, Democrats won fourteen out of seventeen presidential elections there. Since 2000, however, we've lost every time, by increasingly bigger margins. In 2012 Obama lost to Mitt Romney by nearly two to one. It's hard to look at that trend and conclude that it is all about me or about Trump.
The most prominent explanation, though an insufficient one on its own, is the so-called war on coal. Democrats' long-standing support for environmental regulations that protect clean air and water and seek to limit carbon emissions has been an easy scapegoat for the misfortunes of the coal industry and the communities that have depended on it. The backlash reached a fevered pitch during the Obama administration, despite strong evidence that government regulation is not the primary cause for the industry's decline.
The Obama administration was slow to take on this false narrative. When it was getting ready to announce the sweeping new Clean Power Plan, which was seen as the most anti-coal policy yet, I thought the President should consider making the announcement in Coal Country and couple it with a big effort to help miners and their families by attracting new investments and jobs. That might have softened the blow a little.
In the end, President Obama announced the new regulations in the White House alongside his administrator of the U.S. Environmental Protection Agency (EPA). That was seen by many folks in West Virginia as another signal that Democrats didn't care about them. Once that perception takes hold, it's hard to dislodge.
That said, Democrats' problems with white working-class voters started long before Obama and go far beyond coal.
After John Kerry lost to George W. Bush in 2004, the writer Thomas Frank popularized the theory that Republicans persuaded whites in places like West Virginia to vote against their economic interests by appealing to them on cultural issues—in other words, "gays, guns, and God." There's definitely merit in that explanation. Remember my earlier description of the man in Arkansas who said Democrats wanted to take his gun and force him to go to a gay wedding?
Then there's race. For decades, Republicans have used coded racial appeals on issues such as school busing, crime, and welfare. It was no accident that Ronald Reagan launched his general election campaign in 1980 with a speech about "states' rights" near Philadelphia, Mississippi, where three civil rights workers had been murdered in 1964. In 2005 the chairman of the Republican National Committee formally apologized for what's been called the southern strategy. But in 2016 it was back with a vengeance. Politics was reduced to its most tribal, "us" versus "them," and "them" grew into a big list: blacks, Latinos, immigrants, liberals, city dwellers, you name it. Like so many demagogues before him, Trump encouraged a zero-sum view of life where if someone else is gaining, you must be losing. You can hear the resentment in the words of that protestor in Williamson: "We're tired of all the darn handouts; nobody takes care of us."
It's hard to compete against demagoguery when the answers you can offer are all unsatisfying. And years of economic pain provided fertile ground for Republicans' cultural and racial appeals. Union membership, once a bulwark for Democrats in states like West Virginia, declined. Being part of a union is an important part of someone's personal identity. It helps shape the way you view the world and think about politics. When that's gone, it means a lot of people stop identifying primarily as workers—and voting accordingly—and start identifying and voting more as white, male, rural, or all of the above.
Just look at Don Blankenship, the coal boss who joined the protest against me on his way to prison. In recent years, even as the coal industry has struggled and workers have been laid off, top executives like him have pocketed huge pay increases, with compensation rising 60 percent between 2004 and 2016. Blankenship endangered his workers, undermined their union, and polluted their rivers and streams, all while making big profits and contributing millions to Republican candidates. He should have been the least popular man in West Virginia even before he was convicted in the wake of the death of twenty-nine miners. Instead, he was welcomed by the pro-Trump protesters in Williamson. One of them told a reporter that he'd vote for Blankenship for President if he ran. Meanwhile, I pledged to strengthen the laws to protect workers and hold bosses like Blankenship accountable—the fact that he received a jail sentence of just one year was appalling—yet I was the one being protested.
Some on the left, including Bernie Sanders, argue that working-class whites have turned away from Democrats because the party became beholden to Wall Street donors and lost touch with its populist roots. It's hard to believe that voters who embrace Don Blankenship are looking for progressive economics. After all, by nearly every measure, the Democratic Party has moved to the left over the past fifteen years, not to the right. Mitt Romney was certainly not more populist than Barack Obama when he demolished him in West Virginia. And Republicans are unabashedly allied with powerful corporate interests, including the coal companies trying to take away health care and pensions from retired miners. Yet they keep winning elections. During my visit, the Republican Majority Leader in the U.S. Senate, Mitch McConnell from Kentucky, was blocking West Virginia Senator Joe Manchin's legislation to protect coal miners' pensions. Why? Senator Brown said it was "because he doesn't like the United Mine Workers Union," which endorsed his Democratic opponent in 2014. Yet there was virtually no anti-Republican backlash, and to date, no political consequences for one of the most callous displays of disregard for the needs of coal miners I can remember.
Now, I've met a lot of open-minded, big-hearted men and women who live and work in poor, rural communities. It's hard to fault them for wanting to shake things up politically after so many years of disappointment. But anger and resentment do run deep. As Appalachian natives such as author J. D. Vance have pointed out, a culture of grievance, victimhood, and scapegoating has taken root as traditional values of self-reliance and hard work have withered. There's a tendency toward seeing every problem as someone else's fault, whether it's Obama, liberal elites in the big cities, undocumented immigrants taking jobs, minorities soaking up government assistance—or me. It's no accident that this list sounds exactly like Trump's campaign rhetoric.
But just because a situation can be exploited for political gain doesn't mean there's not a problem. The pain—and panic—that many blue-collar whites feel is real. The old world they talk wistfully about, when men were men and jobs were jobs, really is gone.
Don't underestimate the role of gender in this. In an economy where most women don't have any choice but to work and few men earn enough to support a family on their own, traditional gender roles get redefined. Under the right circumstances, that can be liberating for women, good for kids, and even good for men, who now have a partner in shouldering the economic burden. But if the changes are caused by the inability of men to make a decent living when they want to work and can't find a job, the toll on their sense of self-worth can be devastating.
It all adds up to a complex dynamic. There's both too much change and not enough change, all at the same time.
When people feel left out, left behind, and left without options, the deep void will be filled by anger and resentment or depression and despair about those who supposedly took away their livelihoods or cut in line.
Trump brilliantly tapped into all these feelings, especially with his slogan: Make America Great Again. Along with that were two other powerful messages: "What have you got to lose?" and "She's been there for thirty years and never did anything." What he meant was: "You can have the old America back once I vanquish the immigrants, especially Mexicans and Muslims, send the Chinese products back, repeal Obamacare, demolish political correctness, ignore inconvenient facts, and pillory Hillary along with all the other liberal elites. I hate all the same people you do, and, unlike the other Republicans, I'll do something to make your life better."
When my husband was a little boy, his uncle Buddy in Hope, Arkansas, liked to say: "Anybody who tries to make you mad and stop you from thinking is not your friend. There's a lot to be said for thinking." Like so much wisdom I've heard in my life, it's easier to say than to live by. The far easier choice is to play the pin-the-tail-on-the-donkey blame game—which is what has happened to Democrats in too many places.
One of the most important but least recognized facts in American politics is that Republicans tend to win in places where more people are pessimistic or uncertain about the future, while Democrats tend to win where people are more optimistic. Those sentiments don't track neatly with the overhyped dichotomy between the coasts and the heartland. There are plenty of thriving communities in both blue and red states that have figured out how to educate their workforces, harness their talents, and participate in the twenty-first-century economy. And some of the most doom-and-gloom Americans are relatively affluent middle-aged and retired whites—the very viewers Fox News prizes—while many poor immigrants, people of color, and young people are burning with energy, ambition, and optimism.
As an example, in 2016 I got whacked in Arkansas as a whole, but I won Pulaski County, home of Little Rock, the state's vibrant capital city, by 18 points. I lost Pennsylvania, but I won Pittsburgh with 75 percent of the vote. Trump may think of that city as an emblem of the industrial past—he contrasted it with Paris when he pulled out of the global climate agreement in 2017—but the reality is that Pittsburgh has reinvented itself as a hub of clean energy, education, and biomedical research. As I saw when I campaigned there many times, people in Pittsburgh are determined and optimistic about the future.
So I can't say what was in the hearts and minds of those men and women standing in the rain in Williamson chanting "Go home Hillary!" Did they despise me because they'd heard on Fox that I wanted to put coal miners out of business? Did some think I turned my back on them after they'd voted for me in the Democratic primary in 2008? Did they turn against me because I served as Obama's Secretary of State and believed climate change was a real threat to our future? Or did their rage flow from deeper tribal politics? All I knew for certain was they were angry, they were loud, and they hated my guts. I gave them a big smile, waved, and went inside.
* * *
* * *
Dr. Dino Beckett, the director of the Williamson Health and Wellness Center, was waiting for me, along with about a dozen locals and Senator Joe Manchin. They were eager to tell me about how they were working to turn around their struggling community. They had started an incubator to help local entrepreneurs get new small businesses off the ground. The county was trying to turn abandoned mining properties into industrial parks that could attract new employers. They knew they needed better housing infrastructure, so they put people to work refurbishing homes and businesses. They realized that many of their neighbors were struggling with opiate addiction and other chronic health issues such as diabetes, so they opened a nonprofit health clinic. A recovering drug addict who had become a counselor told me how meaningful the work was, even if stemming the epidemic of substance abuse was a Sisyphean endeavor.
To make sure I heard a cross section of perspectives, Dr. Beckett had invited a laid-off coal worker he knew from their children's school soccer team, Bo Copley, along with his wife, Lauren. Bo was a Republican and a fervent Pentecostal, with a T-shirt that said "#JesusIsBetter." He lost his job as a maintenance planner at a local mining operation the year before. Now the family was getting by on what Lauren could earn through her small business as a photographer. When it was Bo's turn to speak, his voice was heavy with emotion.
"Let me say my apologies for what we've heard outside," Bo began, with the chants of the protesters still audible. "The reason you hear those people out there saying some of the things that they say is because when you make comments like 'We're going to put a lot of coal miners out of jobs,' these are the kind of people that you're affecting."
He passed me a picture of his three little children, a son and two daughters. "I want my family to know that they have a future here in this state, because this is a great state," he said. "I've lived my entire life here. West Virginians are proud people. We take pride in our faith in God. We take pride in our family. And we take pride in our jobs. We take pride in the fact that we're hard workers."
Then he got to the heart of the matter. "I just—I just want to know how you can say you're going to put a lot of coal miners out of jobs and then come in here and tell us how you're going to be our friend, because those people out there don't see you as a friend."
"I know that, Bo," I replied. "And I don't know how to explain it other than what I said was totally out of context from what I meant." I badly wanted him to understand. I didn't have a prayer of convincing the crowd outside, but maybe I could make him see that I wasn't the heartless caricature I had been made out to be. I said how sorry I was and that I understood why people were angry.
"I'm going to do everything I can to help," I told him. "Whether or not people in West Virginia support me, I'm going to support you."
Bo looked at me and pointed to the photograph of his children. "Those are the three faces I had to come home and explain to that I didn't have a job," he said. "Those are the three faces I had to come home to and explain that we're going to find a way; that God would provide for us, one way or another, that I was not worried, and I had to try to keep a brave face so they would understand."
He said that earlier in the day he had picked up his young son from school and suggested they stop to get something to eat. "No, Daddy," his son replied, "I don't want us to use up our money." It was hard to hear that.
After the meeting ended, I went off to the side with Bo and Lauren. I wanted to let them know I appreciated their candor. Bo told me how he leaned on his Christian faith in a difficult time. It was everything to him. I shared a little about my faith, and, for a minute, we were just three people bonding over the wisdom of the prophet Micah: "To act justly, to love mercy, and to walk humbly with your God."
Bo was a proud man, but he knew he and his community needed help. Why, he asked, weren't there more programs in place already to help people who were ready and willing to work to find good jobs to replace the ones that had disappeared? Why wasn't there anywhere for someone like him to turn? I told him about my plans to bring new employers to the area and to support small businesses like his wife's. They weren't going to solve the region's problems overnight, but they would help make life better. And if we could get some positive results, people might start believing again that progress was possible. But I knew that campaign promises would go only so far. As we drove off for Charleston, I called my husband. "Bill, we have to help these people."
* * *
* * *
How do we help give people in rural counties such as Mingo and McDowell a fighting chance?
The most urgent need right now is to stop the Trump administration from making things a whole lot worse.
I hope by the time you read this, Republicans will have failed to repeal Obamacare, but that's far from certain. Trump's health care plan would have devastating consequences in poor and rural areas, especially for older people and families who rely on Medicaid. And at a time when opiate addiction is ravaging communities across rural America, Trump and Republicans in Congress proposed scrapping the Affordable Care Act's requirement that insurers cover mental health services and addiction treatment. It alarms me to think about what this would mean for the recovering addicts, family members, doctors, counselors, and police officers I met in West Virginia and across the country who were all struggling to deal with the consequences of this epidemic.
Beyond health care, Trump wants to eliminate nearly all federal support for economic diversification and development in Coal Country. He's proposed shutting down the Appalachian Regional Commission, which has invested more than $387 million in West Virginia alone, helped create thousands of jobs, and supported community efforts such as the Williamson Health and Wellness Center. Appalachia needs more investment, not less; more access to fast, affordable, and reliable broadband for businesses and homes; more high-quality training programs that do a better job of matching students to jobs that actually exist, not just providing certificates that look nice in a frame on the wall but don't lead anywhere; and incentives such as the New Markets Tax Credit that can attract new employers beyond the coal industry and build a more sustainable economy.
Trump's promises are ringing increasingly hollow. After the election, he took a lot of credit for persuading the air-conditioning maker Carrier to keep hundreds of manufacturing jobs in Indiana rather than moving them to Mexico. Since then, we've learned it was essentially a bait and switch: Carrier received millions in subsidies from taxpayers and is still shipping out 630 jobs anyway. That kind of bait and switch shouldn't surprise anyone who's followed Trump's career.
Trump also promised to reopen coal mines and revive the industry to its former glory. But despite what he says, and what a lot of people want to believe, the hard truth is that coal isn't coming back. As Trump's own director of the National Economic Council, Gary Cohn, admitted in a moment of candor in May 2017, "Coal doesn't even make that much sense anymore." Politicians owe it to communities that have relied on the industry for generations to be honest about the future.
The entire debate over coal unfolds in a kind of alternative reality. Watching the news and listening to political speeches, you'd think coal is the only industry in West Virginia. Yet the truth is that the number of coal miners has been shrinking since the end of World War II. During the 1960s, fewer than fifty thousand West Virginians worked in the mines. By the end of the eighties, it was fewer than twenty-eight thousand. The numbers have gone up and down as the price of coal fluctuates, but it's been twenty-five years since the industry accounted for even 5 percent of total employment in the state. Today far more West Virginians work in education and health care, which makes protecting the Affordable Care Act vital to protecting West Virginian jobs.
Across the country, Americans have more than twice as many jobs producing solar energy as they do mining coal. And think about this: since 2001, a half million jobs in department stores across the country have disappeared. That's many times more than were lost in coal mining. Just between October 2016 and April 2017, about eighty-nine thousand Americans lost jobs in retail—more than all the people who work in coal mining put together. Yet coal continues to loom much larger in our politics and national imagination.
More broadly, we remain locked into an outdated picture of the working class in America that distorts our policy priorities. A lot of the press coverage and political analysis since the election has taken as a given that the "real America" is full of middle-aged white men who wear hard hats and work on assembly lines—or did until Obama ruined everything. There are certainly people who fit that description, and they deserve respect and every chance to make a decent living. But fewer than 10 percent of Americans today work in factories and on farms, down from 36 percent in 1950. Most working-class Americans have service jobs. They're nurses and medical technicians, childcare providers and computer coders. Many of them are people of color and women. In fact, roughly two-thirds of all minimum-wage jobs in America are held by women.
Repealing Obamacare or starting a trade war with China won't do anything to make these Americans' lives better. But raising the minimum wage would. It would help a lot. So would a large program to build and repair our bridges, tunnels, roads, ports, and airports and expand high-speed internet access to neglected areas. Strengthening unions and making it easier for workers to organize and bargain for better pay and benefits would help rebuild the middle class. Supporting overstretched families with paid leave and more affordable childcare and elder care would make a huge difference. So would a "public option" for health care and allowing more people to buy into Medicare and Medicaid, which would help expand coverage and bring down costs.
The other thing we should be honest about is how hard it's going to be, no matter what we do, to create significant economic opportunity in every remote area of our vast nation. In some places, the old jobs aren't coming back, and the infrastructure and workforce needed to support big new industries aren't there. As hard as it is, people may have to leave their hometowns and look for work elsewhere in America.
We know this can have a transformative effect. In the 1990s, the Clinton administration experimented with a program called Moving to Opportunity for Fair Housing, which gave poor families in public housing vouchers to move to safer, middle-income neighborhoods where their children were surrounded every day by evidence that life can be better. Twenty years later, the children of those families have grown up to earn higher incomes and attend college at higher rates than their peers who stayed behind. And the younger the kids were when they moved, the bigger boost they received.
Previous generations of Americans actually moved around the country much more than we do today. Millions of black families migrated from the rural South to the urban North. Large numbers of poor whites left Appalachia to take jobs in Midwestern factories. My own father hopped a freight train from Scranton, Pennsylvania, to Chicago in 1935, looking for work.
Yet today, despite all our advances, fewer Americans are moving than ever before. One of the laid-off steelworkers I met in Kentucky told me he found a good job in Columbus, Ohio, but he was doing the 120-mile commute every week because he didn't want to move. "People from Kentucky, they want to be in Kentucky," another said to me. "That's something that's just in our DNA." I understand that feeling. People's identities and their support systems—extended family, friends, church congregations, and so on—are rooted in where they come from. This is painful, gut-wrenching stuff. And no politician wants to be the one to say it.
I believe that after we do everything we can to help create new jobs in distressed small towns and rural areas, we also have to give people the skills and tools they need to seek opportunities beyond their hometowns—and provide a strong safety net both for those who leave and those who stay.
Whether it's updating policies to meet the changing conditions of America's workers, or encouraging greater mobility, the bottom line is the same: we can't spend all our time staving off decline. We need to create new opportunities, not just slow down the loss of old ones. Rather than keep trying to re-create the economy of the past, we should focus on making the jobs people actually have better and figure out how to create the good jobs of the future in fields such as clean energy, health care, construction, computer coding, and advanced manufacturing.
Republicans will always be better at defending yesterday. Democrats have to be in the future business. The good news is we have a lot of ideas to help make life better in our modern economy. As you saw earlier, I proposed a whole raft of them in my campaign. So even as Democrats play defense in Trump's Washington, we have to keep pushing new and better solutions.
* * *
* * *
On that trip to West Virginia, I spent some time with a group of retired miners who were concerned about losing the health care and pensions they had been promised for years of dangerous labor, often in exchange for lower wages.
One retiree told me a story that has stuck in my memory ever since.
Many years ago, when he first went into the mines, he told his wife, "You're not going to have to worry. We're union. We'll have our health care, we'll have our pensions, you won't have to worry about nothing." But quietly, he still worried about his neighbors who didn't have the same benefits.
In 1992, he decided to vote for the first time in his life. He wanted to vote for Bill. When his friends at the mine asked him why, he said the only reason was health care. "You've got health care; what are you worried about?" they asked. But he was adamant. "There are other people that don't have health care," he would say. And when Obamacare was finally passed, he thought it didn't go far enough.
Now some coal companies were trying to take away benefits that had been promised long ago. The security he had assured his wife was rock solid was now in jeopardy.
"People need to worry about one another," he told me. "We are our brother's keeper, and we need to worry about other people. Me, personally, I have faith; I know God is going to get us through it. But we need to be worrying about our brother."
Most of the folks I met in places like Ashland, Kentucky, and Williamson, West Virginia, were good people in a bad situation, desperate for change. I wish more than anything that I could have done a better job speaking to their fears and frustrations. Their distrust went too deep, and the weight of history was too heavy. But I wish I could have found the words or emotional connection to make them believe how passionately I wanted to help their communities, and their families.
Where there's a will to condemn, evidence will follow.
—Chinese proverb
## Those Damn Emails
Imagine you're a kid sitting in history class thirty years from now learning about the 2016 presidential election, which brought to power the least experienced, least knowledgeable, least competent President our country has ever had. Something must have gone horribly wrong, you think. Then you hear that one issue dominated press coverage and public debate in that race more than any other. "Climate change?" you ask. "Health care?" "No," your teacher responds. "Emails."
Emails, she explains, were a primitive form of electronic communication that used to be all the rage. And the dumb decision by one presidential candidate to use a personal email account at the office—as many senior government officials had done in the past (and continued to do)—got more coverage than any other issue in the whole race. In fact, if you had turned on a network newscast in 2016, you were three times more likely to hear about those emails than about all the real issues combined.
"Was there a crime?" you ask. "Did it damage our national security?"
"No and no," the teacher replies with a shrug.
Sound ridiculous? I agree.
For those of you in the present, you've most likely already heard more than your fill about my emails. Probably the last thing you want to read right now is more about those "damn emails," as Bernie Sanders memorably put it. If so, skip to the next chapter—though I wish you'd read a few more pages to understand how it relates to what's happening now. But there's no doubt that a big part of me would also be very happy to never think about the whole mess ever again.
For months after the election, I tried to put it all out of my mind. It would do me no good to brood over my mistake. And it wasn't healthy or productive to dwell on the ways I felt I'd been shivved by then-FBI Director Jim Comey—three times over the final five months of the campaign.
Then, to my surprise, my emails were suddenly front-page news again. On May 9, 2017, Donald Trump fired Comey. The White House distributed a memo by Deputy Attorney General Rod Rosenstein that excoriated Comey for his unprofessional handling of the investigation into my emails. They said that was the reason for firing him. (You read that right. Donald Trump said he fired Comey because of how unfair the email investigation was to . . . me.) Rosenstein cited the "nearly universal judgment" that Comey had made serious mistakes, in particular his decisions to disparage me in a July press conference and to inform Congress that he was reopening the investigation just eleven days before the election. Testifying before Congress on May 19, 2017, Rosenstein described Comey's press conference as "profoundly wrong and unfair."
I read Rosenstein's memo in disbelief. Here was Trump's number two man at the Justice Department putting in writing all the things I'd been thinking for months. Rosenstein cited the opinions of former Attorneys General and Deputy Attorneys General of both parties. It was as if, after more than two years of mass hysteria, the world had finally come to its senses.
But the story quickly fell apart. On national television, Trump told NBC's Lester Holt that the real reason he fired Comey was the FBI's investigation into possible coordination between the Trump campaign and Russian intelligence. Or, as Trump called it, "this Russia thing." I wasn't surprised. Trump knew that, for all of Comey's faults, he wouldn't lie about the law. He had insisted that there was no case against me, despite Republican (and internal FBI) pressure to say there was, so when he confirmed the FBI's Russia investigation to Congress in 2017, I figured he was on borrowed time.
Still, it was incredible to see Comey go from villain to martyr in five seconds flat.
To make sense of this, you have to be able to keep two different thoughts in your head at the same time: Rosenstein was right about the email investigation, and Comey was wrong. But Trump was wrong to fire Comey over Russia. Both of those statements are true. And both are frustrating.
As painful as it is to return to this maddening saga, it's now more important than ever to try to understand how this issue ballooned into an election-tipping controversy. A lot of people still don't understand what it was all about; they just know it was bad. And I can't blame them: they were told that over and over again for a year and a half. For most of the general election campaign, the word email dominated all others when people were asked to name the first word that came to mind about me.
Right off the bat, let me say again that, yes, the decision to use personal email instead of an official government account was mine and mine alone. I own that. I never meant to mislead anyone, never kept my email use secret, and always took classified information seriously.
During the campaign, I tried endlessly to explain that I'd acted in good faith. I tried to apologize, though I knew the attacks being lobbed at me were untrue or wildly overstated, and motivated by partisan politics. Sometimes I dove deep into the tedious details. Other times I tried to rise above it all. Once I even told a bad joke. No matter what, I never found the right words. So let me try again:
It was a dumb mistake.
But an even dumber "scandal."
It was like quicksand: the more you struggle, the deeper you sink. At times, I thought I must be going crazy. Other times, I was sure it was the world that had gone nuts. Sometimes I snapped at my staff. I was tempted to make voodoo dolls of certain members of the press and Congress and stick them full of pins. Mostly, I was furious at myself.
Given my inability to explain this mess, I decided to let other voices tell the story this time. I hope that it helps to better connect the dots and explain what did and, equally important, didn't happen.
Nothing can undo what's done, but it does help with my frustration—and that's clearly good for my mental health!
Our best information is that she set it up as a matter of convenience.
—FBI Director Jim Comey, in congressional testimony, July 7, 2016
Yes, it was supposed to be convenient. Some doubted that explanation. But that's what the FBI concluded after months of investigation. And it's the truth.
A lot of young people today are used to carrying around multiple devices and having both a personal phone and one provided by their work. But I'm not a digital native. (I couldn't even have told you what that term meant until fairly recently.) I didn't send a single email while I was in the White House as First Lady or during most of my first term in the U.S. Senate. I've never used a computer at home or at work. It was not until about 2006 that I began sending and receiving emails on a BlackBerry phone. I had a plain old AT&T account like millions of other people, and used it both for work and personal email. That was my system, and it worked for me.
Adding another email account when I became Secretary of State would have meant juggling a second phone, since both accounts could not be on the same State Department device. I knew that former Secretary of State Colin Powell had used personal email exclusively. I also knew that email wasn't where the bulk of a Secretary's work was done. All this added up to me not giving this much thought when I took office—there was a lot else going on—although, of course, I now wish I had.
In early 2009, I moved my email account from AT&T's server to one that my husband's office had previously set up in our Chappaqua home, which is guarded by the Secret Service. People have asked, "Why did you set up that server?" But the answer is that I didn't; the system was already there. My husband had been using an office server for years and had recently upgraded it. It made sense to me to have my email account on that same system. So I just moved my account onto it. I could keep using my BlackBerry in exactly the same way as I always had.
I emailed regularly with Chelsea and with Bill's team—he does not personally use email, and we are still phone people—and with relatives and friends. But very little of my work was via email during the next four hectic years. I held lots of meetings, talked on the telephone (on both regular and secure lines), read stacks of briefing papers, and traveled nearly a million miles to 112 countries to see people face-to-face.
When we went back later on and collected all my work-related emails, we found a lot like this:
From: | H
---|---
To: | John Podesta
Sent: | Sunday, September 20, 2009 10:28 PM
Subject: | Re: When could we talk?
I'm on endless calls about the UN. Could I call you early tomorrow? Would btw 6:30 and 8:00 be too early? Please wear socks to bed to keep your feet warm.
Yes, that's me telling my friend John to wear warm socks. Or, there's this one, where I struggle to use my fax machine:
From: | H
---|---
To: | Huma Abedin
Sent: | Wednesday, December 23, 2009 2:50 PM
Subject: | Re: can you hang up the fax line, they will call again and try fax
I did.
—Original Message—
From: | Huma Abedin
---|---
To: | H
Sent: | Wed Dec 23 14:43:02 2009
Subject: | Re: can you hang up the fax line, they will call again and try fax
Yes but hang up one more time. So they can reestablish the line.
—Original Message—
From: | H
---|---
To: | Huma Abedin
Sent: | Wed Dec 23 14:39:39 2009
Subject: | Re: can you hang up the fax line, they will call again and try fax
I thought it was supposed to be off hook to work?
Here's one more that still makes me chuckle:
From: | H
---|---
To: | Huma Abedin
Sent: | Wednesday, February 10, 2010 3:19 PM
Subject: | Re: Diane Watson to retire
I'd like to call her.
But right now I'm fighting w the WH operator who doesn't believe I am who I say and wants my direct office line even tho I'm not there and I just [gave] him my home # and the State Dept # and I told him I had no idea what my direct office # was since I didn't call myself and I just hung up and am calling thru Ops like a proper and properly dependent Secretary [of] State—no independent dialing allowed.
In the end, what was meant to be convenient turned out to be anything but. If I had known all that at the time, there's no question I would have chosen a different system. Just about anything would have been better. Carving messages in stone and lugging them around town would have been better.
Laws and regulations did not prohibit employees from using their personal email accounts for the conduct of official Department business.
—Report by the State Department Inspector General, May 2016
Sounds definitive, right? Every department in the federal government has an internal Inspector General who oversees legal and regulatory compliance. The State Department Inspector General and his top aides, one of whom had formerly worked for Republican Senator Chuck Grassley, were no friends of mine. They looked for every opportunity to be critical. Yet when they examined all the rules in place when I was Secretary of State, they came to the above conclusion. There was a lot of confusion and consternation in the press about this question—in part because some of the rules changed after I left office. But as the Inspector General of the State Department spokesman confirmed: there was no prohibition on using personal email.
Prior to Secretary Kerry, no Secretary of State used a state.gov email address.
—Karin Lang, the career diplomat responsible for managing the staff supporting the Secretary of State, in a June 2016 deposition
The use of private email didn't start with me. It also didn't end with me. Colin Powell exclusively used an AOL account. Secretary Kerry, who was the first Secretary of State to use a government email address, has said that he continued using his preexisting personal email for official business well into 2015. None of this was particularly remarkable. Nor was it a secret. I corresponded with more than a hundred government officials from my personal email account, including the President and other White House officials. The IT staff at the State Department often assisted me in using my BlackBerry, particularly when they realized how technologically challenged I was.
As for record keeping, because the overwhelming number of people with whom I was exchanging work-related emails were government personnel on their ".gov" email addresses, I had every reason to think the messages I sent should have been captured by the government's servers, archived, and made available for Freedom of Information Act (FOIA) requests.
With respect to potential computer intrusion by hostile actors, we did not find direct evidence that Secretary Clinton's personal email domain, in its various configurations since 2009, was successfully hacked.
—FBI Director Jim Comey, in a press conference on July 5, 2016
A lot of people suggested that the server maintained by my husband's office might be vulnerable to hacking. As it turned out, the State Department network and many other highly sensitive government systems, including at the White House and the Pentagon, were all hacked. Colin Powell's emails were hacked. But, as Comey stated, there has never been any evidence that my system was ever compromised. Ironically, it turns out it may have been one of the safest possible places for my email.
Everybody thought Hillary Clinton was unbeatable, right? But we put together a Benghazi special committee, a select committee. What are her numbers today? Her numbers are dropping.
—Republican Majority Leader Representative Kevin McCarthy, on Fox News, September 29, 2015
Here's where the story takes a turn into the partisan swamp. Republicans spent years shamelessly trying to score political points off the terrorist attack in Benghazi, Libya, in September 2012. It was a tragedy, and I lay awake at night racking my brain about what more could have been done to stop it. After previous tragedies, including the bombings of our embassy and Marine barracks in Beirut in 1983 that killed 241 Americans, and the bombings of our embassies in Kenya and Tanzania in 1998 that killed 12 Americans and hundreds of Africans, there were good-faith bipartisan efforts to learn lessons and improve security. But after the attacks in Benghazi, Republicans turned the deaths of four brave Americans into a partisan farce. They weren't satisfied that seven congressional investigations (five of them led by Republicans) and an independent review board conducted thorough factual reviews and concluded that neither President Obama nor I were personally to blame for the tragedy. The Republican committee chairmen had done their jobs, but their leaders weren't satisfied. They wanted to score more political points. So they set up a "new" special committee to damage me as much as possible.
As Kevin McCarthy, the number two House Republican, explained in his moment of rare and unintentional candor, something had to be done to hurt me. He was also trying to become Speaker and needed to impress the right wing.
It wasn't until October 2015 that the Republicans finally asked me to testify. By then, the investigation into the terrorist attack had long since been overshadowed by their obsession with my emails. The Republicans running the committee had scrapped ten planned hearings about security and other issues, and instead focused solely on me. I had already testified about the attack in both the House and the Senate in 2013, so there wasn't much new ground to cover. Nonetheless, I answered questions for eleven hours. As overtly partisan as the whole exercise was, I was happy to have the chance to set the record straight.
The Republicans had delivered a massive binder of emails and memos to me just before the hearing began, warning that they planned to ask about any or all of them. Some I'd never seen before. The questioners tried to outdo one another in search of a "Gotcha!" moment that would play on the news. It was all a little ham-handed. One Congressman pointed portentously to a paragraph in one of my emails, insisting it contained some damning revelation of wrongdoing. I directed his attention to the next paragraph, which proved the opposite. And so it went.
Afterward, the Republican chairman Trey Gowdy sheepishly admitted the whole exercise had failed to achieve much of anything. When asked what new information had emerged over eleven hours of grilling, he paused for several seconds and then couldn't come up with anything. I was down the hall in a small conference room, where I hugged my staff, who had labored so hard to prepare me for the hearing. I invited them back to my house in Northwest Washington, where we ate takeout Indian food and decompressed.
The press agreed that the committee was a bust for the Republicans. But I was experienced enough in the ways of Washington scandals to know that some damage had already been done. Accusations repeated often enough have a way of sticking, or at least leaving behind a residue of slime you can never wipe off.
There is no question that former Secretary Clinton had authority to delete personal emails without agency supervision.
—Department of Justice court filing, September 2015
The Benghazi Committee sent the State Department a blizzard of requests for documents. In August 2014, among 15,000 pages of emails provided to the committee were eight emails to or from me. At the time, nobody raised any questions to me about why I was using a non-state.gov account.
A few months later, during the fall of 2014, the State Department, in an attempt to complete its record keeping, sent a letter to each of the four previous Secretaries of State—me, Condoleezza Rice, Colin Powell, and Madeleine Albright—for copies of all work emails we might still have in our possession. None of the other Secretaries produced anything. Nothing about weapons of mass destruction and the deliberations that led up to the Iraq War. Nothing about the fallout over the mistreatment of detainees at Abu Ghraib prison or the use of torture. Nothing at all. Madeleine said she never used email at the State Department. Neither did Condi, although senior aides of hers used personal email accounts. Powell said he didn't keep any of his emails.
I directed my attorneys to collect and provide to the department any messages I had that could conceivably be considered related to official business. That came to more than 30,000 emails. They were intentionally expansive in what they determined to be work related. The State Department and the National Archives and Records Administration later determined that 1,258 of them were, in fact, purely personal, and did not need to be provided to the department.
More than 30,000 emails sounds like a lot. But that's over four years, and a lot of those consisted of "Thx," or "Pls Print"—or no reply at all. One of my aides once calculated the average number of emails he sent and received every day. Over four years, it was hundreds of thousands. That helps put the numbers in context.
Another 31,000 of the emails I had were personal and not related in any way to my job as Secretary of State. I got a lot of grief for saying they were about yoga sessions and wedding planning. But these messages also included communications with lawyers and doctors, information about my mother's estate, reports from family and friends about things happening in their personal lives, both happy and sad—in short, clearly private personal content. Naturally I didn't want strangers reading them.
So we checked to make sure we were following the rules, providing every relevant email I had, and deleted the personal ones.
Critics later pounced on the fact that I deleted my personal emails and accused me of acting improperly. But as the Justice Department said, the rules were clear, and they would have applied to personal emails sent on a government account as well. And for good reason: nobody wants his or her personal emails made public.
Lock her up!
—Trump advisor Michael Flynn at the Republican National Convention, July 18, 2016
This quote could have been pulled from nearly any Trump rally of the entire campaign, but there's a certain poetic justice now in remembering how enthusiastic Michael Flynn was about sending me to jail.
The endless chants of "Lock her up!" once again exposed the viciousness of the Republican smear merchants and their most devoted followers. It was all depressingly familiar. For decades, political adversaries have accused me of every crime under the sun—even murder—and promised that I'd end up in jail one day.
You'd think that this history might have prompted fair-minded journalists to hesitate before setting off on another scandal jamboree. Or that voters might look at a long pattern of false accusations and be skeptical of new claims. But you'd be wrong. The vaguely remembered history of past pseudoscandals ended up reinforcing the general perception that "something shady must be going on with her" and fueling the much-discussed phenomenon of "Clinton fatigue."
Throughout the 2016 campaign, I watched how lies insinuate themselves into people's brains if hammered often enough. Fact checking is powerless to stop it. Friends of mine who made calls or knocked on doors for me would talk to people who said they couldn't vote for me because I had killed someone, sold drugs, and committed any number of unreported crimes, including how I handled my emails. The attacks were repeated so frequently that many people took it as an article of faith that I must have done something wrong.
The hysteria over emails kicked off in earnest in March 2015. On a Saturday night, my attorney, David Kendall, received an email from the New York Times asking several questions about my email practices and asking for responses "by late Sunday or early Monday at the latest." We scrambled to answer as many of the Times's questions as we could. Clearly something was up. The Times article appeared online late Monday, March 2, with the headline "Hillary Clinton Used Personal Email Account at State Dept., Possibly Breaking Rules."
As the Inspector General's report eventually made clear, this was baloney. The Times observed darkly: "The revelation about the private email account echoes long-standing criticisms directed at both the former Secretary and her husband, former President Bill Clinton, for a lack of transparency and inclination toward secrecy." It wasn't until the eighth paragraph that the story noted, "Mrs. Clinton is not the first government official—or first Secretary of State—to use a personal email account on which to conduct official business."
The Times's argument was that using personal email reinforced the narrative that I had a penchant for secrecy, but I've always found that charge odd. People know more about me and Bill than anybody in public life. We've made public thirty-eight years of our tax returns (thirty-eight years more than a certain someone), all my State Department emails, the Clinton Foundation tax returns and donors, medical information—yet we were secretive? When we sometimes did draw a line after going further than anyone in public life to be transparent, we didn't do it to be secretive—we did it to keep ourselves sane. Not to mention that someone trying to keep her email secret would be pretty dumb to use @clintonemail.com!
The facts didn't stop the hamster wheel of Washington scandal from spinning into rapid motion, as other media outlets sought to follow a story that must be important, because the New York Times had put it on the front page.
In an effort to calm things down, two days after the Times article appeared, I called for the public release of all the emails I had provided the State Department. I knew that would be a level of transparency unheard of in public life. In fact, more of my emails are now publicly available than every other President, Vice President, and Cabinet Secretary in our country's history combined. I had nothing to hide, and I thought that if the public actually read all of these thousands of messages, many people would see that my use of a personal account was never an attempt to cover up anything nefarious. The vast majority of the emails weren't particularly newsworthy, which may be why the press focused on any gossipy nugget it could find and otherwise ignored the contents. There were no startling revelations, no dark secrets, no tales of wrongdoing or negligence. They did, however, reveal something I felt was worth seeing: the hard work and dedication of the men and women of the State Department.
Once people did start reading, I was amused by some of the reactions, as I always am when people discover that I am, in fact, a real person. "I was one of the most ardent Hillary haters on the planet . . . until I read her emails," one writer declared. "I discovered a Hillary Clinton I didn't even know existed," she continued, "a woman who cared about employees who lost loved ones . . . who, without exception, took time to write notes of condolence and notes of congratulations, no matter how busy she was . . . who could be a tough negotiator and firm in her expectations, but still had a moment to write a friend with encouragement in tough times." Unfortunately, most people didn't read the emails; they just knew what the press and the Republicans said about them, so they figured they must contain some dark, mysterious secrets.
On March 10 I held a press conference. It wasn't a pleasant experience. The press was ravenous, and I was rusty, having been out of partisan politics for several years. "Looking back, it would've been better if I'd simply used a second email account and carried a second phone," I said. "But at the time, this didn't seem like an issue." That was true. And it didn't satisfy anyone. Right then and there, I should have known there would never be some magical words to prove how silly it was and make it go away.
Losing the story to another news outlet would have been a far, far better outcome than publishing an unfair story and damaging the Times's reputation for accuracy.
—New York Times public editor Margaret Sullivan on July 27, 2015
Late on July 23, 2015, the Times delivered another bombshell. A front-page article headlined "Criminal Inquiry Is Sought in Clinton Email Use" reported that two Inspector Generals had asked the DOJ "to open a criminal investigation into whether sensitive government information was mishandled in connection with the personal email account Hillary Rodham Clinton used as Secretary of State." Now my campaign had to deal with questions about whether I was being measured for an orange jumpsuit.
The Justice Department, however, clarified quickly that it had "received a referral related to the potential compromise of classified information" but "not a criminal referral." The Times had to publish two corrections and an editor's note explaining why it had "left readers with a confused picture."
Representative Elijah Cummings, the ranking Democrat on the Benghazi Committee, helped explain what happened: "I spoke personally to the State Department Inspector General on Thursday, and he said he never asked the Justice Department to launch a criminal investigation of Secretary Clinton's email usage. Instead, he told me the Intelligence Community IG [Inspector General] notified the Justice Department and Congress that they identified classified information in a few emails that were part of the FOIA review, and that none of those emails had been previously marked as classified."
Looking back after the election, the Times described the mix-up as "a distinction without a difference," because we now know that there was an investigation under way. But we also now know that there was a disagreement between the Department of Justice and the FBI about how to describe it appropriately. The DOJ's approach, reflected in the clarification to the Times story issued by its spokesperson, was intended to adhere to the long-standing policy of not confirming or denying the existence of an investigation—a rule that Comey respected scrupulously when he refused to say anything at all about the investigation into possible ties between Russia and the Trump campaign. But when it came to my emails, he had plenty to say. Regardless, the Times got into trouble because it gave its readers only one side of the story. The paper's Margaret Sullivan published a scathing postmortem headlined, "A Clinton Story Fraught with Inaccuracies: How It Happened and What Next?" Sullivan took the Times to task for its shoddy reporting. "You can't put stories like this back in the bottle—they ripple through the entire news system," she wrote. "It was, to put it mildly, a mess."
If all these respected, senior foreign service officers and experienced ambassadors are sending these emails, then this issue is not about how Hillary Clinton managed her email, but how the State Department communicates in the 21st century.
—Phil Gordon, a former Assistant Secretary of State and National Security Council official, who had some of his emails to me classified retroactively, in the Times, May 10, 2016
The Department of Justice's investigation, and pretty much everything else that followed, turned on questions of classification. The issue was no longer using personal email on the job. The question now was what should be considered classified, and did I or anyone else intend to mishandle it?
Despite its science-y name, classification isn't a science. Five people asked to look at the same set of documents could easily come to five different decisions. We see this every day across the government as different agencies disagree about what information should be considered classified. When I was Secretary, it was not uncommon for one of our Foreign Service Officers talking to foreign diplomats and journalists to report back on political or military developments in a country and file this information in an unclassified form. But a CIA agent in the same country, using covert informants and techniques, might gather the very same facts yet classify the report as secret. The very same information: Is it classified or not? Experts and agencies frequently disagree.
That's what happened when the State Department and the intelligence agencies reviewed my emails for release. Remember, I had asked for all of them to be published so that the American people could read them and judge for themselves. There were also a number of Freedom of Information Act requests working their way through the courts. The easiest thing to do would have been to just dump every email onto a website and be done with it, but the government has rules it has to follow in FOIA cases. You don't want to accidentally publish someone's Social Security number or cell phone number.
When reviewing my thirty thousand emails, in a number of instances, representatives of various U.S. intelligence agencies sought to retroactively classify messages that had not previously been marked as classified. Many State Department diplomats with long experience conducting sensitive diplomacy disagreed with those decisions. It was like a town changing speed limits and retroactively fining drivers who had complied with the old limit but not the new one.
For example, an email from Dennis Ross, one of our country's most experienced diplomats, was declared classified retroactively. It described back-channel negotiations he'd conducted with Israelis and Palestinians as a private citizen back in 2011. Government officials had already cleared him to publish the same information in a book, which he had done, but now different officials were trying to classify it. "It shows the arbitrariness of what is now being classified," Dennis observed.
Something similar happened to Henry Kissinger around the same time. The State Department released the transcript of a 1974 conversation about Cyprus between then-Secretary of State Kissinger and the director of the CIA, but much of the text was blacked out because it was now considered classified. This puzzled historians because State had published the full, unredacted transcript eight years before in an official history book . . . and on the department's website!
Another veteran diplomat, Ambassador Princeton Lyman, was also surprised to find some of his run-of-the-mill emails to me retroactively designated as classified. "The day-to-day kind of reporting I did about what happened in negotiations did not include information I considered classified," he told the Washington Post.
That is an absurdity. We might as well shut the department down.
—Former Secretary of State Colin Powell in the Times on February 4, 2016, after learning that two messages sent to his personal email account were being classified retroactively
Like Colin, I thought it was ridiculous that some in the intelligence agencies were now trying to second-guess the judgment of veteran diplomats and national security professionals in the State Department about whether messages they sent should be classified. It was doubly ridiculous to suggest that I should have second-guessed them in the moment.
Given all this, it's no surprise that many experts say that overclassification has become a big problem across the government. Even FBI Director Comey admitted as much in a Senate hearing, agreeing that a great deal of material that gets classified is, in fact, widely known to the public and poses little or no risk to national security.
Comey also confirmed that none of my emails was properly marked as classified, and therefore I would reasonably conclude they were not. His full exchange with Congressman Matt Cartwright of Pennsylvania in a congressional hearing on July 7, 2016, is worth reading:
CARTWRIGHT: You were asked about markings on a few documents—I have the manual here—marking national classified security information. And I don't think you were given a full chance to talk about those three documents with the little c's on them. Were they properly documented? Were they properly marked according to the manual?
COMEY: No.
CARTWRIGHT: According to the manual, if you're going to classify something, there has to be a header on the document? Right?
COMEY: Correct.
CARTWRIGHT: Was there a header on the three documents that we've discussed today that had the little c in the text someplace?
COMEY: No. There were three emails. The c was in the body, in the text, but there was no header on the email or in the text.
CARTWRIGHT: So if Secretary Clinton really were an expert about what's classified and what's not classified, and we're following the manual, the absence of a header would tell her immediately that those three documents were not classified. Am I correct in that?
COMEY: That would be a reasonable inference.
This is not a situation in which America's national security was endangered.
—President Barack Obama, on 60 Minutes, October 11, 2015
This wasn't just the view of the Commander in Chief. Many top foreign policy officials from both parties agreed, and endorsed me for President—like Michael Chertoff, George W. Bush's Secretary of Homeland Security. "She's going to do a good job protecting the country," Chertoff told NPR. "In a world at war, you've got to focus on the top priority which is protecting the United States and protecting our friends and allies."
The American people are sick and tired of hearing about your damn emails! Enough of the emails. Let's talk about the real issues facing America.
—Senator Bernie Sanders, in the first Democratic debate, October 13, 2015
I couldn't have said it better myself. I remain grateful for Bernie's wise comment in our first debate. There was a reason the crowd cheered so heartily. He was right that the whole controversy was nonsense. If only the press had treated it that way. I wish I could end this story right here. Unfortunately, the saga continued.
Our judgment is that no reasonable prosecutor would bring such a case.
—FBI Director Jim Comey, in a press conference on July 5, 2016
The FBI's security inquiry was thorough, professional—and slow. My lawyer wrote to the Department of Justice way back in August 2015, repeating my public pledge to cooperate completely and offering for me to appear voluntarily to answer questions. I wanted my interview to take place as quickly as possible, since the first Democratic primaries were looming. But we were repeatedly told, "Not yet."
It became clear that I would likely be the last witness interviewed. I understood this was the logical sequence, but I chafed at being unable to dispel the cloud of uncertainty looming over me.
Finally, in June 2016, they were ready to talk to me. We agreed to an interview on July 2, a sleepy Saturday on a hot holiday weekend. To avoid press hoopla as much as possible, we set it for 8:00 A.M. at the FBI Headquarters in the J. Edgar Hoover Building in downtown Washington.
An elevator whisked me and my team up from the basement parking lot to the eighth floor, where we were brought to a secure conference room. Eight DOJ and FBI lawyers and agents were waiting for us. One of my attorneys, Katherine Turner, was eight and a half months pregnant, so there was a lot of baby-related small talk to help break the ice.
The interview lasted three and a half hours and was conducted largely by two FBI agents, although all the government lawyers asked some questions. They wanted to know how I had decided to use my personal email at the State Department, who I'd talked to, what I'd been told, what I knew about maintenance of the system, how I'd had the emails sorted, and other things. The agents were professional, precise, and courteous. Their questions were phrased carefully and not argumentative, and when they obtained an answer, they didn't try to badger. I thought it was conducted efficiently. When they said they had no further questions and thanked me, I apologized to them all, saying that I was sorry they'd had to spend so much time on this matter.
Director Comey had not been present during my Saturday interview. But three days later, on Tuesday, July 5, he held a very unusual press conference. It came as a complete surprise to us. We had no warning and had heard no feedback at all after the Saturday session.
Comey made a double-barreled announcement. First, he said that no criminal charges would be brought against anyone, stating that "no reasonable prosecutor" would bring a criminal case of mishandling classified information in this situation. We had expected that. Nonetheless, it was good to hear those words.
The second shot was both completely unexpected and inappropriate. Comey said that although my State Department colleagues and I had not violated the law about handling classified information, we—all three hundred of us who had written emails later classified—were nevertheless "extremely careless." He said the FBI had found that "the security culture of the State Department in general, and with respect to use of unclassified email systems in particular, was generally lacking in the kind of care for classified information found elsewhere in the government." It was one thing to go after me, but disparaging the entire State Department was totally out-of-bounds and revealed how much age-old institutional rivalries between agencies colored this entire process.
Much of the public and press reaction to Comey's announcement rightly focused on the overall conclusion that after months of controversy, there was no case. Critics predicting my imminent indictment were bitterly disappointed. But I was angry and frustrated that Comey had used his public position to criticize me, my staff, and the State Department, with no opportunity for us to counter or disprove the charge.
I felt a little like Ray Donovan, President Reagan's Secretary of Labor, who, after being acquitted of fraud charges, asked, "Which office do I go to to get my reputation back?"
My first instinct was that my campaign should hit back hard and explain to the public that Comey had badly overstepped his bounds—the same argument Rod Rosenstein would make months after the election. That might have blunted the political damage and made Comey think twice before breaking protocol again a few months later. My team raised concerns with that kind of confrontational approach. In the end, we decided it would be better to just let it go and try to move on. Looking back, that was a mistake.
The Director laid out his version of the facts for the news media as if it were a closing argument, but without a trial. It is a textbook example of what federal prosecutors and agents are taught not to do.
—Deputy Attorney General Rod Rosenstein, in his May 9, 2017, memo to Attorney General Jeff Sessions
Rosenstein's damning memo about Comey's handling of the email investigation may have been exploited by the Trump White House to justify firing the FBI Director in a bid to shut down the Russia investigation, but its conclusions should still be taken seriously. After all, Rosenstein is a veteran prosecutor who once again proved his independence by appointing respected former FBI Director Bob Mueller as Special Counsel.
According to Rosenstein, at the July 5 press conference, Comey "usurped" the Attorney General's authority, "violated deeply engrained rules and traditions" at the Justice Department, and "ignored another long-standing principle: we do not hold press conferences to release derogatory information about the subject of a declined criminal investigation."
Comey's excuse for breaking protocol and denouncing me in public was that this was "a case of intense public interest." But as Matt Miller, the Justice Department's Public Affairs Officer from 2009 to 2011, pointed out the day after the press conference, "The Department investigates cases involving extreme public interest all the time." He said that Comey's "willingness to reprimand publicly a figure against whom he believes there is no basis for criminal charges should trouble anyone who believes in the rule of law and fundamental principles of fairness."
Comey decided to go ahead with the press conference because of supposed concerns he had with his boss, Attorney General Loretta Lynch. His decision was reportedly influenced by a forged Russian document that sought to discredit Lynch. It was fake, but Comey was still concerned (more on that in the next chapter). Comey has also pointed to the fact that Lynch and my husband had a brief, unplanned conversation on a tarmac in Phoenix in late June 2016, when their planes happened to be next to each other. Nothing inappropriate was said in any way, but both of them came to regret exchanging pleasantries that day because of the firestorm that followed. There's no doubt that the optics were bad, but that didn't give Comey carte blanche to ignore Justice Department policies and overstep his bounds. The implication that Lynch, a distinguished career prosecutor, was suddenly compromised and couldn't be trusted is outrageous and insulting. It's also insulting to the former Deputy Attorney General Sally Yates and all the other senior Justice Department officials who were in the chain of command.
Unfortunately, that wasn't Comey's last—or most damaging—mistake.
He violated every rule in the book governing the conduct of federal law enforcement officials and did so in a way that was partisan and that indubitably affected the outcome of the election.
—Elliott Jacobson, one of Comey's former colleagues in the U.S. Attorney's Office for the Southern District of New York who has served as a prosecutor for nearly thirty-seven years, in a letter to the editor of the New York Times, April 26, 2017
On October 28 I was headed to Cedar Rapids, Iowa, for a rally with the leaders of several major women's advocacy groups. My friend Betsy was with me on the plane. Annie Leibovitz, the legendary photographer, was along as well to snap candid photos of life on the trail. The election was just eleven days away, and early voting was already in full swing in thirty-six states and the District of Columbia. I was taking nothing for granted, but I was feeling good about our momentum coming out of three successful debates, strong poll numbers, and early-vote projections.
When we landed in Cedar Rapids, Robby Mook, Nick Merrill, and communications director Jennifer Palmieri said they had some news to share. "We have something to tell you, and it's not good," Jennifer said. I had a sinking feeling. Things had been going too well for too long. We were due for trouble. "What now?" I asked. "Jim Comey . . ." Jennifer began, and I immediately knew it was bad.
We didn't have a lot of information, because the internet had been very spotty on the flight, but Jennifer said it seemed that Comey had sent a brief, vaguely worded letter to eight different congressional committees saying that in connection with an unrelated case, "the FBI has learned of the existence of emails that appear to be pertinent" to the previously closed investigation into my handling of classified information—although "the FBI cannot yet assess whether or not this material may be significant."
Jason Chaffetz, the then-Chairman of the House Oversight Committee, immediately tweeted with glee: "Case reopened."
Was this a bad joke? It had to be. The FBI wasn't the Federal Bureau of Ifs or Innuendoes. Its job was to find out the facts. What the hell was Comey doing?
I got off the plane and into the waiting motorcade, beckoning Betsy to join me in the car. What a relief to have my friend with me.
By the time we finished the rally and got back to the plane, the team had learned more. I sat back down in my seat, across from Huma and Betsy, and asked Jennifer to fill me in. How much crazier could this story get?
A lot.
The unrelated federal investigation turned out to be the one into Huma's estranged husband, Anthony Weiner. His lawyers had turned over a laptop of his to the U.S. Attorney's Office. FBI agents from the New York field office searched the computer and found emails between Huma and me.
When we heard this, Huma looked stricken. Anthony had already caused so much heartache. And now this.
"This man is going to be the death of me," she said, bursting into tears.
After more than twenty years working with Huma, I think the world of her, and seeing her in such distress broke my heart. I looked at Betsy, and we both got up to comfort her. I gave her a hug while Betsy patted her shoulder.
In the days that followed, some people thought I should fire Huma or "distance myself." Not a chance. She had done nothing wrong and was an invaluable member of my team. I stuck by her the same way she has always stuck by me.
The more we learned, the more infuriating the story became. The FBI didn't ask Huma or me for permission to read the emails it found, which we would have granted immediately. In fact, they didn't contact us at all. At the time, the FBI had no idea if the emails were new or duplicates of ones already reviewed, or if they were personal or work related, let alone whether they might be considered classified retroactively or not. They didn't know anything at all. And Comey didn't wait to learn more. He fired off his letter to Congress two days before the FBI received a warrant to look at those emails.
Why make a public statement like this, which was bound to be politically devastating, when the FBI itself couldn't say whether the new material was important in any way? At the very end of his July 5 press conference, Comey had declared sanctimoniously, "Only facts matter," but here the FBI didn't know the facts and didn't let that stop it from throwing the presidential election into chaos.
Comey's actions were condemned swiftly by former Justice Department officials of both parties, including Republican Attorneys General Alberto Gonzales and Michael Mukasey, the latter of whom said that Comey "stepped way outside his job."
The Department of Justice's Inspector General also opened an investigation into Comey's conduct.
Before Comey sent his letter, Justice Department officials reminded Comey's deputies of the long-standing policy to avoid any activity that could be viewed as influencing an election. According to reporting by the New York Times, they also said there was no need to inform Congress before the FBI determined if the emails were pertinent. A member of Comey's team at the FBI also raised concerns. If Comey had waited until after the FBI had reviewed the emails, he would have learned quickly that there was no new evidence. Comey sent his letter anyway.
The result, according to Deputy Attorney General Rosenstein, was so damaging that "the FBI is unlikely to regain public and congressional trust until it has a Director who understands the gravity of the mistakes and pledges never to repeat them."
So why did Comey do it?
In a Senate Judiciary Committee hearing on March 3, 2017, Comey testified that he saw only two choices: "speak" or "conceal." But as Rosenstein noted in his memo, " 'Conceal' is a loaded term that misstates the issue. When federal agents quietly open a criminal investigation, we are not concealing anything; we are simply following the long-standing policy that we refrain from publicizing nonpublic information. In that context, silence is not concealment."
I can't know what was in Comey's head. I don't know if he had anything against me personally, or if he thought I was going to win the election and worried that if he didn't speak out he'd later be attacked by Republicans or his own agents. What I do know, though, is that when you're the head of an agency as important as the FBI, you have to care a lot more about how things really are than how they look, and you have to be willing to take the heat that goes along with the big job.
Whatever Comey was feeling or fearing, there is reason to be concerned about what was going on inside the FBI.
There's a revolution going on inside the FBI, and it's now at a boiling point.
—Rudy Giuliani on Fox News, October 26, 2016
According to Rudy and others with close ties to the FBI, there was a vocal faction within the bureau that was livid that, in their view, Comey had "let me off the hook" in July. "The agents are furious," Jim Kallstrom, the former head of the FBI's New York office and a close ally of the ex–New York Mayor, told the press. Kallstrom also endorsed Trump and described me as a "pathological liar" and member of "a crime family." Kallstrom claimed to be in touch with hundreds of FBI agents, both retired and current. "The FBI is Trumpland," is how another agent put it. The agent said I was regarded by some as "the Antichrist personified." The New York Post reported that "FBI agents are ready to revolt."
There was a rash of leaks designed to damage my campaign, including the quickly debunked false claim that indictments were coming relating to the Clinton Foundation.
Then Rudy, one of Trump's top surrogates, went on Fox News on October 26 and promised "a surprise or two that you're going to hear about in the next two days." It was just two days later that Comey sent his letter.
On November 4 Rudy was back on Fox News and confirmed that he had advance warning. "Did I hear about it? You're darn right I heard about it," he said. At the same time, he tried to backpedal on his statement.
Several months later, Comey was questioned about this in that same Senate Judiciary Committee hearing.
"Did anybody in the FBI during this 2016 campaign have contact with Rudy Giuliani about the Clinton investigation?" asked Senator Pat Leahy of Vermont. Comey said it was "a matter the FBI is looking into" and that he was "very, very interested" to learn the truth. "I don't know yet, but if I find out that people were leaking information about our investigations whether to reporters or private parties, there will be severe consequences," Comey said. This is a crucial question that must be answered. Comey owes it to the American people to say whether anyone at the FBI inappropriately provided Giuliani, Kallstrom, or anyone else with information. The bureau's new leaders and the Justice Department Inspector General have a responsibility to investigate this matter fully and ensure accountability.
It's galling that Comey took pains during the same period to avoid saying anything at all about the investigation into possible connections between the Trump campaign and Russian intelligence. This double standard has still never been explained adequately and it leaves me astonished.
The final week of the 2016 campaign was dominated by swirling questions about my emails and talk that the prayers of Trump supporters might finally be answered, and I'd somehow wind up in prison.
After nine days of turmoil—nine days in which millions of Americans went to the polls to vote early—and just thirty-six hours before Election Day, Comey sent another letter announcing that the "new" batch of emails wasn't really new and contained nothing to cause him to alter his months-old decision not to seek charges.
Well, great. Too little, too late. The rest is history.
There is one more angle worth considering before I turn the page on this sordid chapter: the role of the press.
The ongoing normalization of Trump is the most disorienting development of the presidential campaign, but the most significant may be the abnormalization of Clinton.
—Jonathan Chait in New York magazine, September 22, 2016
"Abnormalization" is a pretty good description of how it felt to live through the maelstrom of the email controversy. According to Harvard's Shorenstein Center, over the entire election, negative reports about me swamped positive coverage by 62 percent to 38 percent. For Trump, however, it was a more balanced 56 percent negative to 44 percent positive.
Coverage of my emails crowded out virtually everything else my campaign said or did. The press acted like it was the only story that mattered. To take just one egregious example, by September 2015, the then Washington Post political reporter Chris Cillizza had already written at least fifty pieces about my emails. A year later, the Post editorial board realized the story was out of control. "Imagine how history would judge today's Americans if, looking back at this election, the record showed that voters empowered a dangerous man because of . . . a minor email scandal," they wrote in a September 2016 editorial.
No need to imagine. It happened.
The Post went on: "There is no equivalence between Ms. Clinton's wrongs and Mr. Trump's manifest unfitness for office."
That was one of many editorials and endorsements that got it right. I was glad to be endorsed by nearly every newspaper in the country, including some that hadn't backed a Democrat in decades, if ever. Unfortunately, I don't think many undecided voters read editorials, and they almost never influence broadcast or cable news. It's the political stories on the front page that get read and picked up on TV. So even though some journalists and editors came to regret losing perspective and overdoing the coverage of my emails—and after the election, a few even shared their remorse in confidence—the damage was irreparable.
Considered alongside the real challenges that will occupy the next President, that email server, which has consumed so much of this campaign, looks like a matter for the help desk.
—New York Times endorsement of me for President, September 2016
The Times, as usual, played an outsized role in shaping the coverage of my emails throughout the election. To me, the paper's approach felt schizophrenic. It spent nearly two years beating me up about emails, but its glowing endorsement applied some sanity to the controversy. Then, in the homestretch of the race, when it mattered most, the paper went right back to its old ways.
First, it devoted the entire top half of its front page to Comey's October 28 letter, even though there was zero evidence of any wrongdoing and very few facts of any kind, and continued to give it breathless coverage for the rest of the week. Then, on October 31, the Times ran one of the single worst stories of the entire election, claiming the FBI saw no link between the Trump campaign and Russia. The truth was that a very serious counterintelligence investigation was picking up steam. The paper must have been sold a bill of goods by sources trying to protect Trump. It should have known better than to publish it days before the election. In both cases, it seemed as if speculation and sensationalism trumped sound journalism.
The Times was taken to task by its ombudsman for downplaying the seriousness of Russia's meddling. "This is an act of foreign interference in an American election on a scale we've never seen, yet on most days, it has been the also-ran of media coverage," wrote Liz Spayd on November 5, three days before Election Day. In stark contrast to reporting on my emails, "what was missing is a sense that this coverage is actually important." In a follow-up column in January, Spayd noted that the Times knew in September the FBI was investigating the Trump organization's ties to Russia, possibly including secret warrants from the Foreign Intelligence Surveillance Court, yet didn't tell the public. "It's hard not to wonder what impact such information might have had on voters still evaluating the candidates," she wrote. Good question! It gives a whole new meaning to what Bill likes to call "majoring in the minors."
Over the years, going all the way back to the baseless Whitewater inquisition, it's seemed as if many of those in charge of political coverage at the New York Times have viewed me with hostility and skepticism. They've applied what's sometimes called the "Clinton Rules." As Charles Pierce put it in Esquire magazine, "the Clinton Rules state that any relatively commonplace political occurrence or activity takes on mysterious dark energy when any Clinton is involved." As a result, a lot of journalists see their job as exposing the devious machinations of the secretive Clinton Machine. The Times has by no means been the only—or even the worst—offender, but its treatment has stung the most.
I've read the Times for more than forty years and still look forward to it every day. I appreciate much of the paper's terrific non-Clinton reporting, the excellent op-ed page, and the generous endorsements I've received in every campaign I've ever run. I understand the pressure that even the best political journalists are now under. Negative stories drive more traffic and buzz than positive or evenhanded ones. But we're talking about one of the most important news sources in the world—the paper that often sets the tone for everyone else—which means, I think, that it should hold itself to the highest standard.
I suppose this mini-rant guarantees that my book will receive a rip-her-to-shreds review in the Times, but history will agree that this coverage affected the outcome of the election. Besides, I had to get this off my chest!
This may shock you: Hillary Clinton is fundamentally honest.
—former New York Times editor Jill Abramson in the Guardian, March 28, 2016
Jill Abramson, who oversaw years of tough political coverage about me, came to this conclusion by looking at data from the fact-checking organization PolitiFact, which found I told the truth more than any other presidential candidate in 2016, including both Bernie Sanders and Donald Trump, who was the most dishonest candidate ever measured. The fact that this was seen as surprising says a lot about the corrosive effect of the never-ending email controversy, and all the decades of baseless attacks that preceded it.
But her emails!
—the internet, 2017
The further we've gotten from the election, the more outlandish our excessive national focus on emails has seemed. "But her emails!" became a rueful meme used in response to the latest Trump revelations, outrages, and embarrassments.
As hard as it is to believe or explain, my emails were the story of 2016. It didn't matter that the State Department Inspector General said there were no laws or regulations prohibiting the use of personal email for official business. It didn't matter that the FBI found no reasonable legal grounds to bring any kind of case.
The original decision to use personal email was on me. And I never figured out how to make people understand where I was coming from or convince them that I wasn't part of some devious plot. But it wasn't me who determined how Comey and the FBI handled this issue or how the press covered it. That's on them.
Since the election, we've learned that Vice President Mike Pence used private email for official business when he was Governor of Indiana, like so many other state and federal officials across our country (including, by the way, many staff in the Bush White House, who used a private RNC server for government business and then "lost" more than twenty million emails). We've learned that Trump's transition team copied highly sensitive documents and removed them from a secure facility. We've learned that members of Trump's White House staff use encrypted messaging apps that seem to evade federal records laws. And we know now that Trump associates are under federal investigation for far more serious things. Yet most of the fulminating critics have gone silent. It's almost as if they never really cared about the proper maintenance of government records or the finer points of retroactive classification, and the whole thing was just a convenient political piñata.
The further we get from the election, the stranger it seems that this controversy could swing a national election with such monumental consequences. I picture future historians scratching their heads, trying to understand what happened. I'm still scratching mine, too.
When reason fails, the devil helps.
—Fyodor Dostoevsky
## Trolls, Bots, Fake News, and Real Russians
Some people are blessed with a strong immune system. Others aren't as lucky. Their defenses have been worn down by disease or injury, so they're susceptible to all kinds of infections that a healthy person would easily fight off. When that happens to someone you love, it's terrible to watch.
The "body politic" works in much the same way. Our democracy has built-in defenses that keep us strong and healthy, including the checks and balances written into our Constitution. Our Founding Fathers believed that one of the most important defenses would be an informed citizenry that could make sound judgments based on facts and reason. Losing that is like losing an immune system, leaving a democracy vulnerable to all manner of attack. And a democracy, like a body, cannot stay strong through repeated injuries.
In 2016 our democracy was assaulted by a foreign adversary determined to mislead our people, enflame our divisions, and throw an election to its preferred candidate. That attack succeeded because our immune system had been slowly eroded over years. Many Americans had lost faith in the institutions that previous generations relied on for objective information, including government, academia, and the press, leaving them vulnerable to a sophisticated misinformation campaign. There are many reasons why this happened, but one is that a small group of right-wing billionaires—people like the Mercer family and Charles and David Koch—recognized long ago that, as Stephen Colbert once joked, "reality has a well-known liberal bias." More generally, the right spent a lot of time and money building an alternative reality. Think of a partisan petri dish where science is denied, lies masquerade as truth, and paranoia flourishes. Their efforts were amplified in 2016 by a presidential candidate who trafficked in dark conspiracy theories drawn from the pages of supermarket tabloids and the far reaches of the internet; a candidate who deflected any criticism by attacking others with made-up facts and an uncanny gift for humiliating zingers. He helped to further blur news and entertainment, reality TV and reality.
As a result, by the time Vladimir Putin came along, our democracy was already far sicker than we realized.
Now that the Russians have infected us and seen how weak our defenses are, they'll keep at it. Maybe other foreign powers will join them. They'll also continue targeting our friends and allies. Their ultimate goal is to undermine—perhaps even destroy—Western democracy itself. As the former Director of National Intelligence, James Clapper, told Congress, "If there has ever been a clarion call for vigilance and action against a threat to the very foundation of our democratic political system, this episode is it."
This should concern all Americans—Republicans, Democrats, Independents, everyone. We need to get to the bottom of it. The 2016 election may be over, but we have new elections coming up soon. I'm going to lay out what is known in as much detail as I can, so we can try to understand what happened and what we can do to prevent it from happening again. There's a lot we still don't know, investigations are ongoing, and the story changes daily with breaking news. Trump, his allies, and others have vigorously denied accusations of wrongdoing. You can look at the facts and decide for yourself. But what should be beyond doubt is that foreign interference in our elections is wrong, period. And the threat we face, from without and within, is bigger than one campaign, one party, or one election. The only way to heal our democracy and protect it for the future is to understand the threat and defeat it.
### V for Vendetta (and Vladimir)
President Obama once compared Vladimir Putin to a "bored kid at the back of the classroom." "He's got that kind of slouch," Obama said. When I sat with Putin in meetings, he looked more like one of those guys on the subway who imperiously spread their legs wide, encroaching on everyone else's space, as if to say, "I take what I want," and "I have so little respect for you that I'm going to act as if I'm lounging at home in my bathrobe." They call it "manspreading." That was Putin.
I've dealt with a lot of male leaders in my life, but Putin is in a class by himself. A former KGB spy with a taste for over-the-top macho theatrics and baroque violence (a public inquiry in the United Kingdom concluded that he probably approved the killing of one of his enemies in London by poisoning his tea with polonium-210, a rare radioactive isotope), Putin has emerged in the popular imagination as an arch-villain straight out of a James Bond movie. Yet he's also perennially misunderstood and underestimated. George W. Bush famously said that after looking Putin in the eye, he found him "very straightforward and trustworthy," and was "able to get a sense of his soul." My somewhat tongue-in-cheek response was: "He was a KGB agent—by definition, he doesn't have a soul." I don't think Vladimir appreciated that one.
Our relationship has been sour for a long time. Putin doesn't respect women and despises anyone who stands up to him, so I'm a double problem. After I criticized one of his policies, he told the press, "It's better not to argue with women," but went on to call me weak. "Maybe weakness is not the worst quality for a woman," he joked. Hilarious.
Putin still smolders over what he views as the humiliations of the 1990s, when Russia lost its old Soviet dominions, and the Clinton administration presided over NATO's expansion. And things got a lot worse between us during my time as Secretary of State.
When President Obama and I came into office in 2009, Putin and his prime minister, Dmitry Medvedev, had swapped jobs as a way of thwarting constitutionally required term limits. Surprisingly, Medvedev showed some independence and a willingness to pursue better relations with the United States. We knew Putin was still the real power in Russia but decided to see if we could find some areas of shared interest where progress might be possible. That was the origin of the much-maligned "reset." It led to several concrete successes, including a new nuclear arms control treaty, new sanctions on Iran and North Korea, a much-needed supply route to equip our troops in Afghanistan, increased trade and investment, and expanded counterterrorism cooperation. In the spring of 2011, President Medvedev agreed to abstain on the UN Security Council resolution authorizing the use of force to protect civilians in Libya from the dictator Colonel Muammar Gaddafi, a decision that angered Putin.
President Obama and I agreed that seeking pragmatic cooperation with Russia on certain issues was not inconsistent with also standing up for our values and showing support for the democratic aspirations of the Russian people. I felt a responsibility to speak out against the Kremlin's repression of human rights in Russia, especially the intimidation and murder of journalists and political opponents. In October 2009, I was in Moscow and did an interview with one of the last remaining independent radio stations in the country. I expressed support for human rights and civil society, and I said that I thought a lot of Russians wanted the thugs who attacked journalists brought to justice. I knew Putin wouldn't be happy with me saying these things on his own turf, but I felt that if the United States accepted a gag order on these issues, that decision would reverberate, not just in Russia but also around the world.
The KGB taught Putin to be suspicious of everyone. Russia's troubles in the 1990s and the "color revolutions" of the 2000s—the string of popular revolts that toppled authoritarian regimes in several former Soviet bloc countries—took him from suspicious to paranoid. He came to view popular dissent as an existential threat. When he heard me and other Western leaders voice support for civil society in Russia, he saw it as a plot to undermine him.
For Putin, a pivotal moment came in 2011. In September he announced he would run for President again. In December there were widespread reports of fraud in parliamentary elections, which sparked domestic protests and international condemnation. At a conference in Lithuania focused on promoting democracy and human rights in Europe, I expressed America's concerns. "The Russian people, like people everywhere, deserve the right to have their voices heard and their votes counted," I said, "and that means they deserve fair, free, transparent elections and leaders who are accountable to them." Tens of thousands of Russians took to the streets amid chants of "Putin is a thief," an unprecedented popular challenge to his iron grip on the country. Putin, more paranoid than ever, thought it was a conspiracy orchestrated from Washington. He blamed me in particular, saying I "gave them a signal."
Putin quashed the protests and once again became President, but he was now running scared and seething with anger. In the fall of 2011, Putin had published an essay promising to regain Russia's regional and global influence. I read it as a plan to "re-Sovietize" the lost empire and said so publicly. Once back in office, Putin moved to put his vision into action. He consolidated power and cracked down on any remaining domestic dissent. He also took a more combative tone toward the West and nursed his personal grudge against me. By the way, that's not just how I saw it; grudge is also the word the U.S. government used in its official assessment.
In a series of memos, I warned President Obama that things were changing in Russia, and America would have to take a harder line with Putin. Our relationship was likely to get worse before it got better, I told the President, and we needed to make it clear to Putin that aggressive actions would have consequences.
### There's a Bear in the Woods
During Obama's second term, when I was out of office, things did indeed go from bad to worse. When popular protests in Ukraine forced the country's corrupt, pro-Moscow leader to flee, Putin swung into action. He launched an operation to subvert and seize Ukraine's Crimean Peninsula, a vacation destination for wealthy Russians. That was followed by further efforts to destabilize eastern Ukraine, home to many ethnic Russians, eventually leading to a protracted civil war.
Watching from the sidelines, I was struck by the sophistication of the operation. It was much more effective than Russia's 2008 invasion of Georgia. Nationalist propaganda on television, radio, and social media radicalized ethnic Russians, while cyberattacks muzzled opposing voices. Undercover Russian paramilitary special forces swept into Crimea to organize protests, seize buildings, and intimidate or co-opt Ukrainian officials. Meanwhile, the Kremlin denied it all, despite the fact that the whole world could see photos of Russian soldiers carrying Russian weapons, driving Russian vehicles, and speaking with Russian accents. Putin called them indigenous "self-defense groups." Ukrainians called them "little green men." Once the occupation was a fait accompli, the Russians staged a rigged referendum to give themselves a patina of popular sovereignty and then annexed the peninsula, formally making it part of Russia.
The Russians did one other thing, which didn't get enough attention at the time but in retrospect was a sign of things to come. In early 2014, they released on Twitter and YouTube what they claimed was an audio recording of a private conversation between two veteran American diplomats, our Ambassador to Ukraine, Geoff Pyatt, and my friend and former advisor Toria Nuland, who was then the top State Department official for Europe. On the Russian tape, Toria used colorful language to express her exasperation about European foot-dragging over Ukraine. Moscow clearly hoped her words would drive a wedge between America and our allies. The incident didn't have lasting diplomatic repercussions, but it did show that the Russians were not just stealing information for intelligence purposes, as all countries do; they were now using social media and strategic leaks to "weaponize" that information.
In the wake of Russia's Ukraine operations, I expressed my concerns to some of my former national security colleagues. Moscow had clearly developed new capabilities in psychological and information warfare and was willing to use them. I was worried the United States and our allies weren't prepared to keep up or respond. I knew that in 2013, one of Russia's top military officers, Valery Gerasimov, had written an article laying out a new strategy for hybrid warfare. In previous generations, the Soviet military had planned to fight large-scale conflicts with massive conventional and nuclear forces. In the twenty-first century, Gerasimov said, the line between war and peace would blur, and Russia should prepare for under-the-radar conflicts waged through propaganda, cyberattacks, paramilitary operations, financial and energy manipulation, and covert subversion. The operations in Crimea and eastern Ukraine (and, I would argue, the harboring of NSA leaker Edward Snowden) proved that Putin was putting Gerasimov's theory into practice.
Sometimes these tactics are called "active measures." Thomas Rid, a professor of security studies at King's College London, offered a good primer in testimony before the Senate Intelligence Committee in March 2017. "Active measures are semicovert or covert intelligence operations to shape an adversary's political decisions," he explained. "The tried and tested way of active measures is to use an adversary's weaknesses against himself," and the rise of the internet and social media has created many new opportunities. As Senator Sheldon Whitehouse put it, "The Russians have been at this for a long time," and now "they've adapted old methods to new technologies—making use of social media, malware, and complex financial transactions."
I was also alarmed to see Russian money, propaganda, or other support aiding right-wing nationalist parties across Europe, including Marine Le Pen's National Front in France, Alternative for Germany (AfD), and Austria's Freedom Party. According to the Washington Post, the Kremlin has also cultivated leaders of right-wing American organizations such as the NRA, the National Organization for Marriage, and individuals like the evangelist Franklin Graham. Putin has positioned himself as the leader of an authoritarian, xenophobic international movement that wants to expel immigrants, break up the European Union, weaken the Atlantic Alliance, and roll back much of the progress achieved since World War II. People laugh when Putin has himself photographed riding horses shirtless, winning judo matches, and driving race cars. But the macho stunts are part of a strategy. He has made himself an icon to traditionalists everywhere who resent their increasingly open, diverse, and liberal societies. That's why he formed a close alliance with the Russian Orthodox Church, passed vicious antigay laws, and decriminalized domestic violence. It's all about projecting an image of traditional masculinity, Christian morality, and white nationalist purity and power.
During the campaign, I asked my team to start working on a more aggressive strategic approach toward Russia. I didn't want to be dragged into a new Cold War, but the best way to avoid conflict and keep the door open for future cooperation would be to send Putin a message of strength and resolve on Day One. It's been said that he subscribes to Vladimir Lenin's old adage: "Probe with bayonets. If you encounter mush, proceed; if you encounter steel, withdraw." I wanted to be sure that when Putin looked to America, he saw steel, not mush.
I wanted to go further than the Obama administration, which resisted providing defensive arms to the Ukrainian government or establishing a no-fly zone in Syria, where Putin had launched a military intervention to prop up the murderous dictator Bashar al-Assad. I also intended to increase our investment in cybersecurity and pursue an all-hands-on-deck effort to secure cooperation between the government and the private sector on protecting vital national and commercial infrastructure from attacks, including nuclear power plants, electrical grids, dams, and the financial system.
All of this is to say that I had my eyes open. I knew Putin was a growing threat. I knew he had a personal vendetta against me and deep resentment toward the United States.
Yet I never imagined that he would have the audacity to launch a massive covert attack against our own democracy, right under our noses—and that he'd get away with it.
Since the election, we've learned a lot about the scope and sophistication of the Russian plot, and more information comes to light every day. But even during the campaign, we knew enough to realize that we were facing, in the words of Senator Harry Reid, "one of the gravest threats to our democracy since the Cold War." And it just got worse from there. I won't try to provide you a definitive account of every twist and turn of this saga—there are plenty of other sources for that—but I will try to share what I experienced, how it felt, and what I think we need to do as a nation to protect ourselves for the future.
### The Budding Bromance
It was strange from the start. Why did Donald Trump keep blowing kisses to Vladimir Putin? He said he would give Putin an A for leadership, and described the Russian President as "highly respected within his country and beyond." Trump reveled in reports that Putin had called him "brilliant," even though the more accurate translation was "colorful." In a particularly telling exchange on MSNBC's Morning Joe, Trump defended Putin's alleged murder of journalists. "At least he's a leader, unlike what we have in this country," Trump said. As if that wasn't bad enough, he added, "I think our country does plenty of killing also." No previous American presidential candidate would ever have dreamt of trashing our country like that or suggesting moral equivalency between American democracy and Russian autocracy. No wonder Putin liked Trump.
What was going on here? I was genuinely puzzled. This was far outside the bounds of normal American politics, especially for a Republican. How was the Party of Reagan letting itself become the Party of Putin?
I thought there were three plausible explanations for the budding Trump-Putin "bromance."
First, Trump has a bizarre fascination with dictators and strongmen. He praised Kim Jong-un, the murderous young ruler of North Korea, for his skill at consolidating power and eliminating dissent—"You've gotta give him credit," Trump said. He also talked admiringly about the 1989 Chinese massacre of unarmed student protesters at Tiananmen Square; he said it showed strength. Strength is what it's all about. Trump doesn't think in terms of morality or human rights, he thinks only in terms of power and dominance. Might makes right. Putin thinks the same way, albeit much more strategically. And Trump appears to have fallen hard for Putin's macho "bare-chested autocrat" act. He doesn't just like Putin—he seems to want to be like Putin, a white authoritarian leader who could put down dissenters, repress minorities, disenfranchise voters, weaken the press, and amass untold billions for himself. He dreams of Moscow on the Potomac.
Second, despite his utter lack of interest in or knowledge of most foreign policy issues, Trump has a long-standing worldview that aligns well with Putin's agenda. He is suspicious of American allies, doesn't think values should play a role in foreign policy, and doesn't seem to believe the United States should continue carrying the mantle of global leadership. Way back in 1987, Trump spent nearly $100,000 on full-page ads in the New York Times, the Washington Post, and the Boston Globe criticizing Ronald Reagan's foreign policy and urging America to stop defending allies who should be taking care of themselves. Trump said the world was taking advantage of the United States and laughing at us. Nearly thirty years later, he was saying the same things. He referred to America's alliances as if they were protection rackets, where we could extort weaker countries to pay tribute in exchange for safety. He threatened to abandon NATO and bad-mouthed the European Union. He insulted the leaders of countries such as Britain and Germany. He even got into a Twitter fight with Pope Francis! Given all this, it's no surprise that, once he became President, Trump bickered with our allies and refused to commit to the bedrock principle of mutual defense at a NATO summit. America's lost prestige and newfound isolation were embodied in the sad image of the other leaders of Western democracies strolling together down a lovely Italian street while Trump followed in a golf cart, all by himself.
All this was music to Putin's ears. The Kremlin's top strategic goal is to weaken the Atlantic Alliance and reduce America's influence in Europe, leaving the continent ripe for Russian domination. Putin couldn't ask for a better friend than Donald Trump.
The third explanation was that Trump seems to have extensive financial ties to Russia. In 2008, Trump's son Don Jr. told investors in Moscow, "Russians make up a pretty disproportionate cross section of a lot of our assets" and "we see a lot of money pouring in from Russia," according to the Russian newspaper Kommersant. In 2013, Trump himself said in an interview with David Letterman that he did "a lot of business with the Russians." A respected golf journalist named James Dodson reported that Trump's other son, Eric, told him, "We don't rely on American banks" to fund Trump golf projects, "we have all the funding we need out of Russia."
Without seeing Trump's tax returns, it's impossible to determine the full extent of these financial ties. Based on what's already known, there is good reason to believe that despite repeated bankruptcies and even though most American banks refused to lend to him, Trump, his companies, or partners, according to USA Today, "turned to wealthy Russians and oligarchs from former Soviet republics—several allegedly connected to organized crime." This was based on a review of court cases and other legal documents. Additionally, in 2008, Trump raised eyebrows by selling a mansion in Palm Beach to a Russian oligarch at an inflated price—$54 million more than he paid for it just four years earlier. In 2013, his Miss Universe pageant in Moscow was partly financed by a billionaire ally of Putin. To build Trump SoHo New York hotel, he partnered with a company called the Bayrock Group and a Russian immigrant named Felix Sater, formerly linked to the mafia, who was previously convicted of money laundering. (USA Today has done great reporting on all of this, if you want to learn more.)
Trump's advisors also had financial ties to Russia. Paul Manafort, whom Trump hired in March 2016 and promoted to campaign chairman two months later, was a Republican lobbyist who had spent years serving autocrats overseas, most recently making millions working for pro-Putin forces in Ukraine. Then there was Michael Flynn, the former head of the Defense Intelligence Agency who had been fired for good cause by President Obama in 2014. Then Flynn accepted money from Putin's Western-facing propaganda network, Russia Today (RT), and in December 2015 attended RT's tenth-anniversary gala in Moscow, where he sat at Putin's table (along with Green Party presidential candidate Jill Stein). There was also Carter Page, a former advisor to the Russian gas giant Gazprom, who traveled back and forth to Moscow frequently—including in July 2016, in the middle of the campaign. He seemed to be reading from the Kremlin's anti-American talking points.
Learning all this over the course of 2015 and 2016 was surreal. It felt like we were peeling an onion, and there was always another layer.
If you add together all these factors—Trump's affection for tyrants and hostility toward allies, sympathy for Russia's strategic aims, and alleged financial ties to shady Russian actors—his pro-Putin rhetoric starts to make sense. And this was all out in the open and well known throughout the campaign. It came to a head in late April 2016, when Trump called for improved relations with Russia in a major foreign policy speech at the Mayflower Hotel in Washington. The Russian Ambassador to the United States, Sergey Kislyak, applauded from the front row. (He later attended the Republican National Convention, but avoided ours.)
Republican national security experts were appalled by Trump's embrace of Putin. So was I. At every opportunity, I warned that allowing Trump to be Commander in Chief would be profoundly dangerous and play directly into Russia's hands. "It'll be like Christmas in the Kremlin," I predicted.
### Breach
Then things got stranger.
In late March 2016, FBI agents met with my campaign lawyer, Marc Elias, and other senior staffers at our Brooklyn headquarters to warn us that foreign hackers could be targeting our campaign with phishing emails that tried to trick people into clicking links or entering passwords that would open up access to our network. We were already aware of the threat, because scores if not hundreds of these phishing emails were pouring in. Most were easy to spot, and we had no reason at the time to believe any were successful.
Then, in early June, Marc got a disturbing message from the Democratic National Committee. The DNC's computer network had been penetrated by hackers thought to be working for the Russian government. According to the New York Times, the FBI had apparently discovered the breach months earlier, in September 2015, and had informed a tech support contractor at the DNC, but never visited the office or did much to follow up. As a former head of the FBI Cyber Division told the Times later, that was a bewildering oversight. "We are not talking about an office that is in the middle of the woods of Montana," he said. The offices were just a mile and a half apart. After the election, FBI Director Comey admitted, "I might have walked over there myself, knowing what I know now."
Word didn't reach the DNC's leadership until April. They then brought in a respected cybersecurity firm called CrowdStrike to figure out what was going on, kick out the hackers, and protect the network from further penetration. The CrowdStrike experts determined that the hackers had likely come from Russia and that they had gained access to a large trove of emails and documents. All of this would become public when the Washington Post broke the story on June 14.
The news was unsettling but not shocking. The Russian government had been attempting to hack sensitive American networks for years, as had other countries, such as China, Iran, and North Korea. In 2014, Russians had breached the State Department's unclassified system and then moved on to the White House and the Pentagon. They also hacked think tanks, journalists, and politicians.
The general view was that all of these hacks and attempted hacks were fairly run-of-the-mill intelligence gathering, albeit with twenty-first-century techniques. That turned out to be wrong. Something far more insidious was happening. On June 15, one day after the DNC attack became public, a hacker named Guccifer 2.0—thought to be a front for Russian intelligence—claimed credit for the breach and posted a cache of stolen documents. He said he had given thousands more to WikiLeaks, the organization supposedly devoted to radical transparency. Julian Assange, the founder of WikiLeaks, promised to release "emails related to Hillary Clinton," although it wasn't at all clear what that meant.
The publication of stolen files from the DNC was a dramatic turn of events for several reasons. For starters, it showed that Russia was interested in doing more than collecting intelligence on the American political scene—it was actively trying to influence the election. Just as it had done a year earlier with the audio recording of Toria Nuland, Russia was "weaponizing" stolen information. It did not occur to me at the time that anyone associated with Donald Trump might be coordinating with the Russians, but it seemed likely that Putin was trying to help his preferred candidate. After all, he disliked and feared me, and had an ally in Trump. This was underscored when the Trump campaign removed language from the Republican Party platform calling for the United States to provide Ukraine with "lethal defensive weapons"—a gift to Putin that might as well have come with a ribbon and a bow.
Careful analysis of the documents from Guccifer also revealed an alarming prospect: at least one of the files seemed like it could have come from our campaign, not the DNC. Further research suggested that the file might have been stolen from the personal Gmail account of John Podesta, my campaign chairman. We couldn't be sure, but we feared that more trouble was coming.
### Shouting into the Wind
On July 22, WikiLeaks published about twenty thousand stolen DNC emails. It highlighted a handful of messages that included offensive comments about Bernie Sanders, which predictably set off a firestorm among Bernie's supporters, many of whom were still angry about having lost the primaries. But nothing in the stolen emails remotely backed up the charge that the primaries had been rigged. Nearly all of the offending messages were written in May, months after I had amassed an insurmountable vote and delegate lead.
More important, though, was the fact that the Russians or their proxies had the sophistication to find and exploit those handful of provocative stolen emails in order to drive a wedge between Democrats. That suggests a deep knowledge and familiarity of our political scene and its players. Also, imagine how many inflammatory and embarrassing things they would have found if they'd hacked Republican targets. (Spoiler alert: they did, but never released anything.)
The timing of the WikiLeaks release was terrible—and it didn't seem like a coincidence. I had defeated Bernie and locked up the nomination in early June, but he hadn't endorsed me until July 12, and now we were working hard to bring the party together before the Democratic National Convention started in Philadelphia on July 25. Plus, the news hit on the same day I was introducing Tim Kaine as my running mate, turning what should have been one of the best days of our campaign into a circus.
The document dump seemed designed to cause us maximum damage at a critical moment. It worked. DNC chair Debbie Wasserman Schultz resigned two days later, and the opening of the convention was marred by loud boos and catcalls from Sanders supporters. I was sick about the whole thing. After so many long, hard months of campaigning, I wanted the convention to be perfect. It was my best chance until the debates to present my vision for the country directly to the voters. I remembered what a boost Bill received from his convention in Madison Square Garden in 1992, and I hoped to gain similar momentum. Instead, we were now dealing with a divided party and distracted press corps. Democratic leaders, especially Congresswoman Marcia Fudge of Ohio, Reverend Leah Daughtry, and Donna Brazile, helped bring order to the chaos. And Michelle Obama's masterful, moving speech brought the hall together and quieted the dissenters. Then Bernie spoke, endorsed me again, and helped cement the détente.
On July 27, the day before I formally accepted the Democratic nomination, Trump held one of his wild, stream-of-consciousness press conferences. He said that as President he might accept Russia's annexation of Crimea, deflected blame from the Kremlin for the DNC hack, and then, remarkably, urged the Russians to try to hack my email account. "Russia, if you're listening, I hope you're able to find the thirty thousand emails that are missing," he said, referring to the personal, non-work-related emails that were deleted from my account after everything else had been provided to the State Department. "I think you will probably be rewarded mightily by our press." As the New York Times described it, Trump was "urging a power often hostile to the United States to violate American law by breaking into a private computer network."
Katy Tur of NBC News followed up to see if this was a joke or he really meant it. She asked if Trump had "any qualms" about asking a foreign government to break into Americans' emails. Instead of backing off, he doubled down. "If Russia or China or any other country has those emails, I mean, to be honest with you, I'd love to see them," he said. He also refused to tell Putin not to try to interfere in the election: "I'm not going to tell Putin what to do; why should I tell Putin what to do?" This was no joke.
Despite Trump's attempts to cover for Putin, cybersecurity experts and U.S. intelligence officials were confident that the Russians were behind the hack. There still wasn't official consensus about whether their goal was to undermine public confidence in America's democratic institutions or if Putin was actively trying to derail my candidacy and help elect Trump. But I didn't have any doubt. And the timing of the public disclosure, as well as the specific nature of the material (did Russian intelligence really understand the ins and outs of DNC politics and the decisions of Debbie Wasserman Schultz?), raised the strong possibility that the Russians had gotten help from someone with experience in American politics—a truly alarming prospect.
We were doing a million things at once that week. The convention was all-consuming. So it was hard to stop and focus on the gravity of what was happening. But I realized we had crossed a line. This wasn't the normal rough-and-tumble of politics. This was—there's no other word for it—war. I told my team I thought we were at a "break glass" moment. "We're under attack," I said. It was time to take a much more aggressive public posture. Robby Mook did a round of interviews in which he pointed the finger squarely at Russia. He said they weren't trying just to create chaos, they were actively trying to help Trump. That shouldn't have been particularly controversial, but Robby was treated like a kook. Jennifer Palmieri and Jake Sullivan held a series of background briefings for news networks to explain in more detail. After the election, Jennifer wrote an op-ed in the Washington Post titled "The Clinton Campaign Warned You About Russia. But Nobody Listened to Us." She recalled how journalists were generally more interested in the gossipy content of the stolen emails rather than the prospect that a foreign power was trying to manipulate our election. The press treated our warnings about Russia like it was spin we'd cooked up to distract from embarrassing revelations—a view actively encouraged by the Trump campaign. The media was accustomed to Trump peddling crazy conspiracy theories—like that Ted Cruz's dad helped kill John F. Kennedy—and it acted as if the Russian hacking was "our" conspiracy theory, a tidy false equivalency that let reporters and pundits sleep well at night. As Matt Yglesias of the news site Vox described it later, most journalists thought the argument that Moscow was trying to help Trump was "outlandish and borderline absurd," and our attempt to raise the alarm "was just too aggressive, self-serving, and a little far-fetched."
Maybe the press wouldn't listen to us, but I figured they would listen to respected intelligence officials. On August 5, Mike Morell, the former acting director of the CIA, wrote a highly unusual op-ed in the New York Times. Despite being a strictly nonpartisan career professional, he said that he had decided to endorse me for President because of my strong record on national security, including my role in bringing Osama bin Laden to justice. By contrast, he said Trump was "not only unqualified for the job, but he may well pose a threat to our national security." Coming from America's former top spy, that was a shocking statement. But it paled compared with what Morell said next. Putin, he noted, was a career intelligence officer "trained to identify vulnerabilities in an individual and to exploit them." And here's the shocking part: "In the intelligence business," Morell said, "we would say that Mr. Putin had recruited Mr. Trump as an unwitting agent of the Russian Federation."
Morell's argument was not that Trump or his campaign was conspiring illegally with the Russians to rig the election—although he certainly didn't rule it out. It was that Putin was manipulating Trump into taking policy positions that would help Russia and hurt America, including "endorsing Russian espionage against the United States, supporting Russia's annexation of Crimea, and giving a green light to a possible Russian invasion of the Baltic States." That's an important point to keep in mind, because it often gets lost amid the intense focus on potential criminal acts. Even without a secret conspiracy, there was plenty of troubling pro-Putin behavior right out in the open.
Morell's op-ed was the equivalent of pulling the fire alarm in a crowded building. And yet, somehow, most in the media—and many voters—continued to ignore the danger staring us in the face.
### Snakes!
I was not shocked to see the connection between WikiLeaks and the Russian intelligence services. At least that helped further discredit its odious leader, Julian Assange. In my view, Assange is a hypocrite who deserves to be held accountable for his actions. He claims to be a champion of transparency, but for many years, he's been helpful to Putin, one of the most repressive and least transparent autocrats in the world. It's not just that WikiLeaks avoids publishing anything Putin won't like and instead targets Russia's adversaries—Assange actually hosted a television show on RT, Putin's propaganda network, and receives adoring coverage there. And if hypocrisy isn't bad enough, Assange was charged with rape in Sweden. To avoid facing those charges, he jumped bail and fled to the Ecuadorian embassy in London. After years of waiting, Sweden eventually said it would no longer try to extradite him, but promised that if Assange came back to the country, the investigation could be reopened.
Assange, like Putin, has held a grudge against me for a long time. The bad blood goes back to 2010, when WikiLeaks published more than 250,000 stolen State Department cables, including many sensitive observations from our diplomats in the field. As Secretary of State, I was responsible for the safety of our officers around the world, and I knew that releasing those confidential reports put not only them in danger but also their foreign contacts—including human rights activists and dissidents who could face reprisals from their own governments. We had to move fast to evacuate vulnerable people, and, thankfully, we don't believe anyone was killed or jailed as a result. I thought Assange was reckless and wrong, and said so publicly.
The fact that these two old adversaries from my time as Secretary of State—Assange and Putin—seemed to be working together to damage my campaign was maddening. It was bad enough to have to go up against a billionaire opponent and the entire Republican Party; now I also had to take on these nefarious outside forces. The journalist Rebecca Traister observed once that there was "an Indiana Jones–style, 'It had to be snakes' inevitability" about me facing Trump. "Of course Hillary Clinton is going to have to run against a man who seems both to embody and have attracted the support of everything male, white, and angry about the ascension of women and black people in America," she wrote. I was up for the challenge. And I might add: Of course I had to face not just one America-bashing misogynist but three. Of course I'd have to get by Putin and Assange as well.
By midsummer 2016, the whole world knew that Trump and his team were cheering on the Russian attack on our democracy, and doing everything they could to exploit it. Trump never even tried to hide the fact that he was making common cause with Putin. But what if they were doing more than that? What if they were actually conspiring with Russian intelligence and WikiLeaks? There wasn't any evidence of that yet, but the coincidences were piling up.
Then, on August 8, Trump's longtime consigliere Roger Stone, who cut his teeth as one of Richard Nixon's "dirty tricksters," bragged to a group of Florida Republicans that he was in communication with Assange and predicted that an "October surprise" was coming. This was a shocking admission, made in public, from Trump's longest-serving political advisor. Stone made similar statements on August 12, 14, 15, and 18. On August 21, he tweeted, "Trust me, it will soon be Podesta's time in the barrel. #CrookedHillary". This was particularly notable because, as I mentioned earlier, we had determined there was a good chance that John's email might have been hacked, but didn't know for sure. Stone kept at it over the next few weeks, even calling Assange his "hero."
I wasn't the only one who noticed. At the end of August, Harry Reid, one of the congressional "gang of eight" who are briefed on the most sensitive intelligence matters, wrote a letter to FBI Director Comey that cited Stone's claims and asked for a full and thorough investigation. "The evidence of a direct connection between the Russian government and Donald Trump's presidential campaign continues to mount," Reid wrote. He also raised the prospect that there might be an attempt to falsify official election results. This was a reference to public reports that Russian hackers had penetrated voter registration databases in both Arizona and Illinois, prompting the FBI to warn state election officials across the country to upgrade their security. Like Morell's op-ed, Reid's letter was an attempt to shake the country out of its complacency and get the press, the administration, and all Americans focused on an urgent threat. It didn't work.
### Drip, Drip, Drip
As we headed into the fall, troubling reports and rumors continued to swirl. Paul Manafort resigned on August 19 amid growing questions about his financial ties to Russia. On September 5, the Washington Post reported that U.S. intelligence agencies now believed there was "a broad covert Russian operation in the United States to sow public distrust in the upcoming presidential election and in U.S. political institutions." That meant it was much bigger than the DNC hack.
We heard there was a federal interagency task force digging into the Trump team's financial ties, but no reporters could get it confirmed on the record. There was also talk that the FBI was looking into strange computer traffic between Trump Tower and a Russian bank. Reporters were chasing that one, too, and Slate's Franklin Foer eventually broke the story on October 31. Then there were the whispers going around Washington that the Russians had compromising information on Trump, possibly a salacious videotape from a Moscow hotel. But nobody had any proof.
At my first debate with Trump, on September 26, I went after him hard on Russia, and he continued to defend Putin and contradict the conclusions of our intelligence agencies, which they had shared with him personally. "I don't think anybody knows it was Russia that broke into the DNC," Trump insisted. "I mean, it could be Russia, but it could also be China. It could also be lots of other people. It also could be somebody sitting on their bed that weighs four hundred pounds, okay?" What was he talking about? A four-hundred-pound guy in his basement? Was he thinking of a character out of The Girl with the Dragon Tattoo? I wondered who told Trump to say that.
Meanwhile, Roger Stone continued to tweet warnings that WikiLeaks was preparing to drop another bomb on us, one that would destroy my campaign and land me in prison. He was such a bizarre character it was hard to know how seriously to take anything he said. But given what had happened already, who knew what other dirty tricks were coming our way.
Then came October 7, one of the most significant days of the entire campaign. I was in a prep session for the upcoming second debate, trying hard to stay focused on the task at hand.
The first thing that happened was that Jim Clapper, the Director of National Intelligence, and Jeh Johnson, the Secretary of Homeland Security, issued a brief statement that for the first time formally accused "Russia's senior-most officials" of ordering the hacking of the DNC. We already knew this, but the formal statement gave it the full weight of the U.S. government. Strikingly, the FBI did not join in the statement, and we later learned that Comey refused to do so, claiming it was inappropriate so close to the election. (Hmm.)
Then, at 4:00 P.M., the Washington Post broke the news of Trump's Access Hollywood tape, in which he bragged about sexually assaulting women. It was a catastrophe for Trump's campaign. Less than one hour later, WikiLeaks announced it had obtained fifty thousand of John Podesta's emails and published a first batch of about two thousand. It looked like an orchestrated attempt to change the subject and distract voters—and provided further reason to believe that WikiLeaks and its Russian patrons were very much in sync with the Trump campaign.
It turns out, Russian hackers had gained access to John's personal email account back in March, thanks to a successful phishing attack. WikiLeaks continued to release stolen emails almost every single day for the rest of the campaign. For a while, it seemed like the WikiLeaks gambit was failing. The Access Hollywood story dominated the headlines, put Trump on the defensive, and sent his Republican backers scurrying for cover. The press eagerly covered every stolen email that emerged—even reprinting John's favorite risotto recipe—but none of the stories monopolized the news cycle like the Trump tape.
I commiserated with John about the outrageous invasion of privacy—I was one of the few who knew what it felt like—but he took it in stride. He felt bad about some of the language he used. He felt even worse for the friends and colleagues who had sent him private messages and now had to see their words printed for all to see. And WikiLeaks hadn't bothered to redact personal information such as phone numbers and Social Security numbers, which victimized good people who deserved better.
In the end, though, most of John's emails were . . . boring. They revealed the nuts and bolts of a campaign at work, with staffers debating policies, editing speeches, and kibitzing about the daily ups and downs of the election. In fact, Tom Friedman of the New York Times wrote a column about how well the behind-the-scenes correspondence reflected on me and my team. "When I read WikiHillary, I hear a smart, pragmatic, center-left politician," he wrote, and "I am more convinced than ever she can be the President America needs today."
What was harder to see at the time was that the steady stream of stories guaranteed that "Clinton" and "emails" remained in the headlines up until Election Day. None of this had anything at all to do with my use of personal email at the State Department—nothing at all—but for many voters, it would all blend together. And that was before Jim Comey sent his misguided letter to Congress, which made it all much worse. As a result, we faced a perfect storm. And Trump did his best to amplify our problems, citing WikiLeaks more than 160 times in the final month of the campaign. He could barely contain his excitement whenever a new batch of stolen emails appeared.
Comparing the effects of WikiLeaks and Access Hollywood may prove the old Washington cliché about how the "drip, drip" of scandal can be even more damaging over time than a single really bad story. Trump's tape was like a bomb going off, and the damage was immediate and severe. But no other tapes emerged, so there was nowhere else for the story to go. Eventually the press and the public moved on. It's amazing how quickly the media metabolism works these days. By contrast, the WikiLeaks email dumps kept coming and coming. It was like Chinese water torture. No single day was that bad, but it added up, and we could never get past it. WikiLeaks played into people's fascination with "pulling back the curtain." Anything said behind closed doors is automatically considered more interesting, important, and honest than things said in public. It's even better if you have to do a little legwork and google around for the information. We sometimes joked that if we wanted the press to pay attention to our jobs plan, which I talked about endlessly to little avail, we should leak a private email about it. Only then would it be news worth covering.
WikiLeaks also helped accelerate the phenomenon that eventually came to be known as fake news. False story lines started appearing on Facebook, Reddit, Breitbart, Drudge Report, and other sites often claiming to be based on stolen emails. For example, WikiLeaks tweeted on November 6 that the Clinton Foundation paid for Chelsea's wedding, a totally false accusation, as the Washington Post's Glenn Kessler later verified in his Fact Checker column. Kessler, who's never been shy about criticizing me, heard from readers who said this lie helped convince them to vote for Trump. After the election, he investigated and found it to be "a claim lacking any evidence," and he urged readers "to be more careful consumers of the news." The lack of evidence didn't stop the New York Post and Fox News from repeating the lie and giving it mass circulation. That really got under my skin. Bill and I were proud to pay for Chelsea and Marc's wedding and we treasure every memory of it. Lies about me and Bill are one thing, but I can't stand to see lies about Chelsea. She doesn't deserve that.
Russia's propaganda networks, RT and Sputnik, were eager purveyors of fake news. For example, U.S. intelligence agencies later pointed to an August 2016 video produced by RT titled "How 100% of the Clintons' 'Charity' Went to . . . Themselves." It was another lie. Since Bill and I have released our tax returns going back decades, it's public record that since 2001 we've donated more than $23 million to charities such as the Elizabeth Glaser Pediatric AIDS Foundation, educational institutions, hospitals, churches, the Children's Defense Fund, and the Clinton Foundation. And none of us—not Bill, not Chelsea, not me—has ever taken any money from the foundation.
At the time, I was barely aware that such silly Russian smears were circulating on American social media. And yet, according to a U.S. Intelligence assessment, that one RT video alone was viewed more than nine million times, mostly on Facebook.
Even if I had known that, it would have been hard to believe that many voters would take any of it seriously. Still, reporting from BuzzFeed and others was finding that the reach of fake news on Facebook and other outlets was far wider than anyone expected, and that much of it was being generated in faraway countries such as Macedonia. The whole thing was bizarre. And Trump did all he could to help fake news spread and take root, repeating fake headlines from Russian propaganda outlets like Sputnik at his rallies and retweeting extremist memes.
The day before the election, President Obama was campaigning for me in Michigan (yes, we campaigned in Michigan!), and expressed the frustration we all felt: "As long as it's on Facebook and people can see it, as long as it's on social media, people start believing it," he said, "and it creates this dust cloud of nonsense." Nonsense was right.
On October 30, Harry Reid wrote another letter to Jim Comey, trying one last time to focus the nation's attention back on the unprecedented foreign intervention in our election. The former boxer from Searchlight, Nevada, knew we were in the fight of our lives, and he couldn't believe no one was paying attention. Harry had been briefed by intelligence officials and was frustrated they weren't informing the American people about what was really going on. "It has become clear that you possess explosive information about close ties and coordination between Donald Trump, his top advisors, and the Russian government," he wrote to Comey. "The public has a right to know this information." And yet Comey—who was only too eager to speak publicly about the investigation into my emails—continued to refuse to say a word about Trump and Russia.
I was worried that we'd see even more direct tampering on Election Day. But what more could we do? My campaign and I had spent months shouting into the wind. All that was left was to make our strongest case to voters and hope for the best.
### Dragnet
After the election, I tried to unplug, avoid the news, and not think too much about all this. But the universe didn't cooperate.
Just four days after the election, the Russian Deputy Foreign Minister bragged in an interview that his government had "contacts" with Trump's "immediate entourage" during the campaign. Both the Kremlin and Trump's people tried to walk back this remarkable admission, but the bell couldn't be unrung. A few days after that, President Obama ordered the Intelligence Community—the collection of the government's seventeen different intelligence agencies—to conduct a full review into Russian interference into the election.
Then, in early December, a twenty-eight-year-old man from North Carolina drove to Washington, D.C., with a Colt AR-15 assault rifle, a .38-caliber Colt revolver, and a knife. He had read on the internet that a popular local Washington pizzeria was secretly hosting a child sex abuse ring run by John Podesta and me. This particularly disgusting fake news got its start with an innocuous email released by WikiLeaks about John going out for pizza. It was quickly refracted through the dark corners of the internet and emerged as a blood-curdling conspiracy theory. Alex Jones, the right-wing talk show host effusively praised by Trump who claims that 9/11 was an inside job and the Sandy Hook massacre was a hoax, recorded a YouTube video about "all the children Hillary Clinton has personally murdered and chopped up and raped." Soon that young man from North Carolina was in his car on his way to Washington. When he got to the pizzeria, he searched everywhere for the children supposedly being held captive. There weren't any. He fired off one shot before being apprehended by police and eventually sentenced to four years in prison. Thankfully, no one was harmed. I was horrified. I immediately contacted a friend of mine who runs a bookstore on the same street. She told me that her employees also had been harassed and threatened by conspiracy nuts.
In early January, the Intelligence Community reported back to President Obama and published an unclassified version of its findings for the public. The headline was that Putin himself had ordered a covert operation with the goal of denigrating and defeating me, electing Trump, and undermining the American people's faith in the democratic process. That was no surprise to me or anyone else who had been paying attention, although it was notable that it was now the official view of the U.S. government. The real news, however, was that the Russian intervention had gone far beyond hacking email accounts and releasing files. Moscow had waged sophisticated information warfare on a massive scale, manipulating social media and flooding it with propaganda and fake news.
Soon it felt like every day there was a new revelation about the scope of the Russian operation, secret contacts with the Trump campaign, and an ongoing federal investigation digging into all of it. Congressional hearings began. The New York Times and the Washington Post competed to break scoop after scoop. I know I give the press a lot of grief, especially the Times, but this really was journalism at its finest.
I wasn't just a former candidate trying to figure out why she lost. I was also a former Secretary of State worried about our nation's national security. I couldn't resist following every twist and turn of the story as closely as possible. I read everything I could get my hands on. I called friends in Washington and Silicon Valley and consulted with national security experts and seasoned Russia hands. I learned more than I ever imagined about algorithms, "content farms," and search engine optimization. The voluminous file of clippings on my desk grew thicker and thicker. To keep it all straight, I started making lists of everything we knew about the unfolding scandal. At times, I felt like CIA agent Carrie Mathison on the TV show Homeland, desperately trying to get her arms around a sinister conspiracy and appearing more than a little frantic in the process.
That's not a good look for anyone, let alone a former Secretary of State. So instead, let me channel a TV show that I grew up watching as a kid in Park Ridge: Dragnet. "Just the facts, ma'am."
We've learned a lot about what the Russians did, what the Trump campaign did, and how the U.S. government responded. Let's go through it step-by-step.
### What the Feds Did
First, we've learned that the federal investigation started much earlier than was publicly known.
In late 2015, European intelligence agencies picked up contacts between Trump associates and Russian intelligence operatives. Communications intercepts by U.S. and allied intelligence seem to have continued throughout 2016. We know now that by July 2016, the FBI's elite National Security Division in Washington had started investigating whether the Trump campaign and the Russians were coordinating to influence the election. They have also been looking into Paul Manafort's financial ties to pro-Putin oligarchs.
In the summer of 2016, according to the Washington Post, the FBI convinced a special Foreign Intelligence Surveillance Court that there was probable cause to believe that Trump advisor Carter Page was acting as a Russian agent, and they received a warrant to monitor his communications. The FBI also began investigating a dossier prepared by a well-respected former British spy that contained explosive and salacious allegations about compromising information the Russians had on Trump. The Intelligence Community took the dossier seriously enough that it briefed both President Obama and President Elect Trump on its contents before the inauguration. By the spring of 2017, a federal grand jury was issuing subpoenas to business associates of Michael Flynn, who resigned as Trump's national security advisor after lying about his Russian contacts.
We've also learned a lot about how various parts of the U.S. government reacted differently to the intelligence coming in over the course of 2016 about ties between the Trump campaign and Russia. The CIA seems to have been most alarmed and was also convinced that the Russian goal was to help Trump and hurt me. As early as August 2016, CIA Director John Brennan called his counterpart in Moscow and warned him to stop interfering in the election. Brennan also individually briefed the "gang of eight" congressional leaders and shared his concerns. This explains why Harry Reid sought to galvanize public attention on the threat in his August letter.
We've learned that the FBI took a different approach. They launched an investigation in July 2016, but Director Comey didn't inform congressional leaders, was slower than Brennan to come to the conclusion that Russia's goal was electing Trump, and refused to join other intelligence agencies in issuing a joint statement on October 7 because he didn't want to interfere close to an election—something that certainly didn't stop him when it came to trumpeting news about the investigation into my emails. Sources within the FBI also convinced the New York Times to run a story saying they saw "no clear link to Russia," countering Franklin Foer's scoop in Slate about unusual computer traffic between Trump Tower and a Russian bank. This is one of the stories the Times's ombudsman later criticized.
It wasn't until after the election that the FBI finally came around and joined the rest of the Intelligence Community in putting out the January 2017 assessment that Russia had, in fact, been actively helping Trump. And in March 2017, Comey finally confirmed the existence of a federal investigation into possible coordination. Tyrone Gayle, one of my former communications aides, summed up how most of us felt hearing that news: "That sound you just heard was every ex-Clinton staffer banging their heads on the wall from California to D.C." Part of the frustration was knowing that the FBI's silence had helped Putin succeed and that more exposure could have given the American people the information they needed.
While Brennan and Reid had their hair on fire and Comey was dragging his feet, Republican Senate leader Mitch McConnell was actively playing defense for Trump and the Russians. We know now that even after he was fully briefed by the CIA, McConnell rejected the intelligence and warned the Obama administration that if it made any attempt to inform the public, he would attack it for playing politics. I can't think of a more shameful example of a national leader so blatantly putting partisanship over national security. McConnell knew better, but he did it anyway.
I know some former Obama administration officials have regrets about how this all unfolded. Former Homeland Security Secretary Jeh Johnson told the House Intelligence Committee in June 2017 that the administration didn't take a more aggressive public stance because it was concerned about reinforcing Trump's complaints that the election was "rigged" and being "perceived as taking sides in the election." Former Deputy National Security Advisor Ben Rhodes, whom I'd come to trust and value when we worked together in President Obama's first term, told the Washington Post that the Obama administration was focused on a traditional cyber threat, while "the Russians were playing this much bigger game" of multifaceted information warfare. "We weren't able to put all of those pieces together in real time," Ben said.
Mike McFaul, Obama's former Ambassador to Russia, summed it up in a concise tweet:
FACT: Russia violated our sovereignty during the 2016 election.
FACT: Obama exposed that attack.
OPINION: We should have focused on it more.
I understand the predicament the Obama administration faced, with McConnell threatening them and everyone assuming I was going to win regardless. Richard Clarke, President George W. Bush's top counterterrorism advisor on 9/11, has written about how hard it can be to heed warnings about threats that have never been seen before, and certainly it was hard to imagine the Russians would dare to conduct such a massive and unprecedented covert operation. And President Obama did privately warn Putin directly to back off.
I do wonder sometimes about what would have happened if President Obama had made a televised address to the nation in the fall of 2016 warning that our democracy was under attack. Maybe more Americans would have woken up to the threat in time. We'll never know. But what we do know for sure is that McConnell and other Republican leaders did everything they could to leave Americans in the dark and vulnerable to attack.
### What the Trump Team Did
Let's look at what we've learned since the election about the actions of the Trump team.
We know now there were many contacts during the campaign and the transition between Trump associates and Russians—in person, on the phone, and via text and email. Many of these interactions were with Ambassador Kislyak, who was thought to help oversee Russian intelligence operations in the United States, but they included other Russian officials and agents as well.
For example, Roger Stone, the longtime Trump political advisor who claimed that he was in touch with Julian Assange, suggested in August 2016 that information about John Podesta was going to come out. In October, Stone hinted Assange and WikiLeaks were going to release material that would be damaging to my campaign, and later admitted to also exchanging direct messages over Twitter with Guccifer 2.0, the front for Russian intelligence, after some of those messages were published by the website The Smoking Gun.
We also know now that in December 2016, Trump's son-in-law and senior advisor, Jared Kushner, met with Sergey Gorkov, the head of a Kremlin-controlled bank that is under U.S. sanctions and tied closely to Russian intelligence. The Washington Post caused a sensation with its report that Russian officials were discussing a proposal by Kushner to use Russian diplomatic facilities in America to communicate secretly with Moscow.
The New York Times reported that Russian intelligence attempted to recruit Carter Page, the Trump foreign policy advisor, as a spy back in 2013 (according to the report, the FBI believed Page did not know that the man who approached him was a spy). And according to Yahoo News, U.S. officials received intelligence reports that Carter Page met with a top Putin aide involved with intelligence.
Some Trump advisors failed to disclose or lied about their contacts with the Russians, including on applications for security clearances, which could be a federal crime. Attorney General Jeff Sessions lied to Congress about his contacts and later recused himself from the investigation. Michael Flynn lied about being in contact with Kislyak and then changed his story about whether they discussed dropping U.S. sanctions.
Reporting since the election has made clear that Trump and his top advisors have little or no interest in learning about the Russian covert operation against American democracy. Trump himself repeatedly called the whole thing a hoax—and at the same time, blamed Obama for not doing anything about it. As recently as July 2017, he continued to denigrate the Intelligence Community and claimed that countries other than Russia might be responsible for the DNC hack. Former Deputy Attorney General Sally Yates tweeted in response that Trump's "inexplicable refusal to confirm Russian election interference insults career intel pros & hinders our ability to prevent in future."
But there is one area where Trump's team seems to have been intently interested: rolling back U.S. sanctions against Russia. That's what Flynn was discussing with the Russian Ambassador. The Reuters news service reported that Senate investigators want to know whether Kushner discussed it in his meetings as well, including whether Russian banks would offer financial support to Trump associates and organizations in return. And as soon as the Trump team took control of the State Department, it started working on a plan to lift sanctions and return to Russia two compounds in Maryland and New York that the Obama administration had confiscated because they were bases for espionage. Career diplomats at State were so concerned that they alerted Congress. As of this writing, the Trump administration is exploring returning the compounds without any preconditions. All of this is significant because it makes it a lot easier to see how a quid pro quo with Russia might have worked.
We'll surely continue to learn more. But based on what's already in the public domain, we know that Trump and his team publicly cheered on the Russian operation and took maximum advantage of it. In so doing, they not only encouraged but actually helped along this attack on our democracy by a hostile foreign power.
### What the Russians Did
That brings us to what we've learned since the election about what the Russians did. We know already about the hacking and release of stolen messages via WikiLeaks, but that's just one part of a much larger effort. It turns out they also hacked the Democratic Congressional Campaign Committee and fed damaging information to local bloggers and reporters in various congressional districts across the country, which required sophistication. And that's just the beginning.
The official Intelligence Community report explained that the Russian propaganda strategy "blends covert intelligence operations—such as cyber activity—with overt efforts by Russian Government agencies, state-funded media, third-party intermediaries, and paid social media users, or 'trolls.' " Let's try to break down what it all means.
The simplest part is traditional state-run media; in this case, Russian networks such as RT and Sputnik. They use their global reach to push Kremlin talking points over the airwaves and social media, including malicious headlines like "Clinton and ISIS Funded by Same Money." Sputnik frequently used the same Twitter hashtag as Trump: #CrookedHillary. It's hard to know exactly how wide of a reach RT has. A Daily Beast article reported on claims that it had exaggerated its stats. It's probably more than you'd think (maybe hundreds of thousands) but not enough that it would have a big impact on an election by itself. But when RT propaganda gets picked up and repeated by American media outlets such as Fox News, Breitbart, and Alex Jones's Infowars, and posted on Facebook, its reach expands dramatically. That happened frequently during the campaign. Trump and his team also helped amplify Russian stories, giving them an even bigger megaphone.
The Russians also generated propaganda in less traditional ways, including thousands of fake news sites and individual internet "trolls" who posted attacks on Facebook and Twitter. As the Intelligence Community reported, "Russia used trolls as well as RT as part of its influence efforts to denigrate Secretary Clinton . . . some social media accounts that appear to be tied to Russia's professional trolls—because they previously were devoted to supporting Russian actions in Ukraine—started to advocate for President Elect Trump as early as December 2015." Some of the stories created by trolls were blatantly false, like the one about the pope endorsing Trump, but others were simply misleading attacks on me or puff pieces about Trump. Much of this content was then fed into the same amplification process, pushed along by RT and then picked up by American outlets such as Fox.
The Russians wanted to be sure that impressionable voters in key swing states actually saw their propaganda. So they set out to game the internet.
Much of what we see online is governed by a series of algorithms that determine what content appears in our Facebook and Twitter feeds, Google search results, and so on. One factor for these algorithms is popularity. If lots of users share the same post or click on the same link—and if key "influencers" with large personal networks do as well—then it's more likely to pop up on your screen. To manipulate this process, the Russians "flooded the zone" with a vast network of fake Twitter and Facebook accounts, some carefully designed to appear like American swing voters. Some of these accounts were run by trolls (real live people), and others were automated, but the goal was the same: to artificially boost the volume and popularity of Russian and right-wing propaganda. The automated accounts are called "bots," short for robots. The Russians were not the only ones using them, but they took it to a whole other level. Researchers at the University of Southern California have found that nearly 20 percent of all political tweets sent between September 16 and October 21, 2016, were generated by bots. Many of them probably were Russian. These tactics, according to Senator Mark Warner, vice chair of the Intelligence Committee, could "overwhelm" search engines so that the voters' newsfeeds started showing headlines like "Hillary Clinton's Sick" or "Hillary Clinton's Stealing Money from the State Department."
According to Facebook, another key tactic is the creation of fake affinity groups or community pages that could drive conversations online and draw in unwitting users. Imagine, for example, a fake Black Lives Matter group created to push malicious attacks linking Democrats to the KKK and slavery, with the goal of driving down African American turnout. The Russians did things like that. The similarity of their attacks to organic right-wing memes helped. For example, a prominent Trump supporter and evangelical bishop, Aubrey Shines, produced an online video attacking me because Democrats "gave this country slavery, the KKK, Jim Crow laws." This charge was hugely amplified by the conservative media company Sinclair Broadcast Group, which distributed it to all of its 173 local television stations across the country, along with other right-wing propaganda. Sinclair is now poised to grow to 223 stations. It would reach an estimated 72 percent of American households.
When I learned about these fake groups spreading across Facebook and poisoning our country's political dialogue, I couldn't help but think about the millions of my supporters who felt so bullied and harassed on the internet that they made sure their online communities, such as Pantsuit Nation, were private. They deserved better, and so did our country.
Put all this together, and you've got multifaceted information warfare. Senator Mark Warner summed it up well: "The Russians employed thousands of paid internet trolls and botnets to push out disinformation and fake news at a high volume, focusing this material onto your Twitter and Facebook feeds and flooding our social media with misinformation," he said. "This fake news and disinformation was then hyped by the American media echo chamber and our own social media networks to reach and potentially influence millions of Americans."
It gets worse. According to Time magazine, the Russians targeted propaganda to undecided voters and to "soft" Clinton supporters who might be persuaded to stay home or support a third-party candidate—including by purchasing ads on Facebook. It's against the law to use foreign money to support a candidate, as well as for campaigns to coordinate with foreign entities, so a commissioner on the Federal Election Commission has called for a full investigation of this charge.
We know that swing voters were inundated. According to Senator Warner, "Women and African Americans were targeted in places like Wisconsin and Michigan." One study found that in Michigan alone, nearly half of all political news on Twitter in the final days before the election was false or misleading propaganda. Senator Warner has rightly asked: "How did they know to go to that level of detail in those kinds of jurisdictions?"
Interestingly, the Russians made a particular effort to target voters who had supported Bernie Sanders in the primaries, including by planting fake news on pro-Sanders message boards and Facebook groups and amplifying attacks by so-called Bernie Bros. Russian trolls posted stories about how I was a murderer, money launderer, and secretly had Parkinson's disease. I don't know why anyone would believe such things, even if you read it on Facebook—although it's often hard to tell on there what's a legitimate news article and what's not—but maybe if you're angry enough, you'll accept anything that reinforces your point of view. As the former head of the NSA, retired General Keith Alexander, explained to Congress, the Russian goal was clear: "What they were trying to do is drive a wedge within the Democratic Party between the Clinton group and the Sanders group and then within our nation between Republicans and Democrats." Perhaps this is one reason why third-party candidates received more than five million more votes in 2016 than they had in 2012. That was an aim of both the Russians and the Republicans, and it worked.
According to CNN, Time, and McClatchy, the Justice Department and Congress are examining whether the Trump campaign data analytics operation—led by Kushner—coordinated with the Russians to pull all this off. Congressman Adam Schiff, the top Democrat on the House Intelligence Committee, has said he wants to know whether they "coordinated in any way in terms of targeting or in terms of timing or in terms of any other measure." If they did, that also would be illegal.
Think this is bad? There's more. We knew during the campaign that Russian hackers had breached election systems in two states. Now we know that this effort was far more extensive than previously thought. In June 2017, officials from the Department of Homeland Security testified before Congress that election systems in as many as twenty-one states were targeted. Bloomberg News reported that the number could be as high as thirty-nine. According to a leaked NSA report, the accounts of more than a hundred local election officials across the country were also penetrated. In addition, hackers gained access to the software used by poll workers on Election Day. The goal of these intrusions seems to have been accessing voter registration information. Hackers attempted to delete or alter records of particular voters. They could also have used the data to better target their propaganda efforts. According to Time, investigators want to find out if any stolen voter information ended up with the Trump campaign.
I know that the slow unfolding of this news has inured many people to how shocking all this is. It feels a little like the frog in the pot that doesn't realize it's boiling because it happens so gradually. But step back and think about it: the Russians hacked our election systems. They got inside. They tried to delete or alter voter information. This should send a shiver down the spine of every American.
And why stop there? According to the Washington Post, the Russians used old-fashioned forgery to influence the election as well. The Post says Moscow surreptitiously got a fake document to the FBI that described a fabricated discussion between the chair of the Democratic National Committee and an aide to financier and liberal donor George Soros about how Attorney General Lynch had promised to go easy on me in the email investigation. It was a bizarre fantasy straight out of the fever swamp. Jim Comey may well have known the document was a forgery, but the Post says he was concerned that if it became public, it would still cause an outcry. Its existence, however fraudulent, provided him with a new justification to disregard long-standing protocol and hold his infamous July press conference disparaging me. I don't know what Comey was thinking, but the idea that the Russians could have manipulated him into such a damaging misstep is mind-boggling.
Finally, to add one more bit of cloak-and-dagger mystery to this whole story, a lot of Russian officials seem to have had unfortunate accidents since the election. On Election Day itself, an officer in the New York consulate was found dead. The first explanation was that he fell off a roof. Then the Russians said he had a heart attack. On December 26, a former KGB agent thought to have helped compile the salacious Trump dossier was found dead in his car in Moscow. On February 20, the Russian Ambassador to the United Nations died suddenly, also from a heart attack. Russian authorities have also arrested a cybersecurity expert and two intelligence officials who worked on cyber operations and accused them of spying for the United States. All I can say is that working for Putin must be a stressful job.
If all this sounds unbelievable, I know how you feel. It's like something out of one of the spy novels my husband stays up all night reading. Even knowing what the Russians did in Ukraine, I was still shocked that they would wage large-scale covert warfare against the United States. But the evidence is overwhelming, and the Intelligence Community assessment is definitive.
What's more, we know now that the Russians have mounted similar operations in other Western democracies. After the U.S. election, Facebook found and removed tens of thousands of fake accounts in France and the United Kingdom. In Germany, members of Parliament have been hacked. Denmark and Norway say the Russians breached key ministries. The Netherlands turned off election computers and decided to count every vote by hand. And most notably, in France, Emmanuel Macron's campaign was hit by a massive cyberattack just before the presidential election that sparked immediately comparisons with the operation against me. But because the French had watched what happened in America, they were better prepared. Macron's team responded to Russian phishing attacks with false passwords, and they seeded fake documents in with their other files, all in an attempt to confuse and slow down the hackers. When a trove of stolen Macron emails did appear online, the French media refused to provide the kind of sensationalized coverage we saw here, in part because of a law in France that guards against that happening close to an election. French voters also seem to have learned from our mistakes, and they soundly rejected Le Pen, the right-wing pro-Moscow candidate. I take some comfort knowing that our misfortune helped protect France and other democracies. That's something, at least.
### The War on Truth
As I noted at the beginning of this chapter, one reason the Russian misinformation campaign was successful was that our country's natural defenses had been worn down over several years by powerful interests that sought to make it harder for Americans to distinguish between truth and lies. If you feel like it's gotten tougher to separate out fringe voices from credible journalists, especially online, or you find yourself arguing more and more with people over what should be knowable facts, you're not going crazy. There has been a concerted effort to discredit mainstream sources of information, create an echo chamber to amplify fringe conspiracy theories, and undermine Americans' grasp of objective truth. The McClatchy news service says federal investigators are looking into whether there were direct links between the Russian propaganda war and right-wing organizations such as Breitbart and InfoWars. But even if no direct ties ever come to light, we need to understand how the right-wing war on truth opened the door to the Russian attack.
After the election, a former conservative talk radio host in Wisconsin named Charlie Sykes came forward to explain how this worked. For years, he said, right-wing media and politicians conditioned their supporters to distrust anything they heard from the mainstream media, while pushing paranoid conspiracy theories from people such as Alex Jones and Trump himself—the chief promoter of the racist "birther" lie. "The price turned out to be far higher than I imagined," Sykes said. "The cumulative effect of the attacks was to delegitimize" the mainstream media and "essentially destroy much of the right's immunity to false information." This was useful for Trump when he became a candidate, because it helped him both deflect negative stories from mainstream sources and find a receptive audience for false attacks against me. It did the same for the Russians. And Trump has kept at it in the White House. "All administrations lie, but what we are seeing here is an attack on credibility itself," Sykes said. He quoted Garry Kasparov, the Russian chess grandmaster and Putin opponent who said, "The point of modern propaganda isn't only to misinform or push an agenda. It is to exhaust your critical thinking, to annihilate truth."
Rupert Murdoch and the late Roger Ailes probably did more than anyone else to make all this possible. For years, Fox News has been the most powerful and prominent platform for the right-wing war on truth. Ailes, a former advisor to Richard Nixon, built Fox by demonizing and delegitimizing mainstream media that tried to adhere to traditional standards of objectivity and accuracy. Fox gave a giant megaphone to voices claiming climate change was fake science, the falling unemployment rate was phony math, and you couldn't trust Barack Obama's birth certificate. Ailes and Fox were so successful in polarizing the audience that by 2016, most liberals and conservatives got their news from distinctly different sources and no longer shared a common set of facts.
During the Obama years, the Breitbart News Network, backed by Robert and Rebekah Mercer and led by their advisor Steve Bannon, who is now Trump's top strategist, emerged to give Fox a run for its money. According to the Southern Poverty Law Center, Breitbart embraces "ideas on the extremist fringe of the conservative right." To give you a flavor, here are a few memorable Breitbart headlines:
BIRTH CONTROL MAKES WOMEN UNATTRACTIVE AND CRAZY
* * *
THERE'S NO HIRING BIAS AGAINST WOMEN IN TECH, THEY JUST SUCK AT INTERVIEWS
* * *
GLOBAL TEMPERATURES PLUNGE. ICY SILENCE FROM CLIMATE ALARMISTS
* * *
NAACP JOINS SOROS ARMY PLOTTING DC DISRUPTIONS, CIVIL DISOBEDIENCE, MASS ARRESTS
* * *
HOIST IT HIGH AND PROUD: THE CONFEDERATE FLAG PROCLAIMS A GLORIOUS HERITAGE
* * *
FACT CHECK: WERE OBAMA AND HILLARY FOUNDERS OF ISIS? YOU BET
This would be funny if it wasn't so scary. This kind of garbage "conditioned" Americans, to use Charlie Sykes's word, to accept the Russian propaganda that flooded our country in 2016.
Robert Mercer is a key figure to understand. A computer scientist, Mercer made billions of dollars by applying complex algorithms and data analysis to the financial markets. The hedge fund he helps run, Renaissance Technologies, is wildly successful. By all accounts, Mercer is an extreme antigovernment right-winger. A profile in the New Yorker quoted one former Renaissance colleague as saying Mercer is "happy if people don't trust the government. And if the President's a bozo? He's fine with that. He wants it to all fall down." The New Yorker also reported that another former high-level Renaissance Technologies employee said Mercer hates Bill and me and once accused us of being part of a secret CIA drug-running scheme and of murdering our opponents. If you think these accusations sound batty, you're right. And this man is now one of the most powerful people in America.
Breitbart is only one of the organizations Mercer and his family control. Another is Cambridge Analytica, which has gained notoriety for using Facebook data to target voters for clients such as Trump. It's hard to separate reality from hype when it comes to Cambridge Analytica's track record, but it seems like a mistake to underestimate Mercer. As the New Yorker put it, "Having revolutionized the use of data on Wall Street," he "was eager to accomplish the same feat in the political realm." There's nothing inherently wrong with using big data and microtargeting—every campaign does it, including mine. The problem would come if the data were obtained or used improperly. After reports were published raising questions about whether Cambridge Analytica played a role in Brexit, British authorities are now investigating the company's alleged role with Leave.eu and whether Cambridge's techniques violated British and European privacy laws (which Cambridge denies).
Mercer is not alone. The Koch brothers, who run the second-largest privately held company in America, with extensive oil and gas holdings, have also invested huge sums of money, which has eroded the public's grasp on reality and advanced their ideological agenda. For example, they've spent tens of millions of dollars to fund a network of think tanks, foundations, and advocacy organizations to promote the false science of climate change denial and their agenda. We can expect more of that as the Kochs prepare to spend whatever it takes to consolidate their hold on state governments and expand their power in Washington.
And let's not forget Donald Trump himself. It took a little while for Mercer, the Kochs, and Fox News to realize that Trump could help take their war on truth to the next level, but their eventual support for his candidacy was invaluable. In many ways, Trump is the embodiment of everything they had been working toward, and the perfect Trojan horse for Putin. The journalist Masha Gessen, who covers Putin extensively, has observed: "It's not just that both Putin and Trump lie, it is that they lie in the same way and for the same purpose: blatantly, to assert power over truth itself."
### What Now?
In a Senate hearing in June 2017, Senator Angus King of Maine asked Jim Comey, "Was the Russian activity in the 2016 election a one-off proposition? Or is this part of a long-term strategy? Will they be back?"
"They'll be back," Comey replied emphatically. "It's not a Republican thing or Democratic thing. It really is an American thing."
He returned to the point a few minutes later. "We're talking about a foreign government that, using technical intrusion, lots of other methods, tried to shape the way we think, we vote, we act. That is a big deal. And people need to recognize it," Comey said. "It's not about Republicans or Democrats. They're coming after America."
Comey is absolutely right about this. The January 2017 Intelligence Community report called the Russian influence campaign a "new normal," and predicted Moscow would continue attacking the United States and our allies. Given the success Putin has had, we should expect interference in future elections and even more aggressive cyber and propaganda efforts. Sure enough, since the election, there are new reports that Russia has launched cyberattacks against the U.S. military, including targeting the social media accounts of thousands of American soldiers; that hackers have penetrated companies that run American nuclear power plants; and that Russia is expanding its spy networks inside the United States.
We should also expect the right-wing war on truth to continue. As Trump faces growing political and legal challenges, he and his allies will likely intensify their efforts to delegitimize the mainstream press, the judiciary, and anyone else who threatens his preferred version of reality.
Can anything be done to meet these twin threats and protect our democracy? The answer is yes, if we take this seriously. In 1940, a time of much greater danger for our country, the writer John Buchan wrote, "We have been shaken out of our smugness and warned of a great peril, and in that warning lies our salvation. The dictators have done us a marvelous service to remind us of the true values of life." Americans today need to be similarly alert and determined.
Here are four steps that would help.
First, we need to get to the bottom of what really happened in 2016. Investigators and the press should keep digging. Based on how things are going, it's possible that, as often happens in Washington scandals, the alleged cover-up will become the most serious legal and political problem facing Trump. But no matter what happens, the American people will still need to know the truth about what the Russians did. Therefore, I believe the Special Counsel investigation should be complemented by an independent commission with subpoena power, like the one that investigated 9/11. It should provide a full public accounting of the attack against our country and make recommendations to improve security going forward. It's hard to understand how Republicans, so eager to set up a special committee to go after me over Benghazi, could block such a step.
Second, we need to get serious about cyber warfare. Government and the private sector need to work together more closely to improve our defenses. It will require significant investments to protect our networks and national infrastructure, and Corporate America needs to see this as an urgent imperative, because government can't do it alone. At the same time, our military and intelligence agencies should accelerate development of our own offensive cyber and information warfare capabilities, so that we are prepared to respond to aggression in kind, if need be.
Right now we do not have an effective deterrent to prevent cyber and information warfare the way we do with conventional and nuclear conflicts. Russia, China, and others believe they can operate in a so-called gray zone between peace and war, stealing our secrets, disrupting our elections, manipulating our politics, and harassing our citizens and businesses without facing serious repercussions. To change that calculus, I believe the United States should declare a new doctrine that states that a cyberattack on our vital national infrastructure will be treated as an act of war and met with a proportionate response.
Third, we need to get tough with Putin. He responds only to strength, so that's what we must demonstrate. It was gratifying to see Emmanuel Macron, the new French President, condemn Russian interference and propaganda while standing next to Putin at a press conference in Paris. If the French can do it, surely our own leaders can. Congress recently passed legislation over Trump's objections to ratchet up sanctions on Russia, and he reluctantly signed it. We should keep doing everything we can to isolate Putin. As former Secretary of State Condoleezza Rice said in May, "I'm appalled by what the Russians did, and we ought to find a way, ultimately, to punish it." The Obama administration proved with crippling sanctions against Iran that this kind of pressure can force our adversaries to change course. Russia is a much bigger and more powerful nation, but we have a lot of tools at our disposal, and even Putin is vulnerable to pressure. We also should strengthen NATO; help our allies reduce their dependence on Russian energy supplies, a key source of leverage for Putin; and arm the Ukrainian government so it can resist Moscow's aggression.
Fourth, we need to beat back the assault on truth and reason here at home and rebuild trust in our institutions. Tim Cook, CEO of Apple, has called for "a massive campaign" against fake news. "All of us technology companies need to create some tools that help diminish the volume of fake news," he said.
Companies such as Facebook, Twitter, and Google have already begun taking steps—adjusting algorithms, deactivating bot networks, and partnering with fact-checkers—but they must do more. Facebook is now the largest news platform in the world. With that awesome power comes great responsibility, which it must accept.
The mainstream media also has a responsibility to do more to debunk the lies infecting our public life and more directly hold the liars accountable. American journalists who eagerly and uncritically repeated whatever WikiLeaks dished out during the campaign could learn from the more responsible way the French press handled the hack of Macron. It will also be important to remain vigilant against misinformation like the fake leak that MSNBC's Rachel Maddow exposed in July 2017. "One way to stab in the heart aggressive American reporting on that subject is to lay traps for American journalists," she warned. And while there has been a lot of terrific reporting on the Russia scandal, we need to see the same rigor brought to the blizzard of deception from the administration and Republicans in Congress on everything from the budget to health care to climate change. (I love it when CNN does real-time fact-checking in its on-screen chyron. More of that, please.)
Speaking of Republicans, ultimately it's on them to stop enabling Trump and genuflecting to billionaires such as the Mercers and the Kochs. Aggressive campaign finance reform and a reinvigorated Federal Election Commission would help a lot. But unless principled Republicans step up, our democracy will continue to pay the price.
We all have to do our part if we're going to rebuild trust in one another and our government. As Clint Watts, a former FBI agent and senior fellow at the George Washington University Center for Cyber and Homeland Security, put it in his testimony before the Senate Intelligence Committee: "Until we get a firm basis on fact and fiction in our own country . . . we're going to have a big problem." It's up to each one of us to stay informed and make good decisions with rigorous reasoning and real deliberation. This is especially important when it comes to voting. Choose wisely and don't fall for scams. The same way you try to be careful about where you put your money or the car you buy, be careful and informed with your vote. And we all have the ability to break out of our echo chambers and engage with people who don't agree with us politically. We can keep an open mind and be willing to change our minds from time to time. Even if our outreach is rebuffed, it's worth it to keep trying. We're all going to share our American future together—better to do so with open hearts and outstretched hands than closed minds and clenched fists.
### Worse Than Watergate
As this story continues to unfold, there's a moment from the campaign that I keep replaying in my head over and over again. It was my third debate against Trump. He had just attacked me by quoting out of context a line from an email stolen by the Russians and released by WikiLeaks. The moderator, Chris Wallace of Fox News, was piling on as well. I thought the American people deserved to know what was really going on.
"The most important question of this evening, Chris, is finally, will Donald Trump admit and condemn that the Russians are doing this, and make it clear that he will not have the help of Putin in this election," I said. Trump retreated to his usual pro-Putin talking points: "He said nice things about me. If we got along well, that would be good." Then, turning to me, he added, "Putin, from everything I see, has no respect for this person."
"Well," I fired back, "that's because he would rather have a puppet as President of the United States." Trump seemed befuddled. "No puppet. No puppet. You're the puppet," he stammered.
I think about that line every time I see him on TV now. When he's yucking it up in the Oval Office with the Russian foreign minister and divulging classified information. When he's giving the cold shoulder to the German Chancellor, Angela Merkel, and other European allies. When he's lying through his teeth about Russia or anything else. "No puppet. No puppet. You're the puppet." This man is President of the United States. And no one is happier than Vladimir Putin.
* * *
* * *
In mid-July 2017, as I was putting the finishing touches on this book, Trump met with Putin in Germany. He not only didn't challenge him publicly on interfering in our election—he actually floated the idea of a joint cybersecurity unit, which is a classic example of asking the fox to guard the henhouse. Then, the news broke that Donald Trump Jr., Paul Manafort, and Jared Kushner met in June 2016 with a Russian lawyer connected to the Kremlin who promised to provide damaging information about me and wanted to discuss easing the sanctions on Russia included in the Magnitsky Act. Donald Trump Jr. admitted all this! He was disappointed the dirt didn't pan out the way he'd hoped. You can't make this stuff up. I'm sure there's more to come, so stay tuned.
I know some will dismiss everything in this chapter as me trying to shift blame for my loss in 2016. That's wrong. This is about the future. In the nineteenth century, nations fought two kinds of wars: on land and at sea. In the twentieth century, that expanded to the skies. In the twenty-first century, wars will increasingly be fought in cyberspace. Yet our President is too proud, too weak, or too shortsighted to face this threat head-on. No foreign power in modern history has attacked us with so few consequences, and that puts us all at risk.
I'm not saying this as a Democrat or as a former candidate. I'm saying this as someone who loves our country and will always be grateful for the blessings America has given to me and to the world. I'm worried. I'm worried about our democracy at home, with lies and corruption threatening our bedrock values, institutions, and the rule of law. And I'm worried about the future of democracy around the world. Generations of farsighted leaders on both sides of the Atlantic came together to build a new liberal order out of the ashes of World War II. They defended universal human rights, defied totalitarianism, and delivered unprecedented peace, prosperity, and freedom. As Americans, that is our inheritance. We should be proud of it and we should protect it. But now, between Trump and Putin, all that is at risk.
In June 2017, Jim Clapper was asked how the Russia scandal compared with Watergate. "I lived through Watergate. I was on active duty then in the Air Force. I was a young officer. It was a scary time," he replied. "I have to say, though, I think when you compare the two, Watergate pales, really, in my view, compared to what we're confronting now."
I also lived through Watergate. I was a young attorney working for the House Judiciary Committee's impeachment inquiry into Richard Nixon. I listened to the tapes. I dug into all the evidence of Nixon's crimes. And I agree with Jim Clapper. What we are facing now—an attack on our democracy by our principal foreign adversary, potentially aided and abetted by the President's own team—is much more serious.
In three words I can sum up everything I've learned about life: it goes on.
—Robert Frost
## Election Night
The night of November 8, 2016, started with me chasing my granddaughter and pretending to just miss catching her. Charlotte would squeal with glee and shout, "Again!" and I did it again. This went on for a while. It was almost enough to distract me from the television.
My family and senior staff had gathered at the Peninsula Hotel in New York to watch the returns. I've always dreaded election nights. There's nothing left to do but wait.
Hours earlier, in the predawn darkness, we finished a final whirlwind campaign swing that took me from Pittsburgh to Grand Rapids, Michigan, to a massive rally in Philadelphia with the Obamas and Bruce Springsteen; then to another rally in Raleigh, North Carolina, capped by a raucous late-night duet between Jon Bon Jovi and Lady Gaga; and finally back to Westchester, where a crowd of fired-up supporters met us on the tarmac even though it was close to 4:00 A.M.
I was exhausted but happy and enormously proud of my team. Standing with Bill, Chelsea, Barack, and Michelle in front of tens of thousands of people at Philadelphia's Independence Hall was one of the high points of the entire campaign. The President hugged me and whispered in my ear, "You've got this. I'm so proud of you."
After a quick stop at home to shower and change, Bill and I voted at an elementary school in Chappaqua. People pulled out their cell phones to text friends or discreetly shoot photos of me getting ready to vote. I walked over to the table staffed by diligent volunteers and signed my name in the book of eligible voters. We joked about whether I had identification to prove I was really me. (They didn't make me produce a photo ID, but many Americans would have to do so, and too many would be turned away that day.)
Campaigns are full of minor annoyances and major frustrations, but at the end of the day, it's inspiring to watch our democracy whir into action. When all the arguments are made and rallies are finished and TV ads have aired, it comes down to regular people lining up and having their say. I've always loved that quip from Winston Churchill about how democracy is the worst form of government—except for all the others. I still believe that, even when our system feels totally nuts. (Electoral College, I'm looking at you!)
It's quite something to see your name on a ballot. After twenty months, twelve debates, and more speeches and town halls than I could count, it all came down to this. All over the country, 136 million people were going to look at my name and Donald Trump's name and make a decision that would shape the future of the country and the world.
Before I could mark my ballot, a woman walked up and asked if I would take a selfie with her. (There really are no boundaries for the selfie obsession—not even the sanctity of voting is off limits!) I told her I would be delighted to, as soon as I was finished voting. I filled in the bubbles by my name and the down-ballot candidates, walked the ballot over to the scanner, slid it in, and watched it disappear.
I felt pride, humility, and nerves. Pride because I knew we had given everything we had. Humility because I knew the campaign would be the easy part; governing in this contentious time would be hard. And nerves because elections are always unpredictable. Most of the polling and analysis looked positive. The day before, my chief pollster, Joel Benenson sent me an encouraging report. He said I was leading Trump by 5 points in a direct head-to-head, and by 4 points when third parties were factored in. "You're going to bring this home," Joel told me. Still, I knew our campaign faced hurricane-force headwinds, thanks to Comey and the Russians. Anything was possible.
Voting turned out to be the highlight of the day.
When we arrived at the Peninsula Hotel in the late afternoon, the word was, "Things are looking good." The streets were clogged with police officers and Secret Service agents. Our hotel was just a block away from Trump Tower. Both candidates would be within a stone's throw from each other as the results came in.
I tried to keep my head clear. Unlike my husband, who devours every exit poll and stray anecdote on Election Days, I didn't want to hear it. I'm not convinced the breathless reporting during the day is reliable. And why stress about something you can no longer do anything about? In a few hours, we would all know the outcome.
* * *
* * *
For weeks, I had been carrying around heavy binders full of memos relating to the transition and the first decisions I would have to make as President Elect. There were Cabinet Secretaries to pick, a White House staff to hire, and a legislative agenda to begin working on with Congress. I loved diving into the details of governing, but in the homestretch of the campaign, it was hard to focus on anything past Election Day. Late at night, I would set aside time before bed to read a transition memo or review a few résumés. Sometimes I'd fall asleep halfway through. Other times I'd get fired up and call my team with some idea or plan I wanted us to get ready to pursue on Day One.
On Election Day, with the campaign all but finished, I had a chance to think in earnest about the work ahead. It was exciting. The hundreds of detailed policies we had proposed over the past twenty months hadn't gotten the press attention they deserved, but they provided a solid foundation for getting right to work tackling the nation's problems. I decided that first out of the gate would be an ambitious infrastructure program to create jobs while improving our roads, rails, airports, ports, mass transit systems, and broadband networks. There was a good chance the Democrats would retake the Senate, but I expected to face a hostile Republican majority in the House. In theory, infrastructure should have bipartisan appeal, but we'd learned that partisanship could overwhelm everything. So outreach would have to start right away.
The challenge went well beyond rounding up enough Republican votes to pass an infrastructure package. The election had further divided our country in troubling ways. Trust in government and in our fellow Americans was at historic lows. We were yelling at one another across deep fault lines of class, race, gender, region, and party. It would be my job to try to help bridge those divides and bring the country together. No President could do it alone, but it was important to set the right tone from the beginning. And I knew the press was poised to judge my transition and first hundred days on the basis of how well I reached out to disaffected Trump voters.
My first test—and opportunity—would be the speech on election night, which would be watched by tens of millions of Americans. It would be my final act as a candidate and my first act as President Elect. The advance staff, led by Greg Hale, had built an amazing set in the Javits Center in Midtown Manhattan. I would walk out beneath an actual glass ceiling and stand on a stage the shape of America. The podium would be right over Texas. When the votes were counted, we hoped the symbolic glass ceiling would be shattered forever. I had been thinking about what I wanted to say for a few weeks. My speechwriters Dan Schwerin and Megan Rooney had been working with Jake Sullivan and Jennifer Palmieri on a draft. I knew they also had a draft concession speech under way as well, but I preferred not to think much about that.
Once I got settled in our suite on the top floor of the Peninsula, I asked Dan and Megan to come up. Bill and Jake joined us, and we sat in a small office going over the latest draft. One challenge was how to balance the need to reach out to Trump voters and sound a note of reconciliation, while also giving my supporters the triumphant victory celebration they deserved. There was also history to consider. If everything went as we hoped, I would be giving this speech as the first woman elected President. We had to find a way to mark the significance of the moment without letting it overwhelm everything else.
Most of all, I wanted to reassure Americans about the strength of our democracy. The election had tested our faith in many ways. Trump had violated every norm in the book, including warning that he might not accept the results of the vote if it went against him. The Russians had interfered. So had the Director of the FBI, against long-standing Justice Department policy. And the news media had turned the whole thing into an absurd circus. A lot of Americans wondered what it all meant for our future. I wanted to answer those fears with a strong victory, a smooth transition, and an effective presidency that delivered real results. Winning with a broad coalition would help counter the idea that the country was hopelessly divided. I would argue that despite our differences, a strong majority of Americans had come together in defense of our core values.
We worked on an opening for the speech that would convey that confidence. The election, I would say, showed that "we will not be defined only by our differences. We will not be an 'us versus them' country. The American dream is big enough for everyone." I would promise to be a President for all Americans, not just those who voted for me, and I'd talk about how much I had learned over the course of the campaign by listening to people share their frustrations. I would be candid about how hard it had been to respond to the anger many felt and how painful it was to see our country so divided. But, I'd say, the outcome showed that "if you dig deep enough, through all the mud of politics, eventually you hit something hard and true: a foundation of fundamental values that unite us as Americans."
I wanted to end the speech on a personal note. Throughout the campaign, my mother's story had been an emotional touchstone. Her perseverance spoke to the perseverance our country needed to overcome its own adversity, as well as the long struggle for women's rights and opportunities. With help from the poet Jorie Graham, we had written a closing riff for the speech that made me tear up every time I read it. I want to share it here because, as you know, I never got a chance to deliver it that night:
This summer, a writer asked me: If I could go back in time and tell anyone in history about this milestone, who would it be? And the answer was easy: my mother Dorothy. You may have heard me talk about her difficult childhood. She was abandoned by her parents when she was just eight years old. They put her on a train to California, where she was mistreated by her grandparents and ended up out on her own, working as a housemaid. Yet she still found a way to offer me the boundless love and support she never received herself . . .
I think about my mother every day. Sometimes I think about her on that train. I wish I could walk down the aisle and find the little wooden seats where she sat, holding tight to her even younger sister, alone, terrified. She doesn't yet know how much she will suffer. She doesn't yet know she will find the strength to escape that suffering—that is still a long way off. The whole future is still unknown as she stares out at the vast country moving past her. I dream of going up to her, and sitting down next to her, taking her in my arms, and saying, "Look at me. Listen to me. You will survive. You will have a good family of your own, and three children. And as hard as it might be to imagine, your daughter will grow up and become the President of the United States."
I am as sure of this as anything I have ever known: America is the greatest country in the world. And, from tonight, going forward, together we will make America even greater than it has ever been—for each and every one of us.
The speechwriters went off to make final revisions, and I went back to the waiting game. The polls were starting to close on the East Coast, and results were coming in.
The first warning sign was North Carolina. President Obama had won it in 2008 but lost narrowly in 2012. We had campaigned aggressively there. Now things weren't looking good. It was early still, but black and Latino turnout wasn't as high as we'd hoped, and working-class white precincts likely to go for Trump seemed energized. The same was happening in Florida, the battleground state that in 2000 had decided the entire election. We had been hopeful that this time Florida would be the state that broke the Republicans' back and put our goal of 270 electoral votes within reach. The state's changing demographics, especially its growing Puerto Rican population around Orlando, as well as the pre–Election Day early vote numbers, seemed favorable to us. But when my campaign manager, Robby Mook, came into our suite with the latest numbers, I could tell he was nervous. Robby is as positive a person as you'll ever meet, so I figured the news must be bleak.
Soon the same story was replicated in other key states. In Ohio, the state that decided the 2004 election, things were downright bad. But we had expected that. I reminded myself we didn't have to win everywhere. We just needed to get to 270. Robby and John Podesta kept me and Bill up to date, but there wasn't much to say. All we could do was watch and wait.
Bill was full of nervous energy, chomping on an unlit cigar, calling our longtime friend Governor Terry McAuliffe in Virginia every ten minutes, and eagerly soaking up any information Robby could share. Chelsea and Marc were a calming presence, but they too were on edge. How could you not be? The waiting was excruciating. I decided to do the least likely thing in the world and take a nap. Hopefully, when I woke up, the picture would have improved. I was so bone-tired that even with all the stress, I was able to close my eyes and fall right asleep.
When I got up, the mood in the hotel had darkened considerably. Robby and John looked shaken. Old friends had gathered. Maggie Williams, Cheryl Mills, and Capricia Marshall were there. My brothers and their families were around. Someone sent out for whiskey. Someone else found ice cream—every flavor in the hotel kitchen.
I had won Virginia and Colorado, but Florida, North Carolina, Ohio, and Iowa were all long gone. Now all eyes were on Michigan, Pennsylvania, and Wisconsin, states that we'd counted on and that Democrats had won in every presidential election since 1992. We were getting killed in heavily white, working-class rural and exurban areas. To compensate, we had to run up big margins in the cities, especially Philadelphia, Pittsburgh, Detroit, and Milwaukee, and then everything would be decided in the suburbs. As the hours slipped by, the numbers got worse. Some of the urban precincts were slow to report, but it was getting harder and harder to see how we could find enough votes.
How had this happened? Certainly we'd faced an avalanche of challenges throughout the campaign. Jim Comey's letter eleven days before had knocked the wind out of us. But I thought we had clawed our way back. Things had felt good out on the road. The energy and enthusiasm had been electric. And all our models—as well as all the public polls and predictions—gave us an excellent chance at victory. Now it was slipping away. I felt shell-shocked. I hadn't prepared mentally for this at all. There had been no doomsday scenarios playing out in my head in the final days, no imagining what I might say if I lost. I just didn't think about it. But now it was as real as could be, and I was struggling to get my head around it. It was like all the air in the room had been sucked away, and I could barely breathe.
Not long after midnight, the Associated Press reported that I had won Nevada, which was a relief, and I had a good chance to prevail in New Hampshire, but it wouldn't be enough without Michigan, Wisconsin, and Pennsylvania. The experts were telling us that it might be so close that we'd need a recount or at least another day to sort everything out. After 1:00 A.M., I asked John Podesta to go over to the Javits Center to ask our supporters to go home and get some rest. Win, lose, or draw, I'd wait until Wednesday morning to speak.
Around the same time, John and I both got messages from the White House. President Obama was concerned that drawing out the process would be bad for the country. After so much hand-wringing about Trump undermining our democracy by not pledging to accept the results, the pressure was on us to do it right. If I was going to lose, the President wanted me to concede quickly and gracefully. It was hard to think straight, but I agreed with him. Certainly that's what I would have wanted had the shoe been on the other foot.
At 1:35 A.M., the AP called Pennsylvania for Trump. That was pretty much the ball game. Even with Wisconsin and Michigan outstanding, it was getting impossible to see a path to victory.
Soon there were reports that Trump was preparing to go to his own victory party at the nearby Hilton Hotel. It was time. I decided to make the call.
"Donald, it's Hillary." It was without a doubt one of the strangest moments of my life. I congratulated Trump and offered to do anything I could to make sure the transition was smooth. He said nice things about my family and our campaign. He may have said something about how hard it must have been to make the call, but it's all a blur now, so I can't say for certain. It was all perfectly nice and weirdly ordinary, like calling a neighbor to say you can't make it to his barbecue. It was mercifully brief.
Then I called President Obama. "I'm sorry for letting you down," I told him. My throat tightened. The President said everything right. He told me I'd run a strong campaign, that I had done a great deal for our country, that he was proud of me. He told me there was life after losing and that he and Michelle would be there for me. I hung up and sat quietly for a few moments. I was numb. It was all so shocking.
At 2:29 A.M., the AP called Wisconsin and the election for Trump. He went on TV not long afterward to declare victory.
I sat in the dining room of my hotel suite, surrounded by people I loved and trusted. They were all in as much pain and shock as I was. Just like that, everything we had worked for was gone.
It looked like I was going to win the popular vote, maybe by a significant margin. There was some comfort in that fact. It meant that a majority of Americans hadn't embraced Trump's "us versus them" campaign, and that despite all our troubles, more people chose our platform and vision for the future. I had been rejected—but also affirmed. It was surreal.
I blamed myself. My worst fears about my limitations as a candidate had come true. I had tried to learn the lessons of 2008, and in many ways ran a better, smarter campaign this time. But I had been unable to connect with the deep anger so many Americans felt or shake the perception that I was the candidate of the status quo. And look what they'd thrown at me. I wasn't just running against Donald Trump. I was up against the Russian intelligence apparatus, a misguided FBI director, and now the godforsaken Electoral College. Yes, we knew the rules going in. We knew the states we had to win. Yet, it was infuriating that for the second time in five elections, a Democrat would win more votes but be robbed by this archaic fluke of our constitutional system. I'd been saying since 2000 that the Electoral College gave disproportionate power to less populated states and therefore was profoundly undemocratic. It made a mockery of the principle of "One person, one vote." In a cruel twist of fate, the Founders had also created it as a bulwark against foreign interference in our democracy—Alexander Hamilton cited protecting against foreign influence as a justification for the Electoral College in Federalist Paper No. 68—and now it was handing victory to Vladimir Putin's preferred candidate.
In my head, I heard the vicious "Lock her up!" chants that had echoed through Trump's rallies. In our second debate, Trump had said that if he won, he'd send me to prison. Now he had won. I had no idea what to expect.
The speechwriters gingerly approached with a draft of a concession speech. I honestly wondered why anyone would want to hear from me ever again.
The draft was too combative. It spoke to the fears of millions of Americans about a new President who had campaigned on bigotry and resentment. It said that they weren't alone, that I would keep fighting for them even now that the election was over. Did people even want me to fight for them? Was there any point in making an argument now? Maybe I should just be gracious, concede, and walk away.
Jake pushed back. Yes, he said, being gracious is important. But if we believe what we've said for the past six months about the dangers this guy poses to our country, then you can't act like that's not true anymore. People are scared and worried about what he'll do to their families. They want to hear from you.
A spirited discussion ensued. Eventually I asked the speechwriters to take another crack at a draft that was shorter and more gracious but not sugarcoated.
Bill was watching Trump's speech on television. He couldn't believe it. Neither could I. Eventually everyone left, and it was just us. I hadn't cried yet, wasn't sure if I would. But I felt deeply and thoroughly exhausted, like I hadn't slept in ten years. We lay down on the bed and stared at the ceiling. Bill took my hand, and we just lay there.
* * *
* * *
In the morning, it was real. November 9 dawned raw and rainy. I tried to drink some orange juice, but I didn't have any appetite. I had a job to do. That's what I focused on. By the light of day, I saw more clearly what I needed to say.
The speechwriters came back with a new draft, and I told them I wanted to talk more about what it means to be a democracy. Yes, the peaceful transfer of power was one of our most important traditions—and the mere fact of my conceding honored that. But there's also the rule of law, equality, and freedom. We respect and cherish these things too, and we had to defend them. "Donald Trump is going to be our President," I would say. "We owe him an open mind and the chance to lead." But I would also challenge my supporters and all Americans to keep working for our vision of a better, stronger, fairer America. I was determined that my young staff and supporters not become discouraged. "This loss hurts," I would tell them. "But please, please never stop believing that fighting for what's right is worth it. It is always worth it."
Finally, I wanted to speak directly to the women and girls who had put their faith in me and my campaign. It pained me to think of how they must be feeling. Instead of making history and electing the first woman President, they now had to face a stinging rebuke and come to terms with the fact that the country had just elected someone who objectified women and bragged about sexual assault. A lot of women—and men—were waking up that morning asking whether America was still the country we had thought it was. Would there be a place for them in Trump's America? Would they be safe? Would they be valued and respected?
I couldn't answer those questions. I was asking them myself. But I could use this one last moment on the national stage to tell them how proud I had been to be their champion. I could say that while we didn't break that highest glass ceiling this time, "someday someone will—hopefully sooner than we might think right now." And I could say to all the little girls out there, with every ounce of conviction in my body: "Never doubt that you are valuable and powerful and deserving of every chance and opportunity in the world."
I got dressed and gathered my things. "One day you're going to have to show me pictures of what the stage looked like last night," I told Huma.
"It looked amazing," she replied, "built for a President."
It was time to go. The country was waiting, and this wasn't going to get any easier.
I thought about my mother. There was a time when I was very little, and a neighborhood bully started pushing me around. I ran home to hide, but my mother met me at the door. "There's no room for cowards in this house," she said. "Go back out there." The walk from my front door back to the street was one of the longest of my life. But I went. Mom was right, as usual.
I gathered my family, took a deep breath, and walked out the door.
Victory has a hundred fathers, but defeat is an orphan.
—John F. Kennedy
## Why
I've spent part of nearly every day since November 8, 2016, wrestling with a single question: Why did I lose? Sometimes it's hard to focus on anything else.
I go back over my own shortcomings and the mistakes we made. I take responsibility for all of them. You can blame the data, blame the message, blame anything you want—but I was the candidate. It was my campaign. Those were my decisions.
I also think about the strong headwinds we faced, including the rise of tribal politics in America and across the globe, the restlessness of a country looking for change, excessive coverage of my emails, the unprecedented late intervention by the director of the FBI, the sophisticated misinformation campaign directed from the Kremlin, and the avalanche of fake news. Those aren't excuses—they're things that happened, whether we like it or not.
I think about all that, and about our deeply divided country and our ability to live, work, and reason together.
And that's all before I finish my morning cup of coffee. Then it starts over again.
In the spring of 2017, I was asked by thoughtful journalists such as Nicholas Kristof, Christiane Amanpour, Rebecca Traister, and Kara Swisher to reflect on what happened in 2016 and what lessons all Americans—and Democrats in particular—can learn from my defeat.
This is an important discussion to have. It's not only about the past—not by a long shot. After successfully interfering in one presidential election, Russia will certainly try to do it again. And Democrats are engaged in a vital debate right now about the future of our party, which turns in no small part on the question of what went wrong in 2016 and how to fix it.
Here's an example of the sort of questions I was getting:
"Could the campaign have been better?" Christiane Amanpour asked me. "Where was your message? Do you take any personal responsibility?"
"I take absolute personal responsibility," I replied. "I was the candidate. I was the person who was on the ballot." Then I explained that while we didn't run a perfect campaign, Nate Silver, the widely respected statistician who correctly predicted the winner in 49 states in 2008 and all 50 in 2012, has said that we were on our way to winning until Jim Comey's October 28 letter derailed us. You can agree or disagree with that analysis, but it's what Silver's data said.
The reaction to my interviews was negative, to put it mildly.
"Dear Hillary Clinton, please stop talking about 2016," wrote one columnist in USA Today. CNN, still stuck in false equivalency mode, declared, "Clinton, Trump can't stop airing their 2016 grievances." And one New York Daily News columnist decided the appropriate response was: "Hey, Hillary Clinton, shut the f— up and go away already." Seriously, they printed that in the newspaper.
I understand why some people don't want to hear anything that sounds remotely like "relitigating" the election. People are tired. Some are traumatized. Others are focused on keeping the discussion about Russia in the national security realm and away from politics. I get all that. But it's important that we understand what really happened. Because that's the only way we can stop it from happening again.
I also understand why there's an insatiable demand in many quarters for me to take all the blame for losing the election on my own shoulders and quit talking about Comey, the Russians, fake news, sexism, or anything else. Many in the political media don't want to hear about how these things tipped the election in the final days. They say their beef is that I'm not taking responsibility for my mistakes—but I have, and I do again throughout this book. Their real problem is they can't bear to face their own role in helping elect Trump, from providing him free airtime to giving my emails three times more coverage than all the issues affecting people's lives combined.
Other candidates who have lost the presidency have been allowed—even encouraged—to discuss what went wrong and why. After John Kerry lost the election in 2004, he quite reasonably said that the release of a tape from Osama bin Laden a day before the election had a significant effect on the outcome of the race. The press was interested in what he had to say. They want me to stop talking.
If it's all my fault, then the media doesn't need to do any soul searching. Republicans can say Putin's meddling had no consequences. Democrats don't need to question their own assumptions and prescriptions. Everyone can just move on.
I wish it were that easy. But it's not. So I'm going to try to explain how I understand what happened, both the unexpected interventions that swung the race at the end, and the structural challenges that made it close to begin with. You don't have to agree with my take. But counter with evidence, with a real argument. Because we have to get this right.
Here goes.
### Common Critiques
The election was decided by 77,744 votes out of a total 136 million cast. If just 40,000 people across Wisconsin, Michigan, and Pennsylvania had changed their minds, I would have won. With a margin like that, everyone can have a pet theory about why I lost. It's difficult to rule anything out. But every theory needs to be tested against the evidence that I was winning until October 28, when Jim Comey injected emails back into the election.
For example, some critics have said that everything hinged on me not campaigning enough in the Midwest. And I suppose it is possible that a few more trips to Saginaw or a few more ads on the air in Waukesha could have tipped a couple thousand votes here and there.
But let's set the record straight. We always knew that the industrial Midwest was crucial to our success, just as it had been for Democrats for decades, and contrary to the popular narrative, we didn't ignore those states. In Pennsylvania, where public and private polls showed a competitive race similar to 2012, we had nearly 500 staff on the ground, 120 more than the Obama campaign deployed four years before. We spent 211 percent more on television ads in the state. And I held more than twenty-five campaign events there during the general election. We also blanketed Pennsylvania with high-profile surrogates like President Obama and Vice President Biden. In Michigan, where the polls showed us ahead but not by as much as we'd like, we had nearly 140 more staff on the ground than Obama did in 2012, and spent 166 percent more on television. I visited seven times during the general election. We lost both states, but no one can say we weren't doing everything possible to compete and win.
If there's one place where we were caught by surprise, it was Wisconsin. Polls showed us comfortably ahead, right up until the end. They also looked good for the Democrat running for Senate, Russ Feingold. We had 133 staff on the ground and spent nearly $3 million on TV, but if our data (or anyone else's) had shown we were in danger, of course we would have invested even more. I would have torn up my schedule, which was designed based on the best information we had, and camped out there. As it is, while I didn't visit Wisconsin in the fall, Tim Kaine, Joe Biden, Bernie Sanders, and other high-profile surrogates did. So what went wrong? We'll get to that. But bear in mind that Trump received roughly the same number of votes in Wisconsin that Mitt Romney did. There was no surge in Republican turnout. Instead, enough voters switched, stayed home, or went for third parties in the final days to cost me the state.
Here's the bottom line: I campaigned heavily across Pennsylvania, had an aggressive ground game and lots of advertising, and still lost by 44,000 votes, more than the margin in Wisconsin and Michigan combined. So it's just not credible that the best explanation for the outcome in those states—and therefore the election—was where I held rallies.
Another easy explanation that doesn't stand up to scrutiny is that I lost because I didn't have an economic message. Joe Biden said the Democratic Party in 2016 "did not talk about what it always stood for—and that was how to maintain a burgeoning middle class." He said, "You didn't hear a single solitary sentence in the last campaign about that guy working on the assembly line making sixty thousand bucks a year and a wife making $32,000 as a hostess in a restaurant." I find this fairly remarkable, considering that Joe himself campaigned for me all over the Midwest and talked plenty about the middle class.
Also, it's just not true. Not even close. Vox did an analysis of all my campaign events and found that I talked about jobs, workers, and the economy far more than anything else. As the Atlantic put it in a piece titled, "The Dangerous Myth That Hillary Clinton Ignored the Working Class," I ran on "the most comprehensively progressive economic platform of any presidential candidate in history" and talked more about jobs in my convention speech than Trump did in his, as well as in our first debate, which was watched by eighty-four million people.
Throughout the campaign we always tried to have a positive track of advertising on the air, laying out what I was for and where we needed to go economically. We did that even when we were also running spots highlighting Trump's unfitness for office. We actually filmed one ad outside the Milwaukee offices of a company called Johnson Controls, which was trying to get out of paying taxes in America by moving its headquarters overseas—what's known as a "corporate inversion." It was so cold that day I could barely feel my feet, but I insisted on doing it because I was furious about the shell game the company was playing at the expense of its workers and the American people. I talked about Johnson Controls' tax scheme virtually every day on the trail for months. So we can debate whether my economic message was effective, but you can't claim I didn't have one.
Here's one story that helps explain why this is so frustrating. The day after I accepted the nomination in Philadelphia, Bill and I hit the road with Tim Kaine and his wife, Anne, for a bus tour through factory towns across Pennsylvania and Ohio. It reminded me of our exhilarating bus trip in 1992 with Al and Tipper Gore. That was one of my favorite weeks of the entire '92 campaign. We met hardworking people, saw gorgeous country, and everywhere we went we felt the energy of a country ready for change. Twenty-four years later, I wanted to recapture that. We loaded onto our big blue bus, with "Stronger Together" emblazoned on the sides, and set out on a 635-mile journey. At every stop, Tim and I talked about plans to create jobs, raise wages, and support working families. In Johnstown, Pennsylvania, in rural Cambria County, we shared our ideas with steelworkers in a factory manufacturing wire for heavy industry. Afterward, one of the workers, a crane operator, told a reporter for the Philadelphia Inquirer that he didn't usually vote in presidential elections but might turn out this time because he liked what he heard. "I liked the idea of trying to get better wages for working-class people," he said. "We need them." It was music to my ears.
But you probably don't remember hearing anything about this bus tour. In fact, you may well have heard that I didn't campaign like this at all; that I ignored the Rust Belt, didn't have an economic message, and couldn't connect with working-class voters. Why the disconnect? The very same week that Tim and I were driving around Pennsylvania and Ohio, Donald Trump was picking a high-profile fight with the Khans, the grieving Gold Star parents of a fallen Muslim American war hero. That sucked up all the oxygen in the media. It was a short-term disaster for Trump, and his poll numbers tumbled. But it was also part of a pattern that over the long-term ensured that my economic message never got out and let Trump control the tempo of the race.
### Was I Doomed from the Start?
Some pundits have also said my campaign was doomed from the start, either because of my weaknesses as a candidate or because America was caught up in a historic wave of angry, tribal populism sweeping the world. Maybe. But don't forget that I won the popular vote by nearly three million, roughly the same margin by which George W. Bush defeated John Kerry in 2004. It's hard to see how that happens if I'm hopelessly out of step with the American people.
Still, as I've discussed throughout this book, I do think it's fair to say there was a fundamental mismatch between how I approach politics and what a lot of the country wanted to hear in 2016. I've learned that even the best plans and proposals can land on deaf ears when people are disillusioned by a broken political system and disgusted with politicians. When people are angry and looking for someone to blame, they don't want to hear your ten-point plan to create jobs and raise wages. They want you to be angry, too.
You can see the same dynamic in a lot of personal relationships. I have friends who often get frustrated with their spouses who, instead of listening to them vent about a problem and commiserating, jump straight into trying to solve it. That was my problem with many voters: I skipped the venting and went straight to the solving.
Moreover, I have come to terms with the fact that a lot of people—millions and millions of people—decided they just didn't like me. Imagine what that feels like. It hurts. And it's a hard thing to accept. But there's no getting around it.
Whenever I do a job, such as Senator or Secretary of State, people give me high ratings. But when I compete for a job—by running for office—everything changes. People remember years of partisan attacks that have painted me as dishonest and untrustworthy. Even when they're disproven, those attacks leave a residue. I've always tried to keep my head down and do good work and hope to be judged by the results. That's usually worked, but not this time.
It seems as if many Trump voters were actually voting against me, more than they were voting for him (53 percent to 44 percent, in a September Pew Research Center poll). In exit polls, a significant number of people said they thought Trump was unqualified or lacked the temperament to be President . . . yet voted for him anyway. Of the 61 percent of all voters who said he was unqualified, 17 percent still voted for him. Of the 63 percent who said he didn't have the right temperament, 19 percent voted for him. The exit polls found that 18 percent of all voters viewed both me and Trump negatively, but they went for him 47 percent to 30 percent. Their antipathy toward me must have been even stronger than their concerns about his qualifications and temperament.
I'm not surprised by these findings. Gallup compiled a word cloud depicting everything Americans read, saw, or heard about me during several months of the campaign. It was dominated by a single giant word: email. Much smaller, but also visible were the words lie and scandal. Interestingly, in Trump's word cloud, immigration and Mexico stand out much more than jobs or trade. More on that shortly.
I don't believe all the negative feelings about me were inevitable. After all, I had high approval ratings when I left the State Department. This was the result of a relentless barrage of political attacks and negative coverage. But I also know that it was my job to try to break through all that noise and convince the American people to vote for me. I wasn't able to do it.
So yes, I had my shortcomings as a candidate. And yes, there was indeed a global populist wave and an anti–third term tradition in America. But—and this is important for determining what tilted the outcome of the election—those structural factors didn't pop up as a big surprise at the end. They were in play throughout the campaign. They probably kept the race closer than was justified based on our contrasting policy proposals and conduct, my record in public office, and the achievements of the Obama administration. If these factors were decisive, however, I should have been behind the whole way. And yet, despite consistent headwinds, nearly every public and private poll over two years showed me ahead, often way ahead.
By the homestretch, after two conventions and three debates watched by record numbers of Americans, I had emerged with clear momentum and a solid lead. Vox's Ezra Klein called it "the most effective series of debate performances in modern political history." I was in a stronger position than President Obama had been four years before. So either all those surveys over all those months were wrong, or something changed in the final days of the race to shift enough voters in key states to make a difference.
Were all the polls wrong? We know now that some surveys were off, especially in Wisconsin, especially at the end. It's likely that some Trump voters refused to participate in surveys and so their feedback was missed, and that some people weren't truthful about their preferences. But overall, national polls in 2016 were slightly more accurate than they were in 2012. That year, the final polling average understated President Obama's actual victory by 3.1 points. In 2016, according to the website RealClearPolitics, the final average was off by just 1.2 points. In a race this close, that's not nothing. But it's hardly a massive error.
So no, all the polls weren't wrong. It's possible that my lead throughout the race was slightly overstated—but not significantly. It's reasonable to conclude, therefore, that something important and ultimately decisive happened at the very end.
### The Bottom Falls Out
The evidence backs up the idea that there was a late shift away from me and toward Trump and third-party candidates. My support was strong in early voting across the country, and early-vote turnout roughly matched what our models predicted. But things collapsed in the final days and on Election Day itself.
In real time, it was hard to appreciate how fragile our position was. As I mentioned earlier, Joel Benenson's polling showed a solid lead in the final week. Our data analytics team was also surveying thousands of people each night. "We have seen our margins tighten across the battleground states," Elan Kriegel reported on November 3. But, he continued, "our national toplines have been +3 each of the last four nights." We were up by the same 3-point margin in Michigan, Wisconsin, and Pennsylvania, he said. Democratic Senate campaigns and party committees were seeing similar numbers, and some were even more optimistic.
Exit polls would later find that voters who were still making up their minds in those final days broke strongly for Trump. In Pennsylvania, a state with no early voting allowed at all, the margin among late-deciders was 54 to 37. In Wisconsin, where 72 percent of people voted on Election Day, it was 59 to 30. In Michigan, where 73 percent of people voted on Election Day, it was 50 to 39. And the pattern extended beyond the Midwest. In Florida, late-deciders went for Trump 55 to 38. That late surge was enough to put all these states in Trump's column.
Normally, campaigns have a decent sense of how undecided voters are likely to break, based on their past vote history and demographics. And history shows that most people who tell pollsters they're considering a third-party candidate will "come home" in the end. In the final days of the 2016 campaign, the voters you would expect to return to the Republican Party did so. But that didn't happen on our side. Many Democratic-leaning voters flirting with third-party candidates ended up actually pulling the lever for them. And some undecided voters we expected to ultimately choose us went to Trump instead or stayed home.
That included suburban moderates who might have voted for Republicans in the past but didn't like Trump and had been looking for an acceptable alternative right up until the end. On Election Day, a lot of them held their noses and voted for him anyway. It's revealing to compare the results in the suburbs of Denver and Las Vegas, where the vast majority vote early and I did well enough to carry both Colorado and Nevada, with the results in the Philadelphia suburbs, where nearly everyone voted on Election Day. The final Franklin & Marshall Poll in Pennsylvania, based on interviews nearly all conducted before October 28, found I had a 36-point margin over Trump in the four counties of the Philadelphia suburbs, leading 64 percent to 28 percent. By Election Day, I only beat Trump there by about 13 points. That loss of suburban support in the final week meant I couldn't match Trump's strength in rural areas and ended up narrowly losing the state.
Working-class white women also moved en masse in the final days. Trump led among this group nearly the whole campaign, but according to the NBC–Wall Street Journal poll, I had closed to within just 4 points during the October debates. Then, in the final week, Trump's margin grew to 24 points.
### The Comey Effect
What happened in the homestretch that caused so many voters to turn away from me?
First, and most importantly, there was the unprecedented intervention by then FBI Director Jim Comey.
His October 28 letter about the investigation into my emails led to a week of wall-to-wall negative coverage. A look at five of the nation's top newspapers found that together they published 100 stories mentioning the email controversy in the days after Comey's letter, nearly half of them on the front page. In six out of seven mornings from October 29 to November 4, it was the lead story in the nation's news cycle. Trump understood that Comey's apparent imprimatur gave his "Crooked Hillary" attacks new credibility, and Republicans dumped at least $17 million in Comey-related ads into the battleground states. It worked.
On November 1 and 2, my campaign conducted focus groups with independent, swing voters in Philadelphia and Tampa, Florida. The undecideds weren't ready to jump to Trump yet, but in retrospect, the warning signs were blinking red. "I have concerns about this whole Weiner thing. I find it unsettling. I had been leaning toward Hillary, but now I just don't know," said one Florida voter. "I was never a fan of either one, but this email thing with Clinton has me concerned the past few days. Will they elect her and then impeach her? Was she giving away secret information?" said another.
Outside focus groups were hearing similar things. Researchers who track what consumers are talking about, essentially a word-of-mouth index, found "a sudden change," with a 17-point drop in net sentiment for me, and an 11-point rise for Trump. According to Brad Fay of Engagement Labs, which applies well-established consumer research techniques to study elections, "The change in word-of-mouth favorability metric was stunning, and much greater than the traditional opinion polling revealed."
Those concerns we heard in the focus groups help explain why Comey's letter was so devastating. From the beginning of the general election, we had understood the race to be a contest between voters' fear of risk and desire for change. Convincing Americans that electing Trump was just too big a risk was our best shot at overpowering the widespread desire for a change after eight years of Democratic control. In demographic terms, our strategy depended on compensating for expected weakness with working-class white voters (a trend that had been getting worse for Democrats for a long time) by doing better among college-educated suburban moderates—precisely the people most likely to be concerned about risk.
Before October 28, there was every reason to believe this strategy would work. Voters thought Trump was unqualified and temperamentally unfit. They worried he might blunder into a war. And they thought I was steady, qualified, and safe. Comey's letter turned that picture upside down. Now voters were worried my presidency would be dogged by more investigations, maybe even impeachment. It was "unsettling," as that Florida voter put it. When both candidates seemed risky, then the desire for change reasserted itself and undecideds shifted to Trump or a third party.
In the week that followed Comey's letter, Nate Silver found that my lead in national polling dropped by about 3 points, and my chances of winning the election shrunk from 81 percent to 65 percent. In the average battleground state, my lead was down to just 1.7 points—and the fact that there were few if any polls still in the field that late in the game in places such as Wisconsin meant that the damage could easily have been worse.
Then, on the Sunday afternoon before Election Day, Comey sent another letter explaining that, in fact, there was no new evidence to change his conclusion from July. By then it was too late. If anything, that second letter may have energized Trump supporters even more and made them more likely to turn out and vote against me. It also guaranteed that undecided voters saw two more days of headlines about emails and investigations.
Hours after Comey's second letter hit the news, Trump whipped up the outrage in a rally in Michigan: "Hillary Clinton is guilty. She knows it. The FBI knows it. The people know it," he said. "Now it's up to the American people to deliver justice at the ballot box on November 8." The crowd responded with loud chants of "Lock her up!"
Corey Lewandowski, Trump's former campaign manager, credited Comey's letter with reversing his candidate's fortunes. "With eleven days to go in this election cycle something amazing happened," he said. In his new book, Devil's Bargain: Steve Bannon, Donald Trump, and the Storming of the Presidency, Bloomberg News reporter Joshua Green reveals that the Trump campaign's data scientists thought the effect of Comey's letter was "pivotal." In an internal memo written five days before Election Day, they reported seeing "declining support for Clinton, shifting in favor of Mr. Trump" and predicted, "This may have a fundamental impact on the results." Sadly, they were right.
Silver, whose model had been more conservative than most throughout the race, concluded, "Clinton would almost certainly be President-Elect if the election had been held on Oct. 27 (the day before the Comey letter)." Professor Sam Wang, who runs the Princeton Election Consortium, called Comey's letter "a critical factor in the home stretch" and found a 4-point swing.
Here's a particularly stark way of understanding the impact: Even if Comey caused just 0.6 percent of Election Day voters to change their votes, and even if that swing only occurred in the Rust Belt, it would have been enough to shift the Electoral College from me to Trump.
This is why Paul Krugman, the Nobel Prize–winning economist and New York Times columnist, has started ironically tweeting "Thanks, Comey," every time he sees some new outrage from the Trump White House. Comey made a choice to excoriate me in public in July and then dramatically reopen the investigation on October 28, all while refusing to say a word about Trump and Russia. If not for those decisions, everything would have been different. Comey himself later said that he was "mildly nauseous" at the idea that he influenced the outcome of the election. Hearing that made me sick.
### From Russia with No Love
The second big factor that caused the bottom to fall out at the end of the race was the Russian plot to sabotage my campaign and help elect Trump. Michael Morell, the former acting director of the CIA, has described it as "the political equivalent of 9/11."
The emails Russia stole from John Podesta and provided to WikiLeaks ensured that the words Clinton and emails were in the headlines even before Comey's letter. The subterranean torrent of fake news added to the problem. For voters, the stories merged to create an overpowering fog of scandal and mistrust. Even if there was no fire, there was enough smoke to choke our campaign.
Because no evidence has emerged yet of direct vote tampering, some critics insist that Russian interference had no impact on the outcome at all. This is absurd. The Kremlin's information warfare was roughly equivalent to a hostile super PAC unleashing a major ad campaign, if not worse. Of course it had an impact. (And for those obsessed with actual tampering, since we keep learning more about Russian intrusions into our election systems, maybe this is what the administration and Secretaries of State across the country should be investigating instead of a nonexistent epidemic of voter fraud.)
Nate Silver's website FiveThirtyEight.com looked at Google searches as a measure of how much the WikiLeaks story broke through with actual voters. He found that—except for immediately after Comey sent his letter on October 28—there were more searches about WikiLeaks than the FBI during the final weeks of the race. That did make some sense. The mainstream media provided blanket coverage of Comey, so there was no need to search for more information about that. The WikiLeaks stories, however, could send searchers down deep internet rabbit holes.
Google searches about WikiLeaks were particularly high in swing areas with large numbers of undecided voters, like Cambria County in Pennsylvania and Appleton, Wisconsin. In other words, a lot of people were online trying to get to the bottom of these crazy claims and conspiracy theories before casting their votes. Too often, what they found was more misinformation and Russian-directed propaganda.
Together, the effects of Comey's letter and the Russian attack formed a devastating combination. Silver concluded after the election that if it hadn't been for these two late-breaking factors, I likely would have won Florida, Michigan, Wisconsin, and Pennsylvania by about 2 points. Instead, I lost all four by less than 1 point on average, and Michigan by just two-tenths of a point.
### What Explains Trump's Support?
All of this is depressing, infuriating, and ultimately unsatisfying. Outside interference may help explain why enough votes shifted in the final days to give the Electoral College to Trump. But it doesn't explain why the race was close to begin with, close enough that late movement in a few states could make the difference. It doesn't really explain how sixty-two million people—many of whom agreed Trump was unfit for the job—could vote for a man so manifestly unqualified to be President. This may be the more important question for understanding what's going on in our country right now.
Start with the 13.3 million Republicans who voted for Trump in the primaries. It's safe to say these are mostly hard-core supporters—the ones Trump was talking about when he said, "I could stand in the middle of Fifth Avenue and shoot somebody and I wouldn't lose voters." Thirteen million is a lot of people to strongly support someone most Americans think is unqualified and unfit, but they account for less than half of all Republican primary voters and less than 10 percent of all general election voters. It's a mistake to give those base voters more political weight than they deserve. More interesting and important is how Trump consolidated support among the much larger pool of voters beyond his base.
Besides antipathy toward me, probably the biggest factor pushing Trump skeptics into his camp was pure partisanship. There's an old saying that "Democrats fall in love, Republicans fall in line." That was proven true once again in 2016. I won 89 percent of Democratic voters. Despite the example of a few courageous "Never Trumpers," Trump won 90 percent of Republican voters. Many of them preferred a different candidate in the primaries. Many were surely disgusted by his outrageous behavior, including his treatment of women. Yet when it came down to it, the R next to his name was more important than anything else. Maybe this was about the Supreme Court, or the assumption that he would end up rubber-stamping the congressional GOP's agenda, especially big tax cuts for the rich. Maybe it reflects a deeper partisan element in our politics.
Either way, it stands in stark contrast to what happened in the French election in 2017, when conservatives and socialists alike crossed party lines and rallied behind centrist Emmanuel Macron to stop the extremist Marine Le Pen. In France, patriotism trumped partisanship. Some analysts say French voters watched what happened here and acted to stop it there. So did the Dutch in their election, defeating the right-wing nationalist Geert Wilders. Of course, it helps when the candidate who gets the most votes wins the election. What an idea! If our voters had known more about what Putin was doing on Trump's behalf, would it have made a difference? All I can say is that I believe Americans are just as patriotic as the French and the Dutch.
Partisanship is powerful, but it was far from the only factor fueling Trump's support. As I noted earlier, a desire for change was also important. Exit polls tell us that 39 percent of voters said the ability to bring change was the most important quality in a candidate, and 82 percent of them supported Trump. By comparison, 22 percent of voters said having the "right experience" was most important, and they went for me 90 to 7. The 20 percent who said "good judgment" was most important supported me 65 to 25. And the 15 percent who wanted a candidate who "cares about me" went 57 to 34 for me. In other words, "change" voters provided the bulk of Trump's support.
Change can mean different things to different people. But as I've noted, this was a challenge I grappled with from the very beginning. History shows how hard it is for a party to hold on to the White House for three terms, even after successful presidencies. I castigated Republican obstruction in Congress and offered lots of solutions to make the economy fairer and politics cleaner, but I never escaped being pigeonholed as the candidate of continuity rather than change. Certainly, if voters wanted to "shake things up" or "burn it all down," they were more likely to choose Donald Trump over me. They weren't in any mood to remember that great old Texas saying from Sam Rayburn, the former Speaker of the House: "Any jackass can kick down a barn. It takes a good carpenter to build one."
In polls throughout the campaign, we asked voters what they thought of President Obama and if they wanted to continue in the same direction or go in a fundamentally different direction. You might expect the answers to be linked. And yet, while voters consistently gave the President high marks—in fact, Obama's popularity continued to rise throughout 2016, as did economic forecasts—they just as consistently said they were ready for a new direction. That may show the power of the impulse for change, but it also shows how complicated this is. One might also ask: Why were the vast majority of members of Congress reelected? Incumbents have advantages and gerrymandering has given many of them safe seats, but if there was a real "throw the bums out" wave in this election, we would have seen it down ballot as well.
So, yes, a desire for change was an important factor, but to understand what this was really about we have to look deeper.
### Economic Anxiety or Bigotry
Most postgame analysis has weighed two competing theories: either it was economic anxiety or it was bigotry. A lot of data point toward the latter, but ultimately this is a false choice that misses the complexity of the situation.
Let's start with this: the idea that the 2016 election was purely about economic anxiety just isn't supported by the evidence. There's a perception that Trump was the tribune of the working class while I was the candidate of the elites. And it's true that there was a big divide in this election between voters with a college degree and those without. But this doesn't line up neatly with income levels. There are a lot of middle- and upper-class people without a college degree. As the Washington Post explained in a piece titled, "It's Time to Bust the Myth: Most Trump Voters Were Not Working Class," nearly 60 percent of Trump supporters without a college degree were in the top half of the income distribution. The average income of a Trump voter during the primaries was $72,000, which is higher than for most Americans. And in the general election, voters with incomes below $50,000 preferred me by 12 points.
It's surely true that many blue-collar white voters in Rust Belt communities did like what Trump had to say on the economy. Exit polls found that voters who thought the national economy was in poor shape strongly supported Trump. But that wasn't necessarily their most compelling concern. The same exit polls found that voters who thought the economy was the most important issue in the election (52 percent nationwide) preferred me by a margin of 11 points. This was also true in the key battlegrounds. In Michigan, voters who cared most about the economy went for me 51 to 43. In Wisconsin, it was 53 to 42. In Pennsylvania, 50 to 46. To be fair, there are other ways to look at the numbers. Many Trump supporters who told pollsters they cared most passionately about other issues—especially terrorism and immigration—almost certainly preferred Trump on the economy as well. Nonetheless, the story on the economy is a lot more nuanced than the postelection narrative would have you believe.
Some supporters of Bernie Sanders have argued that if I had veered further left and run a more populist campaign we would have done better in the Rust Belt. I don't believe it. Russ Feingold ran a passionately populist campaign for Senate in Wisconsin and lost by much more than I did, while a champion of free trade, Senator Rob Portman, outperformed Trump in Ohio. Scott Walker, the right-wing Governor of Wisconsin, has won elections there by busting unions and catering to the resentments of conservative rural voters, not by denouncing trade deals and corporations. Sanders himself had a chance to test out his appeal during the primaries, and he ended up losing to me by nearly four million votes—including in Ohio and Pennsylvania. And that was without any pummeling by the Republican attack machine that would have savaged him in a general election.
That said, a small but still significant number of left-wing voters may well have thrown the election to Trump. Jill Stein, the Green Party candidate, called me and my policies "much scarier than Donald Trump" and praised his pro-Russia stance. This isn't surprising, considering that Stein sat with Putin and Michael Flynn at the infamous Moscow dinner in 2015 celebrating the Kremlin's propaganda network RT, and later said she and Putin agreed "on many issues." Stein wouldn't be worth mentioning, except for the fact that she won thirty-one thousand votes in Wisconsin, where Trump's margin was smaller than twenty-three thousand. In Michigan, she won fifty-one thousand votes, while Trump's margin was just over ten thousand. In Pennsylvania, she won nearly fifty thousand votes, and Trump's margin was roughly forty-four thousand. So in each state, there were more than enough Stein voters to swing the result, just like Ralph Nader did in Florida and New Hampshire in 2000. Maybe, like actress Susan Sarandon, Stein thinks electing Trump will hasten "the revolution." Who knows? By contrast, former Massachusetts Governor Bill Weld, a Republican who ran for Vice President on the Libertarian ticket topped by Gary Johnson, told his supporters toward the end that if they lived in swing states they should vote for me. If more third-party voters had listened to Bill Weld, Trump would not be President.
So, if arguments about the power of Trump's economic appeal are overstated, what about his exploitation of racial and cultural anxiety?
Since the election, study after study has suggested that these factors are essential to understanding what happened in the election.
In June 2017, the Voter Study Group, a consortium of academic researchers, published a major new survey that tracked the same eight thousand voters from 2012 to 2016. "What stands out most," concluded George Washington University professor John Sides, are "attitudes about immigration, feelings toward black people, and feelings toward Muslims." Data from the gold standard American National Election Studies also showed that resentment toward these groups was a better predictor of Trump support than economic concerns. And as I previously mentioned, exit polls found that Trump's victory depended on voters whose top concerns were immigration and terrorism, despite his lack of any national security experience and my long record. That's a polite way of saying many of these voters were worried about people of color—especially blacks, Mexicans, and Muslims—threatening their way of life. They believed that the political, economic, and cultural elites cared more about these "others" than about them.
I'm not saying that all Trump voters are racist or xenophobic. There are plenty of good-hearted people who are uncomfortable about perceived antipolice rhetoric, undocumented immigrants, and fast-changing norms around gender and sexual orientation. But you had to be deaf to miss the coded language and racially charged resentment powering Trump's campaign.
When I said, "You could put half of Trump's supporters into what I call the basket of deplorables," I was talking about well-documented reality. For example, the General Social Survey conducted by the University of Chicago found that in 2016, 55 percent of white Republicans believed that blacks are generally poorer than whites "because most just don't have the motivation or willpower to pull themselves up out of poverty." In the same survey, 42 percent of white Republicans described blacks as lazier than whites and 26 percent said they were less intelligent. In all cases, the number of white Democrats who said the same thing was much lower (although still way too high).
Generalizing about a broad group of people is almost always unwise. And I regret handing Trump a political gift with my "deplorables" comment. I know that a lot of well-intentioned people were insulted because they misunderstood me to be criticizing all Trump voters. I'm sorry about that.
But too many of Trump's core supporters do hold views that I find—there's no other word for it—deplorable. And while I'm sure a lot of Trump supporters had fair and legitimate reasons for their choice, it is an uncomfortable and unavoidable fact that everyone who voted for Donald Trump—all 62,984,825 of them—made the decision to elect a man who bragged about sexual assault, attacked a federal judge for being Mexican and grieving Gold Star parents who were Muslim, and has a long and well-documented history of racial discrimination in his businesses. That doesn't mean every Trump voter approved of those things, but at a minimum they accepted or overlooked them. And they did it without demanding the basics that Americans used to expect from all presidential candidates, from releasing tax returns to offering substantive policy proposals to upholding common standards of decency.
"Wait a minute," some critics will say, "President Obama won twice. How could race be a real factor here?"
The important thing to remember is that racial attitudes aren't static and they don't exist in a vacuum. As Christopher Parker, a political science professor at the University of Washington, has explained, the Obama years produced a backlash among white voters: "Every period of racial progress in this country is followed by a period of retrenchment. That's what the 2016 election was about." It's like in physics—every action has an equal and opposite reaction.
Cornell Belcher, a respected Democratic pollster, has studied changing racial attitudes in America extensively and documented this backlash in his book A Black Man in the White House. He described Obama's election as setting off anxiety among many white Americans that built over time. "After a significantly brief honeymoon in November 2008, racial aversion among Republicans climbed precipitously," Belcher wrote, "and stayed at that level until October 2014 when it again spiked—to an all-time high." It's not surprising that those spikes occurred around the two midterm elections, when Republican candidates were working double-time to demonize Obama and he wasn't on the ballot and fully engaged in fighting back.
Other academic researchers have studied a phenomenon they call "racial priming." Their findings show that when white voters are encouraged to view the world through a racial lens and to be more conscious of their own racial identity, they act and vote more conservatively. That's exactly what happened in 2016. John McCain and Mitt Romney made principled decisions not to make their campaigns about race. McCain famously stood up to one of his own voters at a town hall in October 2008 and assured the crowd that rumors about Obama being foreign were false. By contrast, Donald Trump rose to prominence by spreading the racist "birther" lie that President Obama was not born in the United States. Trump launched his campaign for President by calling Mexican immigrants rapists and criminals. And he continued to make racially charged attacks right up until Election Day. All this happened against the backdrop of police shootings and Black Lives Matter protests. It makes sense that by Election Day, more white voters may have been thinking about race and identity than in 2012, when those issues were rarely talked about on either side.
To be fair, I likely contributed to a heightened racial consciousness as well. I called out Trump's bigotry and his appeal to white supremacists and the so-called Alt-Right. In a speech in Reno, Nevada, in August 2016, I laid out a detailed case documenting Trump's history of racial discrimination in his business career and how he used a campaign based on prejudice and paranoia to take hate groups mainstream and help a radical fringe take over the Republican Party. I denounced his decision to hire Stephen Bannon, the head of Breitbart, as campaign CEO. I also spoke positively throughout the campaign about racial justice, immigration, and Muslims.
As a result, some white voters may have decided I wasn't on their side. For example, my meeting with Black Lives Matter activists and support for the Mothers of the Movement was seen by some white police officers as presuming their guilt, in spite of my long-standing support for more police on the street, community policing, and 9/11 first responders. I always said we needed to both reform policing and support police officers. It didn't seem to matter. But this is one issue on which I don't second-guess myself. No parent should fear for the life of an unarmed, law-abiding child when he walks out of the house. That's not "identity politics." It's simple justice.
But back to the question at hand. I find the data on all this to be compelling. Yet I believe that, in the end, the debate between "economic anxiety" and racism or "cultural anxiety" is a false choice. If you listen to many Trump voters talk, you start to see that all these different strands of anxiety and resentment are related: the decline of manufacturing jobs in the Midwest that had allowed white men without a college degree to provide their families with middle-class lives, the breakdown of traditional gender roles, anger at immigrants and other minorities for "cutting in line" and getting more than their "fair share," discomfort with a more diverse and cosmopolitan culture, worries about Muslims and terrorism, and a general sense that things aren't going the way they should and that life was better and easier for previous generations. In people's lives and worldviews, concerns about economics, race, gender, class, and culture all blend together.
The academics see this, too. According to the director of the Voter Study Group, which followed thousands of voters from 2012 to 2016, "Voters who experienced increased or continued economic stress were inclined to have become more negative about immigration and terrorism, demonstrating how economic pressures coincided with cultural concerns."
This isn't new. Back in 1984, Ronald Reagan won by a landslide by flipping formerly Democratic blue-collar whites. The term "Reagan Democrats" came out of a series of famous focus groups conducted in Macomb County, Michigan, by Stan Greenberg, who went on to become Bill's pollster in 1992. Stan found that many working-class white voters "interpreted Democratic calls for economic fairness as code for transfer payments to African-Americans," and blamed blacks "for almost everything that has gone wrong in their lives." After the 2016 election, Stan went back to Macomb County to talk to "Trump Democrats." He found pretty much all the sentiments you would expect—frustration with elites and a rigged political system, and a desire for fundamental change, but also anger at immigrants who compete with them for jobs and don't speak English, fear of Muslims, and resentment of minorities who are seen as collecting more than their fair share of government benefits. Some of the comments sounded like they were ripped straight from the 1984 focus groups.
Stan largely blames President Obama for turning working-class voters away from the Democratic Party by embracing free trade and "heralding economic progress and the bailout of the irresponsible elites, while ordinary people's incomes crashed and they continued to struggle financially." That's another reminder that, despite the heroic work President Obama did to get our economy back on the right track after the financial crisis, many Americans didn't feel the recovery in their own lives and didn't give Democrats credit. Stan also thought my campaign was too upbeat on the economy, too liberal on immigration, and not vocal enough about trade. Still, he notes that coming out of the third debate, I was poised to overperform with white working-class women compared with Obama in 2012 and perhaps achieve "historic numbers," until those voters broke away in the final week and went to Trump.
Stan thinks this happened because I "went silent on the economy and change." But that's baloney. I went back to look at what I said in my final rallies across the battlegrounds. The day before the election, I told a crowd in Grand Rapids, Michigan, "We've got to get the economy working for everybody, not just those at the top. If you believe, as I do, that America thrives when the middle class thrives, then you have to vote tomorrow!" I went on to pledge "the biggest investment in good paying jobs since World War Two," with an emphasis on infrastructure jobs that can't be outsourced, advanced manufacturing that pays high wages, stronger unions, a higher minimum wage, and equal pay for women. I also hit Trump for buying cheap Chinese steel and aluminum for his buildings and for wanting to cut taxes for millionaires, billionaires, and corporations. I spoke directly to "people in our country who feel like they've been knocked down, and nobody cares." I said, "If you give me the honor of being your President, I am going to do everything I can to get this country and everybody in it back up on our feet." I wouldn't call that going "silent on the economy and change."
That said, I do sometimes lie awake at night thinking about how we closed the campaign and if there was anything different we could have done that would have made a difference. It's true that before Comey's letter, I had planned to close with aggressive advertising reminding working families of my plans to change our country and their lives for the better. But after Comey's letter sent my numbers sliding, the consensus on my team was that our best strategy was to hit Trump hard and remind voters why he was an unacceptable choice. Was that a mistake? Maybe. But we were competing against wall-to-wall negative coverage of emails, plus the slime of fake news.
It's easy to second-guess. It's also easy to listen to the ugliest comments in Stan's focus groups and just get furious. But I try to hold on to my empathy. I still believe what I said immediately after my ill-fated comment about the "basket of deplorables," although this part didn't get much attention: many Trump supporters "are people who feel that the government has let them down, the economy has let them down, nobody cares about them, nobody worries about what happens to their lives and their futures, and they're just desperate for change . . . Those are people we have to understand and empathize with as well." Those were people I intended to help.
### Voter Suppression
All of this played out against a landscape shaped by structural factors that didn't get enough scrutiny during the campaign. Most notable is the impact of voter suppression, through restrictive laws as well as efforts to discourage and depress turnout.
An unnamed senior Trump campaign official boasted to the press in late October 2016 that "we have three major voter suppression operations underway," aimed at white liberals, young women, and African Americans. It's worth pausing on this for a moment and reflecting on the fact that they weren't even trying to hide that they were suppressing the vote. Most campaigns try to win by attracting more support. Trump actively tried to discourage people from voting at all. They used some of the same tactics as the Russians, including trafficking in fake news and under-the-radar Facebook attacks. Despicable stuff. After the election, Trump even thanked African Americans for not voting.
But whatever Trump was up to was just the latest in a long-term Republican strategy to discourage and disenfranchise Democratic-leaning voters.
The Supreme Court under Chief Justice John Roberts opened the floodgates by gutting the Voting Rights Act in 2013. When I was in the Senate, we voted to reauthorize the law 98 to 0 and President George W. Bush signed it. But Justice Roberts essentially argued that racism was a thing of the past, and therefore the country no longer needed key protections of the Voting Rights Act. It was one of the worst decisions the court has ever made. By 2016, fourteen states had new restrictions on voting, including burdensome ID requirements aimed at weeding out students, poor people, the elderly, and people of color. Republicans in many states also limited the number and hours of polling places, curtailed early voting and same-day registration, scrapped language assistance for non-English speakers, and purged large numbers of voters from the rolls, sometimes erroneously. Ohio alone has removed up to two million voters since 2011. Much of this national effort was coordinated by Kansas Secretary of State Kris Kobach, who runs a suppression initiative called the Interstate Voter Registration Crosscheck Program.
Kobach is the nation's leading voter suppression advocate and was recently fined for misleading a federal court. He is also the vice chairman of the new commission Trump has created to deal with the phantom epidemic of voting fraud. Studies have found that out of the more than a billion votes cast in the United States between 2000 and 2014, there were just 31 credible cases of voter impersonation. Yet Trump has claimed that millions of people voted illegally in 2016. A review by the Washington Post found only 4 documented instances of voter fraud out of 136 million votes cast in 2016—including an Iowa woman who voted twice for Trump. As Trump's own lawyers asserted in a Michigan court: "All available evidence suggests that the 2016 general election was not tainted by fraud or mistake." Nonetheless, Kobach and Republicans across the country continue to use false claims about fraud to justify curtailing voting rights.
Since the election, studies have documented how big an impact all this suppression had on the outcome. States with harsh new voting laws, such as Wisconsin, saw turnout dip 1.7 points, compared with a 1.3-point increase in states where the law didn't change. And the drop was particularly acute among black voters. Turnout was down 5 points in heavily African American counties in states with strict new ID laws, but down just 2.2 points in similar counties in states without the new laws.
In Wisconsin, where I lost by just 22,748 votes, a study from Priorities USA estimated that the new voter ID law helped reduce turnout by 200,000 votes, primarily from low-income and minority areas. We know for sure that turnout in the city of Milwaukee fell by 13 percent. By contrast, in neighboring Minnesota, which has similar demographics but did not impose arduous new restrictions on voting, turnout in heavily African American counties declined much less and overall turnout was essentially flat. In Illinois, where the state put in place new measures to make it easier to vote, not harder, turnout was up more than 5 percent overall. Among African Americans, turnout was 14 points higher in Illinois than in Wisconsin. The experience living under a deeply unpopular Trumpian governor there may also have motivated people to show up and reject the even worse national version. In short, voting laws matter. A lot. Before the election, one Republican state representative in Wisconsin predicted the new law would help Trump pull off an upset in the state. It turns out he was right.
The Associated Press profiled several Wisconsinites who were turned away or did not have their votes counted because they did not have the required identification, including a Navy veteran with an out-of-state driver's license, a recent college graduate whose student ID was disqualified because it lacked an expiration date, and a sixty-six-year old woman with chronic lung disease who lost her driver's license just before Election Day. She provided Social Security and Medicare cards and a government-issued bus pass with a photo, but her vote was still not counted. The AP reported that these disenfranchised citizens were "not hard to find."
Reading these stories is both eye-opening and infuriating. The right to vote is the foundation of our free society, and protecting that right is the single most important thing we can do to strengthen our democracy. Yet in state after state, Republicans are still at it. President Trump's obsession to root out nonexistent voter fraud is just cover for further suppression. Already in 2017, more states have imposed new restrictions on voting than in 2015 and 2016 combined. Nearly a hundred bills have been introduced in thirty-one states. This is a problem that will grow only more pervasive and urgent in future elections.
### Where Do Democrats Go from Here?
Republicans have another advantage: a powerful, permanent political infrastructure, particularly online. After Mitt Romney's defeat in 2012, and widespread praise for the Obama campaign's technology, Republicans vowed to catch up. Between 2013 and 2016, the Republican National Committee invested more than $100 million in data operations. Outside groups such as the Mercers and the Koch brothers also spent heavily.
By contrast, the Democratic National Committee was badly outgunned. Tom Perez, the new DNC chair, has said, "We've got to up our game on technology." He's right. Perez pledged to "do a better job of building the data analytics platform that will enable us not only to succeed in elections today but to be the state of the art for decades to come." That's crucial.
If we want to win in the future, Democrats need to catch up and leapfrog ahead. And this isn't just about data. We need an "always-on" content distribution network that can match what the right-wing has built. That means an array of loosely connected Facebook pages, Instagram accounts, Twitter feeds, Snapchat stories, and Reddit communities churning out memes, graphics, and videos. More sophisticated data collection and analysis can support and feed this network. I'm no expert in these matters, but I know enough to understand that most people get their news from screens, so we have to be there 24/7.
There are other lessons I hope Democrats learn from 2016. Since the election, the party has been debating how best to set ourselves up to win in the future, starting with the midterms in 2018. I think most of the perceived drama between the center-left and the left-left on this question is overblown. We're far closer together than any of us are to Trump and the Republicans, who just keep getting more extreme. Bernie Sanders and I wrote the 2016 platform together, and he called it the most progressive one in history. We share many of the same values and most of our differences over policy are relatively minor compared to the stark divide between the two parties.
You'd also be hard pressed to find any Democrat who doesn't agree that we need to continue sharpening our economic pitch and that we should make a sustained effort to win back voters who switched from Obama to Trump. We'll have to convince them that Democrats respect them, care about them, and have a plan to make life better, not just in big cities but also in small towns and rural areas. That might become easier as voters watch Trump break his populist promises and embrace a congressional Republican agenda that tilts the playing field even more toward the wealthy and powerful at the expense of working families. So far, their health care debate is about whether they're going to take it away from 22 million Americans to fund tax cuts for the wealthy!
So yes, we need to compete everywhere, and we can't afford to write off any voter or any state. But it's not all kumbaya in the Democratic Party. We're hearing a lot of misguided rhetoric and analysis that could lead us in the wrong direction.
One argument is about whether pursuing the Russia investigation is distracting from making the case to voters about health care and the economy. This is another false choice. It makes all the sense in the world for congressional candidates to focus on pocketbook issues, and the disastrous Republican health care legislation should be front and center. But that doesn't mean Democrats already in Congress should stop doing their jobs. They should continue providing rigorous oversight and hold the Trump administration accountable. I have confidence that Democrats can walk and chew gum at the same time. Plus, the ever-growing Russia scandal is showing Americans that Trump is a liar, and that will help us convince them that he's lying about health care and jobs, too. And don't underestimate how, if left unchecked, Russia's covert operations can easily be used again in the future to defeat other Democrats. That torrent of misinformation helped drown out my message and steal my voice. It gave Trump cover to escape his own problems. This can all happen again if we don't stop it. Oh, and for any Democratic members of Congress feeling squeamish about pushing too hard, just ask yourselves what Republicans would be doing if the situation were reversed.
Here's another misguided argument. Some of the same people who say that the reason I lost was because I didn't have an economic message now insist that all Democrats need to do to win in the future is talk more about jobs, and then—poof!—all those Trump voters will come home. Both the premise and conclusion are false. Yes, we need to talk as much as we possibly can about creating more jobs, raising wages, and making health care and college more affordable and accessible. But that's exactly what I did throughout 2016. So it's not a silver bullet and it can't be the only thing we talk about.
Democrats have to continue championing civil rights, human rights, and other issues that are part of our march toward a more perfect union. We shouldn't sacrifice our principles to pursue a shrinking pool of voters who look more to the past than the future.
My loss doesn't change the fact that the Democrats' future is tied to America's in a fast-changing world where our ability to make progress depends an increasingly diverse, educated, young electorate. Even when the headlines are bad, there's reason to be optimistic about the trend lines. I was the first Democrat since FDR to win Orange County, California. I made historic gains in the suburbs of Atlanta, Houston, Dallas, and Charlotte, as well as in other traditionally Republican areas across the Sun Belt. Latino turnout jumped nearly 5 percent in Florida and rose in other key areas as well.
It wasn't enough this time, but these trends hold the key to our future. That's why the Republicans have worked so hard to keep young people and people of color away from the polls, and to gerrymander districts that protect incumbents. Democrats will have to work even harder to fight for voting rights, fair redistricting, and high turnout not just in presidential elections, but also in local, state, and federal midterm elections where the people who make the voting laws and draw congressional districts are selected.
I know we can do it. There are enough vulnerable Republican congressional seats in districts I won for Democrats to be well on their way to retaking the House in 2018, many of them in Sun Belt suburbs. And if we can flip some Midwestern blue-collar districts that went for Trump but are now disillusioned by his performance in office, all the better. We need a strategy that puts us in a position to catch a wave if it forms, and compete and win all over the country.
I do believe it's possible to appeal to all parts of our big, diverse nation. We need to get better at explaining to all Americans why a more inclusive society with broadly shared growth will be better and more prosperous for everyone. Democrats must make the case that expanding economic opportunity and expanding the rights and dignity of all people can never be either/or, but always go hand in hand. I tried to do this in 2016. That was the whole point of "Stronger Together." And it's why I emphasized my commitment to help create jobs in every zip code, in neglected urban neighborhoods and in small Appalachian towns. That vision did win the popular vote by nearly three million (yes, I'm going to keep mentioning that). Unfortunately, zero-sum resentment proved more powerful than positive-sum aspiration in the places where it mattered most. But that doesn't mean we give up. It means we have to keep making the case, backed up by bold new policy ideas and renewed commitment to our core values.
As for me, I'm sure I'll keep replaying in my head for a long time what went wrong in this election. As I said in my concession speech, it's going to be painful for quite a while. None of the factors I've discussed here lessen the responsibility I feel or the aching sense that I let everyone down. But I'm not going to sulk or disappear. I'm going to do everything I can to support strong Democratic candidates everywhere. If you're reading this book, I hope you'll do your part, too.
If our expectations—if our fondest prayers and dreams are not realized—then we should all bear in mind that the greatest glory of living lies not in never falling, but in rising every time you fall.
—Nelson Mandela
## Resilience
Three things in human life are important. The first is to be kind.
The second is to be kind. And the third is to be kind.
—Henry James
## Love and Kindness
Politics has always been a rough business. Thomas Jefferson and John Adams hurled insults at each other that would make today's nastiest politicians blush. It's just how the game is played: Every campaign seeks to draw contrasts with opponents and the media want to cover conflict. So it's not surprising that two words you don't hear very often in our knock-down, drag-out political brawls are love and kindness. But you heard them from our campaign.
It started as something I'd occasionally mention at the end of speeches, how our country needed compassion and a spirit of community in a time of division. It eventually became a rallying cry: "Love trumps hate!" Partly this was because the race felt ugly and mean and we wanted to be an antidote to that. But partly it was because I've been thinking for a long time about how our country needs to become kinder and all of us need to become more connected to one another. That's not just a sweet thought. It's serious to me. If I had won the election, this would have been a quiet but important project of my presidency.
* * *
* * *
A few weeks after the election, I picked up a copy of a sermon called "You Are Accepted" by Paul Tillich, the Christian theologian of the mid-twentieth century. I remembered sitting in my church basement in Park Ridge years ago as our youth minister, Don Jones, read it to us. "Grace strikes us when we are in great pain and restlessness . . . Sometimes at that moment, a wave of light breaks into our darkness, and it is as though a voice were saying: 'You are accepted.' " Years later, when my marriage was in crisis, I called Don. Read Tillich, he said. I did. It helped.
Tillich says about grace: "It happens; or it does not happen. And certainly it does not happen if we try to force it upon ourselves." This stuck with me. "Grace happens. Grace happens." In other words, be patient, be strong, keep going, and let grace come when it can.
Now I was sixty-nine and reading Tillich again. There was more here than I remembered. Tillich says sin is separation and grace is reconciliation—it's "being able to look frankly into the eyes of another . . . understanding each other's words . . . not merely the literal meaning of the words, but also that which lies behind them, even when they are harsh or angry." After a divisive election, this resonated in a new way. A lot of Americans were estranged from one another. Reconciliation seemed far away. The whole country was seething. Before the election, it felt as if half the people were angry and resentful, while the other half was still fundamentally hopeful. Now pretty much everyone is mad about something.
Tillich published his sermon the year after I was born. Sometimes people describe the postwar years as a golden age in America. But even then, he sensed a "feeling of meaninglessness, emptiness, doubt, and cynicism—all expressions of despair, of our separation from the roots and the meaning of our life." That could just as easily be America in 2016. How many shrinking small towns and aging Rust Belt cities did I visit over the past two years where people felt abandoned, disrespected, invisible? How many young men and women in neglected urban neighborhoods told me they felt like strangers in their own land because of the color of their skin? The alienation cut across race, class, geography. Back in 1948, Tillich was concerned that technology had removed "the walls of distance, in time and space" but strengthened "walls of estrangement between heart and heart." If only he could have seen the internet!
How are we supposed to love our neighbors when we feel like this? How are we supposed to find the grace that Tillich says comes with reconciliation and acceptance? How can we build the trust that holds a democracy together?
Underneath these questions are ones I've been wrestling with and writing and speaking about for decades.
* * *
* * *
It started in college. Like a lot of kids, I felt stifled by the conservative, dollar-crazed conformity of the Mad Men era. That scene in The Graduate where an older man pulls Dustin Hoffman aside and, with great seriousness, shares the secret of life in one word—"Plastics"—made all of us groan. It's no wonder so many of us were looking for meaning and purpose wherever we could find them. As I put it in my Wellesley graduation speech, we were "searching for more immediate, ecstatic, and penetrating modes of living." (Yes, I'm aware of how idealistic that sounds, but that's how we talked!) I didn't know quite how to put it into words, but what many of us wanted was an integrated life that blended and balanced family, work, service, and a spiritual connection all together. We wanted to feel like we were part of something bigger than ourselves—certainly something bigger than "plastics."
Surprisingly, I found some of what I was looking for not in a New Age manifesto but in a very old book.
In one of my political science classes, I read Democracy in America by Alexis de Tocqueville. He came from France and traveled across the United States in the 1830s trying to understand what made our young nation work. He was amazed by the social and economic equality and mobility he saw here, unheard of in aristocratic Europe, and by what he called our "habits of the heart," the everyday values and customs that set Americans apart from the rest of the world. He described a nation of volunteers and problem solvers who believed that their own self-interest was advanced by helping one another. Like Benjamin Franklin, they formed volunteer fire departments, because they realized that if your neighbor's house is on fire, it's your problem, too. Middle-class women—including a lot of Methodists—went into the most dangerous nineteenth-century slums to help poor children who had no one else standing up for them. Those early Americans came together, inspired by religious faith, civic virtue, and common decency, to lend a hand to those in need and improve their communities. They joined clubs and congregations, civic organizations and political parties, all kinds of groups that bound a diverse country together. De Tocqueville thought that spirit made America's great democratic experiment possible.
Those "habits of the heart" felt distant to me in the turmoil of the 1960s. Instead of pitching in to raise a barn or sew a quilt—or clean up a park or build a school—Americans seemed always to be at one another's throats. And a pervasive loss of trust was undermining the democracy de Tocqueville had celebrated 130 years before. Reading his observations helped me realize that my generation didn't need to totally reinvent America to fix the problems we saw and find the meaning we sought, we just had to reclaim the best parts of our national character. That started, I told my classmates in my graduation speech, with "mutuality of respect between people," another clunky phrase but still a pretty good message.
* * *
* * *
Fast-forward twenty years, to early 1991. I'd gotten what I'd always dreamed of—a loving family, a fulfilling career, and a life of service to others—plus more that I had never imagined. I was the First Lady of Arkansas. Every part of that statement would have surprised my college-age self. Now my husband was thinking about running for President of the United States. I didn't know if he could win—George H. W. Bush's approval rating surpassed 90 percent after winning the Gulf War—but I was sure the country needed him to try. The Reagan years had rebuilt America's confidence but sapped its soul. Greed was good. Instead of a nation defined by "habits of the heart," we had become a land of "sink or swim." Bush had said some of the right things, calling for a "kinder, gentler" country and celebrating the generosity of our civil society as "a thousand points of light." But conservatives used that as an excuse for government to do even less to help the less fortunate. It's easy to forget what this was like. Now that the Republican Party has moved so far to the extreme right in the years since, the 1980s have taken on a retrospective halo of moderation by comparison. And it's true that Reagan gave amnesty to undocumented immigrants, and Bush raised taxes and signed the Americans with Disabilities Act. But their trickle-down economic policies exploded the deficit and hurt working families. I thought they were wrong on most issues, and still do.
In those days, I still read Life magazine, and in the February 1991 issue, I came across something that caught me totally by surprise. It was an article by Lee Atwater, the Republican mastermind who'd helped elect Reagan and Bush with slash-and-burn campaigns that played to our country's worst impulses and ugliest fears. He was the man behind the infamous race-baiting "Willie Horton" ad in 1988, the man who believed in winning at any cost. He was also mortally ill with brain cancer and not yet forty years old.
Atwater's piece in Life magazine read like a death-bed conversion. The bare-knuckled political brawler was having an attack of conscience. And despite coming from someone with whom I disagreed about virtually everything, it was like reading my own thoughts printed out on the page. Here's what he wrote that made such a big impression on me:
Long before I was struck with cancer, I felt something stirring in American society. It was a sense among the people of the country, Republicans and Democrats alike, that something was missing from their lives—something crucial. I was trying to position the Republican Party to take advantage of it. But I wasn't exactly sure what it was. My illness helped me to see that what was missing in society is what was missing in me. A little heart, a lot of brotherhood.
The '80s were about acquiring—acquiring wealth, power, prestige. I know. I acquired more wealth, power, and prestige than most. But you can acquire all you want and still feel empty. What power wouldn't I trade for a little more time with my family? What price wouldn't I pay for an evening with friends? It took a deadly illness to put me eye-to-eye with that truth, but it is a truth that the country, caught up in its ruthless ambitions and moral decay, can learn on my dime.
I don't know who will lead us through the '90s, but they must be made to speak to this spiritual vacuum at the heart of American society—this tumor of the soul.
This was exactly how I felt! Atwater was getting to a question that had been gnawing at me for years. Why, I wondered, in the wealthiest, most powerful country on earth, with the oldest, most successful democracy, did so many Americans feel like we lacked meaning in our individual lives and in our collective national life? What was missing, it seemed to me, was a sense that our lives were part of some greater effort, that we were all connected to one another and that each of us had a place and a purpose.
This was part of why I thought Bill should run for President. Filling America's "spiritual vacuum" wasn't a job for government, but it would help to have strong, caring leadership. Bill was starting to think about how to root a campaign in the values of opportunity, responsibility, and community. Eventually he'd call it a "new covenant," a biblical concept. He hoped it would speak to this feeling, articulated so well by Atwater, that something important was missing in the heart of American life.
I cut out the Life magazine article and showed it to Bill.
(I wonder what Lee Atwater would say about Donald Trump. Would he admire the chutzpah of a campaign that stopped blowing dog whistles and spoke its bigotry in plain English for all to hear? Or would he see Trump as the embodiment of everything he hated about the eighties: one big tumor of the American soul?)
* * *
* * *
Fast-forward again, this time to April 1993. My eighty-two-year-old father was lying in a coma in St. Vincent's Hospital in Little Rock. It had been two weeks since he suffered a massive stroke. All I wanted to do was keep sitting by his bedside, hold his hand, smooth his hair, and wait and hope for him to open his eyes or squeeze my fingers. But nobody knew how long his coma would last, and Chelsea had to get back to school in Washington. For reasons passing understanding, I also had a commitment I couldn't get out of: a speech to fourteen thousand people at the University of Texas at Austin.
I was, to put it mildly, a wreck. On the plane to Austin, I leafed through the little book I keep of quotations, Scripture, and poems, trying to figure out what I could possibly say. Then I turned the page and saw the cutout from Lee Atwater's Life article. Something missing from our lives, a spiritual vacuum—this is what I would talk about. It wouldn't be the most articulate or coherent speech I'd ever given, but at least it would come straight from my wounded heart. I began sketching out a new appeal for the "mutuality of respect" I'd talked about in my graduation speech at Wellesley, a return to de Tocqueville's "habits of the heart."
When I got to Texas, I spoke about the alienation, despair, and hopelessness I saw building just below the surface of American life. I quoted Atwater. And to his question—"Who will lead us out of this spiritual vacuum?"—I answered, "all of us." We needed to improve government and strengthen our institutions, and that's what the new Clinton administration was trying to do, but it wouldn't be enough. "We need a new politics of meaning," I said, "a new ethos of individual responsibility and caring." And that would take all of us doing our part to build "a society that fills us up again and makes us feel that we are part of something bigger than ourselves." I cited de Tocqueville and talked about the importance of networks of family, friendship, and communities that are the glue that hold us together.
There had been so much change in our country, a lot of it positive but also much of it profoundly unsettling. The social and cultural upheaval of the 1960s and 1970s, followed by the economic and technological shifts of the 1980s and 1990s, with the rise of automation, income inequality, and the information economy, all of it seemed to be contributing to a spiritual hollowing out. "Change will come whether we want it or not, and what we have to do is to try and make change our friend, not our enemy," I said.
The changes that will count the most are the millions and millions of changes that take place on the individual level as people reject cynicism; as they are willing to take risks to meet the challenges they see around them; as they truly begin to try to see other people as they wish to be seen and to treat them as they wish to be treated; to overcome all of the obstacles we have erected around ourselves that keep us apart from one another, fearful and afraid, not willing to build the bridges necessary; to fill that spiritual vacuum that Lee Atwater talked about.
People in politics don't normally talk this way. Neither do First Ladies. I soon discovered why.
The day after my speech, my father died. I returned to Washington and found that many in the press had hated my attempt to talk unguardedly about what I thought was wrong in the country. The New York Times Magazine put me on the cover with the mocking headline "Saint Hillary." The writer described the Texas speech as "easy, moralistic preaching couched in the gauzy and gushy wrappings of New Age jargon."
I learned my lesson. Over the next few years, I kept thinking about a "new ethos of individual responsibility and caring," but I didn't talk about it much. I read as much as I could, including a new article by Harvard professor Bob Putnam, which later became a bestselling book titled Bowling Alone. Putnam used declining membership in bowling leagues as an evocative example of the breakdown in America's social capital and civil society—the same problems I'd been worrying about.
I decided to write a book of my own. It would speak to these concerns in a less "gauzy and gushy" way than my Texas speech and offer a practical, kitchen-table vision for what we could do about it. The focus would be the responsibility we all had to help create a healthy, nurturing community for children. I'd call it It Takes a Village, after an African proverb that captured something I had long believed.
I wrote about how frantic and fragmented American life had become for many people, especially stressed-out parents. Extended families didn't provide the support they used to. Crime was still a big problem in a lot of communities, making neighborhood streets places of danger rather than support and solidarity. We were spending more time in our cars and in front of the television and less time participating in civic associations, houses of worship, unions, political parties, and, yes, bowling leagues.
I believed we needed to find new ways to support one another. "Our challenge is to arrive at a consensus of values and a common vision of what we can do today, individually and collectively, to build strong families and communities," I wrote. "Creating that consensus in a democracy depends on seriously considering other points of view, resisting the lure of extremist rhetoric, and balancing individual rights and freedoms with personal responsibility and mutual obligations."
Once again, the response from some quarters was brutal. Republicans caricatured my appeal for stronger families and communities as more big-government liberalism, even "crypto-totalitarianism" in one magazine's words. "We are told that it takes a village, that is collective, and thus the state, to raise a child," Bob Dole said, his voice dripping with disdain, in his acceptance speech at the 1996 Republican National Convention. "I am here to tell you it does not take a village to raise a child. It takes a family to raise a child." The crowd went wild.
You might think it's a little odd for the nominee of a major political party to take time out of the most important speech of the campaign to take a swipe at a book about children written by the First Lady—and you would be right.
It was becoming painfully clear that there was no room in our politics for the kind of discussion I wanted to have. Or maybe I was the wrong messenger. Either way, this wasn't working.
I found more receptive audiences overseas. In a speech at the World Economic Forum in Davos, Switzerland, in 1998, I tried to explain how my "village" concept fit together with a broader global agenda of political and economic reform. I used the metaphor of a three-legged stool, which I'd come back to many times in the years that followed. An open and thriving economy was one leg. A stable and responsive democratic government was a second leg. And the third, too often undervalued in serious foreign policy discussions, was civil society. "It is the stuff of life," I said. "It is the family, it is the religious belief and spirituality that guide us. It is the voluntary association of which we are a member. It is the art and culture that makes our spirits soar."
* * *
* * *
Another twenty years went by. Now I was running for President in a time of deep division and smoldering anger. On the news, there was a seemingly endless series of terrorist attacks and mass shootings. Young black men kept getting killed by police. A candidate for President called Mexican immigrants rapists and encouraged violence at his rallies. On the internet, women were harassed frequently, and it was impossible to have a conversation about politics without enduring a blizzard of invective.
In late May 2015, I was campaigning in Columbia, South Carolina. In between events, we squeezed in a quick stop at the Main Street Bakery so I could get a cupcake and shake some hands. There was only one customer in the place, an older African American gentleman sitting alone by the window, engrossed in a book. I was reluctant to disturb him, but we made eye contact. I walked over to say hello and ask what he was reading.
The man looked up and said, "First Corinthians 13."
I smiled. "Love is patient, love is kind," I said, "it does not envy, it does not boast, it is not proud."
His name was Donnie Hunt, and he was a minister at the First Calvary Baptist Church, getting ready for the day's Bible study. He invited me to sit down.
He told me how rewarding he found it to read these familiar lines again and again. "You always learn something," he said.
"Well, it's alive," I replied. "It's the living word."
We sat and talked for a long time—about books, his church, the local schools, racial tensions in the community, his hope to one day visit the Holy Land. "It's on my bucket list," he told me.
A few weeks later, I was back in South Carolina. This time it was Charleston. I visited a technical college and talked with apprentices hoping their training would lead to a good job and a happy life. It was a diverse group—black, white, Hispanic, Asian—all young, all incredibly hopeful. I listened to their stories and heard the pride in their voices.
I got on a plane for Nevada and didn't hear the news until I landed. A young white man trying to start a race war had massacred nine black worshippers at an evening Bible study at Mother Emanuel Church in Charleston. Emanuel means "God with us," but the news made it hard to feel that way. Nine faithful women and men, with families and friends and so much left to do and contribute in their lives, cut down as they prayed. What is wrong with us? I thought. How did we let this happen in our country? How did we still allow guns to fall into the hands of people whose hearts were filled with hate?
Two days later, police brought the murderer into court. One by one, grieving parents and siblings stood up and looked into his blank eyes, this young man who had taken so much from them, and they said: "I forgive you." In its way, their acts of mercy were more stunning than his act of cruelty.
A friend of mine sent me a note. "Think about the hearts and values of those men and women of Mother Emanuel," he said.
"A dozen people gathered to pray. They're in their most intimate of communities, and a stranger who doesn't look or dress like them joins in. They don't judge. They don't question. They don't reject. They just welcome. If he's there, he must need something: prayer, love, community, something. During their last hour, nine people of faith welcomed a stranger in prayer and fellowship."
My friend said it reminded him of the words of Jesus in Matthew: "I was hungry and you gave me food. I was thirsty and you gave me drink. I was a stranger and you welcomed me."
In a speech in San Francisco, I read my friend's note out loud. Then I looked up, and I said what I was feeling in that moment: "I know it's not usual for somebody running for President to say what we need more of in this country is love and kindness. But that's exactly what we need."
* * *
* * *
"Love and kindness" became a staple for me on the campaign trail. Never the core message of the day, never a full-fledged "new politics of meaning" call to arms, but something I'd come back to again and again, and that audiences nearly always responded to, as if they were thirsty for it. With all the rotten news on television and all the negativity in the race, a lot of people wanted to be reassured about the basic goodness of our country and our hope for a better, kinder future. When we started using the phrase "love trumps hate," it caught on like wildfire among our supporters. There were times when I listened to huge crowds chanting those words, and for a minute I'd get swept up in the swell of positive energy and think it might really carry us all the way.
I've spent many hours since the election wondering whether there was more we could have done to get that message through to an angry electorate in a cynical time. There's been so much said and written about the economic hardships and declining life expectancy of the working-class whites who embraced Donald Trump. But why should they be more angry and resentful than the millions of blacks and Latinos who are poorer, die younger, and have to contend every day with entrenched discrimination? Why were many people who were enchanted by Barack Obama in 2008 so cynical in 2016 after he saved the economy and extended health care to millions who needed it?
I went back to de Tocqueville. After studying the French Revolution, he wrote that revolts tend to start not in places where conditions are worst, but in places where expectations are most unmet. So if you've been raised to believe your life will unfold a certain way—say, with a steady union job that doesn't require a college degree but does provide a middle-class income, with traditional gender roles intact and everyone speaking English—and then things don't work out the way you expected, that's when you get angry. It's about loss. It's about the sense that the future is going to be harder than the past. Fundamentally, I believe that the despair we saw in so many parts of America in 2016 grew out of the same problems that Lee Atwater and I were worried about twenty-five years ago. Too many people feel alienated from one another and from any sense of belonging or higher purpose. Anger and resentment fill that void and can overwhelm everything else: tolerance, basic standards of decency, facts, and certainly the kind of practical solutions I spent the campaign offering.
Do I feel empathy for Trump voters? That's a question I've asked myself a lot. It's complicated. It's relatively easy to empathize with hardworking, warmhearted people who decided they couldn't in good conscience vote for me after reading that letter from Jim Comey . . . or who don't think any party should control the White House for more than eight years at a time . . . or who have a deeply held belief in limited government, or an overriding moral objection to abortion. I also feel sympathy for people who believed Trump's promises and are now terrified that he's trying to take away their health care, not make it better, and cut taxes for the superrich, not invest in infrastructure. I get it. But I have no tolerance for intolerance. None. Bullying disgusts me. I look at the people at Trump's rallies, cheering for his hateful rants, and I wonder: Where's their empathy and understanding? Why are they allowed to close their hearts to the striving immigrant father and the grieving black mother, or the LGBT teenager who's bullied at school and thinking of suicide? Why doesn't the press write think pieces about Trump voters trying to understand why most Americans rejected their candidate? Why is the burden of opening our hearts only on half the country?
And yet I've come to believe that for me personally and for our country generally, we have no choice but to try. In the spring of 2017, Pope Francis gave a TED Talk. Yes, a TED Talk. It was amazing. This is the same pope whom Donald Trump attacked on Twitter during the campaign. He called for a "revolution of tenderness." What a phrase! He said, "We all need each other, none of us is an island, an autonomous and independent 'I,' separated from the other, and we can only build the future by standing together, including everyone." He said that tenderness "means to use our eyes to see the other, our ears to hear the other, to listen to the children, the poor, those who are afraid of the future."
On all my long walks in the woods and quiet days at home, when I'm not losing my mind about something I've read in the newspaper or on Twitter, this is what I'm thinking about. I'm coming around to the idea that what we need more than anything at this moment in America is what you might call "radical empathy."
This isn't too different from the "mutuality of respect" I hoped for at Wellesley all those years ago. I'm older now. I know how hard this is and how cruel the world can be. I'm under no illusions that we'll start agreeing on everything or stop having fierce debates about the future of our country—nor should we. But if 2016 taught us anything, it should be that we have an urgent imperative to recapture a sense of common humanity.
Each of us must try to walk in the shoes of people who don't see the world the way we do. President Obama put it very well in his farewell address. He said white Americans need to acknowledge "that the effects of slavery and Jim Crow didn't suddenly vanish in the sixties; that when minority groups voice discontent, they're not just engaging in reverse racism or practicing political correctness; that when they wage peaceful protest, they're not demanding special treatment but the equal treatment our Founders promised." And, for people of color, it means understanding the perspective of "the middle-aged white man who from the outside may seem like he's got all the advantages, but who's seen his world upended by economic, cultural, and technological change."
And, practicing "radical empathy" means more than trying to reach across divides of race, class, and politics, and building bridges between communities. We have to fill the emotional and spiritual voids that have opened up within communities, within families, and within ourselves as individuals. That can be even more difficult, but it's essential. There's grace to be found in those relationships. Grace and meaning and that elusive sense that we're all part of something bigger than ourselves.
I know this isn't the language of politics, and some will roll their eyes again, just as they always have. But I believe as strongly as I ever have that this is what our country needs. It's what we all need as human beings trying to make our way in changing times. And it's the only way I see forward for myself. I can carry around my bitterness forever, or I can open my heart once more to love and kindness. That's the path I choose.
Concern yourself not with what you tried and failed in, but with what is still possible to do.
—Pope John XXIII
## Onward Together
One day a few months after the election, I called some friends and suggested we make a pilgrimage to Hyde Park, New York. I was feeling restless and needed an emotional boost. I thought it might help to visit Val-Kill, Eleanor Roosevelt's cottage, which is one of my favorite historical sites. That's where Eleanor went when she wanted to think, write, entertain, and plan for the future. Maybe I'd be inspired. If nothing else, it would be a nice day out with friends.
It was a cold but clear March day when we arrived. The cottage, simple and unpretentious, was just as I remembered: the rustic "sleeping porch" with its narrow single bed, some of Eleanor's favorite books, her radio, the portrait of her husband she kept over the mantel. A historian who joined us for the tour was kind enough to share some of Eleanor's letters. Reading the mix of adoring fan mail and nasty, cutting diatribes was a reminder of the love-hate whiplash that women who challenge society's expectations and live their lives in the public eye often receive.
I'd been thinking about Eleanor a lot lately. She put up with so much vitriol, and she did it with grace and strength. People criticized her voice and appearance, the money she made speaking and writing, and her advocacy for women's rights, civil rights, and human rights. An overzealous director of the FBI put together a three-thousand-page file on her. One vituperative national columnist called her "impudent, presumptuous, and conspiratorial," and said that "her withdrawal from public life at this time would be a fine public service." Sound familiar?
There were plenty of people hoping that I, too, would just disappear. But here I am. As Bill likes to say, at this point in our lives, we have more yesterdays than tomorrows. There is no way I am going to waste the time I have. I know there is more good to do, more people to help, and a whole lot of unfinished business.
I can only hope to come close to the example Eleanor had set. After her husband died and she left the White House, in 1945, she grew even more outspoken. She became a stateswoman on the world stage, leading the global movement to write and adopt the Universal Declaration of Human Rights. At the same time, she was an active player in national and local Democratic politics, fighting for the soul of her party and her country in a postwar era marked by fear and demagoguery. When she died in 1962, the New York Times obituary described how she outlasted ridicule and bitter resentment to become "the object of almost universal respect."
Her friends and supporters clamored for Eleanor to run for Senate, Governor, even President, but she decided instead to pour her energy into helping elect others. Her favorite was Adlai Stevenson, the Governor of Illinois who ran for President unsuccessfully in 1952 and 1956. His losses hurt. "Though one may doubt the wisdom of the people," Eleanor wrote in a newspaper column after the second defeat to Dwight Eisenhower, "it is always best to trust that in time the wisdom of the majority of the people will be greater and more dependable and those who are in the minority must accept their defeat with grace." She was right, of course. But I would have loved to have heard her response if Adlai had ended up winning the popular vote but losing the Electoral College. She would have found just the right way to capture the absurdity of it all.
As we walked through the cottage, I tried to picture Eleanor in her chair writing, or holding court at the table, surrounded by friends and comrades in arms. She was, until the end, her own person, despite all the demands and constraints the world placed on her—true to herself and her values. That's a surprisingly rare and special thing.
Back in 1946, when Eleanor was charting her post-FDR course, she said something that resonates with me now as it never has before. "During a long life, I have always done what, for one reason or another, was the thing which was incumbent upon me to do without any consideration as to whether I wished to do it or not," she wrote. "That no longer seems to be a necessity, and for my few remaining years, I hope to be free!"
That's the future I want, too. As Eleanor showed, it's there for the taking.
* * *
* * *
"What do we do now?" That's the question a lot of Democrats asked me in the first months after Trump's victory and inauguration. Many of my campaign staff, donors, and volunteers were eager—desperate, even—to find new ways to keep up the fight for the progressive values we all shared. People came up to me in restaurants, airports, and theaters, asking for direction. They wanted to help but didn't know the best way to do it. Should they be giving everything they could to the American Civil Liberties Union and others trying to stop Trump's travel ban in court? Or throw themselves into the handful of special elections that would fill open House seats in 2017? What about diving into new efforts to fight gerrymandering and voter suppression? Should they run for office themselves? There were so many causes, groups, and candidates looking for support, it was hard to know where to begin. Frankly, I was asking the same questions.
At first, I had intended to keep relatively quiet. Former Presidents and former nominees often try to keep a respectful distance from the front lines of politics, at least for a while. I always admired how both George H. W. Bush and George W. Bush avoided criticizing Bill and Barack, and how Bill ended up working with George H. W. on tsunami relief in Asia and Katrina recovery on the Gulf Coast. And with George W. in Haiti after the earthquake in 2011. That's how it's supposed to work. But these weren't ordinary times, and Trump wasn't an ordinary President.
The Russia scandal was getting more disturbing by the day. Polls showed that respect for the United States around the world was collapsing. The understaffed, overpoliticized Trump administration was consumed by crises of their own making, but I shuddered to think about how they would handle a real emergency, whether it was a clash with nuclear-armed North Korea, a major terrorist attack, a natural disaster like Hurricane Katrina, or a cyberattack on a nuclear power plant. At home, instead of investing in infrastructure and jobs, the new administration was busy rolling back protections for civil rights, worker's rights, and clean air and water. I watched with horror as Republicans in Congress moved methodically to dismantle the Affordable Care Act, which would strip tens of millions of Americans of their health care. Soon it became clear their target was much bigger than Obamacare. They wanted to strike a major blow against Medicaid, too. I had no doubt that Medicare and Social Security would soon be on the chopping block as well. It was a full-on ideological assault on the legacy of the Great Society and the New Deal. They don't just want to erase Barack Obama from the history books—they're coming for LBJ and FDR, too. Hardworking families I'd met across the country were going to pay the price. They needed help getting ahead but instead they were getting stabbed in the back. Watching all this unfold in the early months of the Trump presidency, I knew there was no way I could sit quietly on the sidelines.
Not long after I got back from my Val-Kill visit, I was trying to figure out what to say to a conference of businesswomen in California and I came up with a phrase that was a little silly, but it felt right: "Resist, insist, persist, enlist." It became a mantra of sorts for me over the next few months.
Ever since the Women's March in January, resistance had become the watchword for everyone opposed to Trump and all the protests, large and small, spreading across the country. Mitch McConnell had unintentionally made "persistence" a rallying cry as well, after he tried to justify his outrageous silencing of Elizabeth Warren on the Senate floor by saying, "She was warned. She was given an explanation. Nevertheless, she persisted." That last part was now showing up on signs, T-shirts, and hashtags. Chelsea even decided to write a children's book about thirteen inspiring women who shaped American history called She Persisted.
My new mantra celebrated all that energy and activism, but I thought its most important word was the last one: enlist. Unless people stay engaged and find ways to translate protests into political power, we aren't going to stop Trump's agenda or win future elections. To do that, we need to invest in political infrastructure: rebuilding the Democratic Party, training new candidates and staffers, improving our data and social media operations, beating back efforts to restrict voting rights, and more.
I know there are a lot of people—including a lot of Democrats—who are not eager to see me leading such an effort. They feel burned by my defeat, tired of defending me against relentless right-wing attacks, and ready for new leaders to emerge. Some of that sentiment is totally reasonable. I, too, am hungry for new leaders and ideas to reinvigorate our party. But if Al Gore, John Kerry, John McCain, and Mitt Romney can find positive ways to contribute after their own election defeats, so can I. That doesn't mean I'll ever run for office again—although I was amused and surprised by the brief but fervent speculation over whether I would run for Mayor of New York. It does mean I will speak out on the causes I care about, campaign for other Democrats, and do whatever I can to build the infrastructure we need to succeed.
My thinking on all this crystalized in the spring of 2017 during a series of conversations with Howard Dean, the former Vermont Governor. As a presidential candidate in 2004, Howard pioneered many of the online organizing and fund-raising tactics that would later help elect Barack Obama. As chair of the Democratic National Committee, he led a "fifty-state strategy" that extended the party's organizing into red states that had been neglected for too long. That experience made him the perfect person to talk to about the work Democrats needed to do now and how I could help.
Howard shared my enthusiasm for supporting the next generation of Democratic organizers, and he told me about the growing number of grassroots groups sprouting up in the wake of the election. Letting a thousand flowers bloom was great, he said, but it would be important to help the most promising groups find funding and focus. I agreed, and we decided to start a new organization that would identify and support up-and-coming groups and leaders who might not otherwise get the resources they deserved. We recruited a few like-minded colleagues and got to work.
We did a lot of research and met with many young leaders, which itself was both fun and fascinating. I listened to their presentations and peppered them with questions: What inspired you to start this organization? What are your strategic imperatives? What's the one thing you wish you could do with additional resources? They gave smart, thoughtful answers. I walked out of those meetings feeling more hopeful and optimistic than I had in a long time.
After some tough deliberation, we landed on five initial groups to support with fund-raising and advice. Some were already hard at work helping channel a surge of grassroots energy opposing Trump's attempt to repeal Obamacare and offering practical advice for how people could most effectively make their voices heard on Capitol Hill. Others were mobilizing volunteers in swing districts with the goal of taking back the House in 2018 and recruiting and training talented, diverse Democratic women and young people to run for office and win.
The working name of our new umbrella organization was Our American Future. We created a logo and a website and prepared to go public. Luckily, a friend of mine pointed out that the acronym of Our American Future would be OAF. I imagined the headlines: "Hillary Clinton Lurches Out of the Woods: Here Comes OAF." We needed a new name, stat! After a quick brainstorm, we came up with a better option that combined my campaign slogan, Stronger Together, with "Onward!" the exhortation I'd been using to close personal notes for years. (What can I say? I'm a sentimentalist.) The logo and website got a quick makeover, and we were ready to launch Onward Together.
I hope you'll join us in this effort. Check it out at OnwardTogether.org. Become a member and help us support these fantastic groups and the future of Democratic grassroots organizing.
There are many other ways to resist, insist, persist, and enlist. Register to vote. Help your friends and family do the same. You have to vote in every election, not just during presidential years. It matters. For one, your right to vote is protected or undermined by state and local officials who oversee and conduct elections. Bring as many other people as you can to the polls with you.
Get involved in a cause that matters to you. Just pick one, start somewhere. Women's rights, LGBT rights, workers' rights, voting rights, the environment, health care, campaign finance reform, public education—they all deserve attention. Don't just think about it or talk about it: support a cause with your money, your time, and your talents. Find an organization that's doing work you believe in. It may be a long-standing organization or a newer or smaller one. If it doesn't exist, build it.
Local issues are every bit as important as national and global ones. If you see a problem in your community that needs fixing or an injustice that needs correcting, and you think, "Someone ought to do something about that," guess what? That someone could easily be you. Show up at a city council or school board meeting and suggest a solution. If a problem is affecting your life, it's probably affecting someone else's—and that person might just be willing to join you.
Try to get to know your elected officials at every level and learn where they stand. If you disagree with them, challenge them. Learn when they're holding their next town hall and show up. Don't forget to support and contribute to candidates who will fight for your values and interests. Better yet, run for office yourself.
If you've been keeping your opinions to yourself, try speaking out—whether that's on social media, in a letter to the editor, or in conversations with friends, family, and neighbors. Your views are every bit as valuable as everyone else's. You'll be surprised by how satisfying it can be to express yourself. And chances are, once you take a stand, you'll find you're not standing alone for long. If all else fails, make a sign and show up at a protest.
One of my supporters, Katy from Bellevue, Washington, sent me her five-step plan, which I think is a great road map for anyone looking to make a difference:
1) I have set up a monthly contribution to the ACLU and I will stand by, ready to take action as needed.
2) I'm looking ahead to 2018. I know the Democrats have a rough road ahead, with many seats to defend, but I'm ready to start now. I will become more active in my local Democratic Party.
3) I will join a church or a synagogue (I grew up Methodist and my husband is Jewish) as an avenue for public service and to give my sons a greater sense of community.
4) I am a high school history teacher, but because my older son has autism and requires a lot of therapy I am on leave this year. While on leave, I will volunteer at a local school for a few hours a week so that I can continue educating the next generation.
5) I will be more proactive about teaching my sons to love ALL people. We will have conversations about racism and misogyny. I will help them to understand their privilege and to understand that privilege makes them responsible for others.
There's an African proverb I've always loved: "If you want to go quickly, go alone. If you want to go far, go together." If ever there was a moment to channel that spirit, it's now. We have a long road ahead, and we'll only get there together.
* * *
* * *
In the spring of 2017, I received a letter from a group called Wellesley Women for Hillary. Thousands of current and former students from my alma mater had worked their hearts out during the campaign. They were crushed by the outcome, but the group stayed together, supporting and encouraging one another. Now they wanted my advice about what to do next.
Around the same time, I got an invitation from Wellesley's new President, Dr. Paula A. Johnson, to speak at the college's graduation at the end of May. This would be the third pivotal moment in my life when I addressed a Wellesley graduation. It had been nearly a half century since the first time—at my own graduation in 1969—and doing so again in 2017, in the middle of this long, strange year of regret and resistance, felt fitting. I could try to answer the question posed by the Wellesley Women for Hillary—What do we do now?—for the class of 2017, for our country, and for myself.
I love going back to campus. It's more built up than it used to be but still beautiful and full of memories: swimming in Lake Waban . . . staying up late arguing about the war and civil rights . . . being told by my French teacher, "Mademoiselle, your talents lie elsewhere" . . . placing a panicked collect call back to Park Ridge because I didn't think I was smart or sophisticated enough to cut it at Wellesley, and hearing my father say, "Okay, come home," only to have my mother insist, "There aren't quitters in our family."
Over the years, I've had a chance to spend time with several generations of Wellesley students, and it's always a tonic. They're so smart, engaged, and eager to make their marks on the world. It energizes me, and reminds me of the fire and ambition I felt all those years ago.
In the dizzying, depressing days after my defeat, that's what I needed. I needed to remember who I was, where I came from, what I believed, and why I fought so hard and so long for it. Wellesley helped me find myself as a young woman. Maybe it could help me again now chart my path.
The second time I spoke at a Wellesley graduation was in 1992, during the heat of Bill's first run for the White House. I was trying to adjust to the bright glow of the national spotlight (actually, it often felt more like a scorching flame)—and still smarting from the "cookies and tea" fiasco—but also feeling exhilarated by the passion and optimism of our campaign. It was one of the most remarkable years of my life, and I wanted to share what I'd learned and how it felt with my fellow Wellesley grads. In my speech, I urged the class of '92 to defy the barriers and expectations they still faced as strong, independent women, and focus instead on finding fulfillment in their own unique balance of family, work, and service. I reminded them of Wellesley's Latin motto, Non Ministrari sed Ministrare, which means "Not to be ministered unto, but to minister." That sentiment always appealed to my Methodist sensibilities, and it resonated even more in a year when Bill and I were crisscrossing the country talking about a new birth of responsibility, opportunity, and community.
Since I was speaking at an academic event, I reached for a lofty source of wisdom to give a little oomph to my heartfelt advice about serving others: Václav Havel, the dissident Czech playwright and activist who had recently become his country's first freely elected President. Later, as First Lady, I would meet Havel, and he would take me on a mesmerizing moonlit walk through the old city of Prague. But in 1992 I knew him only through his writing, which was eloquent and compelling. Only "by throwing yourself over and over again into the tumult of the world, with the intention of making your voice count—only thus will you really become a person," he wrote. That's what I wanted those Wellesley graduates to understand and act on. It was a time of hope and change, and they belonged at the vanguard of a rising generation.
Boy, did 2017 feel different. The hope so many of us felt in 1992 was gone, and in its place was a creeping dread about the future. Every day, the new Trump administration was disgracing our country, undermining the rule of law, and telling such bald-faced lies that it seemed as if it really had no shame at all. (According to the New York Times, Trump lied or dissembled at least once every day for the first 40 days of his presidency. The Washington Post counted 623 false and misleading statements he had made over his first 137 days.)
In 1969, my classmates and I had worried about the loss of trust in our leaders and institutions. Those fears were back at full force, amplified for the internet age, when it's so easy to live in echo chambers that shut out contrary voices and inconvenient truths. Our leaders now have tools at their disposal to exploit fear, cynicism, and resentment that were unimaginable in 1969.
And as for me, I had thrown myself "into the tumult of the world," but it had left me bruised and gasping for air. What could I possibly say to the Wellesley class of 2017 in a moment like this?
I thought about Havel. He had persevered through much worse. He and all of Soviet-dominated Eastern Europe had lived for decades under what Havel called "a thick crust of lies." He and other dissidents had managed to punch through those lies and ultimately tear down the authoritarian regimes that propagated them. I went back and reread one of his essays, "The Power of the Powerless," which explains how individuals can wield truth like a weapon, even when they lack all political influence. Havel understood that authoritarians who rely on lies to control their people are fundamentally not that different from neighborhood bullies. They're more fragile than they look. He wrote, "The moment someone breaks through in one place, when one person cries out, 'The emperor is naked!'—when a single person breaks the rules of the game, thus exposing it as a game—everything suddenly appears in another light."
This felt like the right message for 2017. I could warn the Wellesley graduates that they were becoming adults during an all-out assault on truth and reason, especially from a White House specializing in "alternative facts." I could explain how the administration's attempts to distort reality were an affront to the Enlightenment values our country was founded on, including the belief that an informed citizenry and free and open debate are the foundations of a healthy democracy. But Havel's words gave reason to hope. Every one of us has a role to play in defending our democracy and standing up for rational thought. I could remind the graduates of what I'd said in my concession speech: that they are valuable and powerful, and that the skills and values they learned at Wellesley had given them everything they would need to fight back.
It drove me crazy that since the election, pundits had fetishized stereotypical Trump supporters to such a degree that they had started dismissing anyone who lived on the coasts and had a college education as irrelevant and out of touch. I wanted to assure the Wellesley grads that this was nonsense. Their capacity for critical thinking, their commitment to inclusiveness and pluralism, their ethic of serving others—that's precisely what we needed in America in 2017. My advice would be simple: Don't let the bastards get you down. Stay true to yourself and your values. Most of all, keep going.
* * *
* * *
I woke up early on May 26. I had spent the previous evening with Bill and a few former campaign aides, eating Thai food, drinking white wine, and working on my speech. I wanted this one to be good. It would be my first big speech since the concession, and I knew a lot of my supporters across the country were eager to hear from me. Many were scared, angry, and hungry for inspiration. Most of all, the graduates deserved a memorable graduation.
It was raining in Chappaqua, and the weather report said it was drizzling in Boston, too. I felt for all the families at Wellesley who surely had been hoping for a perfect day. I had graduated under a brilliantly clear New England sky. Oh well; some people say rain on a wedding day is good luck. Maybe the same is true for graduations.
I got dressed in Wellesley blue, had a cup of coffee, and found a sweet note from Bill. He had stayed up to all hours reading the latest speech draft and scribbled on the top of the page, "H—I like this speech. Hope these suggestions help make it better—wake me and we'll go over it—I love you." I thought for the ten millionth time how glad I was that I had married my best friend and biggest cheerleader. And yes, like always, his edits made my speech better.
Puttering, I turned on the news and quickly regretted it. Overnight, a Republican congressional candidate in Montana who had body-slammed a reporter for asking tough questions about health care had won his special election. At the NATO summit across the Atlantic, Donald Trump had shoved the prime minister of Montenegro out of the way so he could get a better spot in a group photo. I watched the clip several times, like rubbernecking at a car wreck. It was hard not to see the two stories as related, both symbols of our degraded national life in the Age of Trump. I sighed, turned off the television, gathered my things, headed to the airport, and flew to Massachusetts.
Even in the rain, seeing the old redbrick buildings of Wellesley made me feel better. The campus was humming with the familiar rituals of graduation. Parents and grandparents were fawning over their embarrassed children. Younger siblings were soaking in everything, imagining when it would be their turn. Some of the grads had decorated their mortarboards with flower crowns and rainbow flags. Others sported "I'm With Her" stickers and "Love Trumps Hate" pins, which made me smile. By tradition, every Wellesley class is assigned a color. As it happened, both 1969 and 2017 were green classes. As a result, it felt a little like Saint Patrick's Day all over campus.
President Johnson, whom I knew and admired for her work in medicine and on public health issues, met me and brought me to the aptly named Green Hall, a lovely old Gothic building. There I found my academic robes and tasseled cap. As a general rule, I don't wear silly hats in public, but this was an exception. I resolved to see it as jaunty.
To my delight, before the graduation ceremony began, I was able to steal a few minutes with an old friend. When I was a student at Wellesley, Rev. Paul Santmire was the college chaplain and became an important mentor for me. In my '69 commencement speech, I cited him as a model of integrity at a time when we didn't trust authority figures and hardly anyone at all over thirty. Now, in his early eighties, Paul was as sharp and humane as ever. We embraced, and he told me that he'd driven up to New Hampshire in the fall to go door-to-door for my campaign. We reminisced about the old days when I was a wide-eyed student activist, and he mentioned my favorite line from John Wesley, the call to "Do all the good you can." I assured him it was closer to my heart than ever and that my faith had been a rock in this period when everything else felt topsy-turvy.
I also had a chance to visit briefly with a young woman named Lauren, who was the president of the Wellesley Republicans club—a post I had held as a student myself before realizing my evolving views and values were taking me in a different direction. Lauren seemed to be going through similar soul-searching. Wellesley was a lonely place to be a conservative, but she told me her classmates had been eager to talk through their differences in an open and supportive way. Lauren wasn't a Trump fan and was torn about what to do after he won the nomination. The Wellesley Republicans withheld its endorsement. But like most people, Lauren assumed Trump would lose and things would go back to normal. Now she was wrestling with what it all meant. Join the club, I thought. (Or, quit it! Seriously, if anyone is thinking of quitting the Republican Party, now would be a good time.)
There was one more person to meet. Tala Nashawati was chosen by her classmates to be the student speaker at graduation, just as I was in 1969. The American daughter of Syrian immigrants living in Ohio, she was graceful and poised, with a warm smile. Like so many Wellesley students, Tala was ridiculously accomplished and well rounded: a Middle Eastern Studies major, sought-after kickboxing instructor, and soon-to-be medical student. The night before my graduation speech in 1969, I had stayed up all night writing, pacing, and thinking, and in the morning, I was still in a barely controlled panic. But Tala appeared calm. She had been up late putting the finishing touches on her speech, but she had known for a long time what she wanted to say. And now she was ready.
Tala had brought a photo for me to sign. It was from 1969. There I was, standing at the podium, leaning ever so slightly in toward the microphone, my hair swept back into a bun that I remember thinking was very grown up, big glasses perched on my nose. So young. Behind me, a row of gray-haired faculty and trustees looking very serious. Some of them were probably wondering why President Ruth Adams had allowed a student to speak at graduation at all, something that had never happened before. Or they were struggling to follow my passionate but somewhat incoherent remarks. At the bottom of the photo was printed a quote from my speech: "The challenge now is to practice politics as the art of making what appears to be impossible, possible."
I had borrowed that line from a poem written by a friend. It captured the idealism so many of us felt, despite the war and assassinations and unrest all around us. We really believed we could change the world. Forty-seven years later, I had planned to use the line again in the victory speech I hoped to deliver on election night. "I'm older now. I'm a mother and a grandmother," I would have said. "But I still believe with all my heart that we can make the impossible, possible. Look at what we're celebrating tonight."
But in the end, there was nothing to celebrate. The glass ceiling held. The impossible remained so. I looked at Tala. We had never met before this moment, but in so many ways, I felt like I had been fighting for her and millions like her my entire career. And I had let them all down.
Yet here she was, bright-eyed and full of spirit, asking me to sign this black-and-white photo. It meant something to her. So did those words. Despite my defeat, she still believed in making the impossible possible.
It was time to go. There was a long walk through the snaking halls of the old academic building to get out to the tent where the graduation ceremony would be held. President Johnson and I lined up behind the college's trustees, and the procession began.
We turned a corner and saw young women in black robes lining both sides of the hall. They began to clap and cheer wildly. Around another corner were more students. They went on and on, hundreds of them, the entire senior class, lined up like an honor guard. Their cheers were deafening. It was like they were letting months of pent-up feelings pour out—all the hope and hurt they'd felt since November or perhaps since long before. I felt loved and lifted, carried aloft on a wave of emotion.
Finally, we emerged out into the misty air, with waiting parents and news cameras and all the pomp and circumstance of a college commencement. Sitting on the stage, I tried to compose myself, but my heart was still beating fast. Soon Tala was standing at the podium, just like me in the photo. She looked great up there, and her speech was graceful and heartfelt.
Noting that green was the 2017 color, she compared her classmates to emeralds. "Like us, emeralds are valuable, rare, and pretty durable," she said. "But there's something else emeralds are known for: their flaws. I know it's hard to admit, especially as Wellesley students, but we all have a lot of flaws. We are incomplete, scratched up in some places, jagged around the edges."
I leaned in, curious. This is not what I had expected to hear.
"Flawed emeralds are sometimes even better than flawless ones," Tala went on, "because the flaws show authenticity and character."
There was that word again, authenticity. But she was using it as a balm instead of a bludgeon. Flawed. How often had I heard that word over the past two years. "Flawed Hillary." But here was Tala defiantly reclaiming the word, insisting on the beauty and strength of imperfection.
Now her classmates were leaning in, too. They snapped their fingers instead of clapping, as Tala smiled and built to her close.
"In the words of Secretary Clinton, never doubt that you are valuable and powerful and deserving of every chance in the world to pursue your dreams," she told the class of 2017. "You are rare and unique. Let yourself be flawed. Go proudly and confidently into the world with your blinding hues to show everyone who's boss and break every glass ceiling that still remains."
Now the snaps gave way to cheers. I was among the loudest. I stood and applauded and felt hope and pride rising in my heart. If this was the future, then everything had been worth it.
Things are going to be hard for a long time. But we are going to be okay. All of us.
The rain was ending. It was my turn to speak.
"What do we do now?" I said. There was only one answer: "Keep going."
## Acknowledgments
I dedicated this book to the team that stood with me in 2016.
I will always be grateful to Barack and Michelle Obama and their staffs for all their support before, during, and after the campaign; Tim Kaine, Anne Holton, and their family; everyone who spent endless days and nights working in our Brooklyn headquarters; the state directors and state staffs, field and advance teams, coordinated campaign staff, volunteers, interns, and fellows in all fifty states; our consultants, contractors, and vendors; the team at the DNC; our lawyers at Perkins Coie; House and Senate Democrats, Governors, Mayors, and their staffs; and all the friends and surrogates who poured their hearts into our campaign. I wish I could thank each and every one of you. In fact, I asked the publisher whether we could print all your names here—more than 6,500—but they said it would make this book twice as long. Please know that you are written in my heart, now and always.
What Happened wouldn't have happened without the help and support of another great team. This process has been intensely personal, but there's no way I could have done it alone. I'm grateful to everyone who lent a hand in big ways and small. They proved yet again that we really are stronger together.
This starts with Dan Schwerin, Megan Rooney, and Tony Carrk, who spent many hours with me around my kitchen table in Chappaqua, reliving memories and helping me discover what this book would be.
Dan walked into my Senate office a dozen years ago as a young staffer and has been with me ever since. He helped me with my last book, Hard Choices, led my speechwriting team in 2016, and signed on again with this book. I could not have done this and so much else without him. His keen intellect and superior organizational skills are unmatched. He wrestled to the ground reams of facts and arguments to help me make my case. And he's a calm, steady presence in the midst of crisis, and good company all the rest of the time.
Megan Rooney was part of my team at the State Department and came back as a speechwriter for the campaign. She dove into the rigors of this book with thoughtful intelligence, wit, and a well-honed skill at storytelling, all of which made this better than I could have done alone. She was my partner in feminist mind melds and brought her good humor, mischievous smile, and twinkling eyes to many long nights when we all needed a lift.
She and Dan continued their long writing partnership and I loved watching them sitting side by side on my couch, computers on their laps, working on a piece of text, not talking but understanding each other and the task perfectly.
Tony Carrk joined me on my 2008 campaign as a researcher, and in 2016 took charge of that critical team. Through intense pressure and stressful days, he was the go-to guy who knew whatever we needed. His dedication and decency are evident to all. And he did it while becoming the father of a little girl, Celia, during the campaign and a little boy, Diego, during the book writing.
Huma Abedin, Nick Merrill, Cheryl Mills, Philippe Reines, Heather Samuelson, and Jake Sullivan have been by my side for years, through triumph and heartbreak. As they have so many times before, they supported this project and me with wise advice and perspective.
I'm indebted to everyone who shared memories and insights, offered advice, helped review pages and facts, and supported me and my work throughout this process, including Emily Aden, John Anzalone, Charlier Baker, Kris Balderston, De'Ara Balenger, Shannon Beckham, Daniel Benaim, Joel Benenson, Jonathan Berkon, David Binder, Allida Black, Sid Blumenthal, Susie Buell, Glen Caplin, Dennis Cheng, Corey Ciorciari, Brian Cookstra, Brynne Craig, Jon Davidson, Howard Dean, Karen Dunn, Marc Elias, YJ Fischer, Oren Fliegelman, Oscar Flores, Tina Flournoy, Danielle Friedman, Ethan Gelber, Teddy Goff, Jorie Graham, Shane Hable, Tyler Hagenbuch, Maya Harris, Trevor Houser, Jill Iscol, Jay Jacobs, Beth Jones, Elizabeth Kanick, Grady Keefe, Ron Klain, Jen Klein, Harold Koh, Elan Kriegel, Amy Kuhn, David Levine, Jenna Lowenstein, Bari Lurie, Moj Mahdara, Jim Margolis, Capricia Marshall, Marlon Marshall, Garry Mauro, Michael McFaul, Judith McHale, Kelly Mehlenbacher, Craig Minassian, Robby Mook, Minyon Moore, Lissa Muscatine, Navin Nayak, Kevin O'Keefe, Ann O'Leary, Jennifer Palmieri, Maura Pally, Adam Parkhomenko, Matt Paul, Lauren Peterson, John Podesta, Jacob Priley, Amy Rao, Ed Rendell, Mary Kate Rooney, Emmy Ruiz, Rob Russo, Sheryl Sandberg, Marina Santos, Kristina Schake, Oren Schur, Ella Serrano, Meredith Shepherd, Bill Shillady, David Shimer, Anne-Marie Slaughter, Craig Smith, Burns Strider, Donna Tartt, Mario Testino, Opal Vadhan, Lona Valmoro, Jon Vein, Melanne Verveer, Mike Vlacich, Rachel Vogelstein, Diane von Fürstenberg, Don Walker and the Harry Walker Agency, Maggie Williams, Graham Wilson, Theresa Vargas Wyatt, and Julie Zuckerbrod.
Thanks as well to all the experts and academics who helped me develop the policies mentioned in this book and many more that comprised the most progressive Democratic platform in history. Those policies continue to offer a road map for building a better future. You can read more about them at www.hillaryclinton.com/issues.
I couldn't have gotten through the election and its aftermath without my friends. They kept me sane, took me to the theater, came for visits, went on walks, made me laugh, sustained my spirit, and endured an occasional venting session. I'm so looking forward to spending more time with all of you.
I'm indebted to Simon & Schuster, especially Chief Executive Officer Carolyn Reidy, and my editors Jonathan Karp and Priscilla Painton, all of whom spent many hours advising me and reviewing drafts. Thanks to their team: Tamara Arellano, Phil Bashe, Eloy Bleifuss, Alice Dalrymple, Amar Deol, Lisa Erwin, Jonathan Evans, Tiffany Frarey, Megan Gerrity, Cary Goldstein, Megan Hogan, John Paul Jones, Ruth Lee-Mui, Kristen Lemire, Dominick Montalto, Laura Ogar, Anne Tate Pearce, Emily Remes, Richard Rhorer, Jackie Seow, Elisa Shokoff, Laura Tatham, and Dana Trocker.
Thanks to my attorneys: Bob Barnett, debate prep sparring partner and publishing sage; David Kendall, who lived through the email craziness with me; and their team at Williams and Connolly—Tanya Abrams, Tom Hentoff, Deneen Howell, Michael O'Connor, Adam Perlman, Ana Reyes, Amy Saharia, Katherine Turner, and Steve Wohlgemuth.
To the men and women of the United States Secret Service, thank you for always having my back. Your professionalism and courage are an inspiration.
And to the 65,844,610 Americans who voted for me, thank you for your trust and confidence. We didn't get there this time, but I hope you never lose faith in the vision we share for a better America.
The poet Max Ehrmann says, "Whatever your labors and aspirations, in the noisy confusion of life, keep peace with your soul." My peace is only possible because of the love and support of Bill, Chelsea, Marc, Charlotte, Aidan, and our entire family. Thank you for being the greatest editors, sounding boards, stress relievers, and joy givers in the world. And thanks for being excited that I'm around a lot more these days.
## About the Author
© SERGIO BASTANI
HILLARY RODHAM CLINTON is the first woman in U.S. history to become the presidential nominee of a major political party. She served as the 67th Secretary of State—from January 21, 2009, until February 1, 2013—after nearly four decades in public service advocating on behalf of children and families as an attorney, First Lady, and Senator. She is a wife, mother, and grandmother.
MEET THE AUTHORS, WATCH VIDEOS AND MORE AT
SimonandSchuster.com.au
Authors.SimonandSchuster.com.au/Hillary-Rodham-Clinton
## Permissions
PAGE 30
"Still I Rise" from And Still I Rise: A Book of Poems by Maya Angelou, copyright © 1978 by Maya Angelou. Used by permission of Random House, an imprint and division of Penguin Random House LLC. All rights reserved.
PAGE 31
"Hallelujah" by Leonard Cohen, collected in STRANGER MUSIC: Selected Poems and Songs. © 1993 Leonard Cohen and Leonard Cohen Stranger Music, Inc., used by permission of The Wylie Agency LLC.
PAGE 32
Bill Shillady, "Sunday is Coming," comprised of commentary by Pastor Matt Deuel that originally appeared in the Mission Point Community Church blog, given to Hillary Rodham Clinton November 9, 2016. <http://missionpoint.net/its-friday-but-sundays-coming/>. Used by permission.
PAGE 34
Excerpt from The Return of the Prodigal Son: A Story of Homecoming by Henri Nouwen, copyright © 1992 by Henri J. M. Nouwen. Used by permission of Doubleday Religion, an imprint of the Crown Publishing Group, a division of Penguin Random House LLC. All Rights reserved.
PAGES 38 AND 56
Extracts taken from "East Coker," Four Quartets by T.S. Eliot © Set Copyrights Limited and reprinted by permission of Faber & Faber.
PAGE 129
Excerpt from "The Room Where It Happens" from Hamilton by Lin-Manuel Miranda. Used by permission of author.
PAGE 159
Excerpt from The Guernsey Literary and Potato Peel Pie Society: A Novel by Mary Ann Shaffer and Annie Barrows, copyright © 2008 by The Trust Estate of Mary Ann Shaffer & Annie Barrows. Used by permission of The Dial Press, an imprint of Random House, a division of Penguin Random House LLC. All rights reserved.
PAGE 172
"Giving and Receiving Consolation" from Bread For The Journey: A Daybook of Wisdom and Faith by Henri J.M. Nouwen. Copyright © 1997 by Henri J.M. Nouwen. Reprinted by permission of HarperCollins Publishers.
PAGE 192
Excerpt from "To be of use" from Circles on the Water by Marge Piercy, copyright © 1982 by Middlemarsh, Inc. Used by permission of Alfred A. Knopf, an imprint of the Knopf Doubleday Publishing Group, a division of Penguin Random House LLC. All Rights reserved.
PAGE 396
Copyright Vox Media, created by Javier Zarracina for The most common words in Hillary Clinton's speeches, in one chart by David Roberts, published December 16, 2016; <https://www.vox.com/policy-and-politics/2016/12/16/13972394/most-common-wordshillary-clinton-speech>.
PAGE 400
Gallup, based on research done in collaboration with Georgetown University and the University of Michigan.
ALSO BY HILLARY RODHAM CLINTON
Hard Choices
Living History
It Takes a Village
Dear Socks, Dear Buddy: Kids' Letters to the First Pets
An Invitation to the White House: At Home with History
## Index
A note about the index: The pages referenced in this index refer to the page numbers in the print edition. Clicking on a page number will take you to the ebook location that corresponds to the beginning of that page in the print edition. For a comprehensive list of locations of any word or phrase, use your reading system's search function.
ABC News,
Abedin, Huma, , , , , , , –95, –15, ,
abortion, , , ,
Abrams, Tanya,
Abramson, Jill,
Abu Ghraib,
Access Hollywood tape of Trump's remarks about women, , , , , , –39, , –49, ,
Adams, Abigail,
Adams, John, , ,
Adams, John Quincy,
Adams, Ruth,
Adapt Pharma, –62
Aden, Emily,
Adichie, Chimamanda Ngozi,
Affordable Care Act (ACA; Obamacare), , , , , , , , , , , , , –84, , , ,
Afghanistan,
Africa:
Ebola in, , –49
elephants in,
farmers in,
HIV/AIDS in,
African Americans, , , , , –13, ,
Black Lives Matter, , –6,
in Flint, ,
gun violence and, –75,
police officers and, –78
segregated schools and,
voting and, , –20
see also civil rights
AIDS,
Ailes, Roger, –67
Alaska for America, –39
Alaska Permanent Fund,
Albright, Madeleine, ,
Alexander, Keith,
Ali, Muhammad, –18
Allen, Jon,
Alliance for a Healthier Generation,
Alpha Natural Resources,
Altman, Sam,
Alt-Right, ,
Alzheimer's disease,
Amanpour, Christiane,
American Federation of Teachers (AFT), ,
American Heart Association,
American National Election Studies,
AmeriCorps,
Ana Grace Project,
Angelou, Maya, , –30
anger, , , , –72, –79, , , ,
Anthony, Marc,
Anthony, Susan B.,
Anzalone, John, ,
Appalachia, , , , –70, , ,
Appalachian Regional Commission,
Apple,
Apprentice, The,
approval ratings, , , ,
Arch Coal,
Arellano, Tamara,
Arizona,
Arkansas, , , , , ,
Arkansas Travelers,
artificial intelligence, ,
Assad, Bashar al-,
Assange, Julian, , –45,
Assault on Reason, The (Gore),
Associated Press (AP), –45, , ,
Atlantic,
Atlantic Alliance, ,
Atwater, Lee, –35, , ,
Atwood, Margaret, –27
Austria,
authenticity, –25, ,
authoritarianism,
automobile industry, –10,
Baker, Charlie,
Baker, James,
Balderston, Kris,
Balenger, De'Ara,
Banks, Elizabeth, –51
Bannon, Steve, , ,
Bardack, Lisa,
Barden, Jackie,
Barden, Mark,
Bareilles, Sara,
Barnes, Peter,
Barnett, Bob, , ,
Barrett, John,
Barrie, J. M.,
Barrows, Annie,
Bashe, Phil,
Bayrock Group,
Beard, Mary,
Beatles, ,
Beck, Charlie,
Beckett, Dino,
Beckham, Shannon,
Begala, Paul,
Belcher, Cornell,
Benaim, Daniel,
Benenson, Joel, , –68, , , , ,
Benghazi terrorist attack, , –31, , –99, ,
Berkon, Jonathan,
Bernall, Cassie,
Bernall, Misty,
Bernie Bros, ,
Bernstein, Jared, –81
Better Than Bullying,
Between Two Ferns with Zach Galifianakis, ,
Beyoncé,
Bible, ,
Biden, Jill,
Biden, Joe, , , , , , , , –5, , , ,
Bill & Melinda Gates Foundation,
Binder, David, ,
bin Laden, Osama, , , ,
birth control, ,
Black, Allida,
Black Lives Matter, , –6,
Black Man in the White House, A (Belcher),
Blair, Tony,
Blair Center of Southern Politics and Society,
Bland, Sandra,
Blankenship, Don, , –76
Bleifuss, Eloy,
Bloomberg, Michael, , , ,
Bloomberg News, ,
Bloomer, Amelia,
Blumenthal, Sid,
Bly, Nellie,
Bon Jovi, Jon, ,
Booker, Cory, –50
Bordo, Susan,
Borochoff, Daniel,
Boston Globe,
Bowling Alone (Putnam),
Brady Bill, , ,
brain,
Bratton, Bill,
Brazile, Donna,
breath work,
Breitbart News Network, , , –68,
Brennan, John, ,
Brexit, ,
Britain, , , , ,
Broadway shows,
Brooklyn, Clinton campaign headquarters in, , , , , , , , ,
Brooklyn Navy Yard, , ,
Brown, David, –85
Brown, Michael,
Brown, Sherrod,
Brzezinski, Mika,
Buell, Susie,
Buchan, John,
Buckingham Palace,
Buffett, Jimmy and Jane,
Burns, Ken, –78
Bush, Barbara,
Bush, George H. W., , , , –34,
Bill Clinton's inauguration and,
Bush, George W., , , , , , , , , , , , ,
inauguration of,
Putin and,
at Trump's inauguration, , ,
Bush, Jeb,
Bush, Laura,
Bush dynasty,
Buzzfeed,
Byrd, Robert,
Cairo, –3
California, –45, ,
Cambodia,
Cambridge Analytica,
campaign finance laws, , , , ,
capitalism,
Caplin, Glen,
carbon emissions, , ,
Carnegie Corporation of New York,
Carr, Gwen, , , ,
Carrier Corporation,
Carrk, Tony, –4, –67
Carter, Jimmy, , , ,
Cartwright, Matt, –8
Carville, James,
Castile, Philando,
caucuses, , , , ,
Center for American Progress,
Central Baptist Church,
CGI America,
CGI International,
Chaffetz, Jason, ,
Chait, Jonathan,
change, –215, , , –10, –18, –37
and Hillary Clinton falsely viewed as defender of status quo, ,
progressive, , , –79, , , , , –27, –31, ,
social, , , ,
Chappaqua, N.Y., Clintons' home in, , , , –85,
Charity Navigator,
CharityWatch,
Charleston church shooting,
Cheng, Dennis, –66,
Chertoff, Michael, –9
Chicago Cubs, –101
childcare, , , , ,
children, , , , , –9
with disabilities, –201
Children's Defense Fund (CDF), , –201, , , ,
Children's Health Insurance Program (CHIP), , ,
China, , , , , , , , , ,
Tiananmen Square massacre in,
Chinese proverb,
Chipotle, –60
Chisholm, Shirley,
Christie, Chris,
Chung, Jason,
Churchill, Winston,
CIA, , , , ,
Cillizza, Chris,
Ciorciari, Corey,
Citizens United v. FEC, ,
civil rights, , , , , , , ,
Sessions and,
Civil War,
Clapper, James, , ,
Clarke, Richard,
Clarkson, Kelly,
Clean Power Plan,
climate change, , , , , , , , , ,
Clinton, Bill, , , , , , , , , , , , , , , , , , , , , , , –65, , , , , –48, , , , , , , , –60,
Arkansas gubernatorial election of 1980 lost by, ,
Chelsea and, , –50, , , –59,
at Democratic National Convention, , , ,
Democratic Party and, –35
early life of, ,
on Election Night (2016), , , –88
first presidential inauguration of, ,
gun laws and, ,
heart surgery of,
Hillary's concession speech and, ,
and Hillary's decision to run for president, , , , –48,
Hillary's marriage to, , –61, , , –60
Hillary's mother and, –61
Lynch and,
office server of, ,
philanthropy of, –43,
presidential administration of, see Clinton administration
presidential campaign of 1992, , , , , , , , , , , , ,
Secret Service and, –90
tax returns of, ,
Thanksgiving hosted by, –29
television watching of,
transparency of,
at Trump's inauguration, –8, –13
at Trump's wedding to Melania,
welfare reform and, –8
women accusers of,
Clinton, Chelsea, , , , , , , , –59, , , , , ,
Bill and, , –50, , , –59,
childhood of, –97, , –43, –54,
at Democratic National Convention, –49, , , –57,
and her grandmother, ,
health care issues and, , –55,
Hillary's 2016 campaign and, , , , , –56, , ,
philanthropy of, , ,
as President's daughter, –54
She Persisted,
wedding of, , ,
Clinton, Hillary Rodham:
accomplishments and history of public service, ,
activist identity of, –202
approval ratings of, , , ,
books and reading of, , ,
Broadway shows attended by,
childhood of, , , –48, , ,
at Chipotle, –60
clothing of, –89,
"cookies and tea" remark of, –19, ,
as "divisive,"
emails of, see email controversy
as First Lady, , , , , , ,
friends of, , –71
hair and makeup of, –88,
Hard Choices, , ,
health of,
home of, , , –29, , –85,
It Takes a Village, –39
law career of, , –19, , , ,
in law school, , , ,
letters to, –25
marriage of, , –61, , , –60
as mother, –59, ,
motorcades for, –91
name of,
origami cranes sent to, –26
pneumonia of, –2
presidential campaign of 2008, , , , , , , , –64, , , , , , , , , –44, ,
religious faith of, –32, , , ,
as Secretary of State, , , , , , , , –61, , , , , –3, , , , , , , ,
Secret Service and, , , –90, , , ,
senate campaign of, , ,
senate reelection campaign of,
as Senator, , , , , , , , , , , , , , , , ,
sign in house of,
speaking engagements of, –46,
speaking voice of, –25
tax returns of, ,
tearful moment of, –24
television watching of,
Thanksgiving hosted by, –29
transparency of,
at Trump's inauguration, –8, –13
University of Texas speech of, –37
vitriol toward, –27,
at Wellesley College, , , , ,
Wellesley College graduation speeches of, –57, , , , , , –64
Whitewater investigations and, ,
yoga and breath work practiced by, ,
Clinton, Hillary Rodham, 2016 presidential campaign of:
air travel in,
announcement video for,
assembling team for, –72,
birthdays and holidays on the road,
Brooklyn headquarters of, , , , , , , , ,
Chelsea Clinton and, , , , , –56, , ,
children at events for, ,
concession and speech, , , –19, , , , , –88, , –59
data analytics and, , , –76,
debate prep sessions in, , –7,
debates with Trump in, –39, , , –74
debate with Sanders in, –31,
early days of, –81
Election Day and Night, –89, –3
election loss, –23, ,
final whirlwind swing in,
food and, –93
fund-raising for, –98
Hillary viewed as defender of status quo during, ,
Hillary's "basket of deplorables" comment and, ,
historic nature of, , , –59,
life during, –107
logo for, , ,
"Mirrors" ad in, –38
NBC's "Commander in Chief Forum" and, –22
nomination, xii, xiv, –59,
OTR (off the record) visits in, ,
policy team for, ,
press corps traveling with, –99
rallies in, –96, , , , , ,
reasons for running, –57, ,
reflections on reasons for loss in, –425
Roosevelt Island launch of, , –81,
roundtable events in, , , –97
selfies and, ,
staff of, –23,
"Stronger Together" slogan of, , , , –55, , ,
town hall meetings in, , , , , ,
victory speech prepared, –83
votes received, xiv, , , , –87, ,
word frequency of Hillary's speeches in,
and working class and rural communities, –87, –98
Clinton, Virginia (mother of Bill),
Clinton administration, , , ,
gun laws and, ,
health care reform and, , , , ,
impact of, –35
Moving to Opportunity for Fair Housing program of,
welfare reform and, –8
Clinton dynasty,
Clinton fatigue, ,
Clinton Foundation, –42, , , , , ,
Adapt Pharma and, –62
Clinton Global Initiative (CGI), –44
Clinton Rules, –21
Clue of the Tapping Heels, The (Keene),
Clyburn, Jim,
CNN, , , , ,
coal miners, , , –66, –76, –80, –83,
Upper Big Branch Mine disaster, , –76
Cohen, Leonard,
Cohn, Gary,
Colbert, Stephen, ,
Cold War, , ,
Coleman, Bernard,
college, ,
costs of, , , , , , , ,
Colorado, , ,
Columbia Journalism Review,
Columbine High School massacre,
Comey, Jim, , , ,
DNC computer hacking and,
email investigation and, –92, , –20, , , ,
October 28 letter to Congress from, –14, , –20, , , , –7, ,
press conference of, –12,
Reid's letters to, –46, –51
Russia investigation and, , –5, , , , , , ,
Russian forged document and,
Trump's firing of, –91
Commander in Chief Forum, –22
Congress, U.S., , , , , , , , , , , , , ,
Comey's October 28 letter to, –14, , –20, , , , –7, ,
Flint water crisis and,
see also Senate, U.S.
conspiracy theories, , , , , , ,
Constitution,
Khan and,
Second Amendment to, , –88
Nineteenth Amendment to, ,
Consumer Financial Protection Bureau,
Conway, Kellyanne,
Cook, Tim,
Cookstra, Brian,
Cooper, Anderson,
Copley, Bo, –81
Copley, Lauren, ,
Cornyn, John,
corporate power, , ,
Costa, Kristina,
Cotton, Tom,
Crabtree's Kittle House Restaurant and Inn,
crack epidemic,
Craig, Brynne, ,
crime, ,
organized,
see also law enforcement and criminal justice
Crimean Peninsula and Ukraine, –31, , , –41, , , ,
Crowdstrike,
Cruz, Ted, ,
Cummings, Elijah,
Cuomo, Mario,
cyber warfare, , , , –56, , , , –71, –75
Daily Show, The,
Daley, Richard,
Dalrymple, Alice,
Daou, Peter,
data analytics, , , –76, , , –22
Daughtry, Leah,
Davidson, Jon,
Davis, Jordan,
Day, Andra,
Dean, Howard, –53,
Declaration of Independence,
Declaration of Sentiments, ,
Defense Intelligence Agency,
de la Renta, Oscar and Annette,
democracy, , , , , , , , ,
partisan politics and,
Russian attacks on, , –26, , , , , ; see also Russia
Democracy in America (de Tocqueville),
Democratic Congressional Campaign Committee,
Democratic National Committee (DNC), , ,
hacking attack on, –42, –48,
Democratic National Convention of 1968, –98
Democratic National Convention of 2016, , , , , –57, ,
Bill Clinton at, , , ,
Chelsea Clinton at, –49, , , –57,
Hillary Clinton at, xii, , , –57
Michelle Obama at, ,
Democrats, Democratic Party, , , , –50, , –56, , , , , , , –38, , –86, , , , , , , , –68
Bill Clinton and, –35
Eleanor Roosevelt and,
environmental issues and, –74
future of, –25, –55,
guns and, , –89
health care and,
optimism and,
Reagan and,
Russian propaganda and,
Sanders and, ,
sexism and, –28
third-party candidates and,
Trump supporters among, –17,
working class and, , –74, , , –17
Denmark, ,
Deol, Amar,
Depression, Great, , ,
Des Moines Register,
Destruction of Hillary Clinton, The (Bordo),
Detroit, Mich., ,
Deuel, Pastor Matt,
Devil's Bargain: Steve Bannon, Donald Trump, and the Storming of the Presidency (Green),
Diane D. Blair Center of Southern Politics and Society,
Dickens, Charles,
Dionne, E. J.,
Dodson, James,
Doe, Emily, –41
Dole, Bob, ,
Donald J. Trump Foundation, –47,
Donovan, Ray,
Dostoevsky, Fyodor,
Douglass, Frederick,
Dowd, Katie,
Downton Abbey,
Drane, LaDavia,
Dreamers,
Drew, Nancy,
Drudge Report,
drug abuse, , –68,
crack epidemic,
opioid epidemic, , –62, , , –82
Dunn, Karen, , ,
Earhart, Amelia,
"East Coker" (Eliot), , –57
eBay,
Ebeling, Betsy, –98, , , ,
Ebola epidemic, , –49
economy, , , , , , , , , , , , , , , , , , –18, –24
financial crisis of 2008–2009, , , , , , , ,
Hillary Clinton's proposals for, –36
voters' anxiety over, –18
see also jobs
Edelman, Marian Wright, , , –201, –8,
Edelman, Peter,
Education for All Handicapped Children Act,
Edwards, John, ,
Egypt, –3,
Ehrmann, Max,
Eisenhower, Dwight, ,
Electoral College, , –87, ,
Elias, Marc, ,
Eliot, T. S., , –57
Elizabeth II, Queen,
Elizabeth Glaser Pediatric AIDS Foundation,
email controversy, , –73, , , , , –23, –323, , –6,
and classification of documents, –8, –11
Comey and, –92, , –20, , , ,
Comey's October 28 letter to Congress and, –14, , –20, , , , –7, ,
Comey's press conference and, –21,
and convenience of email setup, –95
and deletions of emails, –300,
hacking vulnerability and,
Hillary Clinton's press conference on,
investigations in, , , , –92, , –5, –15, , ,
media coverage of, , , , –23, , , , –5, –21, , , , , ,
national security and, , –22, , –10
New York Times and, –5, , , , –20
public release of emails in, –3,
Sanders on, ,
State Department and, –96, –96, , –300, –3, , , ,
Weiner and, –15
Emerson, Ralph Waldo (attributed),
EMILY's List,
empathy, , –44
employment, see jobs
energy production, , , , –40,
coal miners and, see coal miners
fossil fuels, , ,
Engagement Labs,
Enlightenment,
Environmental Protection Agency (EPA),
environmental regulations, –74
Ephron, Nora,
Ernie,
Erwin, Lisa,
Esquire,
European Union, ,
Brexit and, ,
Evans, Jonathan,
Everytown for Gun Safety,
exercise,
Exeter, N.H.,
Facebook, , , , , , , , , , , , ,
fake groups and accounts on, , –65
Pantsuit Nation group on, ,
Russian propaganda on, –62
facts, see truth and facts
faith, –32,
fake news, –52, –61, , , ,
Fallon, Brian,
false equivalency, –20,
Fay, Brad,
FBI, , , –17, , , , ,
DNC hacking and,
email investigations of, , , , –92, , , –10, ,
Russia investigation of, , , –5, , , , , , –55
Russian fake document sent to, –64
Weiner and, –15
Federal Election Commission, ,
Feingold, Russ, ,
Feinstein, Dianne,
feminism, ,
defining,
see also women's movement
Ferguson, Jesse,
Ferrante, Elena,
Ferraro, Geraldine,
financial crisis of 2008–2009, , , , , , , ,
financial industry, , , , –26, , , , ,
Finch, Charles,
Finney, Karen,
Fiorina, Carly,
First Calvary Baptist Church,
Fischer, YJ,
FiveThirtyEight.com,
Fliegelman, Oren,
Flint water crisis, –15,
Flores, Oscar, , ,
Florida, , , ,
Flournoy, Tina,
Flynn, Michael, –301, , , –58,
focus groups,
Foer, Franklin, ,
food stamps, , ,
foreign policy,
NBC's "Commander in Chief Forum" and, –22
Trump and, , –35
see also national security
Forman, James, Jr.,
fossil fuels, , ,
Four Freedoms Park,
Fox News, , , , , , , , , , –67, ,
France, , , ,
Francis, Pope, , ,
Frank, Thomas,
Franklin, Benjamin,
Franklin & Marshall Poll, –3
Frarey, Tiffany,
Frazier, Joe,
Freedom of Information Act (FOIA), , ,
Freeman, Jelani,
Friedman, Danielle,
Friedman, Tom,
friendships, –69
of Hillary Clinton, , –71
Frost, Robert,
Fudge, Marcia,
Fulton, Sybrina, ,
Funny or Die,
Gaddafi, Muammar,
Galifianakis, Zach, ,
Gallup, ,
García Márquez, Gabriel,
Garner, Eric, ,
Gates, Bill,
Gates, Melinda,
Gates Foundation,
Gayle, Tyrone, ,
Gazprom,
Gelber, Ethan,
General Social Survey,
Gensler, Gary,
Georgetown University,
George Washington Bridge,
George Washington University, ,
Georgia,
Gerasimov, Valery,
Germany, , ,
Gerrity, Megan,
Gessen, Masha,
Gibran, Kahlil,
Giffords, Gabby, ,
Gillibrand, Kirsten,
Ginsburg, Ruth Bader, , ,
Giuliani, Rudy, –17
globalization, ,
Goetz, Isabelle,
Goff, Teddy, ,
Goldstein, Cary,
Gonzalez, Alberto,
Goodlander, Maggie,
Google, , , ,
Gordon, Phil,
Gore, Al, , ,
in presidential election of 2000, ,
Gore, Tipper,
Gorkov, Sergey,
government, size and role of,
Gowdy, Trey, –99
Graduate, The,
Graham, Franklin,
Graham, Jorie, ,
Grassley, Chuck, –96
grassroots organizing, , , , –55,
gratitude,
Great Britain, , , , ,
Great Depression, , ,
Great Expectations (Dickens),
Great Recession,
Great Society,
Green, Joshua,
Greenberg, Stan, –17,
Ground Zero first responders, , ,
Grunwald, Mandy, , , ,
Guardian,
Guccifer, , ,
GuideStar,
guns, , –91, ,
accountability for makers and sellers of, , –87,
background checks and, , ,
Brady Bill and, , ,
Clinton administration and, ,
Columbine High School massacre,
Democrats and, , –89
Giffords and, ,
hunting and, –82
law-abiding owners of, –82
loopholes in laws on,
Michael Brown shooting,
Mother Emanuel Church massacre, , –41
Mothers of the Movement and, –76, –80, –85, , ,
no-fly list and, ,
NRA and, , , –83, –87, ,
Obama and, ,
police officers and, –80, –85, ,
Pulse nightclub shooting,
race and, –75,
Republicans and,
safety laws for, , , , , ,
Sanders and, –87,
Sandy Hook Elementary School shooting, , –91,
Second Amendment and, , –88
Trayvon Martin shooting, –75,
Trump and, –88,
Umpqua Community College shooting,
Hable, Shane,
Hagan, Kay,
Hagenbuch, Tyler,
Haiti, ,
Hale, Greg, ,
"Hallelujah" (Cohen),
Hamilton,
Hamilton, Alexander,
Hamilton, Dontre,
Hamilton, Maria,
Handmaid's Tale, The (Atwood),
Hannah,
Hannon, Stephanie,
Hard Choices (Clinton), , ,
Harkin, Tom,
Harris, Kamala,
Harris, Maya, , , ,
Harvard Law School,
Harvard University,
Shorenstein Center on Media, Politics and Public Policy, , –23,
Havel, Václav, ,
Hawking, Stephen,
HBO,
Head Start,
health care, , , , –63, , , , , , , , , , , , , , , –23
Affordable Care Act, , , , , , , , , , , , , –84, , , ,
Alzheimer's disease,
Chelsea Clinton and, , –55,
Children's Health Insurance Program, , ,
Clinton administration's efforts to reform, , , , ,
Democrats and,
Flint water crisis, –15,
Ground Zero first responders, , , ,
HIV/AIDS,
lead paint poisoning,
Medicaid, , –7, , , , , ,
Medicare, , , , , ,
opioid epidemic, , –62, , , –82
Sanders' plan for, –55,
Trump and, , , , ,
women's services and reproductive rights, , –32, , ,
Height, Dorothy,
Hentoff, Tom,
Herman, Alexis,
heroin addiction, ,
HIV/AIDS,
Hochsprung, Dawn, –91
Hockley, Nicole, –90
Hoffer, Eric,
Hofstra University,
Hogan, Megan,
Holly,
Holt, Blair, –79
Holt, Lester, ,
Holt, Ron, ,
Holton, Anne, , ,
Homeland,
Homeland Security, Department of, ,
Hornbrook, Alex,
Horton, Willie,
Hotel at Kirkwood Center,
House Intelligence Committee, ,
House of Prayer Missionary Baptist Church,
Houser, Trevor,
Howe, Rosemarie,
Howell, Deneen,
Huffington, Arianna,
human rights,
see also civil rights; women's movement
Human Rights Campaign,
humility, ,
Hunt, Donnie,
hunting, –82
Hurricane Katrina, ,
immigration, immigrants, , , , , , , , , , , –17
Mexican, and Trump, , , –25, , , , ,
Indiana,
income,
inequality in, , , , , , , , , , ,
using shared national resources to pay dividends, –39
wages, , , , , , , , , , ,
Indiana,
Infowars, ,
infrastructure, , , , , , , ,
International AIDS Conference,
internet and social media, , , , ,
algorithms used in,
"bots" and, –61
Facebook, see Facebook
Russian propaganda and, –62, –70,
"trolls" and, –61
Twitter, see Twitter
YouTube, , , ,
Intrepid, U.S.S., ,
"Invictus" (Henley),
Iowa, , , –64, , , , , , ,
Iran, , , , ,
Iraq, , , , , ,
Iscol, Jill,
ISIS, –49, , , ,
Israel, ,
It Takes a Village (Clinton), –39
Jackson, Andrew,
Jacob K. Javits Convention Center, , ,
Jacobs, Jay,
Jacobson, Elliott,
James, Henry,
Janelle,
Jaylon, –13,
Jay-Z,
Jefferson, Thomas, ,
Joan of Arc,
jobs, , , , –36, , –87, , , –17, ,
automation and, , , ,
in coal mines, see coal miners
family and medical leave for, , ,
in retail,
in steel industry, , ,
training in, , ,
wages in, , , , , , , , , , ,
women and, , ,
see also working class
John XXIII, Pope,
Johnson, Gary,
Johnson, Jeh, ,
Johnson, Lyndon, ,
Johnson, Paula A., , ,
Johnson Controls,
Jones, Alex, , , ,
Jones, Beth, ,
Jones, Don,
Jones, John Paul,
Jordan, Barbara,
journalists, see media
Journal News,
Justice Department, U.S., , , , –63
in email controversy, , , , , , , –13, ,
see also FBI
Kaine, Anne,
Kaine, Tim, –19, , , , , ,
Kallstrom, Jim, –17
Kanick, Elizabeth,
Karp, Jonathan,
Kasparov, Garry,
Katy, –55
Keefe, Grady,
Keigher, Connolly, , , ,
Keith,
Keller, Helen,
Kelley, Virginia Clinton,
Kelly, Mark, ,
Kelly, Megyn,
Kendall, David, ,
Kennedy, Jim, –80
Kennedy, John F., ,
Kennedy, Robert F., ,
Kent State shootings, ,
Kentucky, , , , ,
Kenya,
Kenyon College,
Kerry, John, , , , , ,
Kessler, Glenn,
KGB,
Putin in, ,
Khan, Ghazala, , ,
Khan, Humayun, , ,
Khan, Khizr, , ,
Kim Jong-un,
kindness and love, –45
King, Angus,
King, Billie Jean,
King, Coretta Scott, ,
King, Martin Luther, Jr., , ,
Kinney, Barbara, ,
Kirkwood Community College,
Kislyak, Sergey, , –58
Kissinger, Henry,
Klain, Ron, , , , ,
Klein, Ezra,
Klein, Jen,
Kobach, Kris, –20
Koch, Charles and David, , –69, ,
Koh, Harold,
Kommersant,
Kos, Sierra,
Kriegel, Elan, , –2,
Kristin,
Kristof, Nicholas, ,
Krugman, Paul,
Kuhn, Amy,
Kushner, Jared, , , ,
Lacy, Barbara,
Lady Gaga,
Lakoff, George,
Lamott, Anne, –32,
Lang, Karin,
Laos,
LaPierre, Wayne,
Latinos, , , ,
Lauer, Matt, –22
Lauren,
Lauren, Ralph,
law enforcement and criminal justice, , –77, , , ,
incarcerating teenagers with adults, –200
police officers, –80, –85, , –6,
Violent Crime Control and Law Enforcement Act, –5
lead poisoning:
Flint water crisis, –15,
from paint,
League of Their Own, The, xvi
League of Women Voters,
Leahy, Pat,
Lean In: Women, Work, and the Will to Lead (Sandberg),
Lee-Mui, Ruth,
Left, , , ,
Legal Services Corporation,
Legend, John,
Legislative Correspondents Association, –7
Leibovitz, Annie,
Lemire, Kristen,
Lenin, Vladimir,
Leon, Donna,
Le Pen, Marine, , ,
Letizia, Marianne,
Let's Move!,
Letterman, David,
Levine, David,
Lewandowski, Corey,
Lewis, John,
LGBT people, , ,
marriage equality and, , ,
Pulse nightclub shooting and,
Libya,
Benghazi terrorist attack in, , –31, , –99, ,
Life,
Atwater article in, –35, , ,
life expectancy, ,
Lincoln, Abraham,
lobbyists,
Locking Up Our Own: Crime and Punishment in Black America (Forman),
Lopez, Jennifer,
Lott, Trent,
Louis-Dreyfus, Julia,
love and kindness, –45
Lowenstein, Jenna, ,
Lurie, Bari,
Lyman, Princeton,
Lynch, Loretta, –13,
Macron, Emmanuel, , , ,
Madame Tussauds New York, –7
Maddow, Rachel,
Magnitsky Act,
Mahdara, Moj,
Manafort, Paul, , , ,
Manchin, Joe, ,
Mandela, Nelson, , , ,
Manning, Greg,
Manning, Lauren,
manufacturing and industry, , , , ,
automobile, –10,
steel, , , ,
see also jobs
Marcia, –58
Margolis, Jim, , , , ,
Márquez-Greene, Nelba,
marriage equality, , ,
Marshall, Capricia, –101, ,
Marshall, Marlon, ,
Martin, Trayvon, –75,
Mauro, Garry,
McAuliffe, Terry, ,
McBath, Lucia,
McCain, John, , –15,
McCarthy, Eugene, ,
McCarthy, Joseph,
McCarthy, Kevin, ,
McCartney, Paul,
McClatchy Company, , –66
McConnell, Mitch, , , ,
McDowell County, W.Va., ,
McFaul, Michael, ,
McGovern, George, , ,
McHale, Judith,
Mckesson, DeRay,
McKinnon, Kate, ,
McSpadden, Lezley,
media, , , , ,
Clinton Foundation and,
Clinton Rules and, –21
email controversy and, , , , –23, , , , –5, –21, , , , , ,
fake news and, –52, –61, , , ,
false equivalencies and, –20,
in France,
Hillary Clinton's health and,
nightly newscasts,
political press corps, , –69, , –99
public policy coverage in, –23, , ,
and right-wing war on truth, –69,
storylines in,
Trump and, , , , , –400
word clouds of coverage of Hillary Clinton vs. Trump, ,
see also internet and social media
Medicaid, , –7, , , , , ,
Medicare, , , , , ,
Medvedev, Dmitry,
Meet the Press,
Mehlenbacher, Kelly,
Mercer, Robert and Rebekah, , –68, , ,
Merkel, Angela, ,
Merkley, Jeff,
Merrill, Nick, , , , , , ,
Methodism, , , , –97, ,
Mexican immigrants, , , –25, , , , ,
Mexico,
Mezvinsky, Aidan, , , , , , , , ,
birth of, ,
Mezvinsky, Charlotte, , , , , , , , , , , , , ,
birth of, ,
dance recital of,
Mezvinsky, Marc, , , , , , , , , , ,
wedding of, , ,
Micah,
Michigan, , , , , , , , , , , , ,
Detroit, ,
Flint water crisis in, –15,
Michigan Department of Environmental Quality,
middle class, , , , , , , , , , ,
Middleton, Clay,
midterm elections:
of 1994,
of 2014,
of 2018,
Mikulski, Barbara,
military,
Miller, Matt,
Mills, Cheryl, , ,
Minassian, Craig,
Miranda, Lin-Manuel,
misogyny,
in presidential election,
Republican Party and,
sexism vs., –15
see also sexism
Missouri,
Miss Universe pageant,
mistakes,
Mohonk Mountain House,
Moms Demand Action,
Mondale, Walter,
Montalto, Dominick,
Montgomery, Mike,
Mook, Robby, , , , , –84,
Moore, Michael,
Moore, Minyon, ,
Moore, Ryan,
Morell, Mike, –43, ,
Morning Joe,
Mother Emanuel Church massacre, , –41
Mothers of the Movement, –76, –80, –85, , ,
moving, –85
Moving to Opportunity for Fair Housing,
Moynihan, Daniel Patrick,
MSNBC, , ,
Mubarak, Hosni,
Mueller, Bob,
Muir, David, –44,
Mukasey, Michael,
Murdoch, Rupert,
Muscatine, Lissa,
Musk, Elon,
Muskie, Ed,
Muslim Brotherhood,
Muslims, , , , , , –17
Trump and, , ,
NAACP, , ,
Nader, Ralph,
Nakiya, –13
naloxone (Narcan), –62
Nance-Holt, Annette, –79
NASA,
Nashawati, Tala, –64
National Archives and Records Administration,
National Building Museum,
National Economic Council,
National Organization for Marriage,
National Park Service,
National Rifle Association (NRA), , , –83, –87, , ,
national security, , ,
Hillary Clinton's emails and, , –22, , –10
NBC's "Commander in Chief Forum" and, –22
Russia and, see Russia
see also terrorism
National Security Agency (NSA), , ,
National September 11 Memorial Museum,
NATO, , , ,
Nayak, Navin, ,
NBC, ,
Commander in Chief Forum, –22
Meet the Press,
News, ,
Netherlands, , –9
Nevada, , , , , ,
New Bedford, Mass.,
New Deal, ,
New Hampshire, –62, , , , , , ,
New Haven Legal Services Clinic,
New Jersey,
New Labour Party,
New Markets Tax Credit,
New York,
New York (state), ,
New York City, –3
9/11 and, , ; see also September 11 attacks
Pride Parade in, –3
New York Daily News, ,
New Yorker,
New Yorker Hotel, –18
New York Post, , ,
New York Times, , , , –21, , , , , , ,
DNC hacking and, –38
Eleanor Roosevelt obituary in,
email controversy and, –5, , , , –20
Hillary Clinton endorsed by,
and Trump's ties to Russia, , –55,
New York Times Magazine,
New York Yankees,
Nietzsche, Friedrich,
Nikkels, Santa,
9/11 attacks, see September 11 attacks
Nineteen Eighty-Four (Orwell),
Nineteenth Amendment, ,
Nixon, Richard, , , , , ,
Noah, Trevor,
No Ceilings: The Full Participation Project,
North America's Building Trades Unions (NABTU),
North Carolina, , , ,
North Dakota,
North Korea, , , ,
Norway,
Nouwen, Henri, , ,
NPR, ,
NRA (National Rifle Association), , , –83, –87, ,
nuclear power plants,
nuclear weapons, , , ,
Nuland, Toria, ,
Nunn, Michelle,
Nyad, Diana,
Obama, Barack, xiv, , , , , , –53, , , , , , , , , , , , , , , , , , , , , , , , –401, –10, , , , , , ,
Benghazi attack and,
birth certificate of, , , –67,
at Democratic National Convention (2016), , –543
early life of, –12
email controversy and,
energy policies of, ,
farewell address of,
Flynn and,
gun laws and, ,
Hillary Clinton appointed Secretary of State by, ,
Hillary Clinton's 2016 campaign and, , , , –68, , , , , , , ,
inauguration of,
presidential campaign of 2008, , , , , , –44
presidential campaign of 2012, , , ,
Putin and, ,
racism and,
Russia and, , , , –56
and Russian interference with election, , , , ,
Trump's accusations of wiretapping by, –10
at Trump's inauguration,
working-class voters and,
Obama, Michelle, , , , , ,
at Democratic National Convention, , ,
at Trump's inauguration,
Obamacare (Affordable Care Act), , , , , , , , , , , , , –84, , , ,
Occupy Wall Street movement,
O'Connor, Flannery,
O'Connor, Michael,
O'Connor, Sandra Day,
Ogar, Laura,
Ohio, –60, , , , –64, , , , , ,
O'Keefe, Kevin,
O'Leary, Ann,
Oliver, Mary, ,
One Hundred Years of Solitude (García Márquez),
On Tyranny: Twenty Lessons from the Twentieth Century (Snyder),
Onward Together, ,
opioid epidemic, , –62, , , –82
Orlando nightclub shooting,
Orwell, George,
Packnett, Brittany,
Page, Carter, , ,
Painton, Priscilla,
Pally, Maura, Palmieri, Jennifer, , , , , ,
Pam, , ,
Panda Principle,
Panetta, Leon,
Pantsuit Nation, ,
Paris,
Parker, Christopher,
Parkhomenko, Adam,
Patterson, Thomas,
Paul, Alice,
Paul, Matt, , ,
Paul, Saint,
Paulson, Hank,
PBS,
Peabody Energy, ,
Pearce, Anne Tate,
Pelosi, Nancy, –12,
Pence, Mike,
Pendleton, Cleo, ,
Pendleton, Hadiya,
Peninsula Hotel, , ,
Pennsylvania, , , , , , , , , , , ,
Penny, Louise,
pension funds,
people of color, , , ,
and economic anxiety vs. bigotry in voters, –18
Latinos, , , ,
Mexican immigrants, , , –25, , , , ,
see also African Americans; Muslims
Perez, Tom, –22
Perkins, Frances,
Perkins Coie,
Perlman, Adam,
Perry, Katy,
Peterson, Lauren,
Petraeus, David,
Pew Research Center, ,
Philadelphia, Pa., , , , , ,
Philadelphia Inquirer,
Pierce, Charles,
Piercy, Marge,
Pittsburgh, Pa., , ,
Planned Parenthood, , , –31
Platten, Rachel,
Plouffe, David, –54,
Podesta, John, –55, , , , , , , , , , , , ,
pizzeria claims and, –52
police officers, –80, –85, , –6,
policy(ies), –41, , , –68
budgets and,
"bumper sticker" ideas in,
Hillary Clinton's campaign team for, ,
inspirational vs. practical approaches to, –25, , , ,
media coverage of, –23, , ,
progressive, , , –79, , , , , –27, –31, ,
putting back into politics,
of Sanders, –31,
targeted programs in,
Trump and, –32,
politics,
authenticity and likeability in, –25,
emotions and crying in, –24
women in, –45,
PolitiFact,
Pollitt, Katha,
pollsters, , , , –5
populism, , , , , , , ,
Portman, Rob,
poverty, , , , , , , ,
and epidemic of despair, –68
in Flint, ,
welfare and, –8,
Powell, Colin, , , , , ,
"Power of the Powerless, The" (Havel),
Praeli, Lorella, –94
prayer, –32
presidential campaigns and elections, ,
of 1992, , , , , , , , , , , , ,
of 2000,
of 2008, , , , , , , , –64, , , , , , , , –44, ,
of 2012, , , ,
presidential election of 2016:
authenticity and likeability issues in, –25,
caucuses in, , , , ,
Democratic National Convention in, see Democratic National Convention of 2016
Election Day and Night, –89, –3
Electoral College in, , –87, ,
first days after, –23
Hillary Clinton's campaign in, see Clinton, Hillary Rodham, 2016 presidential campaign of
press coverage of, see media
primaries in, , , , , , , , , , , , , , –45, , ,
reasons for outcome of, –425
Republican National Convention in, , , ,
Russian interference in, , , , –5, , , , , –46, –65, –70, , , , , , –7, ,
superdelegates in, –45
third-party candidates in, , , , –12
Trump's victory in, –88,
votes for Hillary Clinton in, xiv, , , , –87, ,
press, see media
Pride parades, –3
Priebus, Reince,
Priley, Jacob,
primaries, , , , , , , , , , , , , , –45, , ,
prime ministers,
Princeton Election Consortium,
Priorities USA,
prisoners of war,
Prodigal Son, parable of, ,
progressivism, , , –79, , , , , –27, –31, ,
Prophet, The (Gibran),
Pryor, David,
Pryor, Mark,
Pulse nightclub shooting,
Putin, Vladimir, , –34, –37, , , , ,
Assange and, –44
KGB past of, ,
Morell on,
Obama and, ,
Stein and, , –12
Trump and, , –35, , , , , , , , , –75, ,
Putnam, Bob,
Pyatt, Geoff,
Quinnipiac University,
racial priming, –15
racism, see people of color
Ramsey, Chuck,
Rao, Amy,
Rauvin,
Rawlings, Mike,
Rayburn, Sam,
Ready for Hillary,
Reagan, Ronald, , , , , , –75, , , , , –34
RealClearPolitics,
reality, defining,
see also truth and facts
Reconnecting McDowell, ,
Reddit, ,
Reed-Veal, Geneva,
Reid, Harry, , –46, –51, ,
Reidy, Carolyn,
Reines, Philippe, , , –7,
religious faith, –32,
of Hillary Clinton, –32, , , ,
Remes, Emily,
Remie,
Remington Arms, ,
Renaissance Technologies, –68
Rendell, Ed,
Renteria, Amanda,
reproductive rights, –32, , ,
Republican National Committee (RNC), , , , ,
Republican National Convention (1996),
Republican National Convention (2016), , , ,
Republicans, Republican Party, , , , –50, –56, –68, , , , , , , , , , , , , , –34,
Benghazi attack and, –31, –99
coal communities and, ,
cultural and racial appeals of, –75
Flint water crisis and,
government size and,
guns and,
ideology of, –37
Pelosi and,
pessimism and,
presidential debates of, , ,
racism and, –15
Russian propaganda and,
sexism and misogyny and, –28,
Tea Party, ,
third-party candidates and,
Trump denounced by,
voter suppression by, –29, –21,
at Wellesley,
working-class voters and,
resistance, , ,
Return of the Prodigal Son, The (Nouwen), ,
Reyes, Ana,
Reynolds, Christina,
Reynolds, Diamond,
Rhimes, Shonda,
Rhodes, Ben, –56
Rhorer, Richard,
Rice, Condoleezza, ,
Rice, Tamir,
Richards, Ann,
Richards, Cecile,
Rid, Thomas, –32
Rilke, Rainer Maria,
Rivalsi, Elizabeth,
Rodham, Dorothy Howell (mother of Hillary), , , , , –17, , –48, –67, , , , , –83, ,
Bill and, –61
Chelsea and, ,
childhood of, –64, , –83
death of, ,
living with Hillary and Bill, –66
Rodham, Fiona (niece of Hillary), ,
Rodham, Hugh (brother of Hillary), , –48, , , ,
Rodham, Hugh (father of Hillary), –34, , , , , –48, , , –65, , , , ,
death of, ,
stroke suffered by,
Rodham, Megan (sister-in-law of Hillary), ,
Rodham, Simon (nephew of Hillary), ,
Rodham, Tony (brother of Hillary), , –48, , , , ,
Rodham, Zach (nephew of Hillary), ,
Roe v. Wade, ,
Roger & Me,
Romania,
Romney, Mitt, , , , , , , –15, ,
"Room Where It Happens, The,"
Rooney, Mary Kate,
Rooney, Megan, , ,
Roosevelt, Eleanor, , , , –49
Val-Kill cottage of, –48,
Roosevelt, Franklin Delano, , –79, , , , , , , , ,
Roosevelt, Theodore "Teddy," , –78
Roosevelt Island, , –81,
Roots, the,
Rose Law Firm,
Rosenstein, Rod, –91, –12,
Ross, Dennis,
Rove, Karl,
Rubio, Marco, ,
Ruiz, Emmy, ,
Rukeyser, Muriel,
Russia, –67, , –75, , ,
accidents involving officials from,
"active measures" tactics of, –32
Comey and investigation of, , –5, , , , , , ,
DNC computer hacking and, –42, –48,
election systems hacked by,
embassy compounds in Maryland and New York,
European actions of, –65
FBI and, –64
information warfare and propaganda strategies of, , , –56, –64, –70,
Intelligence Community report on, , , , , –60, ,
and right-wing war on truth, –69
Trump family members and, , , , ,
Trump's financial ties to, –37, , ,
Ukraine and Crimean Peninsula actions of, –31, , , –41, , , ,
U.S. election interference of, , , , –5, , , , , –46, –65, –70, , , , , , –7, ,
U.S. military targeted by, –70
U.S. political divisions sought by,
U.S. sanctions against, , ,
Wikileaks and, –40, , , –48, , , ,
Russian Orthodox Church,
Russia Today (RT), , , , –60, –12
Russo, Rob, ,
Ryan, Tim,
Saharia, Amy,
Saletan, Will,
Samuelson, Heather,
Sandberg, Sheryl, –26,
Sandburg, Carl,
Sanders, Bernie, , , , , , , –31, , , , , , , , , , ,
attacks on Hillary Clinton, –30
college plan of, , ,
in debate with Hillary Clinton, –31,
at Democratic National Convention,
Democratic Party and, ,
on email controversy, ,
endorsement of Hillary Clinton, ,
fossil fuels and,
gun policies and, –87,
health care plan of, –55,
policies of, –31,
reproductive rights and,
Russian propaganda and,
supporters of, , , ,
Sandy Hook Elementary School shooting, , –91,
Sandy Hook Promise, –90
Santmire, Paul, –61
Santos, Marina,
Sarandon, Susan,
Sater, Felix,
Saturday Night Live, ,
Saudi Arabia,
Schake, Kristina, ,
Schiff, Adam,
Schmidt, Eric,
Schultz, Debbie Wasserman, ,
schools:
and children with disabilities, –201
segregated,
STEM teachers in,
Schroeder, Pat,
Schumer, Chuck, ,
Schur, Oren,
Schwerin, Dan, , –55, ,
Second Amendment, , –88
Secretary of State,
Hillary Clinton as, , , , , , , , –61, , , , , –3, , , , , , , ,
Secret Service, , , –90, , , , ,
segregated schools,
Senate, U.S.,
Armed Services Committee,
Hillary Clinton in, , , , , , , , , , , , , , , , ,
Intelligence Committee, , ,
Judiciary Committee,
Seneca Falls Convention, , , , –59
Seow, Jackie,
September 11 attacks, , , , , ,
Ground Zero first responders, , , ,
September 11 Memorial Museum,
Serrano, Ella,
Sessions, Jeff, , , , ,
sexism, –28,
misogyny vs., –15
in presidential election,
problems of recognizing, –16
see also women
sexual harassment and assault, , –40
Trump's bragging about, , , , , , –39, , –49, ,
Shaffer, Mary Ann,
Shaheen, Jeanne,
Shaw, George Bernard,
She Persisted (Chelsea Clinton),
Shepherd, Meredith,
Shillady, Bill, –33, ,
Shimer, David,
Shines, Aubrey,
Shokoff, Elisa,
Shorenstein Center on Media, Politics and Public Policy, , –23,
Shur, Oren,
Sides, John, –13
Silicon Valley, , ,
Silver, Melissa,
Silver, Nate, , ,
Sinclair Broadcast Group,
Situation Room, , , ,
60 Minutes,
Slate, , ,
Slaughter, Anne-Marie,
small businesses, ,
Smegielski, Erica,
Smith, Craig,
Smith, Margaret Chase,
Smoking Gun, The,
Snowden, Edward,
Snyder, Timothy,
social change, , , ,
Socialism, , , , ,
social media, see internet and social media
Social Security, , , , ,
Solow, Sara,
Somoza, Anastasia,
Soros, George,
South Carolina, , , –200, –40
Southern Poverty Law Center,
Soviet Union, , , , , ,
in Cold War, , ,
Spayd, Liz,
Spence, Roy, –55
Springsteen, Bruce,
Sputnik, ,
Square Deal,
Stanton, Elizabeth Cady,
State Department, , , , ,
Benghazi Committee and,
classified documents and, –7, –11
Hillary Clinton as Secretary of State, , , , , , , , –61, , , , , –3, , , , , , , ,
Hillary Clinton's emails and, –96, –96, , –300, –3, , , ,
Inspector General of, –96,
press corps of,
Russian compounds and,
Wikileaks and,
steel industry, , , ,
Stein, Jill, , –12
Steininger, Ruline, –96
STEM teachers,
Stevenson, Adlai, , –49
Stone, Elizabeth, –76
Stone, Roger, , ,
Strayed, Cheryl,
Strider, Burns,
suffragettes and voting rights, –14, , , , ,
Sullivan, Jake, , , , , , , –55, , , ,
Sullivan, Margaret, ,
superdelegates, –45
super PACs,
Supreme Court, , ,
campaign financing and, , ,
presidential election of 2000 and,
Roe v. Wade, ,
Voting Rights Act and, ,
Sweden, –40
Swisher, Kara,
Sweet Maple Cafe,
Sykes, Charlie, ,
Syria, , , , ,
Taft, William Howard,
Tanzania,
Tarbell, Ida,
Tartt, Donna,
Tatham, Laura,
taxes, , , , , , , ,
of Clintons, ,
of Trump, ,
Tea Party, ,
technology, , –71, , –41, ,
artificial intelligence, ,
automation, , , ,
internet, see internet and social media
terrorism, , , , , , , , ,
Benghazi attack, , –31, , –99, ,
ISIS, –49, , , ,
see also September 11 attacks
Testino, Mario,
Texas,
Thanksgiving, –29
There's Something About Mary,
third-party candidates, , , , –12
Tiananmen Square massacre,
Tillich, Paul, –31
Time, , –62,
Tocqueville, Alexis de, , ,
Todd, Charles (pen name),
Todd, Chuck (television journalist),
Too Small to Fail,
torture, ,
Totti, Sofia,
trade, –36, , ,
Traister, Rebecca, ,
Trayvon Martin Foundation, ,
Trocker, Dana,
True Believer, The (Hoffer),
Trump, Donald, , , , –50, , –76, –81, , , , , , –37, , , , , , , , , , , , , , , ,
administration of, –24, –33, –51,
business career of, , ,
coal communities and, , , ,
Comey fired by, –91
"Crooked Hillary" campaign of, , , ,
crowd at inauguration of, –13
debate preparation eschewed by,
in debates, , –7, –39, , , –74
Democratic supporters of, –17,
dictators admired by, ,
domineering style of, –35,
election victory of, –88,
explanations for support for, –10
financial ties to Russia, –37, , ,
first hundred days in office, –33
foreign policy and, , –35
guns and, –88,
health care and, , , , ,
Hillary Clinton's debates with, –39, , , –74
Hillary Clinton's prep sessions for debates with, , –7,
inaugural address of, –8, –11
inauguration of, –8, –13
Khan family and, , ,
"Make America Great Again" slogan of,
media and, , , , , –400
Mexican immigrants and, , , –25, , , , ,
mistakes as viewed by, ,
Muslims and, , ,
in NBC's "Commander in Chief Forum," –22
Obama's birth certificate and, , ,
opioid epidemic and,
policy and, –32,
Pope Francis and, , ,
populist appeal of, , ,
presidential candidacy declared by,
Putin and, , –35, , , , , , , , , –75, ,
rallies of, , –88, , , ,
Republican convention speech of, ,
Republicans' denunciation of,
and sanctions against Russia, , ,
"Second Amendment people" remark of,
sexual assault comments of, , , , , , –39, , –49, ,
taxes of, ,
Trump Foundation and, –47,
Trump University and, ,
in video spoof for Legislative Correspondents dinner, –7
voter fraud alleged by, –21
votes against Hillary Clinton vs. votes for,
wall-building idea of, –25, ,
wedding to Melania,
WikiLeaks and, –49
wiretapping accusations against Obama, –10
women as viewed and treated by, , , , , –39, , –49, ,
Women's March protesting, , , ,
Trump, Donald, Jr., ,
Trump, Eric,
Trump, Melania,
Trump, Tiffany,
Trump Foundation, –47,
Trump SoHo,
Trump University, ,
Truth, Sojourner,
truth and facts, –9, , , , ,
conspiracy theories and, , , , , , ,
and defining reality,
fake news and, –52, –61, , , ,
right-wing war on, –69,
"truthiness,"
Tubman, Harriet, x, xiv
Tur, Katy,
Turner, Katherine, ,
Twitter, , , , , , , , , , , , , ,
"bots" and,
propaganda and, –62
Women's March and, , ,
Uber,
Ukraine, –31, , , –41, , , ,
Ulrich, Laurel Thatcher,
UltraViolet,
Umpqua Community College shooting,
unions, , , , , , ,
United Kingdom, , , , ,
United Methodist Church, , , , –97, ,
United Mine Workers of America, –70,
United Nations, ,
Security Council,
Universal Declaration of Human Rights,
University of Arkansas,
University of Chicago,
University of Southern California,
University of Texas at Austin, –37
Upper Big Branch Mine disaster, , –76
USA Today, ,
Vadhan, Opal,
Valdez, Lupe,
Val-Kill, –48,
Valmoro, Lona, –86,
Van Buren, Martin,
Vance, J. D.,
Veep,
Vein, Jon,
Verveer, Melanne,
veterans,
Vietnam War, , , , –99,
Vilsack, Tom,
Violence Against Women Act,
Violent Crime Control and Law Enforcement Act, –5
Virginia,
Vital Voices,
Vlacich, Mike, ,
Vogelstein, Rachel,
Vogue,
von Fürstenberg, Diane,
Voter Study Group, ,
voting, voters, –15, , ,
African Americans and, , –20
Republican Party and, –29, –21,
suppression of, , –29, , –21,
Trump's allegations of fraud in, –21
womens' fight for voting rights, –14, , , , , ,
women voters, –14,
Voting Rights Act of 1965, ,
Vox, , ,
Walker, Don,
Walker, Scott,
Wallace, Chris,
Wallace, David Foster,
Wallace, Nicolle,
Wall Street, , , , –26, , , , ,
Wall Street Journal, ,
Wang, Sam,
Warner, Mark, –62
Warren, Elizabeth, , , –26,
Washington Post, , , , , , , , ,
Access Hollywood tape and,
email controversy and, , –19
Russia and, , , , , –57, –64
Washington State,
Watergate, ,
Watson, Diane,
Watts, Clint,
Weaver, Karen, , ,
Weber, Max,
Weiner, Anthony, –15,
Weingarten, Randi,
Weld, Bill,
welfare, –8,
Wellesley College,
Hillary Clinton as student at, , , , ,
Hillary Clinton's graduation speeches at, –57, , , , , , –64
Wellesley Republicans,
Wellesley Women for Hillary, –56
Wesley, John, ,
West Virginia, –76, –83, –87
White House, , , ,
Whitehouse, Sheldon,
White House Correspondents' Association,
Whitewater Development Corporation, , ,
Whittier, John Greenleaf,
WikiLeaks, , –49, ,
pizzeria conspiracy theory and, –52
Russia and, –40, , , –48, , , ,
State Department emails released by,
Trump's citing of,
Wilders, Geert, –9
wildlife conservation,
Williams, Maggie, , ,
Williams, Pharrell,
Williams and Connolly,
Wilson, Graham,
Wilson, Woodrow, , –14
Winspear, Jacqueline,
Wintour, Anna,
Wisconsin, , , , –95, , , , , –21
With Liberty and Dividends for All: How to Save Our Middle Class When Jobs Don't Pay Enough (Barnes),
Wohlgemuth, Steve,
Wollstonecraft, Mary,
women, , , –13, –48, , –89
apologies to Hillary Clinton from, –15
campaign donations from,
Clinton campaign's "Mirrors" ad and, –38
confidence of,
creating opportunities for, ,
emotional labor and, –34, –36
friendships between, –69
health services and reproductive rights for, , –32, , ,
jobs and, ,
journalists,
leaders,
maternity leave for,
"nasty,"
in parliamentary vs. presidential systems,
in politics, –45,
as President, –28, , –45, , , ,
reactions toward advocacy by, –26
representation and, –43
and sexual harassment and violence, , –40
speeches by,
Trump's attitudes toward, , , , , –39, , –49, ,
voters, –14,
words used about, –20
working-class, , , ,
see also misogyny; sexism; women's movement
Women in the World, –35
Women's March, , , ,
women's movement, , –14, ,
civil rights movement and,
Seneca Falls Convention, , , , –59
suffragettes and voting rights, –14, , , , , ,
Wonder, Stevie,
Woodward, Charlotte, –59
working class, , , –87, –98, , ,
Democratic Party and, , –74, , , –17
economic anxiety and bigotry in, –18
unions and, , , , , , ,
use of term,
women in, , , ,
see also jobs
World Economic Forum,
World Series, –101
World War II, , , ,
Wrinkle in Time, A (L'Engle),
Wyatt, Theresa Vargas,
Yahoo News,
Yale Child Study Center,
Yale Law School, , , , , ,
Yale-New Haven Hospital,
Yale University,
Yale University Art Gallery,
Yates, Sally, ,
Yeats, William Butler,
Yglesias, Matt,
yoga, ,
YouTube, , , ,
Zika virus,
Zinke, Ryan,
Zuckerbrod, Julie, ,
First published in the US by Simon & Schuster, Inc., 2017
This general edition published 2017 by Simon & Schuster Australia
Suite 19A, Level 1, Building C, 450 Miller Street, Cammeray, NSW 2062
A CBS Company
Sydney New York London Toronto New Delhi
Visit our website at www.simonandschuster.com.au
Copyright © 2017 by Hillary Rodham Clinton
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission of the publisher.
Permissions can be found on pages 493–494.
The author and publishers have made all reasonable efforts to contact copyrightholders for permission, and apologise for any omissions or errors in the form of credits given. Corrections may be made to future printings.
National Library of Australia Cataloguing-in-Publication entry
Author: Hillary Rodham Clinton
Title: What Happened
ISBN 978-1-9255-9669-4
ISBN 978-1-9255-9671-7 (ebook)
Interior design by Ruth Lee-Mui
Front endpaper: Adam Schultz
Back endpaper: Stuart Sipkin/Alamy Stock Photo
| {
"redpajama_set_name": "RedPajamaBook"
} | 6,425 |
We were close to the beach now. The wives were in the car taking pictures of the "stars"
And here is Bela, smiling like nothing happened.
Bobo waving to the crowds.
Bela got into the picture also.
Harold in the aero position.
The brothers still in good shape.
Bela looks like streching a bit. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,808 |
{"url":"https:\/\/www.clutchprep.com\/physics\/practice-problems\/145801\/a-small-object-moves-along-the-x-axis-with-acceleration-ax-t-0-0320m-s3-15-0s-t--1","text":"Position Functions and Instantaneous Velocity Video Lessons\n\nConcept\n\n# Problem: A small object moves along the x-axis with acceleration ax(t) =-(0.0320m\/s3)(15.0s-t). at t=0 the object is at x=-14.0m and has velocity v0x =4.50 m\/s.\u00a0What is the x-coordinate of the object when t=10.0s?\n\n###### FREE Expert Solution\n\nIn this problem, we are given an acceleration function. We need to determine the position function with the aid of the diagram below:\n\n2D&3D Motion with Calculus\n\n$\\mathbit{P}\\begin{array}{c}{\\mathbf{\u2190}}\\\\ {\\mathbf{\\to }}\\end{array}\\underset{\\frac{\\mathbit{d}}{\\mathbit{d}\\mathbit{t}}}{\\overset{{\\mathbf{\\int }}{\\mathbit{d}}{\\mathbit{t}}}{\\mathbit{V}}}\\begin{array}{c}{\\mathbf{\u2190}}\\\\ {\\mathbf{\\to }}\\end{array}\\mathbit{A}$\n\n87% (282 ratings)\n###### Problem Details\n\nA small object moves along the x-axis with acceleration ax(t) =-(0.0320m\/s3)(15.0s-t). at t=0 the object is at x=-14.0m and has velocity v0x =4.50 m\/s.\n\nWhat is the x-coordinate of the object when t=10.0s?","date":"2020-12-01 09:00:33","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\": 0.2727856934070587, \"perplexity\": 2199.735921105781}, \"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\/1606141672314.55\/warc\/CC-MAIN-20201201074047-20201201104047-00180.warc.gz\"}"} | null | null |
Institut Sup'Biotech de Paris er et fransk ingeniør-institut tilknyttet IONIS Education Group.
Instituttet blev oprettet i 2003 (Institut Sup'Biotech de Paris) i 2005 (Sup'Biotech Paris) og har i dag omkring 700 studerende.
Berømte alumne
Cyprien Verseux, Astrobiologi
Bibliografi
Biotechnologies. Les promesses du vivant., Villejuif, FYP Éditions, 2015, 256 p. ()
Uddannelsesinstitutioner i Frankrig
Tekniske universiteter | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,923 |
Q: Instance of 'Controller' has no 'type' member pynput module I am fairly new to Python, I recently made this program to automatically click a text box in a program and type text (hello). But everytime I run the program, it says:
Instance of 'Controller' has no 'type' member.
I am using pynput and Python 3.8.1 32bit. I installed pynput manually through the console with
pip install pynput
Here is my code:
import time
from pynput.keyboard import Key, Controller
from pynput.mouse import Button, Controller
def controlMouse(x, y):
mouse = Controller()
mouse.position = (x, y)
def controlKeyboard(txt):
keyboard = Controller()
keyboard.type(txt)
def clickMouse():
mouse = Controller()
mouse.click(Button.left, 1)
def pressKeyboard(key):
keyboard.press(Key.key)
keyboard.release(Key.key)
mouse = Controller()
controlMouse(268, 1030)
time.sleep(1)
clickMouse()
time.sleep(1)
controlMouse(400, 955)
time.sleep(1)
clickMouse()
controlKeyboard('Hello')
pressKeyboard(enter)
A: You have this:
from pynput.keyboard import Key, Controller
from pynput.mouse import Button, Controller
After that, Controller refers to pynput.mouse.Controller (because it was the last time Controller was defined). If you want to be able to refer to both Controller types, you should do something like this:
from pynput.keyboard import Key, Controller as KeyboardController
from pynput.mouse import Button, Controller as MouseController
You can then use KeyboardController and MouseController to refer to the right kind of Controller.
Alternatively, you can:
import pynput.keyboard
import pynput.mouse
You can then just refer to pynput.keyboard.Controller and pynput.mouse.Controller.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,147 |
\section{Introduction}
Cylindrical martingale problems (MPs) associated with L\'evy generators can be considered as the martingale formulation of (analytically and probabilistically) weak and mild solutions to (semilinear) stochastic (partial) differential equations (S(P)DEs) driven by L\'evy noise.
As in the classical finite-dimensional case, the martingale formulation gives access to weak conditions for the strong Markov property and Girsanov-type theorems, see \cite{criens18,EJP2924}.
Another application of MPs, which was impressively exploited by Stroock and Varadhan \cite{SV} and Jacod and Shiryaev \cite{JS} in the finite-dimensional case, are limit theorems.
In this article, we show the following: A sequence of solutions to MPs whose initial laws converge weakly and whose coefficients converge uniformly on compact sets to continuous coefficients converge weakly to a solution of the MP associated with the limiting initial law and the limiting coefficients.
Moreover, we prove that under a uniqueness and existence assumption on the limiting MP a localized tightness condition implies weak convergence. This observation can be used to verify tightness under boundedness or moment conditions.
Let us mention two consequences of our observations.
Following Stroock and Varadhan \cite{SV}, we call a family of solutions to a well-posed MP a Feller family (or simply Feller) if it is weakly continuous w.r.t. their initial values.
The limit theorem shows that a family of well-posed MPs with continuous coefficients is Feller if and only if a tightness condition holds. This observation generalizes results known for finite- and infinite-dimensional cases, see \cite{EJP2924,Stroock75,SV}.
The limit theorem can also be used to construct solutions to MPs from solutions of approximate MPs and hence provides existence results in the spirit of Skorokhod's theorem for finite-dimensional SDEs.
For illustration we discuss two applications: First, we derive an existence theorem for weak solutions to infinite-dimensional SDEs of the type
\begin{align}\label{int: SDE}
d} %{\operatorname{d}\hspace{-0.05cm} Y_t = b(Y_{t-})d} %{\operatorname{d}\hspace{-0.05cm} t + \sigma (Y_{t-})d} %{\operatorname{d}\hspace{-0.05cm} W_t + \int v(x, Y_{t-})(p - q)(d} %{\operatorname{d}\hspace{-0.05cm} x, d} %{\operatorname{d}\hspace{-0.05cm} t),
\end{align}
where \(W\) is a cylindrical Brownian motion and \(p - q\) is a compensated Poisson random measure.
To explain our result in more detail, let \(J\) be a positive symmetric compact operator on a separable Hilbert space \(\mathbb{B}\). Under the assumption that \(b, \sigma\) and \(v\) satisfy a continuity and local boundedness assumption on \(\mathbb{B}\) and a linear growth condition on \(J(\mathbb{B})\), we show that the SDE \eqref{int: SDE} has a weak solution with values in \(\mathbb{B}\).
For our second application we consider MPs corresponding to stochastic evolution equations of the form
\begin{align}\label{SPDE}
d} %{\operatorname{d}\hspace{-0.05cm} Y_t = \left(A Y_t + b(Y_t)\right)d} %{\operatorname{d}\hspace{-0.05cm} t + \sigma(Y_t)d} %{\operatorname{d}\hspace{-0.05cm} W_t,
\end{align} where \(A\) is the generator of a compact \(C_0\)-semigroup. We adapt the compactness method from \cite{doi:10.1080/17442509408833868} to show that a localized version of tightness holds if the non-linearities satisfy local boundedness conditions.
It follows from this observation that solution families to well-posed diffusion-type MPs with continuous and locally bounded non-linearities are Feller. To the best of our knowledge, this result is new. In addition, we derive limit theorems either under a well-posedness and a local boundedness condition or a uniqueness and a linear growth condition. Our results apply, for instance, to non-linear stochastic heat equations.
Next, we comment on related literature in infinite-dimensional frameworks.
For settings allowing jumps we are only aware of limit theorems for semimartingales given in \cite{XIE1995277}.
We also think that the literature contains no existence result for infinite-dimensional SDEs with jumps which is comparable to ours. For continuous noise an existence theorem similar to ours was given in \cite{GMR09}. We stress that the setting in \cite{GMR09} is not necessarily Markovian. Our result strengthens the Markovian version of the theorem from \cite{GMR09} by replacing one of the linear growth conditions with a local boundedness condition.
A limit theorem for diffusions under a tightness and local boundedness condition can be found in \cite{EJP2924}. Our result extends the theorem from \cite{EJP2924} by showing that the tightness is implied by a well-posedness assumption.
Under well-posedness, continuity, linear growth and moment conditions on the initial laws, limit theorems for time-inhomogeneous SPDEs driven by Wiener noise were proven in \cite{doi:10.1080/07362999708809484}. For the time-homogeneous case we extend these results by replacing the linear growth conditions with local boundedness conditions and confirm the conjecture from \cite{doi:10.1080/07362999708809484} that no moment assumption on the initial laws is needed.
The Feller property of S(P)DEs with Wiener noise is under frequent investigation. We mention two related papers: \cite{doi:10.1080/17442508.2012.712973, Maslowski1999}.
In \cite{doi:10.1080/17442508.2012.712973} the martingale formulation is used to identify the transition semigroup of the studied Cauchy problem, while the core argument is based on a perturbation result for semigroups. The approach in \cite{Maslowski1999} is based on Girsanov's theorem.
The article is structured as follows: In Section \ref{2.1} we introduce the MP, following the exposition given in \cite{criens18}. In Section \ref{sec: MR} we state our main results, in Section \ref{sec:sm} we discuss the existence of weak solutions to SDEs of the type \eqref{int: SDE} and in Section \ref{sec:3} we discuss the diffusion case. The proofs are collected in Section \ref{sec: Proofs}.
\section{Cylindrical Martingale Problems} \label{2.1}
Let \((\mathbb{B}, \|\cdot\|)\) be a real separable reflexive Banach space, which we equip with its norm topology, and let \(\mathbb{B}^*\) be its (topological) dual, which we equip with the operator norm \(\|\cdot\|_o\) and the corresponding topology. It is well-known that \((\mathbb{B}^*, \|\cdot\|_o)\) is also a real separable reflexive Banach space.
For \(x^*\in \mathbb{B}^*\) and \(x \in \mathbb{B}\) we write
\[
x^*(x) \triangleq \langle x, x^*\rangle.
\]
We define \(\Omega\) to be the Skorokhod space of all c\`adl\`ag functions \(\alpha \colon \mathbb{R}_+\to \mathbb{B}\) and equip it with the Skorokhod topology, which turns it into a Polish space, see \cite{EK,JS}.
The coordinate process \(X\) on \(\Omega\) is defined by \(X_t(\alpha) = \alpha(t)\) for all \(\alpha \in \Omega\) and \(t \geq 0\). Moreover, we set \[\mathscr{F} \triangleq \sigma(X_s, s \geq 0), \quad\mathscr{F}_t \triangleq \sigma(X_s, s \in [0, t]), \quad \mathbf{F}\triangleq (\mathscr{F}_t)_{t \geq 0}.\]
It is well-known that \(\mathscr{F}\) is the Borel \(\sigma\)-field on \(\Omega\).
Except otherwise stated, all terms such as stopping time, martingale, local martingale etc. refer to \(\mathbf{F}\) as the underlying filtration.
For a stopping time \(\xi\) we write
\[
\mathscr{F}_{\xi} \triangleq \big\{ A \in \mathscr{F} \colon A \cap \{\xi \leq t\} \in \mathscr{F}_t \textup{ for all } t \geq 0\big\},
\]
which is easily seen to be a \(\sigma\)-field.
An operator \(Q \colon \mathbb{B}^* \to \mathbb{B}\) is called positive if \(\langle Q x^*, x^*\rangle \geq 0\) for all \(x^* \in \mathbb{B}^*\) and symmetric if \(\langle Q x^*, y^*\rangle = \langle Q y^*, x^*\rangle\) for all \(x^*, y^* \in \mathbb{B}^*\).
We denote by \(S^+(\mathbb{B}^*, \mathbb{B})\) the set of all linear, bounded, positive and symmetric operators \(\mathbb{B}^* \to \mathbb{B}\).
For a topological space \(E\) we denote the corresponding Borel \(\sigma\)-field by \(\mathscr{B}(E)\).
Next, we introduce the parameters for the martingale problem:
\begin{enumerate}
\item[(i)]
Let \(A \colon D(A) \subset \mathbb{B} \to \mathbb{B}\) be a linear, densely defined and closed operator.
Here, \(D(A)\) denotes the domain of the operator \(A\).
\item[(ii)]
Let \(b \colon \mathbb{B} \to\mathbb{B}\) be Borel and such that for all bounded sequences \((y^*_n)_{n \in \mathbb{N}} \subset \mathbb{B}^*\) and all bounded sets \(G \subset \mathbb{B}\) it holds that
\begin{align*}
\sup_{n \in \mathbb{N}} \sup_{x \in G} |\langle b(x), y^*_n\rangle| < \infty.
\end{align*}
\item[(iii)]
Let \(a\colon \mathbb{B} \to S^+(\mathbb{B}^*, \mathbb{B})\) be bounded on bounded subsets of \(\mathbb{B}\) and Borel, i.e. \(x \mapsto a(x) y^*\) is Borel for all \(y^* \in \mathbb{B}^*\). Here, bounded refers to the operator norm.
\item[(iv)]
Let \(K\) be a Borel transition kernel from \(\mathbb{B}\) into \(\mathbb{B}\), such that for all bounded sequences \((y^*_n)_{n \in \mathbb{N}} \subset \mathbb{B}^*\), all bounded sets \(G \subset \mathbb{B}\) and all \(\epsilon > 0\) it holds that
\begin{align*}
\sup_{n \in \mathbb{N}} &\sup_{x \in G} \int_{\mathbb{B}} \mathbf{1}_{\{\|y\| \leq \epsilon\}} |\langle y, y^*_n\rangle|^2K(x, d} %{\operatorname{d}\hspace{-0.05cm} y) < \infty,\end{align*}\begin{align*}
\sup_{x \in G} K(x, \{z \in \mathbb{B} \colon \|z\| \geq \epsilon\}) < \infty,
\end{align*}
and \(K(\cdot, \{0\}) = 0\).
\item[(v)]
Let \(\eta\) be a probability measure on \((\mathbb{B}, \mathscr{B}(\mathbb{B}))\).
\end{enumerate}
Let \(A^*\) be the Banach adjoint of \(A\)
and let \(C^2_{c}(\mathbb{R}^d)\) be the set of twice continuously differentiable functions \(\mathbb{R}^d\to \mathbb{R}\) with compact support.
The set of test functions for the MP is given by the following:
\[\mathcal{C} \triangleq \big\{g(\langle \cdot, y^*_1\rangle, \dots, \langle \cdot, y^*_n\rangle) \colon g \in C^2_c(\mathbb{R}^n), y^*_1, \dots, y^*_n \in D(A^*), n \in \mathbb{N}\big\}.\]
If \(g\) is twice continuously differentiable and \(f = g(\langle \cdot, y^*_1\rangle, \dots, \langle \cdot, y^*_n\rangle)\), we write \(\partial_{i} f\) for the partial derivative \[(\partial_{i} g)(\langle \cdot, y^*_1\rangle, \dots, \langle \cdot, y^*_n\rangle)\] and \(\partial^2_{ij} f\) for the partial derivative
\[
(\partial^2_{ij} g)(\langle \cdot, y^*_1\rangle, \dots, \langle \cdot, y^*_n\rangle).
\]
A bounded Borel function \(h\colon \mathbb{B} \to \mathbb{B}\) is called truncation function if there exists an \(\epsilon > 0\) such that \(h(x) = x\) for all \(x \in \mathbb{B}\) with \(\|x\| \leq \epsilon\). Throughout the article we fix a truncation function \(h\).
For \(f = g(\langle \cdot, y^*_1\rangle, \dots, \langle \cdot, y^*_n\rangle) \in \mathcal{C}\) we set
\begin{equation} \label{K}
\begin{split}
\mathcal{K}f (x) \triangleq \sum_{i = 1}^n (& \langle x, A^* y^*_i\rangle + \langle b(x), y^*_i \rangle)\partial_i f(x) + \frac{1}{2} \sum_{i=1}^n\sum_{j = 1}^n \langle a(x)y^*_i, y^*_j\rangle \partial^2_{ij}f(x)
\\&+ \int_{\mathbb{B}} \Big( f(x + y) - f(x) - \sum_{i = 1}^n \langle h(y), y^*_i\rangle \partial_i f(x) \Big) K(x, d} %{\operatorname{d}\hspace{-0.05cm} y).
\end{split}
\end{equation}
We are in the position to define the martingale problem.
\begin{definition} \label{def: MP}
We call a probability measure \(P\) on \((\Omega, \mathscr{F})\) a \emph{solution to the martingale problem (MP) \((A, b,a,K, \eta)\)}, if the following hold:
\begin{enumerate}
\item[\textup{(i)}]
\(P \circ X^{-1}_0 = \eta\).
\item[\textup{(ii)}]
For all \(f \in \mathcal{C}\) the process
\begin{equation}\label{f - K}
\begin{split}
M^f \triangleq f(X) - f(X_0) - \int_0^{\cdot} \mathcal{K}f (X_{s-})d} %{\operatorname{d}\hspace{-0.05cm} s
\end{split}
\end{equation}
is a local \(P\)-martingale.
\end{enumerate}
The set of solutions is denoted by \(\mathcal{M}(A, b, a, K, \eta)\).
We say that the MP is \emph{well-posed}, if there exists a unique solution for all degenerated initial laws, i.e. for all \(\eta = \varepsilon_x\), \(x \in \mathbb{B}\), where \(\varepsilon_x\) is the Dirac measure on \(x \in \mathbb{B}\).
\end{definition}
For reader's convenience, we have collected some important results for MPs in Appendix \ref{app: 1}.
In particular, due to Proposition \ref{prop: A2} in Appendix \ref{app: 1}, the set
\begin{align*}
\mathcal{D} \triangleq \left\{g(\langle \cdot, y^*\rangle)\colon g \in C^2_c(\mathbb{R}), y^* \in D(A^*)\right\} \subset \mathcal{C}
\end{align*}
determines the solutions of a MP and, due to Proposition \ref{prop: A1} in Appendix \ref{app: 1}, if \(P \in \mathcal{M}(A, b,a, K, \eta)\), then \(M^f\) is a local \(P\)-martingale for all
\begin{align}\label{eq: B}
f \in \mathcal{B} \triangleq \big\{ g (\langle \cdot, y^*\rangle) \colon g \in C^2_b(\mathbb{R}), y^* \in D(A^*) \big\},
\end{align}
where \(C^2_b(\mathbb{R})\) denotes the set of bounded twice continuously differentiable functions with bounded gradient and bounded Hessian matrix.
\section{Limit Theorems for Cylindrical Martingale Problems}\label{sec: MR}
In this section we state our main results. We start with the limit theorem as described in the introduction.
Let us stress that we implicitly assume that all coefficients to MPs satisfy the assumptions introduced in the previous section.
We formulate three conditions:
\begin{enumerate}
\item[\textup{(M1)}]
The map
\(
x \mapsto \mathcal{K} f(x)
\)
is continuous for all \(f \in \mathcal{D}\). Here, \(\mathcal{K}\) is defined as in \eqref{K}.
\item[\textup{(M2)}]
Define \(\mathcal{B}^n\) as in \eqref{eq: B} with \(A^*\) replaced by \((A^n)^*\) and define \(\mathcal{K}^n\) as in \eqref{K} with \((A, b, a, K)\) replaced by \((A^n, b^n, a^n, K^n)\). For all \(f \in \mathcal{D}\) there exists a sequence \((f^n)_{n \in \mathbb{N}}\) with \(f^n \in \mathcal{B}^n\) such that for all \(m \in \mathbb{N}\) \begin{align}\label{eq: bdd assp} \sup_{n \in \mathbb{N}} \sup_{x \in \mathbb{B}} \big| f^n(x)\big| + \sup_{n \in \mathbb{N}} \sup_{\|x\| \leq m} \big| \mathcal{K}^n f^n (x)\big| < \infty,\end{align}
and
\begin{align*} \big|f^n - f\big| +
\big|\mathcal{K}^n f^n - \mathcal{K} f\big| \to 0
\end{align*}
as \(n \to \infty\) uniformly on compact subsets of \(\mathbb{B}\).
\item[\textup{(M3)}] \(\eta^n \to \eta\) weakly as \(n \to \infty\).
\end{enumerate}
We are in the position to state the first main result of this article.
\begin{theorem}\label{theo1}
For all \(n \in \mathbb{N}\) let \(P^n\) be a solution to the MP \((A^n, b^n, a^n, K^n, \eta^n)\) and assume that \textup{(M1), (M2)} and \textup{(M3)} hold.
If \(P\) is a probability measure on \((\Omega, \mathscr{F})\) such that \(P^n \to P\) weakly as \(n \to \infty\), then \(P\) solves the MP \((A, b, a, K, \eta)\).
\end{theorem}
The proof is given in Section \ref{proof: theo1} below. For diffusions a related result is given by \cite[Lemma 4.3]{EJP2924}.
As a first corollary we give an existence result under a tightness condition and a convergence result under a uniqueness assumption.
\begin{corollary}\label{coro: existence}
For all \(n \in \mathbb{N}\) let \(P^n\) be a solution to the MP \((A^n, b^n, a^n, K^n, \eta^n)\) and assume that \textup{(M1), (M2)} and \textup{(M3)} hold.
\begin{enumerate}
\item[\textup{(i)}] If \((P^n)_{n \in\mathbb{N}}\) is tight, then the MP \((A, b, a, K, \eta)\) has a solution.
\item[\textup{(ii)}] If \((P^n)_{n \in \mathbb{N}}\) is tight and the MP \((A, b, a, K, \eta)\) has at most one solution, then MP \((A, b, a, K, \eta)\) has a unique solution \(P\) and \(P^n \to P\) weakly as \(n \to \infty\).
\end{enumerate}
\end{corollary}
\begin{proof}
(i). Because \((P^n)_{n \in \mathbb{N}}\) is tight, we can extract a weakly convergent subsequence due to Prohorov's theorem. Due to Theorem \ref{theo1}, the limit point of this subsequence solves the MP \((A, b, a, K, \eta)\).
(ii). Due to Theorem \ref{theo1}, any accumulation point of \((P^n)_{n \in \mathbb{N}}\) is a solution to the MP \((A, b, a, K, \eta)\). Thus, because this MP is assumed to have at most one solution, we conclude that all accumulation points coincide with the unique solution \(P\) and \(P^n \to P\) weakly as \(n \to \infty\) follows from \cite[Theorem 2.6]{bil99}.
\end{proof}
As a second corollary, we obtain a characterization of the Feller property of MPs. It can be viewed as a generalization of \cite[Corollary 4.4]{EJP2924} to a setup including jumps.
\begin{corollary}\label{coro: Feller}
Assume that \textup{(M1)} holds and that for all \(x \in \mathbb{B}\) the MP \((A, b, a, K, \varepsilon_x)\) has a unique solution \(P_x\).
Then, the following are equivalent:
\begin{enumerate}
\item[\textup{(i)}]
The family \(\{P_x, x \in \mathbb{B}\}\) is Feller, i.e. \(x \mapsto P_x\) is weakly continuous, which means that \(P_{x_n} \to P_x\) weakly as \(n \to \infty\) whenever \(x_n \to x\) as \(n \to \infty\).
\item[\textup{(ii)}] For all sequences \((x_n)_{n \in \mathbb{N}} \subset \mathbb{B}\) with \(x_n \to x \in \mathbb{B}\) as \(n \to \infty\), the sequence \((P_{x_n})_{n \in \mathbb{N}}\) is tight.
\end{enumerate}
\end{corollary}
\begin{proof}
The implication (i) \(\Rightarrow\) (ii) is due to Prohorov's theorem and the implication (ii) \(\Rightarrow\) (i) follows from Corollary \ref{coro: existence} and Proposition \ref{prop: A1} in Appendix \ref{app: 1}.
\end{proof}
\begin{remark}
If \(x \mapsto P_x\) is Borel, the following are equivalent:
\begin{enumerate}
\item[(i)]
The family \(\{P_x, x \in \mathbb{B}\}\) is Feller.
\item[(ii)]
The map \(\eta \mapsto \int P_x \eta(d} %{\operatorname{d}\hspace{-0.05cm} x)\) is weakly continuous, i.e. \(\int P_x \eta^n(d} %{\operatorname{d}\hspace{-0.05cm} x) \to \int P_x \eta(d} %{\operatorname{d}\hspace{-0.05cm} x)\) weakly as \(n \to \infty\) whenever \(\eta^n \to \eta\) weakly as \(n \to \infty\).
\end{enumerate}
This fact is noteworthy, because in case for all \(x \in \mathbb{B}\) the MP \((A, b, a, K, \varepsilon_x)\) has a unique solution \(P_x\), the map \(x \mapsto P_x\) is Borel and \(\int P_x \eta(d} %{\operatorname{d}\hspace{-0.05cm} x)\) is the unique solution to the MP \((A, b, a, K,\eta)\), see Proposition \ref{prop: A3} in Appendix \ref{app: 1}.
\end{remark}
Many conditions for tightness include boundedness or moment conditions. In such cases, it might be easier to consider a localized version of \((P^n)_{n \in \mathbb{N}}\). We introduce the stopping time \begin{align}\label{eq: tau}
\tau_z (\alpha) \triangleq \inf(t \geq 0\colon \|\alpha(t-)\| \geq z \textup{ or } \|\alpha(t)\| \geq z),\quad z \geq 0,\ \alpha \in \Omega,
\end{align}
see \cite[Proposition 2.1.5]{EK}.
As the following theorem shows, if a good candidate for the limit of \((P^n)_{n \in \mathbb{N}}\) exists, it suffices to show tightness for the localized sequences
\((P^n \circ X^{-1}_{\cdot \wedge \tau_m})_{n \in \mathbb{N}}\) and all \(m \in \mathbb{N}\).
In Section \ref{sec:3} below we use this observation together with the compactness method from \cite{doi:10.1080/17442509408833868} to deduce mild conditions for the Feller property of diffusion-type MPs and limit theorems.
\begin{theorem}\label{prop: loc}
For all \(n \in \mathbb{N}\) let \(P^n\) be a solution to the MP \((A^n, b^n, a^n, K^n, \eta^n)\) and assume that \textup{(M1), (M2)} and \textup{(M3)} hold. If for all \(x \in \mathbb{B}\) the MP \((A, b, a, K, \varepsilon_x)\) has a unique solution \(P_x\) and for all \(m \in \mathbb{N}\) the sequence \((P^n \circ X_{\cdot \wedge \tau_m}^{-1})_{n \in \mathbb{N}}\) is tight, then the map \(x \mapsto P_x\) is Borel, \(\int P_x \eta(d} %{\operatorname{d}\hspace{-0.05cm} x)\) is the unique solution to the MP \((A, b, a, K, \eta)\) and \(P^n \to \int P_x \eta(d} %{\operatorname{d}\hspace{-0.05cm} x)\) weakly as \(n \to \infty\).
\end{theorem}
The proof is given in Section \ref{proof: theo2} below. In general, tightness of stochastic processes is well-studied. Sufficient and necessary conditions in various settings can be found in \cite{EK, 10.2307/1427238, metivier1987, XIE1995277}. A frequently used condition is the following version of Aldous's tightness criterion.
\begin{proposition}\label{prop: gen tight}
Let \((P^n)_{n \in \mathbb{N}}\) be a sequence of probability measures on \((\Omega, \mathcal{F})\) such that the following hold: \begin{enumerate}
\item[\textup{(i)}] For all \(t \geq 0\) the sequence \((P^n \circ X^{-1}_t)_{n \in \mathbb{N}}\) is tight.
\item[\textup{(ii)}] For all \(\epsilon > 0, M \in \mathbb{N}\) and all sequences \((\rho_n, h_n)_{n \in \mathbb{N}}\), where \((\rho_n)_{n \in \mathbb{N}}\) is a sequence of stopping times such that \(\sup_{n \in \mathbb{N}} \rho_n \leq M\) and \((h_n)_{n \in \mathbb{N}} \in (0, \infty)\) is a sequence such that \(h_n \to 0\) as \(n \to \infty\), we have
\[
\lim_{n \to \infty} P^n \Big(\|X_{\rho_n + h_n} - X_{\rho_n}\| \geq \epsilon \Big) = 0.
\]
\end{enumerate}
Then, \((P^n)_{n \in \mathbb{N}}\) is tight.
\end{proposition}
\begin{proof}
See \cite[Theorem 6.8]{walshintroduction} and \cite[Corollary p. 120]{10.2307/3212499}.
\end{proof}
We illustrate an application of this proposition and Corollary \ref{coro: existence} in the next section.
\section{Existence of Weak Solutions to Jump-Diffusion SDEs}\label{sec:sm}
In this section we apply our results in a semimartingale setting. Namely, we give continuity and linear growth conditions for the existence of weak solutions to jump-diffusion SDEs of the type
\begin{align}\label{eq: main SDE}
d} %{\operatorname{d}\hspace{-0.05cm} Y_t = b(Y_{t-}) d} %{\operatorname{d}\hspace{-0.05cm} t + \sigma(Y_{t-}) d} %{\operatorname{d}\hspace{-0.05cm} W_t + \int v(x, Y_{t-})(p - q)(d} %{\operatorname{d}\hspace{-0.05cm} x, d} %{\operatorname{d}\hspace{-0.05cm} t),
\end{align}
where \(W\) is a cylindrical standard Brownian motion and \(p - q\) is a compensated Poisson random measure (see \cite[Section II.1]{JS}).
We assume that \(\mathbb{B}\) is a separable Hilbert space. Moreover, let \((E, \mathcal{E})\) be a Blackwell space (see \cite[Section II.1.a]{JS}; any Polish space with its Borel \(\sigma\)-field is a Blackwell space), \(\mathbb{H}\) be a second separable Hilbert spaces and \(q = d} %{\operatorname{d}\hspace{-0.05cm} t \otimes F\) be the compensator of a Poisson random measure on \(\mathbb{R}_+ \times E\) (see \cite[Theorem II.1.8]{JS}). The norm of \(\mathbb{B}\) is denoted by \(\|\cdot\|_\mathbb{B}\) and the corresponding scalar product is denoted by \(\langle \cdot, \cdot \rangle_\mathbb{B}\).
Let \(J \colon \mathbb{B} \to \mathbb{B}\) be a compact operator of the form
\[
J x = \sum_{i = 1}^\infty \lambda_i \langle x, h_i\rangle_\mathbb{B} h_i, \quad x \in \mathbb{B}, \lambda_k > 0 \text{ for all } k \in \mathbb{N},
\]
where \(\sup_{k \in \mathbb{N}} \lambda_k < \infty\) and \((h_k)_{k \in \mathbb{N}}\) is an orthonormal basis of \(\mathbb{B}\).
Symmetric positive compact operators are always of this form except that the coefficients \(\lambda_k\) are not necessarily strictly positive, see \cite[Theorem VI.3.2]{werner2007funktionalanalysis}.
We also define \(J^{-1} \colon J(\mathbb{B}) \to \mathbb{B}\) by
\[
J^{-1} x \triangleq \sum_{i = 1}^\infty \frac{1}{\lambda_i} \langle x, h_i\rangle_\mathbb{B} h_i, \quad x \in J(\mathbb{B}).
\]
Equipped with the scalar product \(\langle \cdot, \cdot\rangle_\mathbb{K} \triangleq \langle J^{-1}\ \cdot\ , J^{-1}\ \cdot\ \rangle_\mathbb{B}\) the space \(\mathbb{K} \triangleq J(\mathbb{B})\) becomes a separable Hilbert space with orthonormal basis \((e_k)_{k \in \mathbb{N}} \triangleq (\lambda_k h_k)_{k \in \mathbb{N}}\), see \cite[Proposition C.0.3]{roeckner15}. We denote the corresponding norm by \(\|\cdot\|_\mathbb{K}\).
As always, we identify \(\mathbb{B},\mathbb{H}\) and \(\mathbb{K}\) with their (topological) duals.
\begin{lemma}\label{lem: emb comp}
The embedding \(\iota \colon \mathbb{K} \hookrightarrow \mathbb{B}\) is compact.
\end{lemma}
\begin{proof} Fix a bounded sequence \((y_n)_{n \in \mathbb{N}} \subset \mathbb{K}\). There exists a sequence \((x_n)_{n \in \mathbb{N}} \subset \mathbb{B}\) such that \(y_n = J x_n\) for \(n \in \mathbb{N}\). Because
\[
\|y_n\|_\mathbb{K}= \| J^{-1} J x_n\|_\mathbb{B} = \|x_n\|_\mathbb{B},
\]
the sequence \((x_n)_{n \in \mathbb{N}}\) is bounded in \(\mathbb{B}\). Consequently, because \(J\) is compact, the sequence \((y_n)_{n \in \mathbb{N}} = (J x_n)_{n \in \mathbb{N}}\) has a convergent subsequence in \(\mathbb{B}\). This shows that \(\iota\) is compact.
\end{proof}
The space of all Hilbert-Schmidt operators \(\mathbb{H} \to \mathbb{K}\) is denote by \(L_2(\mathbb{H}, \mathbb{K})\) and the corresponding Hilbert-Schmidt norms is denoted by
\(\|\cdot\|_{\textup{HS}(\mathbb{K})}\). As always, we denote the space of linear bounded operators \(\mathbb{H} \to \mathbb{B}\) by \(L(\mathbb{H}, \mathbb{B})\). In case the image and preimage spaces are not \(\mathbb{B}\) and \(\mathbb{H}\) the notation is analogously. The operator norm on \(L(\mathbb{H}, \mathbb{B})\) is denoted by \(\|\cdot\|_{L(\mathbb{B})}\).
\begin{theorem}\label{prop: existence}
Let \(b \colon \mathbb{B} \to \mathbb{B}, \sigma \colon \mathbb{B} \to L(\mathbb{H}, \mathbb{B})\) and \(v \colon E \times \mathbb{B} \to \mathbb{B}\) be measurable maps such that the following hold:
\begin{enumerate}
\item[\textup{(i)}]
\(b (\mathbb{K}) \subset \mathbb{K}, \sigma (\mathbb{K}) \subset L_2(\mathbb{H}, \mathbb{K})\) and \(v(E \times \mathbb{K}) \subset \mathbb{K}\).
\item[\textup{(ii)}]
For all \(y \in E\) the maps
\[
\mathbb{B} \ni x \mapsto b(x), \sigma (x), v(y, x)
\]
are continuous. For \(\sigma\) we mean continuity in the operator norm \(\|\cdot\|_{L(\mathbb{B})}\).
\item[\textup{(iii)}]
There exists a Borel function \(\gamma \colon E \to \mathbb{R}_+\) such that \(\int_E \gamma^2(y)F(d} %{\operatorname{d}\hspace{-0.05cm} y) < \infty\) and a constant \(L \in (0, \infty)\) such that for all \(y \in E\) and \(x \in \mathbb{K}\)
\begin{align}
\|b(x)\|_\mathbb{K} + \|\sigma(x)\|_{\textup{HS} (\mathbb{K})} &\leq L\big(1 + \|x\|_\mathbb{K}\big),\label{eq: lg}
\\
\|v(y, x)\|_\mathbb{K} &\leq \gamma(y) \big(1 + \|x\|_\mathbb{K}\big).\nonumber
\end{align}
Moreover, for all bounded sets \(B \subset \mathbb{B}\) we have
\begin{align}\label{eq: lbdd}
\sup_{x \in B} \|b(x)\|_\mathbb{B} + \sup_{x \in B} \|\sigma (x)\|_{L(\mathbb{B})} < \infty,
\end{align}
and there exists a Borel function \(\zeta_B\colon E \to \mathbb{R}_+\) such that \(\int_E \zeta^2_B(z)F(d} %{\operatorname{d}\hspace{-0.05cm} z) < \infty\) and
\begin{align}\label{eq: loc bdd B}
\sup_{x \in B} \|v(y, x)\|_\mathbb{B} \leq \zeta_B (y)
\end{align}
for all \(y \in E\).
\end{enumerate}
For all probability measures \(\eta\) on \((\mathbb{K}, \mathcal{B}(\mathbb{K}))\) there exists a solution to the MP \((0, \mu, a, K, \eta \circ \iota^{-1})\), where for all \(x \in \mathbb{B}\)
\begin{align*}
\mu (x) &\triangleq b(x) + \int_E \big(h(v(y, x)) - v(y, x)\big) F(d} %{\operatorname{d}\hspace{-0.05cm} y),\\
a (x) &\triangleq \sigma (x) \sigma(x)^*,\\
K(x, G) &\triangleq \int_E \mathbf{1}_{G\backslash \{0\}} (v(y, x)) F(d} %{\operatorname{d}\hspace{-0.05cm} y),\quad G \in \mathcal{B}(\mathbb{B}),
\end{align*}
and \(\sigma (x)^* \in L(\mathbb{B}, \mathbb{H})\) denotes the adjoint of \(\sigma (x) \in L(\mathbb{H}, \mathbb{B})\).
\end{theorem}
We prove this theorem in Section \ref{sec: pf sm} below. Lipschitz conditions for the existence of (pathwise) unique solutions to SDEs of the type \eqref{eq: main SDE} can be found in \cite{doi:10.1080/17442501003624407,metivier}. A version of Theorem \ref{prop: existence} for SDEs driven by Wiener noise is given in \cite{GMR09}. We are not aware of any result in the direction of Theorem \ref{prop: existence} which allows L\'evy noise.
\begin{remark}
\begin{enumerate}
\item[\textup{(i)}] In case \(\mathbb{B}\) is finite-dimensional it is possible to take \(J = \textup{Id}\). Then, Theorem \ref{prop: existence} boils down to a classical Skorokhod-type existence result for jump-diffusion SDEs.
\item[\textup{(ii)}] Because there exists an \(\epsilon > 0\) such that \(h(x) = x\) for all \(x \in \mathbb{B} \colon \|x\| \leq \epsilon\), there exists a constant \(l > 0\) such that
\(
\|h(x) - x\|_\mathbb{B} \leq l \|x\|_\mathbb{B}^2.
\)
Thus, \eqref{eq: lbdd} and \eqref{eq: loc bdd B} imply that \(\mu\) as defined in Theorem \ref{prop: existence} satisfies
\[
\sup_{x \in G} \|\mu(x)\|_\mathbb{B} < \infty, \quad G \subset \mathbb{B} \text{ bounded}.
\]
\item[(iii)]
Note that for \(T \in L_2(\mathbb{H}, \mathbb{K})\) we have
\begin{align*}
\|T\|_{\textup{HS}(\mathbb{K})} &= \sum_{i = 1}^\infty\sum_{j = 1}^\infty \langle T u_i, e_j\rangle_\mathbb{K}^2 \\&= \sum_{i = 1}^\infty\sum_{j = 1}^\infty \langle J^{-1} T u_i, J^{-1} e_j\rangle_\mathbb{B}^2
\\&= \sum_{i = 1}^\infty\sum_{j = 1}^\infty \langle J^{-1} T u_i, h_j\rangle_\mathbb{B}^2 \\&= \|J^{-1} T\|_{\textup{HS}(\mathbb{B})},
\end{align*}
where \((u_k)_{k \in \mathbb{N}}\) is an orthonormal basis of \(\mathbb{H}\).
Thus, \eqref{eq: lg} is implied by the linear growth condition (iii\('\)) as defined in \cite[Remark 2]{GMR09}.
In Theorem \ref{prop: existence} the second linear growth condition (ii\('\)) from \cite[Remark 2]{GMR09} is weakened to the local boundedness assumption \eqref{eq: lbdd}.
\end{enumerate}
\end{remark}
Let us comment on the idea of proof. The argument is based on Corollary \ref{coro: existence}, i.e. we construct an approximation sequence and verify its tightness via Aldous's tightness criterion, see Proposition \ref{prop: gen tight}. In infinite-dimensional Hilbert spaces closed balls are not compact and, consequently, moment bounds do not imply tightness. To overcome this problem we construct the approximation sequence on the smaller Hilbert space \(\mathbb{K}\). Because \(\mathbb{K}\) is compactly embedded in \(\mathbb{B}\), moment bounds for the approximation sequence on \(\mathbb{K}\) imply tightness on the larger Hilbert space \(\mathbb{B}\).
\section{A Diffusion Setting}\label{sec:3}
In this section we discuss the diffusion case as an important special case of our setting.
\subsection{The Setup}\label{sec: 5.1}
We slightly adjust our setup. Let \(\Omega\) be the space of all continuous functions \(\mathbb{R}_+ \to \mathbb{B}\), where \(\mathbb{B}\) is assumed to be a separable Hilbert space. As usual, we identify \(\mathbb{B}\) with its (topological) dual and equip \(\Omega\) with the local uniform topology. We set \(X, \mathscr{F}\) and \(\mathbf{F} = (\mathscr{F}_t)_{t \geq 0}\) as in Section \ref{2.1}.
Also in this case, \(\mathscr{F}\) is the Borel \(\sigma\)-field on \(\Omega\).
We define \(\tau_z\) as in Section \ref{2.1}. Due to the continuous paths of \(X\) we have
\[
\tau_z = \inf (t \geq 0 \colon \|X_t\| \geq z).
\]
For diffusions the coefficient \(K\) is not relevant and we remove it from all notations. The MP is defined as in Definition \ref{def: MP}.
Due to \cite[Problem 25, p. 153]{EK}, Theorems \ref{theo1} and \ref{prop: loc} also hold in this setting.
Let \(\mathbb{H}\) be a second separable Hilbert space and let \(b^n\) and \(a^n\) be as follows:
\begin{enumerate}
\item[(a)] The coefficients \(b^n\colon \mathbb{B} \to \mathbb{B}\) are Borel.
\item[(b)] The coefficients \(a^n \colon \mathbb{B} \to S^+ (\mathbb{B}, \mathbb{B})\) have decompositions \(a^n = \sigma^n (\sigma^n)^*\), where \(\sigma^n \colon \mathbb{B} \to L(\mathbb{H}, \mathbb{B})\) is Borel.
\end{enumerate}
Next, we define conditions on the coefficients \((b^n)_{n \in \mathbb{N}}\) and \((a^n)_{n \in \mathbb{N}}\).
\begin{enumerate}
\item[(A1)] For all bounded sets \(G \subset \mathbb{B}\)
\begin{align}\label{eq: tr}
\sup_{n \in \mathbb{N}} \sup_{x \in G} \|b^n(x)\| + \sup_{n \in \mathbb{N}} \sup_{x \in G} \|\sigma^n(x)\|_\textup{HS} < \infty.
\end{align}
\item[(A2)]
There exists a constant \(K > 0\) such that for all \(x \in \mathbb{B}\) and all \(n \in \mathbb{N}\)
\begin{align}\label{eq: tr2}
\|b^n(x)\| + \|\sigma^n(x)\|_\textup{HS} \leq K \big(1 + \|x\|\big).
\end{align}
\item[(A3)]
For all bounded sets \(G \subset\mathbb{B}\)
\begin{align}\label{eq: no tr}
\sup_{n \in \mathbb{N}} \sup_{x \in G} \|b^n(x)\| + \sup_{n \in \mathbb{N}} \sup_{x \in G} \|\sigma^n(x)\|_o < \infty,
\end{align}
where \(\|\cdot\|_o\) denotes the operator norm.
\item[(A4)] There exists a constant \(K > 0\) such that for all \(x \in \mathbb{B}\) and all \(n \in \mathbb{N}\)
\begin{align}\label{eq: no tr2}
\|b^n(x)\| + \|\sigma^n(x)\|_o \leq K \big(1 + \|x\|\big).
\end{align}
\end{enumerate}
It is clear that
\begin{align*}
\textup{(A2)} &\Rightarrow \textup{(A1)},\\ \textup{(A4)} &\Rightarrow \textup{(A3)}.
\end{align*}
Recall
that a \(C_0\)-semigroup \((S_t)_{t \geq 0}\) is called compact if \(S_t\) is a compact operator for all \(t > 0\). Note that a \(C_0\)-semigroup with generator \(A\) is compact if and only if it is continuous on \((0, \infty)\) in the uniform operator topology and the resolvent of \(A\) is compact, see \cite[Theorem 3.3, p. 48]{pazy2012semigroups}. In particular, by \cite[(2.5), p. 235]{pazy2012semigroups}, an analytic semigroup (see \cite[Definition 5.1, p. 60]{pazy2012semigroups}) whose generator has a compact resolvent is compact.
We also formulate conditions on the linearity \(A\):
\begin{enumerate}
\item[\textup{(A5)}] The operator \(A\) is the generator of a compact \(C_0\)-semigroup.
\item[\textup{(A6)}] The operator \(A\) is the generator of a \(C_0\)-semigroup \((S_t)_{t \geq 0}\) and there exists a \(\lambda \in (0, \frac{1}{2})\) and an \(\epsilon > 0\) such that
\begin{align}\label{eq: convSG}
\int_0^\epsilon t^{- 2 \lambda} \|S_t\|^2_\textup{HS} d} %{\operatorname{d}\hspace{-0.05cm} t < \infty.
\end{align}
\end{enumerate}
\begin{lemma}\label{lem: for all conv}
\begin{enumerate}
\item[\textup{(i)}]
\textup{(A6)} \(\Rightarrow\) \textup{(A5)}.
\item[\textup{(ii)}] If \eqref{eq: convSG} holds for some \(\epsilon > 0\), then \eqref{eq: convSG} holds for all \(\epsilon > 0\).
\end{enumerate}
\end{lemma}
\begin{proof}
(i). Fix \(t > 0\) and note that, due to \eqref{eq: convSG}, we find an \(s \in(0, t)\) such that \(S_s\) is Hilbert-Schmidt. Thus, the operator \(S_t\) is Hilbert-Schmidt, because it is the product of the bounded operator \(S_{t - s}\) and the Hilbert-Schmidt operator \(S_s\).
We conclude that \(S_t\) is compact.
(ii). Suppose that \eqref{eq: convSG} holds for \(\epsilon > 0\) and let \(T > \epsilon\). There exists an \(s \in (0, \epsilon)\) such that \(S_s\) is Hilbert-Schmidt. Moreover, because \((S_t)_{t \geq 0}\) is a \(C_0\)-semigroup, there are constants \(M \geq 1\) and \(\alpha \geq 0\) such that
\(
\|S_t\|_o \leq M e^{\alpha t}
\) for all \(t \geq 0\), see \cite[Theorem 2.2, p. 4]{pazy2012semigroups}.
We obtain that
\begin{align*}
\int_0^T t^{-2 \alpha} \|S_t\|^2_\textup{HS} d} %{\operatorname{d}\hspace{-0.05cm} t
&\leq \int_0^\epsilon t^{-2 \alpha} \|S_t\|^2_\textup{HS} d} %{\operatorname{d}\hspace{-0.05cm} t + \int_\epsilon^T t^{-2 \alpha} \|S_s\|^2_\textup{HS} M^2 e^{2\alpha (t - s)} d} %{\operatorname{d}\hspace{-0.05cm} t
\\&\leq \int_0^\epsilon t^{-2 \alpha} \|S_t\|^2_\textup{HS} d} %{\operatorname{d}\hspace{-0.05cm} t + (T - \epsilon) \epsilon^{- 2 \alpha} \|S_s\|^2_\textup{HS} M^2 e^{2 \alpha (T - s)} < \infty.
\end{align*}
This completes the proof.
\end{proof}
\subsection{A Tightness Condition}\label{sec: 5.2}
Next, we study tightness of the sequence \((P^n \circ X^{-1}_{\cdot \wedge \tau_m})_{n \in \mathbb{N}}\) when \(P^n \in \mathcal{M}(A, b^n, a^n, \eta^n)\).
A proof for the following proposition can be found in Section \ref{proof: prop1} below.
\begin{proposition}\label{prop: tight}
Let \(m \in [0, \infty]\) and assume one of the following:
\begin{enumerate}
\item[\textup{(i)}] \(m < \infty\), \textup{(A1)} and \textup{(A5)} hold.
\item[\textup{(ii)}] \(m < \infty\), \textup{(A3)} and \textup{(A6)} hold.
\item[\textup{(iii)}] \(m = \infty\), \textup{(A2)} and \textup{(A5)} hold.
\item[\textup{(iv)}] \(m = \infty\), \textup{(A4)} and \textup{(A6)} hold.
\end{enumerate}
If \(P^n \in \mathcal{M}(A, b^n, a^n, \eta^n)\) and the sequence \((\eta^n)_{n \in \mathbb{N}}\) is tight, then \((P^n \circ X_{\cdot \wedge \tau_m}^{-1})_{n \in \mathbb{N}}\) is tight.
\end{proposition}
\begin{remark}\label{rem1}
\begin{enumerate}
\item[(i)] Because \(\tau_\infty = \infty\), Proposition \ref{prop: tight} includes a tightness criterion for the global sequence \((P^n)_{n \in \mathbb{N}}\) as well as for the localizations \((P^n \circ X^{-1}_{\cdot \wedge \tau_m})_{n \in \mathbb{N}}\). Part (iii) of Proposition \ref{prop: tight} is known, see \cite[Remark 3.2, Lemma 3.3]{doi:10.1080/07362999708809484}.
\item[(ii)]
The proof of Proposition \ref{prop: tight} uses the compactness method from \cite{doi:10.1080/17442509408833868}, which is based on the compactness of the generalized Riemann-Liouville operator and the factorization formula introduced in \cite{doi:10.1080/17442508708833480}. In the presence of jumps, the image space of the generalized Riemann-Liouville operator is not suitable anymore and the factorization formula might fail, see \cite[Section 11.4]{peszat2007stochastic} for comments.
\item[(iii)] Continuity and linear growth conditions for the existence of solutions to MPs can be found in \cite{doi:10.1080/17442509408833868}.
\end{enumerate}
\end{remark}
\subsection{Corollaries}\label{sec: 5.3}
In this section we collect corollaries to the results from Section \ref{sec: MR} and Proposition \ref{prop: tight}.
Let \(b \colon \mathbb{B} \to \mathbb{B}\) and \(a \colon \mathbb{B} \to S^+(\mathbb{B}, \mathbb{B})\) be Borel maps such that \(a = \sigma \sigma^*\) for a Borel map \(\sigma \colon \mathbb{B} \to L(\mathbb{H}, \mathbb{B})\).
We formulate the following conditions:
\begin{enumerate}
\item[(A7)] For all \(y^* \in D(A^*)\) the maps
\[
x \mapsto \langle b(x), y^*\rangle, \langle a(x) y^*, y^*\rangle
\]
are continuous.
\item[(A8)]
For all bounded sets \(G \subset \mathbb{B}\)
\begin{align*}
\sup_{x \in G} \|b(x)\| + \sup_{x \in G} \|\sigma(x)\|_\textup{HS} < \infty.
\end{align*}
\item[(A9)] For all bounded sets \(G \subset \mathbb{B}\)
\begin{align*}
\sup_{x \in G} \|b(x)\| + \sup_{x \in G} \|\sigma(x)\|_o < \infty.
\end{align*}
\end{enumerate}
\begin{corollary}\label{coro: diffusion Feller}
Suppose that one of the following holds:
\begin{enumerate}
\item[\textup{(i)}] \textup{(A5), (A7)} and \textup{(A8)} hold.
\item[\textup{(ii)}] \textup{(A6), (A7)} and \textup{(A9)} hold.
\end{enumerate}
If for all \(x \in \mathbb{B}\) the MP \((A, b, a, \varepsilon_x)\) has the unique solution \(P_x\), then \(\{P_x, x \in \mathbb{B}\}\) is Feller.
\end{corollary}
\begin{proof}
Let \((x_n)_{n \in \mathbb{N}} \subset \mathbb{B}\) and \(x \in \mathbb{B}\) such that \(x_n \to x\) as \(n \to \infty\).
Due to Proposition \ref{prop: tight}, the sequence \((P_{x_n} \circ X_{\cdot \wedge \tau_m}^{-1})_{n \in \mathbb{N}}\) is tight for all \(m \in \mathbb{N}\) and it follows from Theorem \ref{prop: loc} that \(P_{x_n} \to P_x\) weakly as \(n \to \infty\). We conclude that the family \(\{P_x, x \in \mathbb{B}\}\) is Feller.
\end{proof}
This observation generalizes the classical result for the finite-dimensional case given in \cite[Corollary 11.1.5]{SV} and it extends the infinite-dimensional result \cite[Corollary 4.4]{EJP2924} by replacing the tightness assumption with explicit conditions implying it.
We also formulate the following condition:
\begin{enumerate}
\item[(A10)] For all \(y^* \in D(A^*)\) we have
\(
\langle b^n , y^*\rangle \to \langle b, y^*\rangle, \langle a^n y^*, y^*\rangle \to \langle a y^*, y^*\rangle
\)
as \(n \to \infty\) uniformly on compact subsets of \(\mathbb{B}\).
\end{enumerate}
\begin{corollary}\label{coro: uni}
Let \(P^n \in \mathcal{M}(A, b^n, a^n, \eta^n)\) for all \(n \in \mathbb{N}\) and suppose that one of the following holds:
\begin{enumerate}
\item[\textup{(i)}] \textup{(A1), (A5), (A7), (A9)} and \textup{(A10)} hold.
\item[\textup{(ii)}] \textup{(A3), (A6), (A7), (A9)} and \textup{(A10)} hold.
\end{enumerate}
If for all \(x \in \mathbb{B}\) the MP \((A, b, a, \varepsilon_x)\) has a unique solution \(P_x\), then \(x \mapsto P_x\) is Borel, \(\int P_x \eta(d} %{\operatorname{d}\hspace{-0.05cm} x)\) is the unique solution to the MP \((A, b, a, \eta)\) and \(P^n \to \int P_x \eta(d} %{\operatorname{d}\hspace{-0.05cm} x)\) weakly as \(n \to \infty\) whenever \(\eta^n \to \eta\) weakly as \(n \to \infty\).
\end{corollary}
\begin{proof}
This follows from Proposition \ref{prop: tight} and Theorem \ref{prop: loc}.
\end{proof}
Corollary \ref{coro: uni} is a generalization of the classical finite-dimensional result \cite[Theorem 11.1.4]{SV} and it extends the related infinite-dimensional result \cite[Lemma 4.3]{EJP2924} via explicit conditions for tightness.
Part (i) of Corollary \ref{coro: uni} can be compared to \cite[Theorems 2.1]{doi:10.1080/07362999708809484} and part (ii) can be compared to \cite[Theorem 2.3]{doi:10.1080/07362999708809484}. We stress that time-inhomogeneous SPDEs were studied in \cite{doi:10.1080/07362999708809484}. For the time-homogeneous case the assumptions in \cite[Theorems 2.1 and 2.3]{doi:10.1080/07362999708809484} are the following:
\begin{enumerate}
\item[(H1)] For all initial laws \(\eta\) the MP \((A, b, a, \eta)\) has at most one solution.
\item[(H2)] For all \(y \in \mathbb{B}\) the families \(\{\langle b, y\rangle, \langle b^n, y\rangle \colon n \in \mathbb{N}\}\) and \(\{\langle a y, y\rangle, \langle a^n y, y\rangle \colon n \in \mathbb{N}\}\) are uniformly equicontinuous on all open and bounded subsets of \(\mathbb{B}\).
\item[(H3)] The convergence in (A10) holds pointwise.
\item[(H4)] (A2) respectively (A4) holds and a similar linear growth condition also holds for \(b\) and \(a\).
\item[(H5)] The initial laws \(\{\eta, \eta^n \colon n \in \mathbb{N}\}\) satisfy a moment condition and \(\eta^n \to \eta\) weakly as \(n \to \infty\).
\item[(H6)] (A5) respectively a condition comparable to (A6) holds, see \cite[Remark 3]{doi:10.1080/17442509408833868} and \cite[Remark 2.3]{doi:10.1080/07362999708809484}.
\end{enumerate}
In view of \cite[Remark 2.1]{doi:10.1080/07362999708809484}, the MP \((A, b, a)\) is well-posed under the assumptions of \cite[Theorems 2.1 and 2.3]{doi:10.1080/07362999708809484}.
Because for equicontinous families the topologies of pointwise and local uniform convergence coincide (see, e.g., \cite[Lemma 11.3.11]{singh2019introduction}), (H2) and (H3) imply (A7) and (A10).
In \cite[Remark 2.2]{doi:10.1080/07362999708809484} it was conjectured that the moment assumption in (H5) is not necessary and only required by the method of identifying the limit. Indeed, the martingale problem method does not need such an assumption and, consequently, in Corollary \ref{coro: uni} no moment condition on the initial laws is imposed. Moreover, instead of (H4), Corollary \ref{coro: uni} contains only the weaker local boundedness assumptions (A1) and (A9) or (A3) and (A9).
We formulate one last condition:
\begin{enumerate}
\item[(A11)] The MP \((A, b, a, \eta)\) has at most one solution.
\end{enumerate}
In the following corollary we replace the well-posedness assumption in Corollary \ref{coro: uni} by a linear growth condition and a uniqueness assumption for the limiting MP.
\begin{corollary}\label{coro: existence diff}
Let \(P^n \in \mathcal{M}(A, b^n, a^n, \eta^n)\) for all \(n \in \mathbb{N}\) and suppose that one of the following holds:
\begin{enumerate}
\item[\textup{(i)}] \textup{(A2), (A5), (A7), (A9), (A10)} and \textup{(A11)} hold.
\item[\textup{(ii)}] \textup{(A4), (A6), (A7), (A9), (A10)} and \textup{(A11)} hold.
\end{enumerate}
If \(\eta^n \to \eta\) weakly as \(n \to \infty\), then there exists a unique solution \(P\) to the MP \((A, b, a, \eta)\) such that \(P^n \to P\) weakly as \(n \to \infty\).
\end{corollary}
\begin{proof}
This follows from Proposition \ref{prop: tight} and Corollary \ref{coro: existence}.
\end{proof}
\begin{remark}
Condition (A11) holds for instance under local Lipschitz conditions.
Another possibility to obtain conditions for uniqueness and well-posedness is to use Girsanov's theorem, see \cite{criens18} and Lemma \ref{lem: wp} below.
\end{remark}
\subsection{Examples}\label{sec:5.5}
In the following we present an example for an application of Corollary \ref{coro: diffusion Feller} and examples for cases where the assumptions (A5) and (A6) are satisfied.
\begin{example}\label{exp: heat}
Assume that \(\mathbb{B} = \mathbb{H}\), that \(\sigma = \textup{Id}\), that (A6) holds and that for all \(x \in \mathbb{B}\)
\[
\|b(x)\| \leq \textup{const. } (1 + \|x\|).
\]
Furthermore, assume that \(x \mapsto \langle b(x), y\rangle\) is continuous for all \(y \in \mathbb{B}\).
The MP \((A, b, a)\) corresponds to the Cauchy problem
\[
d} %{\operatorname{d}\hspace{-0.05cm} Y_t = (A Y_t + b(Y_t))d} %{\operatorname{d}\hspace{-0.05cm} t + d} %{\operatorname{d}\hspace{-0.05cm} W_t,
\]
where \(W\) is a cylindrical standard Brownian motion.
In this case, we have the following:
\begin{lemma}\label{lem: wp}
The MP \((A, b, a)\) is well-posed.
\end{lemma}
\begin{proof}
Let \(x \in \mathbb{B}\). The MPs \((A, b, a, \varepsilon_x)\) and \((A, 0, a, \varepsilon_x)\) have solutions due to \cite[Theorem 2]{doi:10.1080/17442509408833868}.
Because Ornstein-Uhlenbeck processes have a unique law, the MP \((A, 0, a, \varepsilon_x)\) satisfies uniqueness. Now, \cite[Proposition 3.7]{criens18} yields that also the MP \((A, b, a, \varepsilon_x)\) satisfies uniqueness.
\end{proof}
The previous lemma can be compared to \cite[Theorem 13]{daprato2013}, where a similar result is shown.
Let \(P_x\) be the unique solution to the MP \((A, b, a, \varepsilon_x)\).
The following is a consequence of Corollary \ref{coro: diffusion Feller} and Lemma \ref{lem: wp}.
\begin{corollary}
The family \(\{P_x, x \in \mathbb{B}\}\) is Feller.
\end{corollary}
In \cite{Maslowski1999} it is shown that for all \(t > 0\) and all bounded weakly sequentially continuous functions \(f \colon \mathbb{B} \to \mathbb{R}\) the map \(x \mapsto E_x [f(X_t)]\) is weakly sequentially continuous, too. The proof is based on the observation that the sequential Feller property is preserved by Girsanov's theorem.
\end{example}
\begin{example}\label{ex:2}
Let \(\mathcal{O}\) be a bounded domain in \(\mathbb{R}^d\) with smooth boundary and \(m \in \mathbb{N}\). We take \(\mathbb{B} \triangleq L^2(\mathcal{O})\). For any multiindex \(\alpha\) with \(|\alpha| \leq 2m\) let \(\gamma_\alpha \colon \textup{cl}_{\mathbb{R}^d} (\mathcal{O}) \to \mathbb{R}\) be a sufficiently smooth function.
We define the differential operator
\[
A f (x) \triangleq \sum_{|\alpha| \leq 2m} \gamma_\alpha (x) (\partial^\alpha f) (x), \quad x \in \mathcal{O},
\]
for
\[
f \in D(A) \triangleq H^{2m} (\mathcal{O}) \cap H^m_0(\mathcal{O}).
\]
Moreover, we assume that there exists a constant \(C > 0\) such that
\[
(- 1)^{m + 1} \sum_{|\alpha| = 2m} \gamma_\alpha (x) \xi^\alpha \geq C |\xi|^{2m}
\]
for all \(x \in \mathcal{O}\) and \(\xi \in \mathbb{R}^d.\)
Due to \cite[Theorem 2.7, p. 211]{pazy2012semigroups}, the operator \(A\) generates an analytic semigroup on \(\mathbb{B}\).
\begin{enumerate}
\item[(i)] In case \(m = 1\) the resolvent of \(A\) is compact, see \cite[Remark A.28]{DePrato}, and \(A\) generates a compact \(C_0\)-semigroup, i.e. (A5) holds.
\item[(ii)] In case \(2m > d\) it has been noted in \cite[Example 3]{doi:10.1080/17442509408833868} that there exists a \(\rho \in (0, \frac{1}{2})\) such that \((- A)^{-\rho}\) is Hilbert Schmidt and, due to \cite[Remark 3]{doi:10.1080/17442509408833868}, this implies that (A6) holds.
\end{enumerate}
In particular, if \(d = 1\) and \(A\) is the Laplacian, then (A6) holds.
\end{example}
\section{Proofs}\label{sec: Proofs}
\subsection{Proof of Theorem \ref{theo1}}\label{proof: theo1}
For \(\alpha \in \Omega\) we introduce the following sets:
\begin{align*}
V(\alpha) &\triangleq \left\{t >0 \colon \tau_{t} (\alpha) < \tau_{t+}(\alpha) \right\},\\
V'(\alpha) &\triangleq \left\{ t > 0 \colon \alpha (\tau_t (\alpha)) \not = \alpha(\tau_t(\alpha)-) \text{ and } \|\alpha(\tau_t(\alpha) - )\| = t\right\}.
\end{align*}
We stress that \(\tau_{t+}\) is well-defined, because \(t \mapsto \tau_t\) is increasing.
Due to \cite[Problem 13, p. 151]{EK} and \cite[Propositions VI.2.11]{JS}, the map \(\alpha \mapsto \tau_t(\alpha)\) is continuous at each point \(\alpha\) such that \(t \not \in V(\alpha)\). Furthermore, using \cite[Theorem 3.6.3, Remark 3.6.4]{EK} instead of \cite[Theorem VI.1.14 b)]{JS}, we can argue as in the proof of \cite[Proposition VI.2.12]{JS} and obtain that the map \(\alpha \mapsto\alpha (\cdot \wedge \tau_t(\alpha))\) is continuous at each point \(\alpha\) such that \(t \not \in V(\alpha) \cup V'(\alpha)\).
It follows as in the proof of \cite[Proposition IX.1.17]{JS} that the set
\[
\left\{t \geq 0 \colon P \big(\big\{ \alpha \in \Omega \colon t \in V (\alpha) \cup V'(\alpha)\big\}\big) > 0 \right\}
\]
is at most countable. Therefore, we can choose \(\lambda_m \in [m-1, m]\) such that
\begin{align}\label{lambda_m}
P\big(\big\{\alpha \in \Omega \colon \lambda_m \in V (\alpha) \cup V'(\alpha)\big\}\big) = 0.
\end{align}
We summarize:
\begin{align}\label{eq: SK con}
\alpha \mapsto \tau_{\lambda_m}(\alpha), X_{\cdot \wedge \tau_{\lambda_{m}}(\alpha)}(\alpha) \text{ are continuous up to a } P\text{-null set.}
\end{align}
Next, we show that the process \(M^f_{\cdot \wedge \tau_{\lambda_{m}}}\) is a \(P\)-martingale for all \(f \in \mathcal{D}\). Fix an \(f \in \mathcal{D}\) and let \((f^n)_{n \in \mathbb{N}}\) be the corresponding sequence as in (M2).
Define \(M^{f^n}\) as in \eqref{f - K} with \(f\) replaced by \(f^n\) and \(\mathcal{K} f\) replaced by \(\mathcal{K}^n f^n\). Due to Proposition \ref{prop: A1} in Appendix \ref{app: 1}, the process \(M^{f^n}_{\cdot \wedge \tau_{\lambda_{m}}}\) is a \(P^{n}\)-martingale.
We claim the following: There exists a dense set \(D \subset \mathbb{R}_+\) such that the following hold:
\begin{enumerate}
\item[\textup{(a)}] For any bounded sequence \((t_n)_{n \in \mathbb{N}}\subset D\) and any \(t \in D\) we have \[\sup_{n \in \mathbb{N}} \sup_{\alpha \in \Omega}\big|M^f_{t_n \wedge \tau_{\lambda_{m}} (\alpha)}(\alpha)\big| + \sup_{n \in \mathbb{N}} \sup_{\alpha \in \Omega} \big|M^{f^n}_{t \wedge \tau_{\lambda_m (\alpha)}}(\alpha)| < \infty.\]
\item[\textup{(b)}] For all \(t\in D\) the map \(\alpha \mapsto M^f_{t \wedge \tau_{\lambda_{m}}(\alpha)} (\alpha)\) is continuous up to a \(P\)-null set.
\item[\textup{(c)}] For all \(t\in D\) and all compact sets \(K \subset \Omega\) we have
\begin{align*}
\sup_{\alpha \in K} \left|M^{f^n}_{t \wedge \tau_{\lambda_{m}} (\alpha)} (\alpha) - M^f_{t \wedge \tau_{\lambda_{m}(\alpha)}} (\alpha)\right| \to 0
\end{align*}
as \(n \to \infty\).
\end{enumerate}
Before we check these properties, we show that they imply that the process \(M^f\) is a local \(P\)-martingale.
Let \(t \in D\) and \(k \colon \Omega \to \mathbb{R}\) be bounded and continuous. In this case, (a) and (b) imply that the map
\[\alpha \mapsto k(\alpha) M^f_{t \wedge \tau_{\lambda_{m}}(\alpha)} (\alpha)\] is bounded and continuous up to a \(P\)-null set.
Therefore, by the continuous mapping theorem, \(P^n \to P\) weakly as \(n \to \infty\) yields that
\[
E^{P^n} \left[k M^f_{t \wedge \tau_{\lambda_{m}}}\right] \to E^{P} \left[k M^f_{t \wedge \tau_{\lambda_{m}}}\right]
\]
as \(n \to \infty\).
Fix \(\varepsilon > 0\) and denote
\[
c \triangleq \max \Big( \sup_{\alpha \in \Omega} \big|k(\alpha)\big|,\ \sup_{\alpha \in \Omega} \big| k(\alpha) M^f_{t \wedge \tau_{\lambda_m}(\alpha)}(\alpha)\big|,\ \sup_{n \in \mathbb{N}} \sup_{\alpha \in \Omega} \big| k(\alpha) M^{f^n}_{t \wedge \tau_{\lambda_m}(\alpha)}(\alpha)\big|,\ 1\Big).
\]
Note that \(1 \leq c < \infty\) by (a).
Because \((P^n)_{n \in \mathbb{N}}\) is tight, we find a compact set \(K \subset \Omega\) such that
\[
\sup_{n \in \mathbb{N}} P^n(K^c) \leq \frac{\varepsilon}{4 c}.
\]
Using (c) we find an \(N \in \mathbb{N}\) such that for all \(n \geq N\)
\begin{align*}
E^{P^n} \left[ \left|kM^{f^n}_{t \wedge \tau_{\lambda_{m}}} - k M^{f}_{t \wedge \tau_{\lambda_{m}}}\right| \right] &\leq 2c \sup_{m \in \mathbb{N}} P^m (K^c) + c \sup_{\alpha \in K} \big| M^{f^n}_{t \wedge \tau_{\lambda_{m}}(\alpha)}(\alpha) - M^{f}_{t \wedge \lambda_{m}(\alpha)}(\alpha)\big|
\\&\leq \frac{\varepsilon}{2} + \frac{\varepsilon}{2} = \varepsilon.
\end{align*}
Therefore, using the triangle inequality, we obtain that
\begin{align*}
E^{P^n}\left[ kM^{f^n}_{t \wedge \tau_{\lambda_{m}}}\right] \to E^P \left[k M^{f}_{t \wedge \tau_{\lambda_{m}}}\right]
\end{align*}
as \(n \to \infty\).
Take \(s, t \in \mathbb{R}_+\) with \(s < t\). Since \(D\) is dense in \(\mathbb{R}_+\) we find two sequences \((s_n)_{n \in \mathbb{N}}, (t_n)_{n \in \mathbb{N}}\subset D\) with \(s_n \searrow s\) and \(t_n \searrow t\) as \(n \to \infty\).
For any bounded, continuous and \(\mathscr{F}_s\)-measurable function \(k \colon \Omega \to \mathbb{R}\) we have
\begin{align*}
E^{P} \left[ k \left(M^{f}_{t \wedge \tau_{\lambda_{m}}} - M^f_{s \wedge \tau_{\lambda_{m}}}\right)\right] &=\lim_{i \to \infty} E^{P} \left[ k \left(M^{f}_{t_i \wedge \tau_{\lambda_{m}}} - M^f_{s_i \wedge \tau_{\lambda_{m}}}\right)\right]
\\&= \lim_{i \to \infty} \lim_{n \to \infty} E^{P^n} \left[ k \left(M^{f^n}_{t_i \wedge \tau_{\lambda_{m}}} - M^{f^n}_{s_i \wedge \tau_{\lambda_{m}}}\right)\right]
\\&= \lim_{n \to \infty} E^{P^n} \left[ k \left(M^{f^n}_{s \wedge \tau_{\lambda_{m}}} - M^{f^n}_{s \wedge \tau_{\lambda_{m}}}\right)\right] = 0,
\end{align*}
by the dominated convergence theorem, which we can apply due to (a), the right-continuity of \(M^f_{\cdot \wedge \tau_{\lambda_{m}}}\) and the \(P^n\)-martingale property of \(M^{f^n}_{\cdot \wedge \tau_{\lambda_{m}}}\). We claim that this already proves that \(M^f_{\cdot \wedge \tau_{\lambda_{m}}}\) is a \(P\)-martingale.
Take \(g \in C_b(\mathbb{B})\) and let \((m_k)_{k \in \mathbb{N}} \subset (0, \infty)\) be such that \(m_k \searrow 0\) as \(k \to \infty\). We set
\[
g^k (q) \triangleq \frac{1}{m_k} \int_{q}^{q+ m_k} g(X_r)d} %{\operatorname{d}\hspace{-0.05cm} r,\quad k \in \mathbb{N}, q \in \mathbb{R}_+,
\]
and note that \(g^k (q) \colon \Omega \to \mathbb{R}\) is continuous, bounded and \(\mathcal{F}_{q + m
_k}\)-measurable and that
\(g^k(q) \to g(X_q)\) as \(k \to \infty\). Thus, using an approximation argument, we can deduce from the fact that \(E^{P} \big[ k M^f_{t \wedge \tau_{\lambda_m}} \big] = E^{P} \big[ k M^f_{s \wedge \tau_{\lambda_m}} \big]\) holds for all \(s < t\) and all continuous, bounded and \(\mathcal{F}_s\)-measurable \(k\) that
\[
E^{P} \Big[ M^f_{t \wedge \tau_{\lambda_m}} \prod_{i = 1}^l g_i(X_{q_i}) \Big]
= E^{P} \Big[ M^{f}_{s \wedge \tau_{\lambda_m}} \prod_{i = 1}^l g_i(X_{q_i}) \Big],
\]
for all \(s < t\), \(l \in \mathbb{N}\), \(g_1, \dots, g_l\in C_b(\mathbb{B})\) and \(q_1, \dots, q_l \in [0, s]\).
Using a monotone class argument shows that \(M^f_{\cdot \wedge \tau_{\lambda_m}}\) is a \(P\)-martingale.
Since \(\lambda_m \in [m-1, m]\), we have \(\lambda_m \nearrow \infty\) as \(m \to \infty\) and therefore also \(\tau_{\lambda_{m}} (\alpha) \nearrow \infty\) as \(m \to \infty\) for all \(\alpha \in \Omega\). In other words, \(M^f\) is a local \(P\)-martingale.
Due to Proposition \ref{prop: A2} in Appendix \ref{app: 1}, solutions to MPs are determined by the test functions in \(\mathcal{D}\).
Thus, to conclude that \(P \in \mathcal{M}(A, b, a, K, \eta)\) it remains to show that \(P \circ X_0^{-1} = \eta\). Because \(\alpha \mapsto \alpha(0)\) is continuous, we have
\[
\eta^n = P^n \circ X_0^{-1} \to P \circ X_0^{-1}
\]
weakly as \(n \to \infty\). The uniqueness of weak limits and (M3) yield the identity \(P \circ X_0^{-1} = \eta\).
Consequently, \(P \in \mathcal{M}(A, b, a, K, \eta)\) and the theorem is proven.
It remains to check (a) -- (c). The finiteness of the first term in (a) follows from Proposition \ref{prop: A1} in Appendix \ref{app: 1}. The second term is finite due to \eqref{eq: bdd assp} in (M2).
Next, we check (b).
Set
\[
D \triangleq \left\{t \geq 0 \colon P\big(X_{t \wedge \tau_{\lambda_{m}}} \not = X_{(t \wedge \tau_{\lambda_{m}})-}\big) = 0\right\}.
\]
By \cite[Lemma 3.7.7]{EK}, the complement of \(D\) in \(\mathbb{R}_+\) is countable. Thus, \(D\) is dense in \(\mathbb{R}_+\). For each \(t \in D\) set
\[
U_t \triangleq \big\{\alpha \in \Omega \colon \alpha (t \wedge \tau_{\lambda_{m}}(\alpha)) \not = \alpha((t \wedge \tau_{\lambda_{m}}(\alpha))-) \big\},
\]
which is a \(P\)-null set by the definition of \(D\).
Let \(N \in \mathscr{F}\) be a \(P\)-null set such that the maps \(\alpha \mapsto \tau_{\lambda_{m}} (\alpha), X_{\cdot \wedge \tau_{\lambda_{m} (\alpha)}}(\alpha)\) are continuous at all \(\alpha \not \in N\), see \eqref{eq: SK con}. Take \(t \in D\) and \(\alpha \not \in N \cup U_t\). Recalling \cite[VI.2.3]{JS}, we see that the functions \(\omega \mapsto \omega(t \wedge \tau_{\lambda_{m}} (\omega))\) and \(\omega \mapsto \omega(0)\) are continuous at \(\alpha\). Thus, \(M^f_{t \wedge \tau_{\lambda_{m}}}\) is continuous at \(\alpha\) if the map
\[
\omega \mapsto I_{t \wedge \tau_{\lambda_m}(\omega)} (\omega) \triangleq \int_0^{t \wedge \tau_{\lambda_{m}}(\omega)} \mathcal{K} f(\omega(s-))d} %{\operatorname{d}\hspace{-0.05cm} s
\]
is continuous at \(\alpha\).
Because the set of all \(a > 0\) such that \(\tau_a\) is not continuous at \(\alpha\) is at most countable (see \cite[Lemma VI.2.10, Proposition VI.2.11]{JS}) and \(\tau_a (\alpha) \nearrow \infty\) as \(a \to \infty\), we find a \(\hat{\lambda}_m < \infty\) such that \(\lambda_m \leq \hat{\lambda}_m\), \(\tau_{\hat{\lambda}_m}\) is continuous at \(\alpha\) and \(\tau_{\hat{\lambda}_m} (\alpha) > t\). Let \((\alpha_k)_{k \in \mathbb{N}} \subset \Omega\) be such that \(\alpha_k \to \alpha\) as \(k \to \infty\). Due to the continuity of \(\tau_{\hat{\lambda}_m}\) at \(\alpha\), there exists an \(N \in \mathbb{N}\) such that \(\tau_{\hat{\lambda}_m} (\alpha_k) > t\) for all \(k\geq N\).
Due to Proposition \ref{prop: A1} in Appendix \ref{app: 1}, we have \(C \triangleq \sup_{\|x\| \leq \hat{\lambda}_m} |\mathcal{K} f (x)|< \infty\).
Now, for all \(k \geq N\) we have
\begin{align*}
\big| I_{t \wedge \tau_{\lambda_m}(\alpha)} (\alpha) &- I_{t \wedge \tau_{\lambda_m}(\alpha_k)} (\alpha_k)\big| \\&\leq \big| I_{t \wedge \tau_{\lambda_m}(\alpha)} (\alpha) - I_{t \wedge \tau_{\lambda_m}(\alpha)} (\alpha_k)\big| + \big| I_{t \wedge \tau_{\lambda_m}(\alpha)} (\alpha_k) - I_{t \wedge \tau_{\lambda_m}(\alpha_k)} (\alpha_k)\big|
\\&\leq \big| I_{t \wedge \tau_{\lambda_m}(\alpha)} (\alpha) - I_{t \wedge \tau_{\lambda_m}(\alpha)} (\alpha_k)\big| + C \big|t \wedge \tau_{\lambda_m}(\alpha) - t \wedge \tau_{\lambda_m}(\alpha_k)\big|.
\end{align*}
Because for all \(k \geq N\) and all \(s \leq t \wedge \tau_{\lambda_m} (\alpha) < \tau_{\hat{\lambda}_m}(\alpha) \wedge \tau_{\hat{\lambda}_m}(\alpha_k)\) we have
\[
\big| \mathcal{K} f (\alpha(s-)) - \mathcal{K} f(\alpha_k(s-))\big| \leq 2 C,
\]
the first term goes to zero as \(k \to \infty\) by (M1), the dominated convergence theorem and \cite[VI.2.3, Lemma VI.3.12]{JS}. The second term goes to zero as \(k \to \infty\) by the continuity of \(\tau_{\lambda_{m}}\) at \(\alpha\).
We conclude that (b) holds.
Finally, we check (c). Due to \cite[Problem 16, p. 152]{EK}, for each compact set \(K \subset \Omega\) and each \(t \geq 0\) there exists a compact set \(K_t \subset \mathbb{B}\) such that \(\alpha (s) \in K_t\) for all \(\alpha \in K\) and \(s \in [0, t]\). Thus, (M2) implies that
\begin{align*}
\sup_{\alpha \in K} \Big| M^{f^n}_{t \wedge \tau_{\lambda_{m}}(\alpha)} &(\alpha)- M^f_{t \wedge \tau_{\lambda_{m}}(\alpha)} (\alpha)\Big|
\\&\leq 2 \sup_{x \in K_t} \big|f^n(x) - f(x)\big| + t \sup_{x \in K_t}\big| \mathcal{K}^nf^n (x) - \mathcal{K} f(x)\big| \to 0
\end{align*} as \(n \to \infty\).
Therefore, (c) holds and the proof is complete.
\qed
\subsection{Proof of Theorem \ref{prop: loc}}\label{proof: theo2}
Proposition \ref{prop: A3} in Appendix \ref{app: 1} yields that the map \(x \mapsto P_x\) is Borel and that \(P \triangleq \int P_x \eta(d} %{\operatorname{d}\hspace{-0.05cm} x)\) is the unique solution to MP \((A, b, a, K, \eta)\). We show that \(P^n \to P\) weakly as \(n \to \infty\). It is well-known that \(P^n \to P\) weakly as \(n \to \infty\) if and only if each subsequence of \((P^n)_{n \in \mathbb{N}}\) has a further subsequence which converges weakly to \(P\), see, e.g., \cite[Theorem 2.6]{bil99}. If we show that \((P^n)_{n \in \mathbb{N}}\) is tight, Prohorov's theorem yields that any subsequence of \((P^n)_{n \in \mathbb{N}}\) has a weakly convergent subsequence, and Theorem \ref{theo1}, together with the uniqueness of \(P\), yields that this subsequence converges weakly to \(P\). In summary, it suffices to prove that \((P^n)_{n \in \mathbb{N}}\) is tight.
We define the following modulus of continuity:
\begin{align*}
w'(\alpha, \theta, N) &\triangleq \inf_{\{t_i\}} \max_{i} \sup_{s, t \in [t_{i-1}, t_i)} \|\alpha(s) - \alpha(t)\|,
\end{align*}
where \(\{t_i\}\) ranges over all partitions of the form \(0 = t_0 < t_1 < \dots < t_{n -1} < t_n \leq N\) with \(\min_{1 \leq i < n}(t_i - t_{i-1}) \geq \theta\) and \(n \geq 1\).
Now, recall the following fact (see \cite[Corollary 3.7.4]{EK}):
\begin{fact}\label{fact}
A sequence \((\mu^n)_{n \in \mathbb{N}}\) of probability measures on \((\Omega, \mathscr{F})\) is tight if and only if the following hold:
\begin{enumerate}
\item[\textup{(a)}]
For all \(t \in \mathbb{Q}_+\) and \(\epsilon > 0\) there exists a compact set \(C(t, \epsilon) \subset \mathbb{B}\) such that
\[
\limsup_{n \to \infty} \mu^n(X_t \not \in C(t, \epsilon))\leq \epsilon. \]
\item[\textup{(b)}]
For all \(\epsilon > 0\) and \(t > 0\) there exists a \(\delta > 0\) such that
\[
\limsup_{n \to \infty} \mu^n(w'(X, \delta, t) \geq \epsilon) \leq \epsilon.
\]
\end{enumerate}
\end{fact}
In the remainder of this proof, we show that \((P^n)_{n \in \mathbb{N}}\) satisfies (a) and (b) in Fact \ref{fact}. We start with a few preparations.
In what follows let \(m \in \mathbb{N}\) be arbitrary. Denote \(P^{n, m} \triangleq P^n \circ X^{-1}_{\cdot \wedge \tau_m}\) and fix \(t \geq 0\).
Let \(Q^m\) be an accumulation point of \((P^{n, m})_{n \in \mathbb{N}}\).
Using the same arguments as in the proof of Theorem \ref{theo1}, we find a \(\lambda_m \in [m-1, m]\) such that for all \(f \in \mathcal{D}\) the process \(M^f_{\cdot \wedge \tau_{\lambda_{m}}}\) is a \(Q^m\)-martingale and \(Q^m \circ X^{-1}_0 = \eta\).
Due to Proposition \ref{prop: A3} in Appendix \ref{app: 1}, the assumption that the MP \((A, b, a, K)\) is well-posed implies that
\begin{align*}
Q^m = P \text{ on } \mathscr{F}_{\tau_{\lambda_{m}}}.
\end{align*}
We note that the choice of \(\lambda_m\) depends on \(Q^m\), see \eqref{lambda_m}. However, for any accumulation point of \((P^{n, m})_{n \in \mathbb{N}}\) we find an appropriate \(\lambda_m\) in the interval \([m-1, m]\).
Thus, any accumulation point of \((P^{n, m})_{n \in \mathbb{N}}\) coincides with \(P\) on \(\mathscr{F}_{\tau_{m-1}}\).
Due to \cite[Problem 13, p. 151]{EK} and \cite[Lemma 15.20]{HWY}, the map \[\alpha \mapsto M^*_t (\alpha) \triangleq \sup_{s \in [0, t]} \|\alpha(s)\|\] is upper semicontinuous. Thus, the set
\[
\{\tau_{m-1} \leq t\} = \{M^*_t \geq m-1\}
\]
is closed in the Skorokhod topology. We deduce from the Portmanteau theorem that
\begin{equation}\label{port}\begin{split}
\limsup_{n \to \infty}\ P^{n, m} (\tau_{m-1} \leq t) \leq P (\tau_{m-1} \leq t).
\end{split}\end{equation}
Fix \(\epsilon > 0\).
Since \(P(\tau_{m-1} \leq t) \searrow 0\) as \(m \to \infty\), we find an \(m^o \in \mathbb{N}_{\geq 2}\) such that
\begin{align}\label{eq: P bound}
P(\tau_{m^o -1} \leq t) \leq \tfrac{\epsilon}{2}.
\end{align}
Because \((P^{n, m^o-1})_{n \in \mathbb{N}}\) is tight, we deduce from Fact \ref{fact} that there exists a compact set \(C(t, \epsilon) \subset \mathbb{B}\) such that
\begin{align}\label{eq: t imp}
\limsup_{n \to \infty} P^n (X_{t \wedge \tau_{m^o-1}} \not \in C(t, \epsilon)) \leq \tfrac{\epsilon}{2}.
\end{align}
Due to Galmarino's test, see \cite[Lemma III.2.43]{JS}, we have \(\tau_{m^o-1} = \tau_{m^o-1} \circ X_{\cdot \wedge \tau_{m^o}}\). Thus, we obtain
\begin{align*}
P^n (X_t \not \in C(t, \epsilon)) & = P^n(X_{t \wedge \tau_{m^o-1}} \not \in C(t, \epsilon), \tau_{m^o-1} > t) + P^n(X_t \not \in C(t, \epsilon), \tau_{m^o-1} \leq t)
\\&\leq P^n (X_{t \wedge \tau_{m^o-1}} \not \in C(t, \epsilon)) + P^{n, m^o}(\tau_{m^o-1} \leq t).
\end{align*}
From this, \eqref{port}, \eqref{eq: P bound} and \eqref{eq: t imp}, we deduce that
\[
\limsup_{n \to \infty} P^n(X_t \not \in C(t, \epsilon)) \leq \epsilon.
\]
This proves that the sequence \((P^n)_{n \in \mathbb{N}}\) satisfies (a) in Fact \ref{fact}.
Next, we show that \((P^n)_{n \in \mathbb{N}}\) satisfies (b) in Fact \ref{fact}. Let \(\epsilon, t\) and \(m^o\) be as before. Because \((P^{n, m^o-1})_{n \in \mathbb{N}}\) is tight there exists a \(\delta > 0\) such that
\begin{align}\label{eq: t imp2}
\limsup_{n \to \infty} P^n \left(w' (X_{\cdot \wedge \tau_{m^o-1}}, \delta, t) \geq \epsilon\right) \leq \tfrac{\epsilon}{2}.
\end{align}
On the set \(\{\tau_{m^o-1} > t\}\) we have \(w' (X, \delta, t) = w'(X_{\cdot \wedge \tau_{m^o-1}}, \delta, t)\).
Thus, using \eqref{port}, \eqref{eq: P bound} and \eqref{eq: t imp2}, we obtain
\begin{align*}
\limsup_{n \to \infty}&\ P^n (w'(X, \delta, t) \geq \epsilon) \\&\leq \limsup_{n \to \infty}P^n (w'(X_{\cdot \wedge \tau_{m^o-1}}, \delta, t) \geq \epsilon) + \limsup_{n \to \infty} P^{n, m^o} (\tau_{m^o-1} \leq t) \leq \epsilon.
\end{align*}
In other words, \((P^n)_{n \in \mathbb{N}}\) satisfies (b) in Fact \ref{fact} and the proof is complete.
\qed
\subsection{Proof of Theorem \ref{prop: existence}}\label{sec: pf sm}
For each \(n \in \mathbb{N}\) let \(\phi^n \colon \mathbb{R}^n \to [0, 1]\) be the standard mollifier on \(\mathbb{R}^n\), see, e.g., \cite[p. 147]{gilbarg2001elliptic}. Recall that \(\phi^n\) is supported on the Euclidean unit ball. Set \(\lambda_\textup{max} \triangleq \sup_{k \in \mathbb{N}} \lambda_k < \infty\).
We fix a sequence \((\epsilon_n)_{n \in \mathbb{N}} \subset (0, \infty)\) such that \(\epsilon_n \leq \tfrac{1}{n} \min_{k = 1, \dots, n} \lambda_k\) for all \(n \in \mathbb{N}\). Clearly, we have \(\epsilon_n \leq \frac{1}{n}\lambda_\textup{max} \to 0\) as \(n \to \infty\).
Define
\[
\theta_n x \triangleq \big(\langle x, h_1\rangle_\mathbb{B}, \dots, \langle x, h_n\rangle_\mathbb{B} \big), \quad x \in \mathbb{B},
\]
and set
\[
v^n (y, x) \triangleq \frac{1}{\epsilon_n^n}\int_{\mathbb{R}^n} \phi^n \Big(\frac{z - \theta_n x}{\epsilon_n}\Big)v\Big(y, \sum_{i = 1}^n \frac{z^i e_i}{\lambda_i}\Big) d} %{\operatorname{d}\hspace{-0.05cm} z, \quad y \in E, x \in \mathbb{B}.
\]
We define \(b^n\) and \(\sigma^n\) in the same manner.
Here, recall that \((h_k)_{k \in \mathbb{N}}\) is an orthonormal basis of \(\mathbb{B}\) and that \((e_k)_{k \in \mathbb{N}} = (\lambda_k h_k)_{k \in \mathbb{N}}\) is an orthonormal basis of \(\mathbb{K} = J(\mathbb{B})\).
Next, we check properties of \(v^n, b^n\) and \(\sigma^n\).
\begin{lemma}\label{lem: 1}
For all \(m \in \mathbb{N}\) and all \(x, z \in \mathbb{K}\) with \(\|x\|_\mathbb{K}, \|z\|_\mathbb{K} \leq m\) there exist constants \(L = L(n, m) \in (0, \infty)\) and \(l = l(n, m) \in (0, \infty)\) such that \[
\int_E \|v^n (y, x) - v^n(y, z)\|_\mathbb{K}^2 F(d} %{\operatorname{d}\hspace{-0.05cm} y) \leq L \|x - z\|_\mathbb{K}^2
\]
and
\[
\|b^n (x) - b^n(z)\|_\mathbb{K} + \|\sigma^n(x) - \sigma^n(z)\|_{\textup{HS} (\mathbb{K})} \leq l \|x - z\|_\mathbb{K}.
\]
\end{lemma}
\begin{proof}
We only prove the claim for \(v^n\). For \(b^n\) and \(\sigma^n\) it follows in the same manner.
Fix \(m \in \mathbb{N}\) and let \(y \in E\) and \(x, z \in \mathbb{K}\) with \(\|x\|_\mathbb{K}, \|z\|_\mathbb{K} \leq m\). Define \[G (n, m) = G \triangleq \{u \in \mathbb{R}^n \colon \|u\|_{\mathbb{R}^n} < \|\iota\|_o m + \epsilon_n\},\]
where \(\|\cdot\|_{\mathbb{R}^n}\) denotes the Euclidean norm on \(\mathbb{R}^n\) and \(\|\iota\|_o\) denotes the operator norm of \(\iota\).
Using the Parseval identity, we obtain
\[
\|\theta_n x \|_{\mathbb{R}^n}^2 = \sum_{i = 1}^n \langle x, h_i\rangle_\mathbb{B}^2 \leq \|x\|_\mathbb{B}^2 \leq \|\iota\|^2_o \|x\|_\mathbb{K}^2.
\]
For all \(u \not \in G\) we have
\[
\| u - \theta_n x\|_{\mathbb{R}^n} \geq \|u\|_{\mathbb{R}^n} - \|\theta_n x\|_{\mathbb{R}^n} \geq \|u\|_{\mathbb{R}^n} - \|\iota\|_o m \geq \epsilon_n.
\]
Because smooth functions with compact support are Lipschitz continuous, the function \(\phi^n\) is Lipschitz continuous and we denote the corresponding Lipschitz constant by \(L = L(n)\).
Furthermore, we have for all \(u \in G\)
\[
\Big\| \sum_{i = 1}^n \frac{u^i}{\lambda_i} e_i\Big\|_\mathbb{K} \leq \sum_{i = 1}^n \frac{\|\iota\|_o m + \epsilon_n}{\lambda_i} \triangleq C = C(n, m).
\]
Now, we deduce from the linear growth assumption, i.e. hypothesis (iii), that
\begin{align*}
\|v^n (y, x) - v^n(y, z)\|_\mathbb{K} &\leq \frac{1}{\epsilon_n^n} \int_{\mathbb{R}^n} \Big|\phi^n\Big(\frac{u - \theta_n x}{\epsilon_n}\Big) - \phi^n\Big(\frac{u - \theta_n z}{\epsilon_n}\Big)\Big| \Big\|v\Big(y, \sum_{i = 1}^n \frac{u^i}{\lambda_i} e_i\Big)\Big\|_\mathbb{K} d} %{\operatorname{d}\hspace{-0.05cm} u
\\&=\frac{1}{\epsilon_n^n} \int_{G} \Big|\phi^n\Big(\frac{u - \theta_n x}{\epsilon_n}\Big) - \phi^n\Big(\frac{u - \theta_n z}{\epsilon_n}\Big)\Big| \Big\| v\Big(y, \sum_{i = 1}^n \frac{u^i}{\lambda_i} e_i \Big) \Big\|_\mathbb{K} d} %{\operatorname{d}\hspace{-0.05cm} u
\\&\leq \frac{\gamma(y) (1 + C ) L \|\iota\|_o |G| }{\epsilon^{n+1}_n} \|x - z\|_\mathbb{K},
\end{align*}
where \(|G|\) denotes the Lebesgue measure of \(G\).
Thus, we have
\[
\int_E \|v^n (y, x) - v^n(y, z)\|_\mathbb{K}^2 F(d} %{\operatorname{d}\hspace{-0.05cm} y) \leq \int_E \gamma^2(y)F(d} %{\operatorname{d}\hspace{-0.05cm} y)\Big(\frac{(1 + C ) L \|\iota\|_o |G| }{\epsilon^{n+1}_n}\Big)^2 \|x - z\|_\mathbb{K}^2.
\]
This completes the proof.
\end{proof}
\begin{lemma}\label{lem: 2}
There exists a constant \(l \in (0, \infty)\) such that for all \(y \in E\) and \(x \in \mathbb{K}\)
\begin{align*}
\|v^n(y, x)\|_\mathbb{K}^2 &\leq l \gamma^2(y) \big(1 + \|x\|_\mathbb{K}^2 \big), \\
\|b^n(x)\|_\mathbb{K}^2 + \|\sigma^n(x)\|^2_{\textup{HS} (\mathbb{K})} &\leq l \big(1 + \|x\|_\mathbb{K}^2\big).
\end{align*}
\end{lemma}
\begin{proof}
For all \(u \in \mathbb{R}^n\) with \(\|u\|_{\mathbb{R}^n} \leq 1\) the triangle and the Cauchy-Schwarz inequality yield that
\[
\Big\| \sum_{i = 1}^n \frac{\epsilon_n u^i}{\lambda_i} e_i\Big\|_\mathbb{K} \leq \sum_{i = 1}^n \frac{\epsilon_n}{\lambda_i} |u^i| \leq \frac{\|u\|_{\mathbb{R}^n}}{\sqrt{n}} \leq 1.
\]
Thus, we deduce from the linear growth assumption, i.e. hypothesis (iii), that for all \(y \in E\) and \(x \in \mathbb{K}\)
\begin{align*}
\|v^n(y, x)\|_\mathbb{K} &= \Big\| \int_{\mathbb{R}^n} \phi^n(u) v \Big(y, \sum_{i = 1}^n \Big( \frac{\epsilon_n u^i}{\lambda_i} + \frac{\langle x, h_i\rangle_\mathbb{B}}{\lambda_i} \Big) e_i \Big) \Big\|_\mathbb{K}
\\&\leq \int_{\mathbb{R}^n} \phi^n(u) \Big\|v\Big(y, \sum_{i = 1}^n \Big(\frac{\epsilon_nu^i}{\lambda_i} + \frac{\langle x, h_i\rangle_\mathbb{B}}{\lambda_i} \Big) e_i\Big)\Big\|_\mathbb{K} d} %{\operatorname{d}\hspace{-0.05cm} u \\&\leq \gamma(y) \Big(2 + \Big\| \sum_{i = 1}^n \frac{\langle x, h_i\rangle_\mathbb{B}}{\lambda_i} e_i\Big\|_\mathbb{K} \Big) \int_{\mathbb{R}^n} \phi^n(u)d} %{\operatorname{d}\hspace{-0.05cm} u
\\&= \gamma(y)\Big(2 + \Big\| \sum_{i = 1}^n \frac{\langle x, h_i\rangle_\mathbb{B}}{\lambda_i} e_i\Big\|_\mathbb{K} \Big).
\end{align*}
Note that for \(x \in \mathbb{K}\)
\begin{align*}
\langle x, h_i\rangle_\mathbb{B} = \lambda_i \langle J^{-1} x, h_i\rangle_\mathbb{B} = \lambda_i \langle J^{-1} x, J^{-1} e_i\rangle_\mathbb{B} = \lambda_i \langle x, e_i\rangle_\mathbb{K}
\end{align*}
and that
\begin{align*}
\Big(2 + \Big\| \sum_{i = 1}^n \langle x, e_i\rangle_\mathbb{K} e_i\Big\|_\mathbb{K} \Big)^2 &\leq 8 + 2 \Big\| \sum_{i = 1}^n \langle x, e_i\rangle_\mathbb{K} e_i\Big\|^2_\mathbb{K}
\\&= 8 + 2 \sum_{i = 1}^n \langle x, e_i\rangle_\mathbb{K}^2
\\&\leq 8 \big(1 + \|x\|_\mathbb{K}^2\big),
\end{align*}
where we use the Parseval identity and the elementary inequality \((a_1 + a_2)^2 \leq 2 a^2_1 + 2 a^2_2\) for all \(a_1, a_2 \in \mathbb{R}\).
Thus, we obtain
\[
\|v^n(y, x)\|_\mathbb{K}^2 \leq 8 \gamma^2(y) \big(1 + \|x\|_\mathbb{K}^2\big).
\]
A similar argument applies for \(b^n\) and \(\sigma^n\).
\end{proof}
\begin{lemma}\label{lem: 3}
For all \(y \in E\) we have \[
\|v^n(y, \cdot) - v(y, \cdot)\|_\mathbb{B} + \| b^n - b\|_\mathbb{B} + \| \sigma^n - \sigma\|_{L(\mathbb{B})} \to 0\]
as \(n \to \infty\) uniformly on compact subsets of \(\mathbb{B}\). Moreover, for any compact set \(K \subset \mathbb{B}\) it holds that
\[
\int_E \sup_{n \in \mathbb{N}} \sup_{x \in K} \| v^n(y, x)\|_\mathbb{B}^2 F(d} %{\operatorname{d}\hspace{-0.05cm} y) < \infty.
\]
\end{lemma}
\begin{remark}
We stress that \(y \mapsto \sup_{n \in \mathbb{N}} \sup_{x \in K} \|v^n(y, x)\|_\mathbb{B}\) is \(\mathcal{E}\)-measurable. To see this, recall that compact metric spaces are separable, i.e. there exists a countable dense (w.r.t. \(\|\cdot\|_\mathbb{B}\)) set \(K' \subset K\). Because \(x \mapsto v(y, x)\) is continuous for all \(y \in E\), we conclude that the map \[
y \mapsto \sup_{n \in \mathbb{N}} \sup_{x \in K} \|v^n(y, x)\|_\mathbb{B} = \sup_{n \in \mathbb{N}} \sup_{x \in K'} \|v^n(y, x)\|_\mathbb{B}
\]
is \(\mathcal{E}\)-measurable as the countable supremum over \(\mathcal{E}\)-measurable functions.
\end{remark}
\begin{proof}
Again, we only show the claim for \(v^n\).
Fix \(y \in E\) and \(\varepsilon > 0\) and let \(K \subset \mathbb{B}\) be compact.
We set
\[
G_n \triangleq \Big\{ \sum_{i = 1}^n \big(\epsilon_n u^i h_i + \langle x, h_i\rangle_\mathbb{B} h_i\big) \colon x \in K, u \in \mathbb{R}^n \text{ with } \|u\|_{\mathbb{R}^n} \leq 1\Big\}.
\]
and \(G \triangleq K \cup \big(\bigcup_{n \in \mathbb{N}} G_n\big)\).
For all \(n \in \mathbb{N}\) the set \(G_n\) is compact in \(\mathbb{B}\) as it is the image of the compact set \(\{u \in \mathbb{R}^n \colon \|u\|_{\mathbb{R}^n} \leq 1\} \times K\) under the continuous map
\[
(u, x) \mapsto \sum_{i = 1}^n \big(\epsilon_n u^i h_i + \langle x, h_i\rangle_\mathbb{B} h_i\big).
\]
We claim that also the set \(G\) is compact in \(\mathbb{B}\). To see this take a sequence \((y_n)_{n \in \mathbb{N}}\subset G\). We have to show that \((y_n)_{n \in \mathbb{N}}\) has a subsequence converging to an element in \(G\). There exists a sequence \((k_n)_{n \in \mathbb{N}} \subset \mathbb{N}\) and two sequences \((x_n)_{n \in \mathbb{N}} \subset \mathbb{B}\) and \((u_n)_{n \in \mathbb{N}}\) with \(u_n \in \mathbb{R}^{k_n}\) and \(\|u_n\|_{\mathbb{R}^{k_n}} \leq 1\) such that
\[
y_n = \sum_{i = 1}^{k_n} \big(\epsilon_{k_n} u^i_n h_i + \langle x_n, h_i\rangle_\mathbb{B} h_i\big),\quad n \in \mathbb{N}.
\]
Suppose that \(k \triangleq \sup_{n \in \mathbb{N}} k_n < \infty\). Then, we have
\(
(y_n)_{n \in \mathbb{N}}\subset\bigcup_{i = 1}^k G_i.
\)
Because \(\bigcup_{i = 1}^k G_i\) is compact as the finite union of compact sets, the sequence \((y_n)_{n \in \mathbb{N}}\) has a subsequence converging to an element in \(\bigcup_{i = 1}^k G_i\subset G\).
Suppose now that \(k = \infty\). Passing to a subsequence if necessary, we can assume that \(k_n \to \infty\) as \(n \to \infty\) and, because \(K\) is compact, we can further assume that there exists an \(x \in K\) such that \(x_n \to x\) as \(n \to \infty\).
Now, we have
\begin{align*}
\Big\| \sum_{i = 1}^{k_n} \big(\epsilon_{k_n} u^i_n h_i &+ \langle x_n, h_i\rangle_\mathbb{B} h_i \big) - x \Big\|_\mathbb{B} \\&\leq \sum_{i = 1}^{k_n} |u^i_n| \epsilon_{k_n} + \Big\| \sum_{i = 1}^{k_n} \langle x_n - x, h_i \rangle_\mathbb{B} h_i - \sum_{i = k_n + 1}^\infty \langle x, h_i\rangle_\mathbb{B} h_i \Big\|_{\mathbb{B}} \\&\leq \frac{\lambda_\textup{max}}{\sqrt{k_n}} + \|x_n - x\|_\mathbb{B} + \sqrt{\sum_{i = k_n + 1}^\infty \langle x, h_i\rangle_\mathbb{B}^2}
\to 0\end{align*}
as \(n \to \infty\). Thus, in the case \(k = \infty\) the sequence \((y_n)_{n \in \mathbb{N}}\) has a subsequence converging to a point in \(K \subset G\). We conclude the compactness of \(G\).
Because \(G\) is compact, hypothesis (ii) implies that the map \(G \ni x \mapsto v (y, x)\) is uniformly continuous. In other words, there exists a \(\delta > 0\) such that for all \(x, z \in G\) with \(\|x - z\|_\mathbb{B} < \delta\) we have
\[
\|v(y, x) - v(y, z)\|_\mathbb{B} \leq \varepsilon.
\]
Let \(\epsilon \leq \delta (2 \sqrt{2})^{-1}\).
Because compact sets are totally bounded, there exists an \(N_1 \in \mathbb{N}\) and points \(x_1, \dots, x_{N_1} \in \mathbb{B}\) such that
\[
K \subset \bigcup_{i = 1}^{N_1} B_{x_i} (\epsilon),
\]
where \(B_{x_i}(\epsilon) \triangleq \{x \in \mathbb{B} \colon \|x - x_i\|_\mathbb{B} \leq \epsilon\}\).
Take \(u \in \mathbb{R}^n\) with \(\|u\|_{\mathbb{R}^n} \leq 1\) and \(x \in K\). We find a \(k \in \{1, \dots, N_1\}\) such that \(\|x - x_k\|_\mathbb{B} \leq \epsilon\). Thus, we have
\begin{align*}
\Big\| \sum_{i = 1}^n \big(\epsilon_n u^i h_i + \langle x, h_i\rangle_\mathbb{B} h_i \big) - x \Big\|_\mathbb{B}
&\leq \frac{\lambda_\textup{max}}{\sqrt{n}} + \sqrt{\sum_{i = n + 1}^\infty \langle x, h_i\rangle_\mathbb{B}^2}
\\&\leq \frac{\lambda_\textup{max}}{\sqrt{n}} + \sqrt{2\epsilon^2 + 2\max_{j = 1, \dots, N_1} \sum_{i = n + 1}^\infty \langle x_j, h_i\rangle_\mathbb{B}^2}
\\&\leq \frac{\lambda_\textup{max}}{\sqrt{n}} + \frac{\delta}{2} + \sqrt{2\max_{j = 1, \dots, N_1} \sum_{i = n + 1}^\infty \langle x_j, h_i\rangle_\mathbb{B}^2}.
\end{align*}
Therefore, we find an \(N_2 \in \mathbb{N}\) and for all \(n \geq N_2\) we have
\[
\sup_{\|u\|_{\mathbb{R}^n} \leq 1} \sup_{x \in K} \Big\| \sum_{i = 1}^n \big(\epsilon_n u^i h_i + \langle x, h_i\rangle_\mathbb{B} h_i \big) - x \Big\|_\mathbb{B} < \delta.
\]
We conclude that for all \(n \geq N_2\)
\begin{align*}
\sup_{x \in K} \|v^n (y, x) &- v(y, x)\|_\mathbb{B}\\&\leq \sup_{x \in K} \int_{\mathbb{R}^n} \phi^n(u) \Big\| v\Big(y, \sum_{i = 1}^n \big(\epsilon_n u^i h_i + \langle x, h_i\rangle_\mathbb{B} h_i\big)\Big) - v\Big(y, x\Big)\Big\|_{\mathbb{B}} d} %{\operatorname{d}\hspace{-0.05cm} u \leq \varepsilon.
\end{align*}
This proves the first claim.
To see that the second claim holds it suffices to note that
\[
\sup_{n \in \mathbb{N}} \sup_{x \in K} \|v^n (y, x)\|_\mathbb{B} \leq \sup_{x \in G} \|v(y, x)\|_\mathbb{B}
\]
and to use hypothesis (iii). The proof is complete.
\end{proof}
\begin{lemma}\label{eq: loc bdd}
For any bounded set \(G \subset \mathbb{B}\) it holds that
\[
\sup_{n \in \mathbb{N}} \sup_{x \in G} \Big( \|b^n(x)\|_\mathbb{B} + \|\sigma^n(x)\|_{L(\mathbb{B})} + \int_E \|v^n(x, y)\|_\mathbb{B}^2 F(d} %{\operatorname{d}\hspace{-0.05cm} y) \Big) < \infty.
\]
\end{lemma}
\begin{proof}
There exists an \(m \in \mathbb{N}\) such that for all \(x \in G\) we have \(\|x\|_\mathbb{B} \leq m\). Thus, for all \(x \in G\) and \(u \in \mathbb{R}^n\) with \(\|u\|_{\mathbb{R}^n} \leq 1\) we have
\begin{align*}
\Big\| \sum_{i = 1}^n \big(\epsilon_n u^i + \langle x, h_i\rangle_\mathbb{B} \big)h_i \Big\|^2_\mathbb{B} &\leq 2 \Big\|\sum_{i = 1}^n \epsilon_n u^i h_i\Big\|^2_{\mathbb{B}} + 2 \sum_{i = 1}^n \langle x, h_i\rangle_\mathbb{B}^2
\leq 2\lambda_\textup{max}^2 + 2 m^2.
\end{align*}
Set \(G' \triangleq \{x \in \mathbb{B} \colon \|x\|_\mathbb{B}^2 \leq 2 \lambda_\textup{max}^2 + 2 m^2\}\).
Thus, using hypothesis (iii), we obtain that
\begin{align*}
\sup_{n \in \mathbb{N}} \sup_{x \in G} \int_E \|v^n(y, x)\|_\mathbb{B}^2 F(d} %{\operatorname{d}\hspace{-0.05cm} y)
\leq \int_E \zeta^2_{G'}(y)F(d} %{\operatorname{d}\hspace{-0.05cm} y) < \infty.
\end{align*}
The remaining claims follow in the same manner.
\end{proof}
Denote by \(\Omega^o\) the Skorokhod space of c\`adl\`ag functions \(\mathbb{R}_+ \to \mathbb{K}\), equip it with the Skorokhod topology and denote the corresponding Borel \(\sigma\)-field by \(\mathcal{F}^o\).
\begin{lemma}\label{lem: sde}
For all \(n \in \mathbb{N}\) the MP \((0, \bar{b}^{n}, \bar{a}^n, \bar{K}^n, \eta)\) has a solution \(\bar{P}^{n}\), seen as a probability measure on \((\Omega^o, \mathcal{F}^o)\), where for all \(x \in \mathbb{K}\)
\begin{align*}
\bar{b}^{n} (x) &\triangleq b^n (x) + \int_E \big(h(v^n(y, x)) - v^n(y, x)\big)F(d} %{\operatorname{d}\hspace{-0.05cm} y),\\ \bar{a}^n (x)&\triangleq \sigma^n (x) \sigma^n (x)^*, \\ \bar{K}^n(x, G) &\triangleq \int_E \mathbf{1}_{G\backslash \{0\}} (v^n(y, x)) F(d} %{\operatorname{d}\hspace{-0.05cm} y),\quad G \in \mathcal{B}(\mathbb{K}).\end{align*}
Here, \(\sigma^n(x)^* \in L (\mathbb{K}, \mathbb{H})\) denotes the adjoint of \(\sigma (x)\in L(\mathbb{H},\mathbb{K})\).
\end{lemma}
\begin{proof}
We show that the SDE \begin{align}\label{eq: SDE loc L}
d} %{\operatorname{d}\hspace{-0.05cm} Y_t = b^n (Y_{t-}) d} %{\operatorname{d}\hspace{-0.05cm} t + \sigma^n(Y_{t-})d} %{\operatorname{d}\hspace{-0.05cm} W_t + \int_E v^n (y, Y_{t-}) (p - q)(d} %{\operatorname{d}\hspace{-0.05cm} y, d} %{\operatorname{d}\hspace{-0.05cm} t),\quad Y_0 = \zeta \sim \eta,
\end{align} has a solution with paths in \(\Omega^o\). Fix a filtered probability space which supports a cylindrical standard Brownian motion \(W\) and a compensated random measure \(p - q\).
As in the proof of \cite[Lemma 34.11]{metivier}, we define for \(m \in \mathbb{N}, y \in E\) and \(x \in \mathbb{K}\)
\begin{align*}
b^{n, m}(x) &\triangleq b^n \big(\big(1 \wedge \tfrac{m}{\|x\|_\mathbb{K}}\big) x\big),\\
\sigma^{n, m}(x) &\triangleq \sigma^n\big(\big(1 \wedge \tfrac{m}{\|x\|_\mathbb{K}}\big) x\big),\\
v^{n, m} (y, x) &\triangleq v^n \big(y, \big(1 \wedge \tfrac{m}{\|x\|_\mathbb{K}}\big) x\big).
\end{align*}
Due to Lemma \ref{lem: 1}, the coefficients \(b^{n, m}, \sigma^{n, m}\) and \(v^{n, m}\) satisfy a global Lipschitz condition, whose Lipschitz constant might depend on \(m\). Thus, we deduce from \cite[Theorem 3.11]{doi:10.1080/17442501003624407}\footnote{\cite[Theorem 3.11]{doi:10.1080/17442501003624407} only applies for square-integrable initial values and trace class Brownian motion. Latter is no restriction due to \cite[Proposition 4.7]{DePrato}. Because, due to Proposition \ref{prop: A3} in Appendix \ref{app: 1} and a Gronwall-type argument, weak existence and pathwise uniqueness holds for all initial laws, a Yamada-Watanabe argument shows that also strong existence holds for arbitrary initial laws.} that for each \(m \in \mathbb{N}\) there exists a c\`adl\`ag adapted \(\mathbb{K}\)-valued process \(Y^m\) with dynamics
\[
d} %{\operatorname{d}\hspace{-0.05cm} Y^m_t = b^{n, m} (Y^m_{t-}) d} %{\operatorname{d}\hspace{-0.05cm} t + \sigma^{n, m} (Y^m_{t-})d} %{\operatorname{d}\hspace{-0.05cm} W_t + \int_E v^{n, m}(y, Y^m_{t-})(p - q)(d} %{\operatorname{d}\hspace{-0.05cm} y, d} %{\operatorname{d}\hspace{-0.05cm} t), \quad Y^m_0 = \zeta.
\]
Define
\[
\tau_m \triangleq \inf (t \geq 0 \colon \|X_{t - }\|_\mathbb{K} \geq m \text{ or } \|X_t\|_\mathbb{K} \geq m).
\]
We note that \(b^n(x) = b^{n, m} (x)= b^{n, m + 1} (x), \sigma^n(x) = \sigma^{n, m} (x)= \sigma^{n, m + 1}(x)\) and \(v^n(y, x) = v^{n, m}(y, x) = v^{n,m + 1}(y, x)\) for all \(x \in \mathbb{K} \colon \|x\|_\mathbb{K} \leq m\) and \(y \in E\). Thus, arguing as in the proof of \cite[Lemma 34.8]{metivier}, the Lipschitz conditions imply that a.s. \(Y^m_t = Y^{m + 1}_t\) for \(t \leq \tau_m \circ Y^m \wedge \tau_m \circ Y^{m + 1}\). Due to Galmarino's test (see \cite[Lemma III.2.43]{JS}), this yields that a.s.
\(
\tau_m \circ Y^m = \tau_m \circ Y^{m + 1}.
\)
Lemma \ref{lem: 2} implies that \(b^{n, m}, \sigma^{n, m}\) and \(v^{n, m}\) satisfy a linear growth condition with a linear growth constant independent of \(m\).
Hence, an argument based on Doob's inequality and Gronwall's lemma (see the proof of Lemma \ref{lem: bounded exp} below) yields that a.s. \(\tau_m \circ Y^m \to \infty\) as \(m \to \infty\).
Finally, we conclude that the process
\[
Y_t \triangleq Y^1_t \mathbf{1} \{t < \tau_1 \circ Y^1\} + \sum_{k = 2}^\infty Y^k_t \mathbf{1} \{\tau_{k - 1} \circ Y^{k-1} \leq t < \tau_k \circ Y^k\}, \quad t \geq 0,
\]
solves the SDE \eqref{eq: SDE loc L}.
Now, \cite[Theorem 3.13]{criens18} yields the claim.
We stress that \(\bar{b}^n\) is well-defined due to Lemma \ref{lem: 2}.
To see this, recall that there exists an \(\epsilon > 0\) such that \(h(x) = x\) for all \(x \in \mathbb{B} \colon \|x\|_\mathbb{B} \leq \epsilon\).
Note that for \(x \in \mathbb{K}\) with \(\|x\|_\mathbb{B} \geq \epsilon\) we have \(\|x\|_\mathbb{K} \geq \|\iota\|_o^{-1} \|x\|_\mathbb{B} \geq \|\iota\|^{-1}_o \epsilon \triangleq \delta\).
Thus, for all \(x \in \mathbb{K}, y \in E\) we have
\begin{align*}
\|h(v(x, y)) - v(x, y)\|_\mathbb{K} &= \| h(v(x, y)) - v(x, y)\|_\mathbb{K} \mathbf{1}_{\{\|v(x, y)\|_\mathbb{K} \geq \delta\}}
\\&\leq \big(\tfrac{\|h\|_\infty}{\delta} + 1 \big) \|v(x, y)\|_\mathbb{K} \mathbf{1}_{\{\|v(x, y)\|_\mathbb{K} \geq \delta\}}
\\&\leq \tfrac{1}{\delta} \big(\tfrac{\|h\|_\infty}{\delta} + 1 \big) \|v(x, y)\|_\mathbb{K}^2.
\end{align*}
Let \(l > 0\) be as in Lemma \ref{lem: 2} and set \(l' \triangleq \frac{l}{\delta} (\tfrac{\|h\|_\infty}{\delta} + 1 )\). We obtain for all bounded \(G \subset \mathbb{K}\) that
\[
\sup_{x \in G} \|\bar{b}^n(x)\|_\mathbb{K} \leq \sqrt{l} \sup_{x \in G} \big(1 + \|x\|_\mathbb{K}\big) + l' \sup_{x \in G} \big(1 + \|x\|_\mathbb{K}^2\big) \int_E\gamma^2(y)F(d} %{\operatorname{d}\hspace{-0.05cm} y) < \infty,
\]
which shows that \(\bar{b}^n\) is well-defined.
\end{proof}
Define by \(P^n (d} %{\operatorname{d}\hspace{-0.05cm} \omega) \triangleq \bar{P}^n \big( (\iota X_t)_{t \geq 0} \in d} %{\operatorname{d}\hspace{-0.05cm} \omega\big)\) a probability measure on \((\Omega, \mathcal{F})\), where \(X\) denotes the coordinate process on \(\Omega^o\).
\begin{lemma}
For each \(n \in \mathbb{N}\) the probability measure \(P^n\) solves the MP \((0, \tilde{b}^{n}, \tilde{a}^n, \tilde{K}^n, \eta \circ \iota^{-1})\), where for all \(x \in \mathbb{B}\)
\begin{align*}
\tilde{b}^{n} (x) &\triangleq b^n(x) + \int \big( h(v^n(y, x)) - v^n(y, x)\big)F(d} %{\operatorname{d}\hspace{-0.05cm} y),\\ \tilde{a}^n (x)&\triangleq \sigma^n (x) \sigma^n (x)^*, \\ \tilde{K}^n(x, G) &\triangleq \int \mathbf{1}_{G\backslash \{0\}} (v^n(y, x)) F(d} %{\operatorname{d}\hspace{-0.05cm} y),\quad G \in \mathcal{B}(\mathbb{B}).\end{align*}
Here, \(\sigma^n(x)^* \in L(\mathbb{B}, \mathbb{H})\) denotes the adjoint of \(\sigma^n(x)\in L (\mathbb{H}, \mathbb{B})\).
\end{lemma}
\begin{proof}
For \(x \in \mathbb{K}\) denotes by \(\sigma^n (x)^\star \in L(\mathbb{K}, \mathbb{H})\) the adjoint of \(\sigma^n(x) \in L(\mathbb{H}, \mathbb{K})\) and by \(\sigma^n(x)^* \in L(\mathbb{B}, \mathbb{H})\) the adjoint of \(\sigma^n(x) \in L(\mathbb{H}, \mathbb{B})\).
Recalling hypothesis (i), for all \(x \in \mathbb{K}\) and \(y, z \in \mathbb{B}\) we obtain that
\begin{align*}
\langle \sigma^n(\iota x) \sigma^n(\iota x)^* z, y\rangle_\mathbb{B}
& = \langle \sigma^n(x) \sigma^n(x)^* z, \iota^* y\rangle_\mathbb{K}
\\&= \langle \sigma^n(x)^* z, \sigma^n(x)^\star i^* z \rangle_\mathbb{H} \\&= \langle z, \sigma^n(x) \sigma^n(x)^\star i^* y\rangle_\mathbb{B}
\\&= \langle \iota^* z, \sigma^n(x) \sigma^n(x)^\star i^* y\rangle_\mathbb{K}
\\&= \langle \sigma^n(x) \sigma^n(x)^\star i^* z, \iota^* y\rangle_\mathbb{K}.
\end{align*}
Denote by \(X\) the coordinate process on \(\Omega^o\), take \(f = g(\langle \cdot, y_1\rangle_\mathbb{B}, \dots, \langle \cdot, y_n\rangle_\mathbb{B}) \in \mathcal{C}\)
and define \(f^* \triangleq g(\langle \cdot, \iota^* y_1\rangle_\mathbb{K}, \dots, \langle \cdot, \iota^* y_n\rangle_\mathbb{K})\). We note that
\begin{align*}
\sum_{i = 1}^n &\langle b(\iota X), y_i\rangle_\mathbb{B} \partial_i f (\iota X) + \frac{1}{2} \sum_{i = 1}^n\sum_{j = 1}^n \langle \sigma^n (\iota X) \sigma^n(\iota X)^* y_i, y_j\rangle_\mathbb{B} \partial_{ij}^2 f (\iota X) \\&\quad\qquad\qquad\qquad + \int_E \Big(f (\iota X + v(\iota X, z)) - f (\iota X) - \sum_{i = 1}^n \langle v(\iota X, z), y_i \rangle_\mathbb{B} \partial_i f(\iota X)\Big) F(d} %{\operatorname{d}\hspace{-0.05cm} z)
\\&= \sum_{i = 1}^n \langle b(X), \iota^* y_i\rangle_\mathbb{K} \partial_i f^* (X) + \frac{1}{2} \sum_{i = 1}^n\sum_{j = 1}^n \langle \sigma^n (X) \sigma^n(X)^\star \iota^* y_i, \iota^* y_j\rangle_\mathbb{K} \partial_{ij}^2 f^* (X) \\&\quad\qquad\qquad\qquad+ \int_E \Big(f^* (X + v(X, z)) - f^* (X) - \sum_{i = 1}^n \langle v(X, z), \iota^* y_i \rangle_\mathbb{K} \partial_i f^*(X)\Big) F(d} %{\operatorname{d}\hspace{-0.05cm} z).
\end{align*}
Now, the claim follows from the definition of the martingale problem and Lemma \ref{lem: sde}. We stress that a similar argument as used for \(\bar{b}^n\) in the proof of Lemma \ref{lem: sde} shows that \(\tilde{b}^n\) is well-defined, see Lemma \ref{eq: loc bdd}.
\end{proof}
\begin{lemma}\label{lem: 4}
The sequence \((P^n)_{n \in \mathbb{N}}\) is tight.
\end{lemma}
\begin{proof}
We start with a moment bound. Fix \(\epsilon > 0\). Because any Borel probability measure on a Polish space is tight, we find a compact set \(K \subset \mathbb{K}\) such that \(\eta (K) \geq 1- \frac{\epsilon}{2}\).
Define \(Z \triangleq \mathbf{1} \{X_0 \in K\}\), which is a random variable on \((\Omega^o, \mathcal{F}^o)\).
\begin{lemma}\label{lem: bounded exp}
For all \(T \in \mathbb{R}_+\) we have
\(\sup_{n \in \mathbb{N}} \bar{E}^n \big[\sup_{t \in [0, T]}\|X_{t}\|^2_\mathbb{K} Z \big] < \infty\).
\end{lemma}
\begin{proof}
For \(m \in \mathbb{N}\) let \(\tau_m\) be defined as in \eqref{eq: tau}. Fix \(t \in [0, T]\).
Using Doob's and H\"older's inequality, \cite[Lemma 4.7]{criens18} and \cite[Proposition II.1.28, Theorems II.1.33, II.2.34]{JS} we obtain that
\begin{align*}
\bar{E}^n \Big[ \sup_{s \in [0, t]} \langle X_{s \wedge \tau_m}, e_k\rangle_\mathbb{K}^2 Z \Big]
\leq 16\ \Big( \bar{E}^n \Big[ Z &\int_0^{t \wedge \tau_m} \langle \bar{a}^n(X_s) e_k, e_k\rangle_\mathbb{K} d} %{\operatorname{d}\hspace{-0.05cm} s + TZ \int_0^{t \wedge \tau_m} \langle b^n(X_s), e_k\rangle_\mathbb{K}^2 d} %{\operatorname{d}\hspace{-0.05cm} s \Big] \\&+ \bar{E}^n\Big[ Z\int_0^{t \wedge \tau_m} \int_{\mathbb{K}} \langle x, e_k\rangle_\mathbb{K}^2 \bar{K}^n(X_s, d} %{\operatorname{d}\hspace{-0.05cm} x) d} %{\operatorname{d}\hspace{-0.05cm} s + Z\langle X_0, e_k\rangle_\mathbb{K}^2\Big]\Big).
\end{align*}
Using the Parseval identity, we obtain
\begin{align*}
\bar{E}^n \Big[ \sup_{s \in [0, t]}\| X_{s \wedge \tau_m}\|_\mathbb{K}^2 Z \Big] &\leq \sum_{k = 1}^\infty \bar{E}^n \Big[ \sup_{s \in [0, t]} \langle X_{s \wedge \tau_m}, e_k\rangle_\mathbb{K}^2 Z \Big] \\&
\leq 16\ \Big( \bar{E}^n \Big[ Z \int_0^{t \wedge \tau_m} \textup{trace}_\mathbb{K} \bar{a}^n(X_s) d} %{\operatorname{d}\hspace{-0.05cm} s + TZ \int_0^{t \wedge \tau_m} \| b^n(X_s)\|_\mathbb{K}^2 d} %{\operatorname{d}\hspace{-0.05cm} s \Big] \\&\hspace{2.5cm}+ \bar{E}^n\Big[ Z\int_0^{t \wedge \tau_m} \int_{\mathbb{K}} \| x\|_\mathbb{K}^2 \bar{K}^n(X_s, d} %{\operatorname{d}\hspace{-0.05cm} x) d} %{\operatorname{d}\hspace{-0.05cm} s + Z\|X_0\|_\mathbb{K}^2\Big]\Big).
\end{align*}
Due to Lemma \ref{lem: 2}, we find two constants \(c_1, c_2 > 0\) independent of \(n, m\) and \(t\), such that
\[
\bar{E}^n \Big[ \sup_{s \in [0, t]} \|X_{s \wedge \tau_{m}}\|_\mathbb{K}^2 Z \Big] \leq c_1 + c_2 \int_0^t \bar{E}^n \Big[ \sup_{s \in [0, r]} \|X_{s \wedge \tau_{m}}\|_\mathbb{K}^2 Z\Big] d} %{\operatorname{d}\hspace{-0.05cm} r.
\]
Gronwall's lemma yields that
\[
\bar{E}^n \Big[ \sup_{t \in [0, T]}\|X_{t \wedge \tau_{m}}\|_\mathbb{K}^2 Z \Big] \leq c_1 e^{c_2 T}.
\]
Finally, Fatou's lemma yields that
\[
\bar{E}^n \Big[ \sup_{s \in [0, T]} \|X_{t}\|_\mathbb{K}^2 Z \Big] \leq \liminf_{m \to \infty} \bar{E}^n \Big[ \sup_{t \in [0, T]} \|X_{t \wedge \tau_{m}}\|_\mathbb{K}^2 Z \Big] \leq c_1 e^{c_2 T}.
\]
This completes the proof.
\end{proof}
Fix \(t \in \mathbb{R}_+\).
Using Chebyshev's inequality, we obtain that
\[
\bar{P}^n \big(\|X_t\|_\mathbb{K} Z \leq R \big) \geq 1 - \frac{\sup_{n \in \mathbb{N}} \bar{E}^n \big[\|X_t\|_\mathbb{K}^2 Z\big]}{R^2}.
\]
Due to Lemma \ref{lem: bounded exp}, we find \(R^* > 0\) such that
\[
\inf_{n \in \mathbb{N}} \bar{P}^n \big(\|X_t\|_\mathbb{K} Z \leq R^* \big) \geq 1 - \tfrac{\epsilon}{2}.
\]
Set
\[
K_1 \triangleq \textup{cl}_\mathbb{B} \big\{\iota x \colon x \in \mathbb{K} \text{ and } \|x\|_\mathbb{K} \leq R^* \big\} \subset \mathbb{B}.
\]
Due to Lemma \ref{lem: emb comp}, the embedding \(\iota\) is compact and, consequently, the set \(K_1\) is compact in \(\mathbb{B}\). We obtain
\begin{align*}
P^n \big(X_t \in K_1\big) &\geq \bar{P}^n \big(\iota X_t \in K_1, X_0 \in K \big)
\\&\geq \bar{P}^n \big(\| X_t \|_\mathbb{K} Z \leq R^*\big) - 1 + \iota(K)
\\&\geq \bar{P}^n \big(\|X_t\|_\mathbb{K} Z \leq R^* \big) - \tfrac{\epsilon}{2}
\\&\geq 1 - \epsilon.
\end{align*}
This shows that \((P^n \circ X_t^{-1})_{n \in \mathbb{N}}\) is tight for all \(t \in \mathbb{R}_+\). In other words, (i) in Proposition \ref{prop: gen tight} holds.
Let \(M > 0\) and \((\rho_n)_{n \in \mathbb{N}}\) be a sequence of stopping times on \(\Omega\) such that \(\sup_{n \in \mathbb{N}} \rho_n \leq M\). Moreover, let \((h_n)_{n \in \mathbb{N}} \subset \mathbb{R}_+\) be a sequence such that \(h_n \to 0\) as \(n \to \infty\).
We can consider \((\rho_n)_{n \in \mathbb{N}}\) as a sequence of stopping times on \(\Omega^o\) by identifying \(\rho_n\) with \(\rho_n \circ \iota\).
Let \(\epsilon > 0, K \subset \mathbb{K}\) and \(Z\) be as above.
We can argue as in the proof of Lemma \ref{lem: bounded exp} and obtain that
\begin{align*}
\bar{E}^n \big[ &\|X_{\tau_m \wedge (\rho_n + h_n)} - X_{\tau_m \wedge \rho_n}\|_\mathbb{K}^2 Z \big] \\&\leq 12\ \Big( \bar{E}^n \Big[ Z\int_{\tau_m \wedge \rho_n}^{\tau_m \wedge (\rho_n + h_n)} \textup{ trace}_\mathbb{K} \bar{a}^n(X_s) d} %{\operatorname{d}\hspace{-0.05cm} s + Z\int_{\tau_m \wedge \rho_n}^{\tau_m \wedge (\rho_n + h_n)} \int_{\mathbb{K}} \| x \|_\mathbb{K}^2 \bar{K}^n(X_s, d} %{\operatorname{d}\hspace{-0.05cm} x) d} %{\operatorname{d}\hspace{-0.05cm} s \Big] \\&\qquad\qquad + \bar{E}^n \Big[ h_nZ \int_{\tau_m \wedge \rho_n}^{\tau_m \wedge (\rho_n + h_n)} \| b^n(X_s)\|_\mathbb{K}^2 d} %{\operatorname{d}\hspace{-0.05cm} s \Big]\Big).
\end{align*}
Thus, due to Lemmata \ref{lem: 2} and \ref{lem: bounded exp}, we find two constants \(c_1, c_2 > 0\) independent of \(n\) and \(m\) such that
\[
\bar{E}^n \big[ \|X_{\tau_m \wedge (\rho_n + h_n)} - X_{\tau_m \wedge \rho_n}\|_\mathbb{K}^2Z \big] \leq c_1 h_n + c_2 h^2_n.
\]
Furthermore, Fatou's lemma yields that
\[
\bar{E}^n \big[ \|X_{\rho_n + h_n} - X_{\rho_n}\|_\mathbb{K}^2Z \big] \leq c_1 h_n + c_2 h^2_n.
\]
Fix \(\delta > 0\) and set \(\bar{\delta} \triangleq \delta \|\iota\|_o^{-1}\). By Chebyshev's inequality, we have
\begin{align*}
\bar{P}^n \big(\|X_{\rho_n + h_n} - X_{\rho_n}\|_\mathbb{K} \geq \bar{\delta}\big) &\leq \bar{P}^n \big(\|X_{\rho_n + h_n} - X_{\rho_n}\|_\mathbb{K} Z \geq \bar{\delta}\big) + \eta(K^c)
\\&\leq \frac{\bar{E}^n \big[ \|X_{\rho_n + h_n} - X_{\rho_n}\|_\mathbb{K}^2Z \big]}{\bar{\delta}^2} + \frac{\epsilon}{2}
\\&\leq \frac{c_1 h_n + c_2 h^2_n}{\bar{\delta}^2} + \frac{\epsilon}{2}.
\end{align*}
Because \(h_n \to 0\) as \(n \to \infty\), we find an \(N \in \mathbb{N}\) such that
\[
\bar{P}^n \big(\|X_{\rho_n + h_n} - X_{\rho_n}\|_\mathbb{K} \geq \bar{\delta}\big) < \epsilon
\]
for all \(n \geq N\).
We conclude that
\[
P^n \big(\|X_{\rho_n + h_n} - X_{\rho_n}\|_\mathbb{B} \geq \delta\big) \leq \bar{P}^n \big(\|X_{\rho_n + h_n} - X_{ \rho_n}\|_\mathbb{K} \geq \bar{\delta}\big) < \epsilon
\]
for all \(n \geq N\),
i.e. (ii) in Proposition \ref{prop: gen tight} holds. This completes the proof.
\end{proof}
Define \(\mathcal{K}\) as in \eqref{K} with \(A = 0\) and \(b\) replaced by \(\mu\) as given in the statement of Theorem \ref{prop: existence} and let \(\mathcal{K}^n\) as in \eqref{K} with \(A = 0\) and \(b\) replaced by \(\tilde{b}^n\), \(a\) replaced by \(\tilde{a}^n\) and \(K\) replaced by \(\tilde{K}^n\).
For all \(f = g(\langle \cdot, y^*\rangle_\mathbb{B}) \in \mathcal{D}\), Taylor's theorem yields that
\[
\big|f(x + v(x, y)) - f(x) - \partial f (x) \langle v(x, y), y^*\rangle_\mathbb{B} \big| \leq \tfrac{1}{2} \|g''\|_\infty \|y^*\|^2_\mathbb{B} \|v(x, y)\|^2_\mathbb{B}, \qquad y \in E, x \in \mathbb{B}.
\]
Thus, due to the continuity assumptions on \(b, \sigma\) and \(v\), \eqref{eq: loc bdd B} and the dominated convergence theorem the map
\[
\mathbb{B} \ni x \mapsto \mathcal{K} f(x)
\]
is continuous for all \(f \in \mathcal{D}\).
Let \(K \subset \mathbb{B}\) be compact and \(f = g(\langle \cdot, y^*\rangle_\mathbb{B}) \in \mathcal{D}\).
Note that for all \(x \in \mathbb{B}\) and \(y \in E\)
\begin{align*}
K^n (x, y) \triangleq \big|f(x + v(x, y)) &- f(x + v^n(x, y)) - \partial f (x) \langle v(x,y) - v^n(x, y), y^*\rangle_\mathbb{B} \big|
\\&\leq \|g'\|_\infty \big|\langle v(x, y) - v^n(x, y), y^*\rangle_\mathbb{B}\big| + \|g'\|_\infty \big| \langle v(x, y) - v^n(x, y), y^*\rangle_\mathbb{B}\big|
\\&\leq 2 \|g'\|_\infty \|y^*\|_\mathbb{B} \|v(x, y) - v^n(x, y)\|_\mathbb{B}.
\end{align*}
Thus, Lemma \ref{lem: 3} yields that for all \(y \in E\)
\begin{align}\label{eq: pw conv}
\sup_{x \in K} K^n(x, y) \to 0 \text{ as } n \to \infty.
\end{align}
Due to Taylor's theorem, we have for all \(x \in \mathbb{B}\) and \(y \in E\)
\begin{align*}
K^n(x, y) &\leq \tfrac{1}{2} \|g''\|_\infty \|y^*\|_\mathbb{B}^2 \big( \|v (x, y) \|_\mathbb{B}^2 + \|v^n(x, y)\|_\mathbb{B}^2\big).
\end{align*}
Consequently, recalling Lemma \ref{lem: 3}, hypothesis (iii) and \eqref{eq: pw conv}, we deduce from the dominated convergence theorem that
\[
\int_E\sup_{x \in K} K^n(x, y) F(d} %{\operatorname{d}\hspace{-0.05cm} y) \to 0 \text{ as } n \to \infty.
\]
Using again Lemma \ref{lem: 3}, we obtain that
\begin{equation*}\begin{split}
\sup_{x \in K}\big| \mathcal{K} f (x) - \mathcal{K}^n f(x)\big| &\leq \|g'\|_\infty \|y^*\|_\mathbb{B} \sup_{x \in K} \|b^n (x) - b(x)\|_\mathbb{B} \\&\qquad + \tfrac{1}{2} \|g''\|_\infty \|y^*\|_\mathbb{B}^2 \sup_{x \in K} \|\sigma^n (x) - \sigma (x)\|_{L(\mathbb{B})}^2 \\&\qquad+ \int_E \sup_{x \in K} K^n(x,y) F(d} %{\operatorname{d}\hspace{-0.05cm} y) \\&\to 0 \text{ as } n \to \infty.
\end{split}
\end{equation*}
Using again Taylor's theorem, Lemma \ref{eq: loc bdd} yields that
\begin{align*}
\sup_{n \in \mathbb{N}} \sup_{\|x\|_\mathbb{B} \leq m} \big| \mathcal{K}^n f (x) \big| &\leq \|g'\|_\infty \|y^* \|_\mathbb{B} \sup_{n \in \mathbb{N}} \sup_{\|x\|_\mathbb{B} \leq m} \|b^n(x)\|_\mathbb{B}
\\&\qquad+ \tfrac{1}{2} \|g''\|_\infty \|y^*\|_\mathbb{B}^2 \sup_{n \in \mathbb{N}} \sup_{\|x\|_\mathbb{B} \leq m} \|\sigma^n(x)\|_{L(\mathbb{B})}^2
\\&\qquad + \tfrac{1}{2} \|g''\|_\infty \|y^*\|_\mathbb{B}^2 \sup_{n \in \mathbb{N}} \sup_{\|x\|_\mathbb{B} \leq m} \int_E \|v^n(x, y)\|_\mathbb{B}^2 F(d} %{\operatorname{d}\hspace{-0.05cm} y) < \infty.
\end{align*}
We conclude from Corollary \ref{coro: existence} and Lemma \ref{lem: 4} that the MP \((0, \mu, a, K, \eta \circ \iota^{-1})\) has a solution.
\qed
\subsection{Proof of Proposition \ref{prop: tight}}\label{proof: prop1}
For \(T \in (0, \infty)\) let \(\Omega^T\) be the space of continuous functions \([0, T] \to \mathbb{B}\), let \(X^T\) be the coordinate process on \(\Omega^T\) and set \(\mathcal{F}^T \triangleq \sigma (X^T_t, t \in [0, T])\).
Due to \cite[Corollary 5]{whitt1970}, the sequence \((P^n \circ X_{\cdot \wedge \tau_m}^{-1})_{n \in \mathbb{N}}\) is tight if and only if for all \(T \in \mathbb{N}\) its restriction to \((\Omega^T, \mathcal{F}^T)\) is tight.
We fix \(T \in \mathbb{N}\).
Our strategy is to adapt the compactness method from \cite{doi:10.1080/17442509408833868}.
In the following we fix \(n \in \mathbb{N}\) and work with the filtered probability space \((\Omega, \mathscr{F}, \mathbf{F}, P^n)\).
Due to \cite[Theorem 3.6]{EJP2924}, we find a cylindrical standard Brownian motion \(W\) (possibly on an extension of \((\Omega, \mathscr{F}, \mathbf{F}, P^n)\)) such that
\[
X_t = S_t X_0 + \int_0^t S_{t - s} b^n(X_s)d} %{\operatorname{d}\hspace{-0.05cm} s + \int_0^t S_{t-s} \sigma^n(X_s) d} %{\operatorname{d}\hspace{-0.05cm} W_s, \quad t \in [0, T].
\]
Let \(\varepsilon > 0\) be fixed.
Because \((\eta^n)_{n \in \mathbb{N}}\) is tight, there exists a compact set \(K \subset \mathbb{B}\) such that
\[
\inf_{n \in \mathbb{N}} \eta^n (K) \geq 1 - \tfrac{\varepsilon}{2}.
\]
Let \(m^* > 0\) be a constant such that \(\|x\| \leq m^*\) for all \(x \in K\).
In the cases (ii) and (iv), let \(\theta \triangleq \lambda\) and choose \(p > 2\) such that \(\tfrac{1}{p} < \theta\). In the other cases (i) and (iii) take \(p > 2\) and choose \(\theta \in (0, \frac{1}{2})\) such that \(\tfrac{1}{p} < \theta\).
In the cases (iii) and (iv), the linear growth conditions and a standard argument based on Gronwall's lemma (see \cite[Theorems 7.2 and 7.5]{DePrato}) yields that
\[
\sup_{s \in [0, T]} E^{P^n}\big[ \mathbf{1}_K (X_0) \|X_{s \wedge \tau_\infty}\|^p\big] = \sup_{s \in [0, T]} E^{P^n}\big[ \mathbf{1}_K(X_0) \|X_s\|^p\big] \leq C_{p, T},
\]
where \(C_{p, T} \in (0, \infty)\) is a constant independent of \(n\).
Note that
\begin{equation}\label{eq: b ineq}
\begin{split}
E^{P^n} \Big[ \mathbf{1}_K(X_0) &\int_0^T \|b^{n}(X_{s \wedge \tau_m})\|^p d} %{\operatorname{d}\hspace{-0.05cm} s \Big] \\&\leq \begin{cases}
T\cdot\big(\sup_{k \in \mathbb{N}} \sup_{\|x\| \leq m \vee m^*} \|b^k(x)\|\big)^p,&\text{if (i) or (ii) holds},\\
TK^p 2^{p} \big(1 + C_{p, T}\big),&\text{if (iii) or (iv) holds}.
\end{cases}
\end{split}
\end{equation}
Let \(L^p([0, T], \mathbb{B})\) be the space of all Borel functions \(f \colon [0, T]\to \mathbb{B}\) such that \(\int_0^T \|f(s)\|^p d} %{\operatorname{d}\hspace{-0.05cm} s < \infty\).
For \(f \in L^p([0, T], \mathbb{B})\), we define
\[
(G_{\xi} f)(t) \triangleq \int_0^{t} (t - s)^{\xi - 1} S_{t - s} f(s) d} %{\operatorname{d}\hspace{-0.05cm} s,\quad \xi \in (\tfrac{1}{p}, 1], t \in [0, T].
\]
Due to \cite[Proposition 8.4]{DePrato}, the operator \(G_\xi\) is compact from \(L^p ([0, T], \mathbb{B})\) into \(\Omega^T\).
We define
\[
Y^{n, m, \theta}_s \triangleq \int_0^s (s - r)^{- \theta} S_{s-r} \sigma^{n}(X_{r \wedge \tau_m})d} %{\operatorname{d}\hspace{-0.05cm} W_r,\quad s \in [0,T].
\]
In either of the cases (i) and (iii), we obtain as in the proof of \cite[Proposition 7.3]{DePrato} that there exists a constant \(\widehat{C}_{p, T} \in (0, \infty)\) such that
\begin{equation}\label{bound sigma}
\begin{split}
E^{P^n}\Big[ \mathbf{1}_K(X_0) &\int_0^T \|Y^{n, m, \theta}_s\|^p d} %{\operatorname{d}\hspace{-0.05cm} s\Big] \\&\leq \widehat{C}_{p, T} \int_0^T E^{P^n} \Big[ \mathbf{1}_K(X_0) \| \sigma^{n} (X_{s \wedge \tau_m}) \|^p_\textup{HS}\Big] d} %{\operatorname{d}\hspace{-0.05cm} s
\\&\leq \begin{cases}
\widehat{C}_{p, T} T \big(\sup_{k \in \mathbb{N}}\sup_{\|x\| \leq m \vee m^*} \|\sigma^k(x)\|_\text{HS}\big)^p,&\text{if (i) holds},\\
\widehat{C}_{p, T} T K^p 2^{p} \big(1 + C_{p, T} \big),&\text{if (iii) holds}.
\end{cases}
\end{split}
\end{equation}
In the cases (ii) and (iv) we have chosen \(\theta = \lambda\) and we obtain as in the proof of \cite[Proposition 6.3.5]{roeckner15} that there exists a constant \(\widehat{C}_{p} \in (0, \infty)\) such that
\begin{equation}\label{bound sigma2}
\begin{split}
E^{P^n}\Big[ \mathbf{1}_K&(X_0) \int_0^T \|Y^{n, m, \theta}_s\|^p d} %{\operatorname{d}\hspace{-0.05cm} s\Big] \\&\leq \widehat{C}_{p} \Big(\int_0^T (T - s)^{- 2 \lambda} \|S_{T - s}\|^2_\textup{HS} E^{P^n} \Big[ \mathbf{1}_K(X_0) \| \sigma^{n} (X_{s \wedge \tau_m}) \|^p_o\Big]^\frac{2}{p} d} %{\operatorname{d}\hspace{-0.05cm} s \Big)^\frac{p}{2}
\\&\leq \begin{cases}
\widehat{C}_{p} \big(\int_0^T s^{- 2 \lambda}\|S_s\|^2_\textup{HS} d} %{\operatorname{d}\hspace{-0.05cm} s\big)^\frac{p}{2} \big(\sup_{k \in \mathbb{N}}\sup_{\|x\| \leq m \vee m^*} \|\sigma^k(x)\|_o\big)^p,&\text{if (ii) holds},\\
\widehat{C}_{p}\big( \int_0^T s^{- 2 \lambda}\|S_s\|^2_\textup{HS} d} %{\operatorname{d}\hspace{-0.05cm} s \big)^{\frac{p}{2}}K^p 2^{p} \big(1 + C_{p, T} \big),&\text{if (iv) holds}.
\end{cases}
\end{split}
\end{equation}
Recall the the r.h.s. is finite due to Lemma \ref{lem: for all conv}.
By \cite[Proposition 1]{doi:10.1080/17442508708833480}, we have the following factorization formula
\[
\int_0^t S_{t-s} \sigma^{n}(X_{s \wedge \tau_m}) d} %{\operatorname{d}\hspace{-0.05cm} W_s = \tfrac{\sin (\pi \theta)}{\pi} \big(G_\theta Y^{n, m, \theta}\big) (t),\quad t \in [0, T].
\]
Thus, due to \cite[Remark A.1]{Brzeniak2005}, for all \(t \in [0, T]\)
\[
\Big(\int_0^\cdot S_{\cdot -s} \sigma^n(X_s) d} %{\operatorname{d}\hspace{-0.05cm} W_s \Big) (t \wedge \tau_m) = \tfrac{\sin (\pi \theta)}{\pi} \big(G_\theta Y^{n, m, \theta}\big) (t \wedge \tau_m).
\]
Consequently, we obtain
\begin{align*}
X_{t \wedge \tau_m}
= S_{t \wedge \tau_m} X_0 + \left(G_1 b^{n} (X_{\cdot \wedge \tau_m})\right)(t \wedge \tau_m) + \tfrac{\sin(\pi \theta)}{\pi} \big(G_\theta Y^{n, m, \theta}\big)(t \wedge \tau_m),\quad t \in [0, T].
\end{align*}
Define \begin{align*}B_R &\triangleq \Big\{u \in L^p ([0, T], \mathbb{B}) \colon \int_0^T \|u(s)\|^p d} %{\operatorname{d}\hspace{-0.05cm} s \leq R \Big\},\\
\Lambda (R, \theta, m) &\triangleq \left\{ \alpha \in \Omega^T \colon \alpha = (G_\theta u)(\cdot \wedge \tau_m(\lambda)), u \in B_R, \lambda \in \Omega\right\},
\\
\Lambda^\star (m) &\triangleq \left\{\alpha \in \Omega^T \colon \alpha = S_{\cdot \wedge \tau_m(\lambda)} x, x \in K, \lambda \in \Omega\right\},
\end{align*}
and
\begin{align*}
\Lambda' &(R, m)
\\&\triangleq \left\{ \alpha \in \Omega^T \colon \alpha = \alpha^1 + \alpha^2 + \tfrac{\sin(\pi \theta)}{\pi} \alpha^3,\ \alpha^1 \in \Lambda^\star (m), \alpha^2 \in \Lambda (R, 1, m), \alpha^3 \in \Lambda (R, \theta, m) \right\}.
\end{align*}
We claim that the sets \(\Lambda^\star (m), \Lambda (R, 1, m)\) and \(\Lambda (R, \theta, m)\) are relatively compact.
To show this, we recall the following version of the Arzel\`a-Ascoli theorem (see \cite[Theorem A.2.1]{Kallenberg} and \cite[Theorem 1.8.23]{tao2010epsilon}):
\begin{fact}\label{fact2} Fix two metric spaces \(U\) and \((V, \rho)\), where \(U\) is compact and \(V\) is complete. Let \(D\) be dense in \(U\). A set \(A \subset C(U, V)\) (the space of all continuous functions \(U \to V\) equipped with the uniform topology) is relatively compact if and only if for all \(t \in D\) the set \(\pi_t (A) \triangleq \{\alpha(t)\colon \alpha \in A\} \subset V\) is relatively compact in \(V\) and \(A\) is equicontinuous, i.e. for all \(s \in U\) and \(\epsilon > 0\) there exists a neighborhood \(N\subset U\) of \(s\) such that for all \(r \in N\) and \(\alpha \in A\)
\[
\rho (\alpha(r), \alpha(s)) < \epsilon.
\]
In that case, even \(\bigcup_{t \in U} \pi_t(A)\) is relatively compact in \(V\).
\end{fact}
Let \(\xi \in \{\theta, 1\}\).
The set \(\Lambda (R, \xi, m)\) is relatively compact if it is equicontinuous and for all \(t \in [0, T]\) the set
\[
C_t \triangleq \{y \in \mathbb{B}\colon y = \alpha(t), \alpha \in \Lambda(R, \xi, m)\}
\]
is relatively compact in \(\mathbb{B}\).
We note that the set \(\Lambda (R, \xi, \infty)\) is relatively compact, because the operator \(G_\xi\) is compact.
Thus, Fact \ref{fact2} yields that the set \[C \triangleq \bigcup_{t \in [0, T]}\{y \in \mathbb{B} \colon y = \alpha(t), \alpha \in \Lambda (R, \xi, \infty)\}\] is relatively compact in \(\mathbb{B}\). For all \(t \in [0, T]\) we have \(C_t \subset C\) and hence also the set \(C_t\) is relatively compact in \(\mathbb{B}\).
Let now \(t \in [0, T]\) and \(\epsilon > 0\).
Again due to Fact \ref{fact2}, there exists a \(\delta> 0\) such that for all \(s \in [0, T]\) with \(|t - s| \leq \delta\) we have
\begin{align*}
\|\alpha (t) - \alpha (s)\| < \tfrac{\epsilon}{2}
\end{align*}
for all \(\alpha \in \Lambda (R, \xi, \infty)\).
Note that
\[
\|\alpha(t \wedge \tau_m(\lambda)) - \alpha (s \wedge \tau_m(\lambda))\| = \begin{cases} \|\alpha(\tau_m(\lambda)) - \alpha(s)\|,& t \geq \tau_m(\lambda)\geq s,\\
\|\alpha(t) - \alpha(\tau_m(\lambda))\|,&t \leq \tau_m(\lambda) \leq s,\\
\|\alpha(t) - \alpha(s)\|,&t, s \leq \tau_m(\alpha),\\
0,&t, s \geq \tau_m(\alpha).\end{cases}
\]
In the first case, we have
\[
\|\alpha(\tau_m(\lambda)) - \alpha(s)\| \leq \|\alpha(\tau_m(\lambda)) - \alpha(t)\| + \|\alpha(t) - \alpha(s)\| < \epsilon,
\]
because \(|t - \tau_m(\lambda)| \leq |t - s| \leq \delta\). In the second case, we have
\[|t - \tau_m(\lambda)| = \tau_m(\lambda) - t \leq s - t \leq \delta,\] and hence
\[
\|\alpha(t) - \alpha(\tau_m(\lambda))\| < \tfrac{\epsilon}{2} \leq \epsilon.
\]
In the third and fourth case, the desired inequality holds trivially. Thus,
the inequality
\[
\|\alpha(t) - \alpha(s)\| < \epsilon
\] holds for all \(\alpha \in \Lambda (R, \xi, m)\) and \(s \in [0, T]\) with \(|t - s| \leq \delta\). We conclude that the set \(\Lambda(R, \xi, m)\) is equicontinuous. Now, Fact \ref{fact2} yields that it is also relatively compact.
The relative compactness of \(\Lambda^\star (m)\) follows from the same argument, if we can show that the set \(\Lambda^\star (\infty)\) is relatively compact.
Because \(K\) and \(S_t\) for all \(t > 0\) are compact, the set
\[
\{y \in \mathbb{B} \colon y = S_t x, x \in K\},\quad t \in (0, T],
\]
is relatively compact in \(\mathbb{B}\). Since \((S_t)_{t \geq 0}\) is a \(C_0\)-semigroup, \cite[Lemma 5.2, p. 37]{engel2006one} yields that the map
\[
[0, T] \times K \ni (t, x) \mapsto S_t x
\]
is uniformly continuous.
In other words, for all \(\epsilon > 0\) there exists a \(\delta > 0\) such that
\[
\|S_t x - S_s x\| < \epsilon
\]
for all \(x \in K\) and \(t, s \in [0, T] \colon |t - s| < \delta\), i.e. the set \(\Lambda^\star (\infty)\) is equicontinuous. Thus, it is relatively compact by Fact \ref{fact2}. We conclude that also \(\Lambda^\star (m)\) is relatively compact.
Finally, it follows that \(\Lambda'(R, m)\) is relatively compact. Using \eqref{eq: b ineq}, \eqref{bound sigma} and \eqref{bound sigma2} together with Chebyshev's inequality, for all \(R > 0\) there exists a constant \(C'\) independent of \(n\) and \(R\) such that
\begin{align*}
P^n &\Big(X_0 \in K\ \text{ and } \int_0^T \|b^n (X_{s \wedge \tau_m})\|^p d} %{\operatorname{d}\hspace{-0.05cm} s \leq R \ \text{ and }\ \int_0^T\|Y^{n, m, \theta}_s\|^p d} %{\operatorname{d}\hspace{-0.05cm} s \leq R\Big)
\\&\geq \eta^n (K)- P^n \Big( \mathbf{1}_K (X_0) \int_0^T \|b^n (X_{s \wedge \tau_m})\|^p d} %{\operatorname{d}\hspace{-0.05cm} s > R\Big) - P^n \Big(\mathbf{1}_K(X_0) \int_0^T\|Y^{n, m, \theta}_s\|^p d} %{\operatorname{d}\hspace{-0.05cm} s > R\Big)
\\&\geq 1 - \frac{\varepsilon}{2} - \frac{1}{R}\ \Big( E^{P^n} \Big[ \mathbf{1}_K(X_0)\int_0^T \|b^n (X_{s \wedge \tau_m})\|^p d} %{\operatorname{d}\hspace{-0.05cm} s\Big] + E^{P^n} \Big[ \mathbf{1}_K(X_0)\int_0^T\|Y^{n, m, \theta}_s\|^p d} %{\operatorname{d}\hspace{-0.05cm} s\Big]\Big)
\\&\geq 1 - \frac{\varepsilon}{2} -\frac{C'}{R}.
\end{align*}
Consequently, there exists an \(R_\varepsilon > 0\) such that
\begin{align*}
\inf_{n \in \mathbb{N}} P^n\big((X_{t \wedge \tau_m})_{t \in [0, T]} \in \Lambda'(R_\varepsilon, m)\big)
\geq 1 - \varepsilon.
\end{align*}
We conclude that the restriction of \((P^n \circ X_{\cdot \wedge \tau_m}^{-1})_{n \in \mathbb{N}}\) to \((\Omega^T, \mathcal{F}^T)\) is tight. Because \(T \in \mathbb{N}\) was arbitrary, this implies that \((P^n \circ X_{\cdot \wedge \tau_m}^{-1})_{n \in \mathbb{N}}\) is tight.
\qed
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,492 |
\section*{1. Introduction}
\par\q Let $[x]$ be the greatest integer not exceeding $x$.
For a prime $p$ let $\Bbb
Z_p$ be the set of rational numbers whose denominator is not
divisible by $p$. Let $\{P_n(x)\}$ be the Legendre polynomials given
by
$$P_0(x)=1,\ P_1(x)=x,\ (n+1)P_{n+1}(x)=(2n+1)xP_n(x)-nP_{n-1}(x)\ (n\ge
1).$$ It is well known that (see [MOS, pp.\;228-232], [B1] and [B2])
$$P_n(x)=\f
1{2^n}\sum_{k=0}^{[n/2]}\b nk(-1)^k\b{2n-2k}nx^{n-2k}
=\sum_{k=0}^n\b nk\b{n+k}k\Ls{x-1}2^k.\tag 1.1$$ From (1.1) we see
that $P_n(-x)=(-1)^nP_n(x)$.
\par Let $p>3$ be a prime. In 2003 Rodriguez-Villegas [RV] conjectured that
$$\aligned&\sum_{k=0}^{p-1}\f{\b{2k}k^2\b{3k}k}{108^k}\e 0\mod{p^2}\qtq{for}
p\e 2\mod 3,
\\& \sum_{k=0}^{p-1}\f{\b{2k}k^2\b{4k}{2k}}{256^k} \e 0\mod{p^2}
\qtq{for} p\e 5,7\mod 8,
\\& \sum_{k=0}^{p-1} \f{\b{2k}k\b{3k}k\b{6k}{3k}}{1728^k}
\e 0\mod{p^2}\qtq{for} p\e 3\mod 4.\endaligned\tag 1.2$$ In 2005
Mortenson [M] proved these congruences modulo $p$, in 2012 Z.W. Sun
[Su3] confirmed (1.2). Motivated by Mortenson's work, in [Su1,Su2]
Z.W. Sun posed many conjectures concerning the following sums modulo
$p^2$:
$$\sum_{k=0}^{p-1}\f{\b{2k}k^3}{m^k},\
\sum_{k=0}^{p-1}\f{\b{2k}k\b{3k}k}{m^k},\
\sum_{k=0}^{p-1}\f{\b{2k}k\b{4k}{2k}}{m^k}\qtq{and} \sum_{k=0}^{p-1}
\f{\b{2k}k\b{3k}k\b{6k}{3k}}{m^k},$$ where $m$ is an integer with
$p\nmid m$. In [S2-S5] the author solved some of his conjectures by
establishing the following congruences:
$$\align &\sum_{k=0}^{p-1}\f{\b{2k}k^3}{m^k}
\e P_{\f{p-1}2}\Big(\sqrt{1-\f{64}m}\Big)^2\mod {p^2},\tag 1.3
\\&\sum_{k=0}^{p-1}\b{2k}k^2\b{3k}k(x(1-27x))^k\e\Big(
\sum_{k=0}^{p-1}\b{2k}k\b{3k}kx^k\Big)^2\mod{p^2},\tag 1.4
\\&\sum_{k=0}^{p-1}\b{2k}k^2\b{4k}{2k}(x(1-64x))^k\e\Big(
\sum_{k=0}^{p-1}\b{2k}k\b{4k}{2k}x^k\Big)^2\mod{p^2},\tag 1.5
\\&\sum_{k=0}^{p-1}\b{2k}k\b{3k}k\b{6k}{3k}(x(1-432x))^k\e\Big(
\sum_{k=0}^{p-1}\b{2k}k\b{3k}k\b{6k}{3k}x^k\Big)^2\mod{p^2}.\tag 1.6
\endalign$$
It is easily seen that (see [S1, pp.1916-1917, 1920], [S3, p.1953] and [S5, p.182])
$$\aligned&\b{-\f 12}k^2=\f{\b{2k}k^2}{16^k},\ \b{-\f
13}k\b{-\f 23}k=\f{\b{2k}k\b{3k}k}{27^k}, \\&\ \b{-\f 14}k\b{-\f
34}k=\f{\b{2k}k\b{4k}{2k}}{64^k},\ \b{-\f 16}k\b{-\f
56}k=\f{\b{3k}k\b{6k}{3k}}{432^k}.\endaligned\tag 1.7$$ Let $p$ be
an odd prime, $a\in\Bbb Z_p$ and let $\ap\in\{0,1,\ldots,p-1\}$ be
given by $a\e \ap\mod p$. In [S6], the author proved that
$$\sum_{k=0}^{p-1}\f{\b{2k}k\b ak\b{-1-a}k}{4^k}\e 0\mod{p^2}
\qtq{for}\ap\e 1\mod 2.$$
Let
$(a)_k=a(a+1)\cdots(a+k-1)=(-1)^kk!\b{-a}k$ and
$${}_rF_s\biggl(\begin{matrix} a_1,\ldots,a_r\\
b_1,\ldots,b_s\end{matrix}
\biggm|z\biggr)=1+\sum_{k=1}^{\infty}\f{(a_1)_k\cdots(a_r)_k}
{(b_1)_k\cdots(b_s)_k}\cdot \f{z^k}{k!}.$$
After
reading the author's preprint (arXiv:1101.1050) involving
(1.4)-(1.6), in the email to the author on January 11, 2011 Wadim
Zudilin wrote: ``It's probably worth mentioning that the proofs of
Theorems 2.1, 2.4 and possibly Theorem 3.1 from your arXiv:1101.1050
can be simplified. Your congruences assume the form
$$\left( \sum_{k=0}^{p-1} \frac{(a)_k (1-a)_k}{k!^2} x^k \right)^2
\e \sum_{k=0}^{p-1} \frac{(a)_k (1-a)_k}{k!^2} \binom{2k}{k}
(x(1-x))^k \mod {p^2}, $$
where $a=1/3$, $1/4$ or $1/6$ ($1/2$ is possible as well). Note that
this follows from the identity
$$ \left( \sum_{k=0}^\infty \frac{(a)_k (1-a)_k}{k!^2} x^k \right)^2
= \sum_{k=0}^\infty \frac{(a)_k (1-a)_k}{k!^2} \binom{2k}{k}
(x(1-x))^k $$
truncated to $p$ terms. If $k>p/2$, then the coefficients on
both sides
are $0\mod {p^2}$ (as you already used in the proof, e.g., of Theorem
2.1)." In the email on January 15, 2011 Zudilin wrote: The
identity is a combination of the Gauss quadratic
transformation ([Ba, p.88, Eq. (2)])
$${}_2F_1\biggl(\begin{matrix} A, \, B \\ A+B+\frac12 \end{matrix}
\biggm|4z(1-z)\biggr) ={}_2F_1\biggl(\begin{matrix} 2A, \, 2B \\
A+B+\frac12 \end{matrix} \biggm|z\biggr),$$ and Clausen's original
identity ([Sl, p.75, Eq.(2.5.7)])
$${}_2F_1\biggl(\begin{matrix} a, \, b \\ a+b+\frac12 \end{matrix}
\biggm|z\biggr)^2 ={}_3F_2\biggl(\begin{matrix} 2a, \, 2b, \, a+b \\
a+b+\frac12, \, 2a+2b \end{matrix} \biggm|z\biggr).$$
\par Let $p$ be an odd prime and $a\in\Bbb Z_p$. In this note,
inspired by Zudilin's
comments we give an elementary proof of the following generalization
of (1.4)-(1.6):
$$\Big(\sum_{k=0}^{p-1}\b ak\b {-1-a}kx^k\Big)^2\e
\sum_{k=0}^{p-1}\b{2k}k\b ak\b {-1-a}k(x(1-x))^k\mod{p^2}.$$ As an
application, for $m\in\Bbb Z_p$ with
$m\not\e 0\mod p$ we show that
$$\sum_{k=0}^{p-1}\f{\b{2k}k\b ak\b{-1-a}k}{m^k}\e 0\mod p
\qtq{implies}\sum_{k=0}^{p-1}\f{\b{2k}k\b ak\b{-1-a}k}{m^k}\e 0\mod
{p^2}.$$
\section*{2. Main results}
\par\q\pro{Lemma 2.1 ([S3, Lemma 3.2])} For any nonnegative integer $n$
we have
$$P_n(\sqrt{1+4x})^2=\sum_{k=0}^n\b nk\b {n+k}k\b{2k}kx^k.$$
\endpro
\par As Zudilin noted, Lemma 2.1 can also be deduced from
Clausen's identity, Gauss' quadratic transformation for
hypergeometic series and (1.1).
\pro{Theorem 2.1} Let $p$ be an odd prime and
$a\in\Bbb Z_p$. Then
$$\sum_{k=0}^{p-1}\b{2k}k\b ak\b{-1-a}kx^k
\e P_{\ap}(\sqrt{1-4x})^2\e P_{p-1-\ap}(\sqrt{1-4x})^2\mod p.$$
\endpro
Proof. By Lemma 2.1,
$$\align P_{\ap}(\sqrt{1-4x})^2
&=\sum_{k=0}^{\ap}\b{2k}k\b{\ap}k\b{\ap+k}k (-x)^k
\\&=\sum_{k=0}^{p-1}\b{2k}k\b{\ap}k\b{\ap+k}k (-x)^k
\\&\e \sum_{k=0}^{p-1}\b{2k}k\b ak\b{a+k}k (-x)^k
\\&=\sum_{k=0}^{p-1}\b{2k}k\b ak\b{-1-a}k x^k\mod p.
\endalign$$
To complete the proof, we note that $P_{p-1-\ap}(t)\e P_{\ap}(t)
\mod p$ by [S4, Lemma 2.2].
\par{\bf Remark 2.1} In the cases $a=-\f 12,-\f 13,-\f 14,-\f 16$,
Theorem 2.2 was given by the author in [S2, Theorem 4.1], [S3,
Theorems 3.2 and 4.2] and [S5, Theorem 4.1].
\pro{Corollary 2.1} Let $p$ be an odd prime and $a,x\in\Bbb Z_p$.
Then $\sum_{k=0}^{p-1}\b{2k}k\b ak\b{-1-a}kx^k\e 0\mod p$ implies
$$P_{\ap}(\sqrt{1-4x})\e P_{p-1-\ap}(\sqrt{1-4x}) \e 0\mod p.$$
\endpro
Proof. By (1.1),
$$P_n(\sqrt{1-4x})=\f 1{2^n}(\sqrt{1-4x})^{n-2[\f n2]}
\sum_{k=0}^{[n/2]}\b nk(-1)^k\b{2n-2k}n(1-4x)^{[\f n2]-k}.$$ Thus
$P_n(\sqrt{1-4x})^2\e 0\mod p$ implies $P_n(\sqrt{1-4x})\e 0\mod p$.
Now applying Theorem 2.1 we deduce the result.
\pro{Lemma 2.2} For any nonnegative integer $n$ we have
$$\sum_{k=0}^n\b ak\b{-1-a}k\b a{n-k}\b{-1-a}{n-k}
=\sum_{k=0}^n\b{2k}k\b ak\b{-1-a}k\b k{n-k}(-1)^{n-k}.$$
\endpro
Proof. Let $S_1(n)$ and $S_2(n)$ be the sums on the left and right
hands of the identity, respectively. Using Maple and the Zeilberger
algorithm we find that for $i=1,2$,
$$n^3S_i(n)=(2n-1)(n^2-n-2a(a+1))S_i(n-1)+(n-1)(2a+n)(2a+2-n)S_i(n-2)\
(n\ge 2).$$ Since $S_1(0)=1=S_2(0)$ and $S_1(1)=-2a(a+1)=S_2(1)$,
applying the above we deduce that $S_1(n)=S_2(n)$.
\par{\bf Remark 2.2} In the cases $a=-\f 13,-\f 14,-\f 16$, the
identity was given by the author in [S2,S3,S5].
\pro{Theorem 2.2} Let $p$ be an odd prime and $a\in\Bbb Z_p$. Then
$$\Big(\sum_{k=0}^{p-1}\b ak\b {-1-a}kx^k\Big)^2\e
\sum_{k=0}^{p-1}\b{2k}k\b ak\b {-1-a}k(x(1-x))^k\mod{p^2}.$$
\endpro
\par Taking $a=-\f 13,-\f 14,-\f 16$ in Theorem 2.2 and
then applying (1.7) we get (1.4)-(1.6). Thus, Theorem 2.2 is a
generalization of (1.4)-(1.6). \par Proof of Theorem 2.2. For
$k\in\{\f{p+1}2,\ldots,p-1\}$ we see that $p\mid \b{2k}k$ and
$$\align \b ak\b {-1-a}k&=(-1)^k\b ak\b{a+k}k
\\&=(-1)^k\f{(a+k)(a+k-1)\cdots (a-k+1)}{k!}\e 0\mod p.\endalign$$
Thus, applying Lemma 2.2 we see that
$$\align&\sum_{k=0}^{p-1}\b{2k}k\b ak\b {-1-a}k(x(1-x))^k
\\&\e \sum_{k=0}^{(p-1)/2}\b{2k}k\b ak\b {-1-a}k(x(1-x))^k
\\&=\sum_{k=0}^{(p-1)/2}\b{2k}k\b ak
\b {-1-a}kx^k\sum_{r=0}^k\b kr(-x)^r
\\&=\sum_{n=0}^{p-1}x^n
\sum_{k=0}^{\min\{n,\f{p-1}2\}}\b{2k}k\b ak\b{-1-a}k\b
k{n-k}(-1)^{n-k}
\\&\e\sum_{n=0}^{p-1}x^n
\sum_{k=0}^n\b{2k}k\b ak\b{-1-a}k\b k{n-k}(-1)^{n-k}
\\&=\sum_{n=0}^{p-1}x^n
\sum_{k=0}^n\b ak\b{-1-a}k\b a{n-k}\b{-1-a}{n-k}
\\&=\sum_{k=0}^{p-1}\b ak\b{-1-a}kx^k\sum_{n=k}^{p-1}
\b a{n-k}\b{-1-a}{n-k}x^{n-k}
\\&=\Big(\sum_{k=0}^{p-1}\b ak\b{-1-a}kx^k\Big)
\Big(\sum_{r=0}^{p-1} \b ar\b{-1-a}rx^r-\sum_{r=p-k}^{p-1} \b
ar\b{-1-a}rx^r\Big)\mod {p^2}.
\endalign$$
For $0\le k\le p-1$ we see that $p\mid \b ak$ for $k>\ap$. For $0\le
k\le \ap$ and $p-k\le r\le p-1$ we see that $r\ge p-k>p-1-\ap$ and
so $p\mid \b{-1-a}r$. Hence for $0\le k\le p-1$ and $p-k\le r\le
p-1$ we have $p\mid \b ak\b{-1-a}r$, $p\mid \b{-1-a}k\b ar$ and so
$p^2\mid \b ak\b{-1-a}k\b ar\b{-1-a}r$. Now combining all the above
we deduce the result.
\pro{Theorem 2.3} Let $p$ be an odd prime and $m\in\Bbb Z_p$ with
$m\not\e 0\mod p$. Then
$$\sum_{k=0}^{p-1}\f{\b{2k}k\b ak\b{-1-a}k}{m^k}\e 0\mod p
\qtq{implies}\sum_{k=0}^{p-1}\f{\b{2k}k\b ak\b{-1-a}k}{m^k}\e 0\mod
{p^2}.$$
\endpro
Proof. Suppose $\sum_{k=0}^{p-1}\f{\b{2k}k\b ak\b{-1-a}k}{m^k}\e
0\mod p$. By Corollary 2.1, $P_{\ap}(\sqrt{1-\f 4m})\e 0\mod p$.
Thus,
$$\align &\sum_{k=0}^{p-1}\b ak\b{-1-a}k\Ls{1-\sqrt{4/m}}2^k
\\&\e \sum_{k=0}^{p-1}\b {\ap}k\b{-1-\ap}k\Ls{1-\sqrt{4/m}}2^k
\\&=\sum_{k=0}^{\ap}\b{\ap}k\b{\ap+k}k\Ls{\sqrt{4/m}-1}2^k
\\&=P_{\ap}\Big(\sqrt{1-\f 4m}\Big)\e 0\mod p.
\endalign$$
By Theorem 2.2,
$$\Big(\sum_{k=0}^{p-1}\b ak\b{-1-a}k\Ls{1-\sqrt{4/m}}2^k\Big)^2\e
\sum_{k=0}^{p-1}\f{\b{2k}k\b ak\b{-1-a}k}{m^k}\mod {p^2}.$$ Thus the
result follows.
Taking $a=-\f 12,-\f 13,-\f 14,-\f 16$ in Theorem 2.3 and then
applying (1.7) we deduce the following result.
\pro{Corollary 2.2}
Let $p$ be an odd prime, and $m\in\Bbb Z_p$ with $m\not\e 0\mod p$.
Then
$$\align &\sum_{k=0}^{p-1}\f{\b{2k}k^3}{m^k}\e 0\mod p
\qtq{implies} \sum_{k=0}^{p-1}\f{\b{2k}k^3}{m^k}\e 0\mod {p^2},
\\&\sum_{k=0}^{p-1}\f{\b{2k}k^2\b{3k}k}{m^k}\e 0\mod p
\qtq{implies} \sum_{k=0}^{p-1} \f{\b{2k}k^2\b{3k}k}{m^k}\e 0\mod
{p^2},
\\&\sum_{k=0}^{p-1}\f{\b{2k}k^2\b{4k}{2k}}{m^k}\e 0\mod p
\qtq{implies} \sum_{k=0}^{p-1} \f{\b{2k}k^2\b{4k}{2k}}{m^k}\e 0\mod
{p^2}\endalign$$ and
$$\sum_{k=0}^{p-1}\f{\b{2k}k\b{3k}k\b{6k}{3k}}{m^k}\e 0\mod p
\qtq{implies} \sum_{k=0}^{p-1}\f{\b{2k}k\b{3k}k\b{6k}{3k}}{m^k}\e
0\mod {p^2}.$$
\endpro
\par We remark that Corollary 2.2 can be easily deduced from [S2, Theorem
4.1], [S3, Theorems 3.2 and 4.2] and [S5, Theorem 4.1].
\pro{Theorem
2.4} Let $p$ be an odd prime and $u\in\Bbb Z_p$.
\par $(\t{\rm i})$ If $u\not\e \f 14,\f 1{16}\mod p$ and
$\sum_{k=0}^{p-1}\b{2k}k^2\b{3k}k\sls{u^2}{(1-4u)^3}^k\e 0\mod p$,
then
$$\sum_{k=0}^{p-1}\b{2k}k^2\b{3k}k\Ls{-u}{(1-16u)^3}^k \e
0\mod{p^2}.$$
\par $(\t{\rm ii})$ If
$u\not\e -\f 13,-\f 1{27}\mod p$ and
$\sum_{k=0}^{p-1}\b{2k}k^2\b{4k}{2k}\sls {u^3}{(1+3u)^4}^k\e 0\mod
p$, then
$$\sum_{k=0}^{p-1}\b{2k}k^2\b{4k}{2k}\Ls u{(1+27u)^4}^k\e
0\mod{p^2}.$$
\endpro
Proof. This is immediate from Corollary 2.2 and [S7, Corollaries 3.1
and 5.2].
\pro{Corollary 2.3} Let $p>3$ be a prime. Then
$$\sum_{k=0}^{p-1}\f{\b{2k}k^2\b{3k}k}{1458^k}\e 0\mod {p^2}
\qtq{for}p\e 5\mod 6$$ and
$$\sum_{k=0}^{p-1}\f{\b{2k}k^2\b{3k}k}{15^{3k}}\e 0\mod {p^2}
\qtq{for}p\e 11,14\mod {15}.$$
\endpro
Proof. Taking $u=-\f 12$ in Theorem 2.4(i) and then applying (1.2)
we obtain the first congruence. Taking $u=1$ in Theorem 2.4(i) and
then applying [S2, Theorems 4.6] we obtain the second congruence.
{\bf Remark 2.3} Let $p$ be a prime of the form $6k+5$. In [S7] the
author proved that $\sum_{k=0}^{p-1}\f{\b{2k}k^2\b{3k}k}{1458^k}\e
0\mod p$ and conjectured that
$\sum_{k=0}^{p-1}\f{\b{2k}k^2\b{3k}k}{1458^k}\e 0\mod {p^3}$.
\par\q
\newline{\bf Acknowledgment}
\par\q
\newline The author is indebted to Wadim Zudilin for his
contribution to Theorem 2.2. See comments in Section 1.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,154 |
Home News Gaming
Lawlz
Legal Battles
Macgasm TV
Apps Of The Week: Burner, Posts, Chronicle, And Olly Low Poly & The Zombie Tower
Suzy Kendrick - August 24, 2012
New Abra-Ca-Bacon Levels Added To Angry Birds Seasons
PS4 Might Not Actually Be So Kind To Used Games, Jack Tretton Clarifies
Strap on as Jetpack Joyride launches on iOS
World Of Goo Finally Gets Updated For iPhone 5
Survive Over 80 Levels And Become A Monkey Ninja
Grant Brünner - June 5, 2012
Sure, you've played a platformer before. Mario, Prince of Persia, and Sonic all have their charms, but we need a platformer for this generation...
Get Ready For A New Multiplayer Sandbox Game Called Yogventures
Grant Brünner - April 23, 2012
Sandbox games have truly taken off in popularity in the last decade. Grand Theft Auto is well loved because of the sandbox aspect of...
Ultimate Tic-Tac-Toe Makes Tic-Tac-Toe Fun Again
Andrew Kunesh - August 15, 2013
Wojciech Siudzinski, an iOS developer, has recently released Ultimate Tic-Tac-Toe into the App Store: a new take on the classic tic-tac-toe paper game. The...
Games of the Week: Icarus Proudbottom Teaches Typing, Worms 3, Dropchord,...
Michael McConnell - August 20, 2013
Last week had some good news for Apple gamers. Dots was updated with some additional content, likely pulling you back in just after you...
Junk Jack released, turns out it's awesome
Marco Fiori - November 10, 2011
Yes! Junk Jack is out. We first spied the Minecraft-esque 2D title back in July and it's been one of our most eagerly awaited...
Anki Drive For iOS Announced, The Toy Of The Future
Toby Wellington - June 10, 2013
The first big announcement Apple made in its WWDC press conference was a bit of a surprise. Apple chose to bring out the new...
Batman: Arkham Asylum to arrive October 13
Corey Tamas - September 19, 2011
Batman: Arkham Asylum, the publicly and critically acclaimed game from Feral Interactive, will be arriving on the Macintosh this coming October 13th (and no,...
Harley Quinn arrives in Batman: Arkham City Lockdown latest update
Elle Cooke - February 23, 2012
Arkham City Lockdown is probably one of my favourite games on iOS right now, and today, it just got a little better. NetherRealm added...
OnLive launches in the UK
Marco Fiori - September 26, 2011
This weekend Eurogamer Expo took place in London and one of the biggest stories was the UK launch of OnLive, the cloud based gaming...
Man Of Steel For iOS And Android Announced For Release This...
Kaylie Moise - June 7, 2013
Warner Bros. announced with a teaser trailer that it will be releasing a Man of Steel game for iOS and Android this month. Based off the... | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,033 |
The 2022 Greek Basketball Super Cup is the 3rd edition of the revived Greek professional domestic basketball super cup competition, under the auspices of the Hellenic Basketball Clubs Association (HEBA), and the 4th overall. The Greek Basketball Super Cup had been played only three times before, in 1986 under the auspices of the Hellenic Basketball Federation (E.O.K.), in 2020, and in 2021. All games were hosted in Kallithea Palais des Sports in Rhodes, Greece.
Olympiacos won the 2022 Greek Super Cup.
Format
The competition will be played in a final-four format and single elimination games, between the teams placed in the four first places of the 2021–22 Greek Basket League, which include the 2021–22 Greek Basketball Cup winner and finalist. Larisa basketball team finished fourth in the 2021–22 Greek Basket League earning the right to participate in the Super Cup final four competition, however, the club decided to forfeit the competition and Kolossos H Hotels replaced them.
Qualified Teams
The following four teams qualified for the tournament.
Bracket
References
External links
Official Hellenic Basketball Federation Site
Official Greek Basket League Site
Greek Basketball Super Cup
2022–23 in Greek basketball | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,073 |
Q: Square CSP Policy needs a quick update
Loading failed for the with source
"blob:https://connect.squareup.com/2d9347c7-e067-4ca1-9aaf-7ce2c40aec44".
frame.html:1
Content Security Policy: The page's settings blocked the loading of a
resource at
blob:https://connect.squareup.com/2d9347c7-e067-4ca1-9aaf-7ce2c40aec44
("script-src 'unsafe-inline' https://browser.sentry-cdn.com").
When will the Square developers please update their CSP policy and address other pending issues?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,881 |
{"url":"https:\/\/math.stackexchange.com\/questions\/701025\/finding-the-dimension-and-basis-of-an-orthogonal-space","text":"# Finding the dimension and basis of an orthogonal space\n\nI am trying to find the basis and dimensions of the the space orthogonal $S$ which is in $\\mathbb R^3$.\n\n$$S = \\begin{bmatrix}1\\\\2\\\\3\\end{bmatrix}$$\n\nSo the dimension would be two because it is $3 - 1$.\n\nThe problem I am having is finding the basis. Would I do\n\n$$1x+2y+3z = 0$$\n\nWhich would give me different basis. Am I on the correct track?\n\nYou just need find two independent vectors $[x~y~z]^T$ that satisfies $1x+2y+3z=0$.\nFor example, let $x_1=-3, y_1=0,z_1=1$, $\\Rightarrow [x_1~y_1~z_1]^TS=-3\\times 1+0\\times 2+3\\times 1=0$, also let $x_2=2, y_1=-1,z_1=0$, then $[x_2~y_2~z_2]^TS=2\\times 1+(-1)\\times 2+3\\times 0=0$.\nTherefore $\\begin{bmatrix}x_1\\\\y_1\\\\z_1\\end{bmatrix}=\\begin{bmatrix}-3\\\\0\\\\1\\end{bmatrix}$, and $\\begin{bmatrix}x_2\\\\y_2\\\\z_2\\end{bmatrix}=\\begin{bmatrix}2\\\\-1\\\\0\\end{bmatrix}$ are such two vectors, because they are also independent:\nif $\\alpha\\begin{bmatrix}-3\\\\0\\\\1\\end{bmatrix}+\\beta\\begin{bmatrix}2\\\\-1\\\\0\\end{bmatrix}=0$, then $\\begin{bmatrix}-3\\alpha\\\\0\\\\\\alpha\\end{bmatrix}+\\begin{bmatrix}2\\beta\\\\-\\beta\\\\0\\end{bmatrix}=0$ , $$\\Rightarrow \\begin{bmatrix}-3\\alpha+2\\beta\\\\-\\beta\\\\\\alpha\\end{bmatrix}=0$$, which implies $\\alpha=\\beta=0$\nWell, the equation $1x+2y+3z=0$ indeed says that the inner product of vectors $S$ and $(x,y,z)^T$ is $0$, that is, they are orthogonal.\nSo we are looking for a basis among its solutions: e.g. you can take $y=1,\\ z=0$ then $y=0,\\ z=1$ and calculate the $x$'s for them.","date":"2022-10-06 10:41:49","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\": 0.9950495362281799, \"perplexity\": 112.66077816156141}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-40\/segments\/1664030337803.86\/warc\/CC-MAIN-20221006092601-20221006122601-00595.warc.gz\"}"} | null | null |
[](https://travis-ci.org/MiCHiLU/gae-tap)
[](https://app.wercker.com/project/bykey/72878e11dca6d30f174e95253d766075)
[](https://landscape.io/github/MiCHiLU/gae-tap/master)
# A full stack framework for the Google App Engine -based
Let's finish the work quickly and go TAP BEER!
Looking for sponsors:
1. [$120 - I get 30L barrel beer!](https://www.gittip.com/MiCHiLU/)
2. [ $60 - I get 15L barrel beer! ](https://www.gittip.com/MiCHiLU/)
3. [ $12 - I get a 1-pint beer! ](https://www.gittip.com/MiCHiLU/)
4. [ $6 - I get 1/2 pint beer! ](https://www.gittip.com/MiCHiLU/)
## Status
* [Travis CI](https://travis-ci.org/MiCHiLU/gae-tap)
* [Wercker CI](https://app.wercker.com/project/bykey/72878e11dca6d30f174e95253d766075)
* [Code Health](https://landscape.io/github/MiCHiLU/gae-tap/master)
## Features
Supports:
* [Google App Engine / Python 2.7](https://cloud.google.com/appengine/docs/python/)
* [Google Cloud Endpoints API](https://cloud.google.com/appengine/docs/python/endpoints/)
* [NDB Asynchronous Operation](https://cloud.google.com/appengine/docs/python/ndb/async)
* [Python NDB Datastore API](https://cloud.google.com/appengine/docs/python/ndb/)
* [Python Module Configuration](https://cloud.google.com/appengine/docs/python/tools/appengineconfig)
* [Google Analytics for feature phone](https://github.com/MiCHiLU/Google-Analytics-for-Mobile--Google-App-Engine)
* I18N / Python, HTML and JavaScript / [babel](http://babel.pocoo.org/)
* Japanese han-kaku characters / 半角 / [zenhan-py](https://github.com/MiCHiLU/zenhan-py)
* OAuth login / [gae-simpleauth](https://github.com/MiCHiLU/simpleauth)
* [Google OAuth 2.0](https://developers.google.com/accounts/docs/OAuth2) authentication-based Users API (alternate of [Google App Engine Users API](https://cloud.google.com/appengine/docs/python/users/))
* generating sitemaps
* [sessions](https://webapp-improved.appspot.com/api/webapp2_extras/sessions.html)
* Google Cloud Endpoints API as a CRUD, avoid method naming conflict in implemented with multiple classes
* [Endpoints Proto Datastore API](https://github.com/GoogleCloudPlatform/endpoints-proto-datastore)
Low cost operating:
* Google Drive Spreadsheets as a database via Google Visualization API
* Google Drive Form-based feedback system
* hosting as a proxy
* DropBox
* Google Drive
* hostname-based multitenancy
* supports robots.txt
* just a few costs permanent caching and key-value store via taskqueue API
* minimum OAuth accounting
* redirecting to Google URL Shortener
Performance:
* pre-compiling jinja2 templates to Python byte code / [jinja2precompiler](https://github.com/MiCHiLU/jinja2-precompiler)
* [uglify-js](https://github.com/mishoo/UglifyJS)
Coding:
* [CoffeeScript](http://coffeescript.org/)
* [HAML](http://haml.info/)
* [SASS](http://sass-lang.com/) / [compass](http://compass-style.org/)
Development:
* [AngularJS](https://angularjs.org/)
* [Appstats](https://cloud.google.com/appengine/docs/python/tools/appstats)
* [Jinja2 2.6](http://jinja.pocoo.org/docs/dev/)
* [Twitter bootstrap](http://getbootstrap.com/)
* [webapp2](https://cloud.google.com/appengine/docs/python/tools/webapp2)
* [file system event-based automation building on Mac OS X 10.7+](https://pypi.python.org/pypi/watchlion)
* [Docker](https://www.docker.com/)
Testing:
* [py.test](http://pytest.org/)
* coverage of tests / [pytest-cov](https://pypi.python.org/pypi/pytest-cov)
* [karma](http://karma-runner.github.io/)
Utils:
* CORS
* CSRF guard
* HMAC
* e-mail reports of errors
* fanstatic
* handling taskqueue
* managing cache records
* memoize
* ring buffer
* token bucket
Continuous Integration Supports:
* [Travis CI](https://travis-ci.org/)
* [Wercker CI](http://wercker.com/)
## Set up
$ git clone --depth 1 https://github.com/MiCHiLU/gae-tap.git
$ cd gae-tap
$ bundle install
$ npm install
$ mkvirtualenv --python=`which python2.7` gae-tap
(gae-tap)$ pip install -r requirements.txt
(gae-tap)$ pip install -r requirements-gae.txt
## Set environ
It need the `GOOGLE_APPENGINE` environ args. Default `GOOGLE_APPENGINE` as below:
GOOGLE_APPENGINE=$HOME/google-cloud-sdk/platform/google_appengine
If you want to set another path, define `GOOGLE_APPENGINE` in environ as below:
$ GOOGLE_APPENGINE=<path to your gae> make
## Docker
Alternatively, Quickly set up environment via Docker:
$ docker pull michilu/gae-tap
## First-time build
First, you must have been build core library:
(gae-tap)$ (cd gae/tap && make release)
Then, if you want to add templates of gae-tap to git repository:
$ git add \
gae/site-packages/tap_templates_compiled.zip \
gae/tap/static/js/admin_response_cache.js \
gae/tap/static/js/admin_response_cache.min.js \
gae/tap/static/js/error_page.js \
gae/tap/static/js/error_page.min.js \
gae/tap/static/js/utils.js \
gae/tap/static/js/utils.min.js
Alternatively, update the core library from releases:
1. Download `gaetap-<release-number>.zip` file from https://github.com/MiCHiLU/gae-tap/releases
2. Then replace with files and directories in your repository.
If you want to start a new project with `make scaffold`, as below:
$ make scaffold
your project name, default 'gae-tap': <type your project name>
your github user name, default 'MiCHiLU': <type your github user name>
your app-id, default 'gae-tap': <type your app-id>
## Build and Test
(gae-tap)$ make
## Run development server
(gae-tap)$ make runserver
then access to:
* admin server: [http://localhost:8000](http://localhost:8000)
* instance server: [http://localhost:8080](http://localhost:8080)
* API Explorer: [http://localhost:8080/_ah/api/explorer](http://localhost:8080/_ah/api/explorer)
## iPython shell with the Google App Engine environment
First, you must be install iPython:
(gae-tap)$ pip install ipython
Then, type `make shell` command as below:
(gae-tap)$ make shell
Python 2.7.5 (default, Mar 9 2014, 22:15:05)
IPython 2.3.1 -- An enhanced Interactive Python.
Doctest mode is: ON
>>>
Access to the Datastore on the development environment in the iPython shell:
(gae-tap)$ make shell
>>> from google.appengine.ext import testbed
>>> tb = testbed.Testbed()
>>> tb.setup_env(app_id='dev~your-app-id')
>>> tb.activate()
>>> tb.init_datastore_v3_stub(datastore_file='../assets/tmp/datastore.db', use_sqlite=True)
>>> tb.init_memcache_stub()
>>> tb.init_taskqueue_stub()
>>> from your-app import model
## Deploy
(gae-tap)$ make deploy
Auto deploy via Wercker CI:
If you want to auto-deploy to the Google App Engine, add an `APP_ENGINE_TOKEN` variable to `Deploy pipeline` of `Deploy targets` in your `App` on the Wercker CI.
The `APP_ENGINE_TOKEN` value is a `refresh_token` of your `$HOME/.appcfg_oauth2_tokens`, like follow:
$ jq .refresh_token ~/.appcfg_oauth2_tokens
"1/ABCDEFGHIJKLMNOPQRSTUVWXYZ_1234567890"
then access to:
* Server: [https://<app-id>.appspot.com/](https://<app-id>.appspot.com/)
* API Explorer: [https://<app-id>.appspot.com/_ah/api/explorer](https://<app-id>.appspot.com/_ah/api/explorer)
* Developers Console: [https://console.developers.google.com/project/<app-id>](https://console.developers.google.com/project/<app-id>)
## Dependencies
* Python 2.7
* [pip 6.x](https://pypi.python.org/pypi/pip/6.1.1)
* Google App Engine
* [Django 1.5.x](https://pypi.python.org/pypi/Django)
* [Third-party Libraries in Python 2.7](https://cloud.google.com/appengine/docs/python/tools/libraries27) on Google App Engine
* [libxml2](http://www.xmlsoft.org/)
* [libxslt](http://xmlsoft.org/XSLT/)
* [lxml](http://www.xmlsoft.org/)
* GNU Make
* [How to install Xcode Command Line Tools](http://railsapps.github.io/xcode-command-line-tools.html)
* [Bundler](http://bundler.io/)
* [Node.js](https://nodejs.org/)
### Optionals
* [virtualenvwrapper](https://pypi.python.org/pypi/virtualenvwrapper)
## Known issues
* The `gcloud app Python Extensions component on the Google Cloud SDK does not include the Django package.
You can run a script:
$ ./assets/fetch_django-1.5.x.sh
* [content-length header of the error status response that generated by endpoints is wrong](https://code.google.com/p/googleappengine/issues/detail?id=10544)
You can patching to Google App Engine SDK:
$ patch -d $GOOGLE_APPENGINE -p0 -i $PWD/gae/tap/endpoints.patch
### on GAE <1.9.27
* [Google Cloud SDK - GAE 1.9.18 produces docker error](https://code.google.com/p/google-cloud-sdk/issues/detail?id=125)
You can patching to Google App Engine SDK:
$ patch -d $GOOGLE_APPENGINE -p0 -i $PWD/gae/tap/docker.patch
## LICENSE
Licensed under the terms of the MIT.
Copyright (c) 2013 ENDOH takanao
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,601 |
Q: bash call variable built in loop some variables are built but I don't know how to call them.
I tried:
echo "$r$z"
echo $($r$z)
echo "$($r$z)"
or
echo "$r$i"
echo $($r$i)
echo "$($r$i)"
here is the way I build the variables:
z=0;for i in {1..3};do y=$(( RANDOM % 10 ));r[z++]=$y;done
or
for i in {1..3};do eval "r$i=$(( RANDOM % 10 ))";done
the expected result should be:
r1r2r3
A: It might be better to store them in an array instead of creating r1, r2 and r3 variables. That's because, afaik, there's not really an way to create variables from other variables.
$ r=(0);
$ z=0;
$ for i in {1..3}; do
(( y = RANDOM % 10 ));
r+=($y);
done
$ for i in ${r[@]}; do echo $i; done
This produces an array with three integers, in my case:
8
1
9
A: The best is design to use arrays instead of handcooked variable names, hence Bayou's answer is what you're looking for.
Now, the way to expand variables the name of which is in another variable, exists in Bash (without using eval) and is called indirect expansion. You'll find some information about this in the Shell Parameter Expansion section of the reference manual.
In your case it will look like this:
for i in {1..3}; do
# You need to create an auxiliary variable with the name of the variable to expand
varname=r$i
# Then use the indirect expansion (it's prefixed with an exclamation mark)
echo "${!varname}"
done
This is considered poor practice and should be avoided whenever possible: the better design is to use arrays.
Just another comment about the way of creating variables without using eval is to use declare or printf. Here's how it goes with printf:
for i in {1..3}; do
printf -v "r$i" "%d" "$((RANDOM % 10))"
done
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,790 |
Dear Reader,
The book you are holding came about in a rather different way to most others. It was funded directly by readers through a new website: Unbound.
Unbound is the creation of three writers. We started the company because we believed there had to be a better deal for both writers and readers. On the Unbound website, authors share the ideas for the books they want to write directly with readers. If enough of you support the book by pledging for it in advance, we produce a beautifully bound special subscribers' edition and distribute a regular edition and e-book wherever books are sold, in shops and online.
This new way of publishing is actually a very old idea (Samuel Johnson funded his dictionary this way). We're just using the internet to build each writer a network of patrons. Here, at the back of this book, you'll find the names of all the people who made it happen.
Publishing in this way means readers are no longer just passive consumers of the books they buy, and authors are free to write the books they really want. They get a much fairer return too – half the profits their books generate, rather than a tiny percentage of the cover price.
If you're not yet a subscriber, we hope that you'll want to join our publishing revolution and have your name listed in one of our books in the future. To get you started, here is a £5 discount on your first pledge. Just visit unbound.com, make your pledge and type `TERRIBLE` in the promo code box when you check out.
Thank you for your support,
Dan, Justin and John
Founders, Unbound
# Contents
1. Superfriends List
2. Introduction
3. Alien Raiders
4. Alien Sidestep
5. Battle Probe
6. Interview: Alan Boiston
7. Bionic Granny
8. Car Race
9. Count Duckula 2
10. Interview: Jeff Minter
11. Crazy Kong
12. Dangerous Streets
13. Graffiti Man
14. Interview: Mentski
15. Button Press 3000
16. Highlander
17. Hunter
18. Interview: Paul Rose AKA Mr Biffo
19. Killer Caverns
20. Killjoy
21. Licence to Kill
22. The State of the Industry
23. Los Angeles SWAT
24. Show-Jump
25. Surprise Surprise
26. Interview: Steve Benway
27. SQIJ
28. Trench
29. Interview: Violet Berlin
30. ULTRA SUPER REFUND ADVENTURE TURBO REVIVAL CHAMPIONSHIP EDITION EX PLUS ALPHA
31. Acknowledgements
32. Index
33. Supporters
# Hello!
I'm Stuart, AKA Ashens. I make videos for YouTube, write comedy scripts and sometimes act in things.
I recently realised that I miss writing articles and stories, so have joined forces with Unbound in an attempt to rectify that by writing books. I live in Norwich, in a house filled with all sorts of useless items that I tell myself I need for my work. I'm obsessed with old video games and things that aren't quite good enough for their intended purpose.
My favourite soup is crab meat and sweetcorn.
@ashens
youtube.com/ashens
questforthegamechild.com
# Superfriends List
Listed here are the Superfriends – people who pledged a substantial amount of money to help ensure that this book became a reality. May their game cassettes never demagnetise.
Leo Baggerreft
Michael Barrett
Alan Boyd
Michael Brown
Dua9in Cameron
Gregor Cameron
Christopher Cobb
Chloe Cresswell
Thomas Edge
Matthew Faulkner
Brent Friedrich
Sam Glennie
Alex "Peggy" Grant
Richard "dragonridley" Hatton
Ian Hopkins
Daniel Fink Jensen
Trent Johnson
Joshua Kahn
Joseph Kawa
Lucas Kmiecik
Kymo Misenica Kobayashi
Ephraim Leadon
Marko Mannonen
Matthew Mitchell
Tanja "Tikal" Pattberg
Jeroen Richters
Dominic Rossetto-White
Aidan Rothnie
Nathan Schlosser
Aaron Scott
Mike Sleeman
Sam Thompson
Mark Tolladay
Tommy Törnqvist :)
Justin Trueland
Adam Unwin
Sean Zoltek
# INTRODUCTION
BY STUART ASHEN
Hello! And welcome to Terrible Old Games You've Probably Never Heard Of, a compendium of some of the most obscure and appalling titles spewed out by the video games industry.
This isn't a guide to the very worst – it's a showcase for games that I personally found intriguing as well as mind-bleedingly awful. I've included a variety of game types and release formats, and largely ignored the prices to find objectively awful games. And most importantly, you won't find the usual suspects like E.T. for the Atari 2600 and Superman for the Nintendo 64 as they're already covered extensively on many different websites and YouTube videos.
For inclusion in this book, a game must have been:
• Released some time between 1980–1995 inclusive
• Sold commercially
• Released for a home computer format, not a games console*
• So utterly terrible that it would be almost impossible for a reasonable person to enjoy playing the game.
A lot of games we played thirty years ago seem crap now, but Terrible Old Games You've Probably Never Heard Of is about the ones that were crap then.
I've also asked some knowledgeable and interesting people what the most disappointing game they ever bought was. Those won't necessarily be terrible games, but they will have made people angry which is as equally entertaining. I even allowed mention of a Nintendo game as it provides a great point about what gaming was like before the Internet.
Giant heaps full of thanks go to the people who pledged to get this book published via Unbound. Now the games mentioned inside will finally receive the recognition and derision they deserve – because they're terrible, they're old, and you probably haven't heard of them.
Stuart Ashen
Norwich, 2015
*For the purposes of this book I've counted the Commodore Amiga CD32 as a computer, because it's essentially an Amiga 1200 with the keyboard chopped off and a CD drive stuck on. So there.
# Alien Raiders
Format: Commodore VIC-20
Year of Release: Approx. 1983
Developer: Harteveld Software
Publisher: Micro-Spec Ltd
Original Price: Unknown
There's confusion with this game before it even starts. The title screen calls the game Alien Raiders, but the next screen calls it Alien Invaders – a name also shown at the top of the screen during the game! For the purposes of this book, I'm going with Alien Raiders as that's what was written on the cartridge, but either name is valid I suppose. If only video games had birth certificates.
The first thing Alien Raiders does is assault you with four seconds of random beeping, which is never a nice thing to experience. It then tells you the controls for left, right and fire, and away you go into possibly the most worthless single-screen shoot 'em up ever made.
You control a classic Space Invaders-style ship that sits on a black line. Four green alien ships jerk down the screen extremely slowly. Occasionally two aliens will start in the same place, which leads to one of them disappearing and there only being three on screen for the rest of the game. They move straight down, one at a time from left to right, then sit still for a second before the movement wave starts again. Your ship moves much faster and can shoot straight up, with a single bullet on screen at any time. When you shoot an enemy ship it turns into a black waffle that blocks your shots until the next time the aliens move, although sometimes they remain on screen until an alien moves over them. When an alien is shot, it's replaced with another from the top of the screen.
Soundwise, Alien Raiders makes only two noises after the initial random beeping. There's a warble when you shoot and a sound like spit hitting a tom-tom drum when an alien is hit.
The fun never starts in Alien Raiders! Or Alien Invaders, for that matter.
The game is written in BASIC, and both the aliens and your ship only move along the 8x8 character blocks of the VIC's standard screen mode. The result is there are only 20 horizontal positions the aliens can be in, and your ship is restricted to the same columns they travel down. A combination of this restriction, the aliens' inability to move sideways, and the speed of your ship means Alien Raiders is painfully easy. It's a very simple task to line yourself up under the extraterrestrial idiots, and you have absolutely ages to do it. If one of the invading raiders reaches the bottom of the screen, it's instantly game over, but that's not going to happen unless you deliberately allow it.
This leads us into the game's strangest design choice. When you shoot an alien, you receive 10 points. When you accumulate 100 points, you win and the game immediately ends. So all you have to do is shoot ten aliens, which takes approximately 36 seconds. It's so easy that I managed to easily complete three versions of the game at once by simultaneously running multiple VIC-20 emulators.
The inevitable outcome of playing Alien Raiders. The correct answer is "NO".
The only chance of losing without it being on purpose is if you encounter a bug that makes the aliens invisible when you shoot them – they sometimes become impossible to shoot and will just progress down the screen unless you can get the score to 100 first. Otherwise, you effectively have to choose to lose. Also, when the game ends, it asks if you want to play again with a Y/N prompt – but entering Y ends the program; you have to enter the whole word YES. Not that anyone would likely want to play the game more than once, but it's annoying anyway.
Alien Raiders is an absolute swindle. It's 36 seconds of utterly tedious gameplay for what was almost certainly a premium price, as it was released on an expensive cartridge rather than a cassette tape.
You won't see this message unless you really want to or if you're the victim of an annoying bug.
The game is also a bit of an enigma. It consists of only 88 lines of BASIC code. Was it designed as a game for toddlers? Was it a magazine type-in that somehow got released commercially? And who was the publisher Micro-Spec? There's no record of them releasing anything other than this game.
A look at the source code reveals an extra final line numbered 65000 that says "Harteveld Software" surrounded with asterisks. Harteveld were a Dutch developer who released the puzzle games Kolom Raden (Guess the Column) and Memory – both simple BASIC games and both of which have the same line 65000 in them. It therefore seems likely they made a game called Alien Invaders that they never released themselves, but that for some reason Micro-Spec published as Alien Raiders. What is the story behind the whole affair? We may never know... or care.
All of the alien types. I call them Harold, Susan, Engelbert, Boffo and Revenge of Boffo.
REVIEW SCORES
None known.
other versions
None. Just play any version of Space Invaders on any machine and you'll almost certainly have more fun.
# Alien Sidestep
Format: Commodore 64
Year of Release: 1983
Developer: Unknown. VIC-20 version
by Kerry Enderson
Publisher: Mr Computer Products
Original Price: Approx. 7 pounds
Space Invaders was a worldwide phenomenon, but five years after release it was getting a little stale. The time had come to put a new spin on a classic. And who better to do that than Mr Computer Products? The answer, tragically, is anybody.
It's been said that the key to a good game is choice. Some games offer multiple ways to beat a challenge, but even the simplest examples need you to make the right choice at the right time to win. Do you move left or right? Do you fire one last time or retreat to the side? Or do you play Alien Sidestep, which effectively eliminates player choice and therefore any potential fun?
This is Strategy Alpha. During Level 2. You will probably be asleep by this point.
Rows of aliens appear on the screen from the top left. They move horizontally to the right, at which point they reappear at the left further down. If they reach the bottom of the screen, then it is officially a bad thing, because the game ends if it happens three times. Nothing revolutionary so far.
BUT! The aliens have mastered the dark art of the sidestep, a bit like the drivers in the fourth The Fast and the Furious movie. This means that when they are about to be hit by a bullet, they stop moving so it passes harmlessly to their right, which presents a massive problem. The bullets fired from your crude blue rocket crawl painfully slowly up the screen and you can only have 16 on the screen at once. This means the usual tactic of aiming at where the aliens will be is useless, as they just stop moving before they're hit.
This is Strategy Omega. And also the least impressive firework display in history.
In fact, to actually progress in Alien Sidestep, there are only two effective battle plans. I shall refer to them as Strategy Alpha and Strategy Omega, and both rely on shooting a bullet directly to the left of the previous bullet.
Strategy Alpha:
1. Move from the left of the screen to the right, hammering the fire button so there isn't a gap in your bullets for the aliens to slip through.
2. Move your ship back to the left as your bullets crawl up the screen.
3. Repeat steps 1 and 2 forever.
Strategy Omega:
1. Move your ship slightly to the left,
then slightly to the right, firing constantly.
2. Repeat step 1 forever.
And that's it! Any divergence from either strategy will result in not shooting anything, and ultimately game over. And Strategy Alpha is far more effective than Strategy Omega, so you can't even mix it up by swapping between them without risking failure. There is no room for deviation, improvisation or fun.
These are all the enemy types. They are worth 10, 20 and 30 points respectively, and they are all suspiciously familiar.
The depressingly repetitive gameplay is further reinforced by a total lack of variety in the game's levels. Shoot enough of the Space Invader rip-off aliens on level 1 and you will get to shoot identically-acting aliens that look slightly different on levels 2 and 3. And if you complete level 3, then the words "POINTS DOUBLE" appear on screen and the charge fanfare that Scrappy-Doo loved so much plays. Then everything starts all over again. And because it never gets more difficult, it's pretty much impossible to lose if you follow Strategy Alpha. You could actually play Alien Sidestep forever – the only real obstacle is maintaining interest through the mind-crushing tedium.
There is only one unpredictable feature in the entire game – sometimes, if you hit an alien (usually on the top row) you get 50 points and the little "you've picked up an item or jumped a barrel!" tune from Donkey Kong plays. It seems to happen at random and is not even 0.001% enough to save the game from being a boring, monotonous chore.
This is the actual game label. Notice the inexplicable wavy quiff encroaching bottom centre.
Alien Sidestep was released by Mr Computer Products (also known as O.E.M. Inc.), who may well rank as one of the worst game publishers in history. They released about eight games, all in 1983, and they're all rubbish at best. Alien Sidestep wasn't even their worst effort – that accolade goes to Close Encounters of the Worst Kind, an astonishingly honest title for a game that is simply a shrieking, pulsating mess of sprites that seems specifically designed to induce a headache.
The much nicer VIC-20 version. Still no fun to play, though.
REVIEW SCORES
None known.
other versions
Commodore VIC-20: All of Mr Computer Products' games were also available on the VIC-20, with the possible exception of their dire Donkey Kong rip-off Mario's Brewery. In fact, their C64 titles seem to be bad ports of the VIC-20 originals! Despite the C64 being a much more powerful machine, its version of Alien Sidestep is slower, jerkier and has annoying sprite flickering. The VIC-20 version has a lower resolution but is otherwise superior in every way.
# Battle Probe
Format: Atari ST
Year of Release: 1988
Developer: Capital Software Designs Ltd
Publisher: Crysys
Original Price: 14.99 pounds
And so Human Kind went out of Earth and, like locust, spread and devoured the Galaxy. The Earth was contaminated but out of the contamination there evolved a new life form which regenerated the land, sea and air until once again greedy Human Kind attempted to return.
That's the text from the back of Battle Probe's disk case. The usual idea for a case is to write an exciting description of the game to entice browsers to buy it. But publisher Crysys decided to provide what seems to be a Russian poem automatically translated into English by faulty software. I don't know if it helped sales, but I suspect not.
That's a very unconvincing star field. The skulls are quite good though.
A simple, vertically-scrolling shoot 'em up, Battle Probe has you controlling a spaceship, flying over space stations of some kind as enemy ships attack you. The only slight deviation from the basic template is that your ship has an ever- diminishing fuel supply you need to replenish, although it never came close to running out when I was playing.
Battle Probe is an amazingly orange game. The status area is orange. Your ship is orange. Most enemies are orange. The backgrounds are orange. Your bullets are orange. Even the stars are orange. This game is more orange than a clownfish addicted to fake tanning lotion.
This emplacement exists to shoot eight eyes into space simultaneously. Warfare in the future is weird.
The graphics themselves are generally well defined, but it can be hard to discern what's going on as so many things are the same colour. There are also a lot of eyes featured. Some enemy ships are eyes, gun turrets spew eyes at you, and different coloured eyes in the backgrounds confer extra lives, fuel and bonus points. If I had to create a single image to sum up this game, it would be an orange eye.
When I first loaded Battle Probe, I was impressed with how smooth the scrolling and the ship's movements were. My positive impressions ended there, sadly.
The player's ship narrowly avoids a space satsuma as two eyeball enemies pass over the game's border, possibly in an attempt to escape into the real world.
As soon as a few enemies appear on screen, the whole game slows to a crawl. Your ship moves so slowly anyway that it's almost impossible to dodge things fired at you. The collision detection – one of the most important parts of a shoot 'em up – is absolutely atrocious, with bullets frequently passing through your ship. Sometimes after losing a life, you restart on a bullet or background obstacle and die again immediately. It's difficult to tell which background objects can be passed over and which will kill you. All the enemy ships have identical attack patterns, appearing in threes and waving left and right. The upshot is that Battle Probe is no fun to play whatsoever.
A row of bonus eyeballs. They trigger the spoken phrases "Another ship!", "Bonus!" and "Gas-o-line!"
Interestingly for the time, the sound consists entirely of sampled audio. The title screen constantly plays a scratchy three second music loop which grates on the nerves after a few plays. The vast majority of the game is silent, punctuated by an explosion effect when an enemy is killed or your ship is destroyed. There are also three different snippets of speech reserved for when you pick up items, although they're almost unintelligible – more due to their odd intonation than the low sample quality.
Battle Probe is a depressingly fun-free experience. The whole package feels painfully cheap, especially considering the substantial £15 asking price. There isn't even a game over message – it just cuts abruptly back to the title screen and the three second music loop.
The box art isn't particularly noteworthy; I just wanted to use a picture that isn't mostly orange.
The developers, Capital Software, produced only Battle Probe before forming a new company called New Dimensions. They then made two very weak games before finding their strength in application software – they went on to re-lease the immensely successful Technosound Turbo audio sampler for the Amiga, which dance group The Prodigy used in their early work.
Publisher Crysys only released Battle Probe and three dull sports management games that all used the same game engine. By 1989 they'd disappeared, which was probably for the best.
REVIEW SCORES
The only magazine to review Battle Probe was ST Action, who awarded it a generous 25%.
other versions
None. Possibly no other computers could handle so much orange on screen at once.
# THE MOST DISAPPOINTING GAME I EVER BOUGHT
by Alan Boiston, racing game journalist and YouTuber
SDI: Strategic Defense Initiative
Format: Amstrad CPC
Year of Release: 1989
Developer: Source Software Ltd
Publisher: Activision
Original Price: 9.99 pounds
Back in the '80s, pocket money was very limited – a few pence a week besides a couple of 10p pieces for the arcade. This encouraged me to play as well as possible to extend those arcade experiences, but that short session was never enough and I always wanted to play those games at home. After weeks or even months of saving, I would eventually be able to buy a new game, usually at Woolworths or WHSmith. On one occasion I was lucky to be taken to Hamleys toy shop in London. On the top floor they featured an amazing selection of all of the latest computer games, and it was there that I saw SDI: Strategic Defense Initiative for the Amstrad for the first time. Wow, the excitement! The box art and screenshots looked amazing. OK, they were screen shots from various formats, but surely the Amstrad version couldn't look too bad? I spent my hard-earned savings and couldn't wait to get home and indulge in hours of Star Wars Defense System action!
I waited for the 20 minutes loading time with building excitement. The loading screen wasn't all that impressive: as the lines came across and built the picture piece by piece, it looked limited colourwise. But no fear, I knew the game was going to be amazing. As I played my first game, however, the shock of disappointment washed over me. No in-game music, poor audio and only a single blue colour used in the entire game. And to top it off, it played super slowly with a terrible frame rate. Everything that I loved about the arcade was gone. Instead it felt like an empty shell.
It was horrible. I'd spent all of my pocket money and was left with a game that wasn't worth playing. If you grew up and played computer games in the '80s, "screenshots from various formats" is a phrase you'll be familiar with. They usually displayed the arcade, Amiga and Atari ST versions on the back. But every now and again they would feature shots from at least the Commodore 64 or Amstrad CPC versions. I felt like I had been completely misled, as it was effectively a conversion of the ZX Spectrum release and not the arcade at all.
I was determined not to be fooled again. From that point forward I was more selective, and if I didn't like a game or if it wasn't as represented on the back of the box, then I would take it back. I also stopped buying a lot of budget software and instead focused on the bigger names even if it meant taking longer to save. With that approach I eventually saved enough to buy Domark's Star Wars Trilogy box set – now that was awesome!
Alan can be found on Twitter at
@VVVGamer
FACT!
Amstrad Action magazine really liked SDI, awarding it 82%. Even though it plays like a particularly dull dog. The 49% given by Amstrad Computer User makes more sense.
# Bionic Granny
Format: Commodore 64
Year of Release: 1984
Developer: Unknown
Publisher: Mastertronic
Original Price: 1.99 pounds
For years I thought that this game was made to cash in on the popularity of Super Gran, a TV series about an elderly Scottish lady who receives super powers. However, it actually predates the show! It seems that unnaturally beefed-up grandmothers were just a popular idea in the mid-eighties.
The cassette inlay describes the titular Granny as lurking outside a school at home time, trying to "zap" children with her laser-powered umbrella. It describes the aim of the game as "Run for your life before she gets you too!" which is nonsense since you actually play as her. It's not a good sign when the people writing the game's description don't know anything about it.
Terrifying skull-faced goons hang out near the school as Bionic Granny goes for the frog-headed child on the right.
More pertinent instructions are given on the game's title screen, but it is so full of grammatical and typographical errors that it would make a middle school English teacher faint. But the aim is clear: you are Bionic Granny, and you must assault as many children as possible. They never say how Granny came to have parts of her body replaced with cybernetic equivalents or why she is compelled to physically injure kids. That's a shame as I'm sure it would be a fascinating and tragic story. I'll have to wait for a novelisation.
On starting the game, you're presented with a road system leading into a school at the top of the screen. A giant clock floating in the air shows the time as four o'clock. Then, children run out of the school and down the screen. Either the scale or perspective is insane – the entire school building is the same width as the road, and the children leaving the school are as big as a quarter of a football pitch.
Granny appears to be firing a rifle in the air, but she is actually just waving a stick.
Bionic Granny herself is stuck at the bottom of the screen, only capable of moving left and right. She has two frames of animation and no leg movement, so she appears to glide around on roller skates. She constantly waves a wooden stick in the air, presumably having lost her laser-powered brolly.
So you can only move left and right, trying to crash into the school kids as they attempt to run off the bottom of the screen. If any touch you, they instantly disappear and points are earned.
Oddly, a giant red face appears when Granny dies. Perhaps it's her soul escaping in the form of a demonic terminator skull.
But you do not stand unopposed in your quest to violently assail innocent youngsters who cannot fight back. The lollipop lady, who has sworn to use her crossing guard powers to stop Bionic Granny, frantically runs around the screen firing stop signs from her infinite supply. This may be possible due to magical powers or futuristic technology – she appears to be the offspring of Skeletor and one of the aliens from Close Encounters of the Third Kind, so she probably has access to both.
And... that's it. You just slide around horizontally, trying to avoid the lollipop lady's projectiles and smack as many kids as possible into oblivion. Not only is it mind-meltingly dull, it is also annoying – the stop signs launched by the lollipop lady move at a terrifying speed and are almost impossible to dodge if you're directly under them. Eventually, your score gets near 5,000 and the supply of kids dries up, leaving only one that runs down the right-hand side of the screen. Breach the 5,000 point barrier and you reach level 2 – which is exactly the same as level 1. The fun never starts with Bionic Granny!
The game's cast: Bionic Granny, lollipop lady, school girl, school boy, school girl 2, school boy 2. Wonderful.
The sound consists of two audio annoyances: a jolly, twinkly tune that plays constantly in the background and an odd noise like a rubber band being pinged against a damp towel that pipes up when you injure a child. Earplugs are recommended.
Bionic Granny is utter, utter tosh. Even for the budget price of £1.99 (about £6 today, taking into account inflation), there's no excuse for such half-baked nonsense. Well, I say half-baked, but frankly this game isn't even one-fifth-baked. It's become infamous in the Commodore 64 community, to the extent that it spawned an enhanced – and differently spelled – remake in 2010 called Bionik Granny Returns.
The game's cover art has a truly terrifying face in the background, like a mummified John Lennon.
The publisher Mastertronic was incredibly prolific, releasing well over 100 games for the Commodore 64. But the actual developers of Bionic Granny remain uncredited and unknown. It's possible, however, that it was written by brothers David and Richard Darling. Bionic Granny was put together using Mirrorsoft's "The Games Creator", an easy-to-use construction kit that required no programming experience but imposed heavy limitations on any game made with it. The Darlings themselves actually made "The Games Creator", and they used it to produce several substandard games for Mastertronic such as BMX Racers and Mind Control. The text on their title screens often included grammatical errors, too. But they went on to found the very successful company Codemasters that still publishes hit games to this day, so even if they did make Bionic Granny, I think we can all collectively forgive them.
REVIEW SCORES
Commodore User magazine's weird scoring system gave Bionic Granny 6 points out of a potential 20, which is at least 4 too many.
other versions
Some online sources mention an Amstrad CPC version – I am very pleased to announce that it doesn't seem to exist. Nice to end on a positive note. Continuing the genre of overpowered pensioners, TV's Super Gran had its own rubbish game released in 1985.
# Car Race
Format: MSX1
Year of Release: 1983
Developer: Ample Software / Panasonic
Publisher: Ample Software
Original Price: approx. 13 pounds
No messing about with the title here – you know exactly what you're getting. It's like calling the latest FIFA game "Ball Kick" or calling Bioshock "Weirdo Shoot". Except it isn't really a race at all, meaning half of the title is actually inaccurate.
Clearly inspired by the arcade game Bump 'n' Jump, Car Race (or Car-Race as it appears in the game) actually involves driving at a high speed down an infinitely long, entirely straight road until you run out of fuel. It's a bit like a nightmare induced by driving on a German autobahn for too long.
Red car goes up, black car goes down. That's the way Car Race goes.
First impressions are that it's a fairly basic affair. The title screen is entirely text-based, and a jolly but repetitive tune plays in the background. Sadly things do not become more sophisticated when you play the game.
The graphics are about as primitive as they can be before you can't tell what they are. The road you race down is entirely blank, and at the sides there is a continual loop of infinite dogs, trees, huts and bicycles. It feels like the game was written in a weekend. Worst of all is the audio, which is a constant, horrible whining sound that's presumably supposed to represent your engine noise. After a few seconds, it feels like there are drugged bees trapped in both your ears.
A road that stretches on forever through an infinitely repeating suburb. This is purgatory.
Your first game of Car Race will inevitably proceed as follows:
You press the space bar to start.
You take in what's on the screen – your car is at the bottom and a straight road leads upwards. A black car is swerving towards you.
You hold down space to accelerate.
The "Game Over" screen appears within five seconds of starting.
You are extremely confused.
The reason for the game ending is that you've run out of fuel, despite your score telling you that you've only travelled about 80 metres. This is because the way Car Race deals with fuel is utterly bonkers – you burn more petrol the slower you go. At the minimum speed your car starts at, the entire tank empties in about 3.5 seconds. The instant the game starts, you have to hold down the space bar and never release it – and even then your 1,000 units of fuel will have reduced to about 350 by the time you get up to speed!
When you crash, the top half of an angel flies off up the road. Although it could be an alien chasing an inner tube.
So, you've worked out how to actually play the game for more than a few seconds and discovered just how barebones it is. Then, black cars appear at the top of the screen, weaving down towards you. There is always exactly one of these cars on the screen at all times. Your car moves left and right quite slowly, and the enemy vehicles are a lot faster – some of them swerve all over the screen at an insane speed, making them effectively impossible to avoid. Collision with one of them makes your car explode and costs you 100 units of fuel, but your car is immediately replaced by one moving at the speed you were last travelling at.
Your ever-diminishing fuel supply can be replenished by running over tiny blue petrol pumps that randomly appear in the road, granting you an extra 100 units. Tragically, they fly down the screen so fast that you can't possibly move over to them in time; you have to hope they will appear pretty much directly in front of you.
Here's a low-quality picture of the cover art, because the screenshots are all the same.
And that is all of Car Race's gameplay. Hold down accelerate and never let go for a second or your fuel evaporates faster than a drop of water on a lightsaber. Shuffle left and right, hoping that a fuel pickup appears in a favourable position and the next black car isn't one of the crazy, swerving ones. The best strategy by far is to move over to the far right of the screen and swerve carefully, as the enemies mostly stay on the left and fuel often appears on the right. By a combination of this and saint-like patience, you can reach the maximum score of 65,535 metres after about 20 solid minutes of mind-numbingly tedious play.
Car Race's biggest sin is that of wasted opportunity. The movement and scrolling are smooth and the collision detection is solid. If they'd actually put some time and thought into the game design, it could be quite good fun. But sadly, it's just a bleak lump of nothing that's so dull you could fall asleep playing it – if the horrifying engine noise didn't keep you awake.
Ample Software released two other games: a bizarre alcoholism-based platformer called Super Drinker and Scramble Eggs, a rubbish, simplified version of Scramble where the enemy spaceships are replaced with eggs. Yes, really.
REVIEW SCORES
None known
other versions
None, but you can play Bump 'n' Jump (AKA Burnin' Rubber) on various systems, and it's pretty much the same game but a million times better.
# Count Duckula 2
Format: Amstrad CPC
Year of Release: 1992
Developer: Unknown
Publisher: Alternative Software
Original Price: 3.99 pounds
The Amstrad CPC suffered from a horrible plague throughout its lifespan that affected many of the games released for it. It was a particularly insidious disease known as Lazy ZX Spectrum Conversions. The only cure was an injection of money and time from game publishers, and as you're probably aware from the contents of this book, that medication was in extremely short supply.
The Amstrad is capable of displaying a low resolution mode with 16 colours, similar to the Commodore 64 but with a larger potential palette and more vivid hues. But it can also produce a higher resolution screen similar to the Spectrum, albeit with only four colours at once. It also shares the same processor which led to developers realising they could just port over the code of a Spectrum game in a few days. It would have fewer colours than the original version and run much slower, as the graphics were converted to the exact Amstrad format in real time. But some companies simply didn't care – the Spectrum had a much bigger market share in the UK so the Amstrad versions were treated as an afterthought. That didn't stop them charging the same money for them though...
This screen appears to feature a fresco of Raggedy Ann after being stabbed in the stomach.
Count Duckula 2 is one of the very worst examples of a lazy conversion. And as the game is distressingly poor in the first place, Alternative Software took something dreadful and made it into something frankly unholy.
The second game to be based on the popular children's cartoon from British animation studio Cosgrove Hall, Count Duckula 2 follows the exploits of the vegetarian vampire duck as he gets stranded on Planet Cute. The entire world is covered with animated toys whose touch slowly kills our hero, apparently because he doesn't like cute things. Fair enough.
That's a bottle of ketchup at the top of the screen. Yes, really.
Things start off well with a colourful and nicely drawn loading screen that leads into a funky remix of the cartoon's title music. Then things fall off a cliff faster than Wile E. Coyote strapped to Acme's finest rocket- powered anvil.
The graphics are absolutely dreadful. A pixelated mess representing Duckula stands in a mostly empty screen peppered with ugly blocks that look like they've escaped from a 1982 magazine type-in. Occasionally there are large images of toys in the corners, but they've been reduced to two colours without being redrawn and are a total mess as a result.
Count Duckula dies because he touched the bottom of his screen. His hair is duplicated due to hideous graphical errors.
Then the graphics move and the true horror begins. Everything is jerky and flickery beyond belief – the top of Duckula's head seems to be detached from the rest of his body as he shuffles and twitches across the platforms. There is no jumping animation, meaning he takes Aled Jones' advice and just walks in the air. The enemies feature minimal animation. Everything runs like it's being updated in real-time by a tranquilised sloth in a bath of treacle. Sound is limited to a handful of beepy spot effects.
The game is based primarily around waiting for constantly moving platforms to be in the correct place to allow you to progress. And when I say "moving" I actually mean "flickering in and out of existence at different points on the screen". As the game runs at half the speed it was designed for, you spend an awful lot of time waiting. The evil toys that sap your strength can be stunned with your ketchup gun, except for the jack-in-the-boxes which can't be shot or avoided.
According to the instructions, the thing saying "CORN" is the torn-off top of a cereal packet. Even the items you collect are things you'd find in a bin.
Beyond the stiflingly tedious game design lie even more technical problems. The controls are painfully unresponsive, with a lag of around half a second between you pressing a button and something actually happening. You frequently merge into the corners of platforms as you try and jump on them. And there's yet another massive problem caused by the lazy conversion from the Spectrum original...
For some reason the Amstrad version stops you jumping off the top of the screen. If you try, Duckula bangs his head and plummets straight down. As the levels were designed assuming you would have this ability, this oversight causes multiple problems. The most serious is that the second screen is impossible to complete by standard means, as any attempt to reach the moving platforms leads to falling off the bottom of the screen and instant death. The only way to progress is to call Tremendous Terrence, a superhero who carries you to the next screen. You can only use this level skip every so often, so it's a kick in the teeth to be forced to use it on screen two, especially since you will need him on the very next screen when you inevitably get your head stuck in the ceiling.
Tremendous Terrence helpfully provides a way to avoid a game-crippling programming oversight.
Count Duckula 2 is an absolute travesty. Amstrad owners deserved better than lazy Spectrum ports, and the people who paid money for the game – possibly on the strength of the first Count Duckula title – certainly deserved better than this digital farce.
The people responsible for producing this dreadful conversion remain unknown as they understandably didn't put their names on it anywhere. Alternative Software released dozens of budget games for the Amstrad, including multiple children's television tie-ins like Postman Pat and Fireman Sam. They also spewed out the nightmarishly dreadful BMX Ninja and Rik the Roadie, and as such are still considered beyond redemption to this day.
The Spectrum version. Still dreadful... just less dreadful.
other versions
Spectrum: As previously mentioned, the original version is effectively the same game except it works properly and there's no sound. The graphics are far more colourful, the crippling bugs aren't present, and it runs literally twice as fast. However it's still an utterly atrocious game – in fact, in 1993 the readers of Your Sinclair magazine voted it the worst Spectrum game of all time by a landslide. (Clearly they had never tried to play SQIJ!)
Commodore 64: This version had a lot more effort put into it and is far superior in every respect as a result. It even has an extra shoot 'em up section at the start. It's not great by any means, but it's the best version by a country mile.
REVIEW SCORES
Amstrad Action felt that 3% was a fair score, and I can't disagree.
# THE MOST DISAPPOINTING GAME I EVER BOUGHT
by Jeff Minter, game coder and founder of Llamasoft }:-D
Asteroids
Format: Commodore Vic-20
Year of Release: 1983
Developer: S. Munnery
Publisher: Bug-Byte
Original Price: 7.00 pounds
Think about the defining characteristics of the coin-op Asteroids: precise, smoothly-animated gameplay that was extremely challenging but ultimately fair; sparsely beautiful and pure vector graphics; simple but effective audio that served to ramp up the tension. Now imagine something with characteristics the diametric opposite of those, and you have Asteroids by S. Munnery. Tiny character mode "asteroids" lurched around the screen in giant character-grid-quantised steps. Occasionally, the game would begin with one of them placed directly on top of your ship, killing you instantly. Your ship was a strange kind of horseshoe-shaped thing that would trundle around the screen forlornly making noises like a Hoover, and when you pressed the FIRE button, a line of full stops would come out of its nose.
It was a complete and utter pile of smeg, and for me, it was one of the final straws that broke the dromedary and convinced me to start Llamasoft. I believe my thinking on the matter was along the lines of "For fuck's sake, even I could do better than that." Inspired, I founded Llamasoft and made a completely shit version of Defender for the Vic-20. I did go on to do some other slightly less shit things later on though.
Playing this game felt like being repeatedly stabbed in the eyes with recently sharpened pencils whilst being comprehensively kneed in the bollocks by Margaret Thatcher. S. Munnery did do another game called Cosmiads on the Vic-20 years later; it was actually marginally less terrible than Asteroids and only made you feel like flushing your own head down the toilet.
Buying Asteroids made me a bit wary of buying games from software houses that sold a bunch of games by different authors. I'd bought a game off Bug-Byte before that hadn't been entirely dreadful, and it was on the strength of that experience that I ponied up seven whole Earth quid for that traumatising Asteroids. There was a lot of a "buy any old crap from shitty programmers and shove it out there because people will buy anything" attitude that a lot of early software houses succumbed to in those days, and this was just Bug-Byte doing that, I suppose. I think that's why Llamasoft ended up being such a one man band in the end. I may have made shitty games myself in the early days, but at least I actively tried to get better at it instead of just selling any old crap because I could get away with it.
Jeff can be found on Twitter at @llamasoft_ox – follow him for Sheep Time on Periscope.
FACT!
S. Munnery is Simon Munnery, who went on to have an extremely successful career in comedy, performing stand-up and writing for TV and radio.
# Crazy Kong
Format: Commodore VIC-20
Year of Release: 1983
Developer: Unknown
Publisher: Interceptor Software
Original Price: 6 pounds
Along with Pac-Man, Donkey Kong was a cultural phenomenon in the early 80s, and every home computer had multiple unlicensed clones made for it. Sadly, most of them were pretty rubbish, and Interceptor's Crazy Kong is certainly no exception.
The usual set-up applies – an oversized gorilla has kidnapped your girlfriend for some reason, and to rescue her you have to climb up some gantries whilst the ape throws barrels at you. The instructions even specifically call the main character Mario. Copyright was not well-respected at the time, to say the least.
Mario's head is not attached to his body. If you suffer from a similar ailment, seek medical help immediately.
Things start badly with an ugly title picture that isn't centred in the middle of the screen and offers no discernible way to start the game. Tragically the game does start up after a while, and your buyer's remorse really kicks in.
According to Interceptor's mail-order advert for Crazy Kong, it "includes some of the best graphics ever seen on the VIC-20". I'm not sure where they're hidden, as all the ones actually displayed on screen would be better described as "adequate". Kong himself is a purple sloth. Mario's girlfriend is a ghost with a bell on her head. The row of blue boats at the bottom of the screen are supposed to be custard pies. And when Mario dies, he turns into a green angel that looks more like some kind of monster from a 50s B movie.
Mario is victorious! Sloth Kong could just run up and punch him, but instead he stays close to his comforting barrels.
Animation is almost absent – things jerk around the screen, and Mario just flicks one leg out behind himself when he's not standing still. The jumping animation is bizarre – Mario slowly hovers into the air, floats forward one character space and lands. Sound is limited entirely to an annoying beep every time you move and a weird laser gun effect every time you jump.
The very first thing you have to do in Crazy Kong is extremely frustrating. You have to walk onto a constantly falling platform just as it teleports back into its starting position – an irritating leap of faith that takes several games to get the hang of. One wrong move and you fall to your death, or you glitch into the conveyor belt below, which forces you to kill yourself by touching one of the deadly yellow blocks. The lethargic controls do not to help.
On death, Mario apparently transforms into the X-Men villain Sauron.
The rest of the level involves jumping over the bright blue pies, which is extremely easy, then dodging the barrels as you make your way to the top. There are no hammers with which to smash the barrels in this version, so you rely entirely on timing your movements and jumping. The barrels alternate between two different paths, so it doesn't take long to figure out an optimum route. The only real threat are the controls, which will occasionally leave you stuck on a ladder when a barrel's coming your way. Oddly, Mario moves faster the closer he gets to the top of the screen; by the time he's reached the third girder, he's zipping around like a coffee-addled businessman on a supercharged Segway.
So you reach Mario's phantasmic, bell-headed sweetheart and the level ends! You are awarded some points and... that's it. The same level starts again, just running slightly faster. As you can easily get to the top in 30 seconds, there's a serious lack of variety and value for money. Eventually it gets too fast to actually complete, or at least it seemed that way to me after playing it for far, far too long.
Our hero gets stuck in the floor. Tragically, his only method of escape is to gnaw his own legs off.
Crazy Kong is one of the worst examples of an early eighties Donkey Kong rip-off, and that's saying something. The graphics are actually better than some other attempts (yes, really!) but everything else conspires to remove any rational reason to play it. It's a buggy, fiddly, annoying mess with almost nothing to it. It's still better than C-Tech's infamous Krazy Kong for the Spectrum, but then so is having explosive diarrhoea on a long train journey.
Interceptor published a huge number of games in the 80s and early 90s, both under their own name and the Players, Players Premier, Pandora and Fun Factory labels. Whilst there were some absolute stinkers amongst their early games, the quality increased hugely as time progressed.
The box art is terrifying. If this was the cover of a VHS tape, I would have rented it without question.
REVIEW SCORES
Computer and Video Games magazine described the game as having "more bugs than a flea-bitten moggy". Yet somehow they gave it 6/10 for both value and playability! They misspelled the name as Krazy Kong and claimed the game cost 95p more than it did, so perhaps they were distracted by a particularly impressive dance routine at the time.
other versions
Commodore 64: Pleasingly, this version is totally different. It has appalling graphics and is brutally difficult, but it is far more fun to play than the VIC-20 version.
# Dangerous Streets
Format: Commodore Amiga CD32
Year of Release: 1993
Developer: Micromania Software
Publisher: Flair
Original Price: 25.99 pounds
Ignited by the home release of Street Fighter II the previous year, the market for fighting games was huge in 1993. The Amiga had few exclusives to call its own – the only one of note was Body Blows, a fairly simple affair with nice graphics. A really solid fighter would be a license to print money, surely? It seems that Micromania Software certainly thought so, but they somehow replaced the word "solid" with "unplayable" in their design documents.
The characters in Dangerous Streets are an odd bunch even for a fighting game. They have a very 70s vibe to their designs, and they mostly seem to be refugees from an Italian disco of that era, with the inexplicable exception of a blue monk who has springs strapped to his feet. The two female characters both wear stripper outfits so skimpy you wouldn't let your kids play the game.
From left to right, top to bottom we have: Sgiosa Capeli (works in a disco), Pinen (lorry driver), Tony (playboy), Luisa (gym teacher), Macalosh (spiritual boss of the Sioux), Ombra (expert palmist), Keo (custodian for an old castle), Lola (top model)
One of the most notable things about Dangerous Streets is that it looks quite pretty in screenshots. The characters are competently drawn and well-defined, and the backgrounds are colourful. This was possibly a marketing strategy to make magazine reviews and the back of the box more impressive, because as soon as you see the characters move, any prettiness flies out of the window with a speed that would startle a cheetah on steroids.
The animation is beyond laughable, to the extent that you begin to wonder if the movements were designed by a primitive computer that had human motion explained to it by a semi-comatose drunkard. The characters jerk and twitch like a low-budget zombie movie that has half its frames missing. A particular favourite is the way Luisa's head twitches alarmingly as she walks, making it seem like she is auditioning for an especially disturbing remake of The Exorcist. And Macalosh's standing pose manages to look ridiculous through using only two frames of animation – he half-squats at a gravity defying angle as if he is trying to defecate in an invisible toilet without his arse cheeks touching the seat.
Macalosh has some kind of bowel problem whilst Keo struggles with his foot springs.
The fighting moves that the characters use are worse still. They're an almost animation-free cavalcade of seemingly random, jerky attacks with no thought put into how they would affect the gameplay. Each character has several ridiculous, wannabe-comedic moves that only further ruin any potential fun: Lola can fire lumps of hair gel out of her hair. Tony can project a small, blue demon from his fingertips to hide behind. Pinen has a hollow chest cavity which opens up to reveal a tiny version of himself that flies along the screen, fists pummelling. Macalosh tries to whip his hair into his opponent's eyes and can turn into a monster so ill-defined that I have no idea what it's supposed to be. Keo can summon a squid to protect himself, whilst Luisa's defence involves turning into a solid block of metal. Sgiosa can make his hideous, fluorescent catsuit glow, which apparently protects him. Ombra somehow dives into the floor and flies back out again further along the screen, a protracted move which actually counts as his forward jump so he does it all the bloody time.
I can only assume that the game designers were trying to make things light-hearted and tongue-in-cheek. But for that to work, it needs to be backed up by charm and wit and not be one of the worst fighting games ever commercially released.
The sound is equally poor. Dull, bleeping Euro disco tracks are streamed from the CD for background music. The contact sound effects only seem to kick in if they feel like it, and some of them are just blasts of white noise. Or possibly the game just blasts white noise every so often, I can't tell. Worst of all are the pre-fight announcements of the characters' names, all of which sound like they were recorded from people shouting across a bathroom into a dodgy microphone.
Top five ridiculous moves! Slab defence, large cap shield, hair gel attack, scalp lash, and mini man attack.
But as bad as the audio-visual horror gets, it's the gameplay that really plumbs the depths of incompetence. Fighting games need to be carefully balanced with tight controls and clear feedback at all times. Dangerous Streets eschews these things in favour of a man who blows into his hat so it expands to giant size and he can hide behind it.
I will now attempt to explain what it's like to play Dangerous Streets without resorting to sexual swearwords. Firstly, the controls make no sense. Some of the four face buttons on the horrible CD32 control pad duplicate each other, but not all the time. Moving your character across the screen quickly is a nightmare due to the bizarre jump animations that most characters have. Hit detection is a joke, and characters don't always react to being hit – add in the almost random sound effects, and most of the time you have no idea if you've actually landed a blow on your opponent. Each character's limited "super-move" is far less effective than his or her standard forward attack. Characters can move slightly off-screen so you can't see them. If both players select the same character, they look identical and there is no way to tell them apart. There is no sense of weight to any of the fighters, and it feels as if you have very little influence over what they do – unless you just hold down one button... you can beat the computer by holding down one button.
Macalosh has turned into a thing. Possibly the offspring of a panther and a gorilla?
Dangerous Streets is an utter travesty. A twitchy, jerking mess far worse than even the infamous fighting game failures Shaq Fu and Rise of the Robots. The CD32 hadn't been out for long and you might think Commodore would want to keep this garbage as far away from their new console as possible before people compared it to Street Fighter II and bought a Super Nintendo. Instead they included the game with all new CD32s and named the resulting bundle the Dangerous Streets pack. I am not making this up.
It also gives you instructions on how to load the game after you have loaded the game.
Commodore had made several questionable business decisions over the years, but this was possibly their most ridiculous. It, of course, did nothing to help sales. After a slew of legal problems and component supply failures, Commodore declared bankruptcy in April 1994 and the Amiga CD32 went off sale only eight months after its release. It was never released in North America.
Developer Micromania were never heard of before or after Dangerous Streets, which is in itself a beautiful mercy. Publisher Flair were responsible for various other CD32 pack-in games and also the execrable Surf Ninjas – an Amiga CD32 exclusive that is so bad the only reason I haven't covered it in this book is because I wrote so much about Dangerous Streets.
Luisa versus Luisa. Can you tell which is which? No? Neither can the players. The Amiga 500/500+/600 version, with smaller fighters and less colours, but all the perverse costumes!
REVIEW SCORES
Amiga Power awarded the game 3%. As in three out of a hundred. At the time I assumed the score was comically low as some kind of protest against substandard games having entire console bundle packs named after them. Then a few months later, I attempted to play it and realised they were entirely serious.
The One magazine gave it 22% and described it as a "freshly laid turd". German magazine Amiga Joker somehow decided it was worth a frighteningly inflated 44%, despite utterly eviscerating the gameplay in their review. But they thought the graphics and sound were good so they may have been mentally incapacitated by paint fumes or something.
other versions
Commodore Amiga 1200 (AGA): This version is extremely similar, as internally the CD32 is essentially an A1200 with an extra chip in the graphics architecture to help take advantage of the added CD drive. However, without said CD drive, the music is reduced to slightly discordant Street Fighter II-style tunes and the loading takes forever. What's more, it comes on three disks so you have to keep swapping them. As a result it's actually worse than the CD32 version.
Commodore Amiga 500/500+/600 (OCS/ECS): Amazingly, this version is worse still! The lesser power of the older Amiga models led to smaller game characters, less colourful backgrounds and no in-game music at all. Even Amiga Joker couldn't stomach this version, which they blessed with a 20% rating as it flew into their rubbish bin.
PC: A rare PC port of an Amiga game! If only it were rarer. The fighters in this version are huge and far more detailed, and if both players select the same character they are actually different colours. But the good news ends there. It is horribly sluggish on the hardware of the time and the soundtrack consists entirely of lifeless jangly music. For reasons I cannot begin to fathom, huge foreground items were added to each stage, obscuring about a third of the screen.
# Graffiti Man
Format: Atari ST
Year of Release: 1987
Developer: ReLINE
Publisher: Rainbow Arts
Original Price: 24.99 POUNDS
The game starts. The screen is filled with grotesquely ugly freaks jerking around everywhere. You move your character slightly, and he apparently touches a freak, despite clearly not being close enough. He instantly explodes in a mess of blood. You lose a life and respawn at the start. You try to move carefully along the screen, but attempting to move vertically in the play area means you can't tell exactly where your character is. He gets near a freak and explodes again. You are now on your last life. You manage to navigate past the freaks for a few seconds then explode for no noticeable reason. The game is over. You have played Graffiti Man for less than 30 seconds, have lost all your lives, and have no idea what happened. You weep hot, bitter tears of anger and frustration.
Graffiti Man is a truly horrible game.The idea is to guide Mickey, "the multi-talented Graffiti Man", across several locations so he can spray some paint on some walls. This will apparently enable him to join a famous graffiti gang. It's never made clear what Mickey's many talents are, but from the game we can assume they don't stretch to being able to see more than a few feet in front of his own nose or move at the speed of a normal human being.
Why is the road that colour? And why do the life counter men appear to have been boiled?
The instant you start, you are thrown into a mess of sensory overload with a screen chock-full of caricatures on a hideous, orangey-brown background. It becomes obvious that you need to run from the left side of the screen to the right, dodging the various freakish stereotypes in your path. The playfield is split into three vertical planes that you can move between. The freaks, unable to change lanes, move horizontally from one side of the screen to the other, looping back round when they disappear off the edge. It sounds simple, and it absolutely is simple. But one thing it is not is easy.
As previously described, your first game of Graffiti Man is likely to last only a few confusing seconds. There is stuff everywhere and it all kills you instantly. But it is only when you understand how things work that the true horror begins.
The bearded man releases tiny clockwork spies from a cardboard box. It's a hobby, I suppose.
The game chugs along, usually around a painfully slow six frames a second, meaning our hero Mickey walks in slow motion as if in a bad dream. This also makes the fast-paced enemy freaks jerk around in an astonishingly ugly manner. The controls are painfully unresponsive, meaning quick reactions to onscreen events are impossible, and it's very difficult to stop on the middle plane. When you reach the right-hand side of the screen, it begins to scroll with very little space in front of Mickey, meaning that freaks can appear and kill you before you can possibly react. Coupled with the dodgy collision detection, the only way to proceed is to predict the behaviour of the looping enemies like some kind of freak-obsessed sociologist.
So! You are now the world's leading expert in predicting freak movement patterns and getting an unresponsive, slow-motion graffiti artist to navigate them. What else do you need to look out for? How about the super-fast projectiles that some enemies fire at random and will kill you if they get anywhere near you? How about the way you can outrun the screen scrolls on level 3 and disappear off into the digital ether? How about the small objects that fire diagonally across the screen and are almost impossible to dodge in certain positions? How about the fact that Mickey can jump and duck, but that both moves are completely useless? How about the way these problems make the game so frustrating that you may furiously punch through the TV connected to your Atari ST? Master all of these and you may make it through all four levels!
Top row: Freakishly ugly roller skater, dangerously barefoot skateboarder, Steve Martin in Roxanne, blatantly racist caricature. Bottom row: Crazy octopus, constantly punching sailor, creepy spy cliché, inexplicable shears-wielding spy.
You start off in a street full of punks and pensioners, move on to a train station full of psychotic porters, pass through some docks filled with deadly sailors and wildlife, and then finally graduate to what appears to be the lawn of the White House covered with spies and dogs. I don't know what part of Washington, DC, Mickey lives in, but I think it's safe to assume the house prices are low and insurance costs are high.
Successfully completing a level leads to a bonus stage, but never has the word "bonus" been used more erroneously. You are presented with a piece of incredibly poor graffiti, such as a stick figure, and the game switches to mouse control to let you spray white pixels over it. The more of it you cover, the more points you get – the instructions say that you fail the bonus stage if you don't reach a certain score, but this is untrue. As there is no high score table, it's utterly pointless and dull. It also means that the pinnacle of Mickey's graffiti prowess is to make other people's crap childish drawings look even worse.
Before and after Mickey's artistic endeavours. No wonder everyone wants to kill him.
By this time you've probably worked out that purchasers of Graffiti Man wouldn't be very happy. Adding to their considerable buyers' remorse is the length of the game – each level takes less than a minute to complete, as does the bonus level. So in the unlikely event that you could make it through the four levels of frustrating dross, you would complete the entire game in well under eight minutes. The final insult is the price: an eye-watering £24.99.
But there are a few positives lying among the wreckage of Graffiti Man. The freakish caricature sprites are generally well drawn and amusing, and the animation of main character Mickey is excellent. The music is comprised of beepy-yet-funky little tunes that fit the game well, although the title theme is oddly bleak until the funk kicks in. And, most amazingly of all, there is actually a proper reward for beating the game! After the final bonus stage, you are treated to a very basic paint program that allows you to make your own crappy-looking graffiti and save it to a disk. That doesn't sound like much, but it's impressive for the time, considering the vast majority of games used to give you nothing more than a message saying "Congratulations!" for playing through them.
Presenting the horrible box art, where someone dressed a mannequin as Clint Ruin then badly airbrushed it!
It's amazing to think that this rubbish was one of the first games released by major publisher Rainbow Arts. It seems to be nothing more than a substandard port of the Amiga version that runs like a dog. Developers ReLINE somehow went on to make a game using the Pink Panther cartoon license as well as a semi-pornographic business management sim for the German market. It's hard to know which stigma was harder for them to bear: the creation of this game or the stupid capitalisation in their company name.
REVIEW SCORES
No known ST reviews, but in their review of the Amiga version, Australian Commodore and Amiga Review understandably said, "I didn't like this one at all!"
other versions
Commodore Amiga: This superior version is far faster and smoother, running at double the frame rate, at least. As a result, the controls feel much more responsive, although the speed increase also means the entire game can be completed in less than five minutes.
Commodore 64: This 8-bit conversion also runs far more smoothly, although the graphics are featureless and drab. The scrolling is replaced with a flip-screen system that makes it possible for enemy freaks to seemingly appear out of nowhere and kill you instantly.
# THE MOST DISAPPOINTING GAME I EVER BOUGHT
by Mentski, Bearded retrospective
idiot and occasional face
Out Run
Format: ZX Spectrum
Year of Release: 1987
Developer: Probe Software
Publisher: U.S. Gold
Original Price: 8.99 pounds
(12.99 pounds for the disk)
The story has many layers...where to begin?
Let's start with a bit of foundation: Back in those days there was a concept that floated around the schoolyard – the quest for the "arcade-perfect" port. Now we all know a Speccy conversion would never be perfect, but we were happy enough if it faithfully recreated the gameplay.
In 1986, Elite released a conversion of Sega's Space Harrier, seemingly doing the impossible and creating a reasonably playable port considering the hardware limitations. We were suitably impressed, and began to ask questions. Converting Space Harrier to the Speccy was considered nigh-impossible; surely there's no way you could ever squeeze Sega's latest arcade hit, Out Run, into Sir Clive's novelty doorstop?
Then some time in 1987 U.S. Gold declared they'd acquired the Out Run license and that it'd be released for home computers in time for Christmas.
The hype for this was huge. U.S. Gold were attempting the impossible. Then we saw the screenshots and our jaws dropped...
The Speccy screenshot showed the iconic Ferrari about to overtake a truck. The sprites were huge and looked like accurate representations of the arcade games graphics (albiet in monochrome of course, because ironically for a computer called the Spectrum, colour wasn't its strong point).
Maybe, just maybe, the programmers had been able to do what we all thought was impossible?
Release time came, and I remember rushing down to my local branch of Boots on a Saturday morning to get a copy. I finally had in my hands a copy of Out Run that I could play at home. On the back of the case were screenshots of the game on multiple formats, including the same shot for the Speccy that had made my mouth water in the magazines... This was it! The time had come!
Here's where it all turns for the worst: first up, the tape containing all the levels was accidentally recorded backwards.
On bringing the game home, I hurriedly loaded it only to find that I couldn't play it due to a bloody tape mastering error! I rushed back to Boots to get a replacement, only to find out all their Spectrum copies had the same error, and I'd have to wait three more days for new stock to arrive!
Three more days of sweaty anticipation. Three days of loading up the main program, staring at the menu, listening to the Speccy's beepy rendition of eminent background tune "Magical Sound Shower", waiting for a replacement copy so I could finally recreate the sheer joy I felt playing the greatest arcade game ever made.
Three days finally passed and I hurried to Boots after school to get my replacement copy. I know I said the time had come last time, but now I really mean it... The time had finally come!
Oh dear.
This was not the game they advertised. I mean, it looked similar, but it was clearly different. The giant sprites? Nowhere to be seen. Everything apart from the car had been shrunk by about 50%. The giant palm trees now looked more like roadside bonsai, and the towering trucks were now barely any taller than your Testarossa. The road was a pixellated, undefined mess... and worst of all was the speed.
Out Run on the ZX Spectrum is very, very slow. This game is supposed to be about driving a 180mph Ferrari through beautiful European-inspired locations. Playing this port made you wonder if you'd get there quicker if you got out and walked!
You'd think something like this would have been trashed in the press, but no! It got favourable reviews! Many said that despite its flaws, it was the best the Spectrum could have done... which was utter bunk too, as we found out shortly later when Ocean ported Chase H.Q. to riotous applause, blowing poor old Out Run out of the water in every possible way.
It was the first time I felt outright lied to by a games publisher. Those screenshots shown before release were pure fabrications (not just the Spectrum but shots for the Amstrad CPC and Atari ST, too!) A bond of trust was broken the day U.S. Gold lied about the quality of this game.
I also felt let down by the magazines of the day – not only for falling for U.S. Gold's propaganda, but for giving the game favourable reviews despite how bad it was and for not once questioning why the finished product didn't resemble the marketing bumpf. In time, older, cynical me would wonder if these magazines were on U.S. Gold's payroll.
Nearly 30 years on and we're still dealing with publisher lies and questioning journalistic integrity. The more things change, the more they stay the same.
And yet it didn't change my attitude to buying games. I still purchased appalling conversions of awesome arcade games for years. After all, it was the only way to play those games at home at the time.
Does anybody want a second-hand copy of Street Fighter II on Atari ST? Only played once...
Mentski can be found on YouTube at youtube.com/mentski and on Twitter at @mentski
FACT!
This is the infamously inaccurate screenshot, stitched together from two sources as tragically the high quality one was only partial. It was used for preview articles in Your Sinclair, Sinclair User and Computer & Video Games magazines as well as the back of the game box. There is no excuse.
# BUTTON PRESS 3000
An exclusive, original terrible game
for you to play!
Simply enter this program into a Sinclair ZX Spectrum and RUN it to experience the dead-souled frustration that only comes from playing a truly dreadful video game!
10 PRINT "PRESS T TO WIN"
20 PAUSE 0
30 IF INKEY$ ="T" THEN GO TO 70
40 IF INKEY$ ="t" THEN GO TO 70
50 IF INKEY$ ="C" THEN GO TO 80
60 CLS : PRINT "WRONG KEY, YOU LOSE": STOP
70 CLS : PRINT "WELL DONE, YOU WIN": STOP
80 CLS : PRINT "CHEAT MODE ACTIVE"
90 PRINT "PRESS T TO WIN"
100 PAUSE 0
110 GOTO 70
Look out for details on how to pre-order the Button Press 3000 Game of the Year Collector's Edition and DLC Season Pass!
# Highlander
Format: ZX Spectrum
Year of Release: 1986
Developer: Canvas
Publisher: Ocean
Original Price: 7.95 pounds
Highlander is without doubt the best film ever made about an immortal Scotsman who only dies if you lop his head off. Unfortunately it spawned several awful sequels, none of which are worth the time it takes to watch them. But it's the 1986 home computer adaptation that takes the filthy, tarnished crown for being the worst of the franchise.
The Highlander game concentrates entirely on the sword fighting aspect of the film, pitting hero Connor MacLeod against three increasingly difficult opponents – friendly mentor Ramírez, creepy murderer Fizir (called Fasil in the film) and vicious maniac The Kurgen. Each opponent is loaded separately from the cassette tape, and you do not have to beat one to progress. This lack of continuity would be a shame if there was any joy to be had from playing the game at all.
You've been knocked over in the corner and will be hacked to bits. Get used to this.
On starting the game, the first thing to hit you is how incredibly ugly the characters are. MacLeod and his opponents are nothing but a mess of big white blocks. They're decently animated big white blocks, but it doesn't matter how well something moves if you can't see what it's supposed to be. The graphics are those used in the Amstrad CPC and Commodore 64 versions, which were designed for a lower screen resolution in multiple colours. The Spectrum's monochrome rendering leaves them an incomprehensible mess.
So the game appears to be two albino Lego models trying to smash each other apart with sticks. And astoundingly, it plays even worse than it looks. None of the sword fighting moves seem to do much – if you're lucky, then your opponent's energy may go down a bit, but you can't really tell who is successfully hitting whom. Generally a fight will last less than a minute as your opponent knocks you over in the corner and depletes your energy, at which point your head falls off. Your energy does start to regenerate if you don't attack or get hit for a second, but it's so hard to move away from your opponent that it's rarely useful.
MacLeod's sword proves too heavy, allowing Fizir to stab him in the eye.
The instruction manual tells you to watch for your enemy's attacks and respond to them, which is effectively impossible due to the clumsy movements and horribly unresponsive controls. You could only effectively respond to an opponent's attack if he sent you details on a postcard a week in advance. The single tactic that seems to have any effect at all is to mash the fire button and hope, turning Highlander into a slapstick routine of two nitwits flailing sticks at each other until one falls over.
The sound is almost non-existent. There is no music whatsoever and just a weird, popping noise if someone gets hit. And the laziness doesn't end there – despite there being three different opponents that you have to load separately, they all have identical moves. They just look different, and some can take more of a beating. I can only assume that Highlander must have been written in an incredible hurry.
Due to illness, The Kurgen has been replaced by Toad of Toad Hall.
Have you ever tried to get an elderly relative to play a video game? Highlander is a way to experience the confusion and bewilderment they feel, even if you're well versed with the medium yourself. What's going on? Why isn't the little man moving? Why does he keep falling over? Why can't I ever win? Can I stop playing and watch Columbo now?
Playing Highlander is one of the least entertaining ways you could possibly spend your time. The fighting feels futile, as if you're just wasting your time watching some unnecessarily large white pixels move around. At least there's a simultaneous two player option so you can have a companion in your misery – until they leave and never speak to you again because you made them play Highlander.
Ramírez absorbs the "quickening" energy from MacLeod's corpse, which seems to turn him into some kind of mole-man.
Developers Canvas also made the crappy TV tie-in Miami Vice. But they also produced conversions of the excellent golf game Leaderboard and the graphic adventure Killed Until Dead, which may have the greatest name of any game ever.
Ocean Software were an absolute powerhouse in the 8-bit days, releasing a huge number of licensed games as well as original titles. The peak of their success on the Spectrum was the brilliant Robocop, which broke records for the longest time spent at number one in the Gallup sales chart. They eventually became the UK arm of Infogrames and released their last game in 1998.
The Amstrad CPC version kindly displays what the characters should actually look like.
This wasn't the last attempt at a game based around Highlander. Nine years later, Lore Design Ltd made Highlander: The Last of the MacLeods for the Atari Jaguar, based on a spin-off cartoon series. It was an interesting game ruined by an overly simple plot and abysmal controls, but it was still far better than Highlander. There was also an original game in production from Eidos Interactive for the Xbox 360, Playstation 3 and PC, but it was cancelled in 2010.
REVIEW SCORES
Sinclair User absolutely slammed the game, describing it as a "Golden Turkey" and awarding it 2/5. Crash described it as "totally boring and quite unplayable" yet gave it a stupidly inflated 57%. Oddly the other major Spectrum magazine Your Sinclair didn't review the game, but it did deservedly appear in their reader poll of worst games ever.
other versions
Amstrad CPC: This version is far prettier and is the definitive Highlander experience for what that's worth. It received around 50% in reviews.Commodore 64: This is also much better but runs slower than the other versions. It was absolutely reviled by reviewers – ZZap!64 magazine gave it 30% and revised the rating to 19% when it was re-released five years later at a cheaper price.
# Hunter
Format: Atari 8-bit series
Year of Release: 1995
Developer: Condor Soft
Publisher: Power Per Post (PPP)
Original Price: Approx.6 POUNDS
In the early nineties, software support for Atari's 8-bit line of computers began to dry up, leaving the format with a dwindling supply of new games. This led to mail order companies, like Germany's Power Per Post (PPP), becoming increasingly important to diehard enthusiasts. This is a shame, really, as it meant they were able to sell them unadulterated garbage like Hunter.
An attempt to recreate the sporting pastime of fatally wounding wild animals by shooting them with a big gun, Hunter spectacularly fails on several levels. It also spectacularly fails at being a video game that anyone could enjoy playing, so at least it's consistent.
I am resorting to using a screenshot of the menu, as all of the in-game shots look the same.
The title screen is promising – a majestic, golden stag stands in front of a stylised sunrise as a funky, crunchy, bass-heavy chiptune plays. Oddly, the music doesn't fit the displayed image or the feel of hunting in a forest at all, implying that it was produced for something else entirely. It is good quality, but sadly this is the last time anything from Hunter will feel as if any effort was put into it.
After dismissing the title screen, four options present themselves, together with another totally incongruous tune. Or possibly three options, as it doesn't actually seem possible to change the "level" setting. It is, however, possible to select ammo values of 80, 160 and 240, the higher numbers doing nothing more than stretching the game out past the point of sanity. It's also possible to turn the sound off completely – and as the only sound is the same astonishingly ill-fitting music played constantly throughout the game, that may be a good idea.
I hope you like this scene, as you won't be seeing any others. Ever.
On starting the game, you are treated to a single static scene of two trees on a grassy landscape. And that's it location-wise, as there is no movement or alternate scenery. The animals, for reasons best known to themselves, start sliding across the screen from right to left. And I mean they literally slide – there is no animation at all, meaning that the animals look like cardboard cut-outs drifting across the screen on roller skates. Once one has disappeared off to the left, another appears immediately and slides across in almost exactly the same place; there are only a few pixels of height variation between the paths they take. The beasts must have politely formed a queue to glide along a hidden train track and be shot one at a time. You can't really blame the hunter for not moving location after finding a hunting ground like that...
Your job, of course, is to stop the animals from reaching the left side of the screen by killing them dead with bullets. This is achieved by moving a circle over the animal and pressing fire. In order to stop that being too easy, the crosshair circle jerks and flickers around to an insane extent. It's not just like the hunter has unsteady hands, it's like he's operating a pneumatic road drill at the same time as aiming. (But on the plus side, "Jerky Crosshair" is an amazing name for a tongue-in-cheek Country and Western music act.)
From left to right we have: Slug / rabbit hybrid (2 points), Dog with head-mounted helicopter blades (4 points), Sock-faced elk (5 points).
If you're lucky enough to press the fire button at the exact moment the circle flails over the animal, then the animal instantly evaporates – a major disappointment for any hunter wanting meat or a trophy, although you do get some points. This task is made easier by your gun being fully automatic, holding all its ammunition in one clip and having a fire rate of approximately 480 rounds a minute. As all the animals take the same path, the most effective strategy is just to position the circle where you know all of them are going to pass and leave it there. You simply hold down the fire button as your prey reaches the circle and release it when they've vanished into the ether. Then the next creature from the queue immediately starts sliding across, and this continues until you run out of ammo. At no point do you enjoy yourself.
Hunter's only shred of variety is that there are three different mammals to slay, they appear in random order, and they are worth different points.
Here we see the crosshair circle in full jitter. Excitement fails to ensue.
Yet another intrinsic flaw with Hunter is that the smaller animals that give fewer points are actually harder to shoot. As there is no time limit and an infinite supply of woodland creatures with a death wish, the best plan is to ignore the slugrabbits and only shoot at the helidogs and sockelks in order to conserve ammunition.
The game finally ends when your bullets run out. At this point, a text box appears telling you that when your ammo hit zero, you turned around and ran away, accidentally smacked into a deer and fell over, and had to spend a few days in hospital. A final insult, although it's at least more colourful than just saying Game Over.
Hunter ends up not being a hunting game at all; instead it seems to focus on a jittery-handed lunatic wielding a huge automatic rifle and raking in an endless stream of wheeled cardboard cut-outs at the edge of a forest. Somehow I doubt this is what the programmers set out to achieve.
This is one of the most egregious examples of a game being knocked out quickly for the cash that I've ever come across. The whole thing feels unfinished on a conceptual level, let alone a practical one. The only decent part is the music, which was clearly not written for the game and was presumably only used because Condor Soft had access to it. I'm filing this one under "Cheeky to charge money for it".
Some PPP games were translated into English and sold by companies in the UK and America, but for reasons that should by now be painfully obvious, they decided to give Hunter a miss. I was unable to find any published reviews of the game, but I really, really hope that a German magazine somewhere was able to warn its readers against throwing money at this quarter-arsed semi-game.
PPP continued to sell games with such evocative titles as Rubber Ball and Glaggs It! well into the 90s. Condor Soft made no other games at all – presumably as they'd already brought the world a premier cardboard-elk-on-roller-skates-shooting simulator, they had nothing else to strive for.
REVIEW SCORES
None known. Which is a tragedy, as I'd love to know what the magazines of the time made of this embarrassment.
other versions
None. Although you could claim that Cabela's Trophy Bucks for the Xbox 360 is a spiritual successor, if you don't mind being completely wrong.
# THE MOST DISAPPOINTING GAME I EVER BOUGHT
by Paul Rose AKA Mr Biffo, Editor of former Teletext games mag, Digitiser-turned-screenwriter
Jack and the Beanstalk
Format: ZX Spectrum
Year of Release: 1984
Developer: Chris & Steve Kerry
Publisher: Thor Computer Software
Original Price: 5.95 pounds
I was sucked in by the graphics on the packaging of Jack and the Beanstalk – which, at least in screenshot form, did a fair job of aping the Ultimate Play the Game aesthetic. Not only did it not live up to the promised visuals, it was infuriatingly difficult. I don't think I ever got past the first level, which had Jack attempting to scale the beanstalk while being knocked off it by the endlessly-circling birds.
I was disappointed, naturally – but more than that, I felt cheated out of my pocket money. Consequently, I attempted to erase the tape using a magnet, then went to my parents and told them that there was something wrong with it. My dad took me back to the shop to get a refund, but the manager refused – of course, he tested out the game, and it worked fine. My dad pressed the point, getting increasingly angry, until the manager caved and said he'd replace it, but only with another copy of the same game. This led to a horrible escalation of events, which culminated in my dad using a racist term and storming out of the shop. The guilt of it haunts me to this day.
The horrible domino effect caused by my initial deceit utterly scarred me. I became much, much more cautious lest any knee-jerk purchases led to a further display of my dad's hitherto – and subsequent – buried racism.
Paul can be found at www.digitiser2000.com and on Twitter at @mrbiffo
FACT!
Jack and the Beanstalk supports the Currah μSpeech, a hardware speech synthesiser add-on for the Spectrum. When plugged in, the unit emits a slurring, mostly unintelligible buzz that is supposed to mimic human speech. When you turn on the game it shrieks "THIZZIZ ZUH SLORY OFF JAFFAND ZUH BEAN STORK," then stops the game and drones rubbish at you when you lose a life. It makes an already almost unplayable game far worse by slowing it down and hurting your ears.
# Killer Caverns
Format: Oric-1
Year of Release: 1983
Developer: Daryl Bowers
Publisher: Virgin Games
Original Price: 6.99 pounds
Have you been waiting all your life for a game about caverns that kill people? Well even if so, I cannot recommend this game. Sorry.
Killer Caverns tells the story of Helpless Harold, a man desperate to get his hands on a certain treasure chest. Usefully, he starts the game standing near it! But less usefully it's at the bottom of a well, and he can't actually reach it. So rather than go and get a rope or something, he decides to search through a nearby cavern system full of lethal dangers to retrieve seventeen parts of a ladder that a madman hid there. Helpless Harold is not a clever man.
This is where "ultra-minimalist" ends and "crap" begins.
The game begins by asking you to select a difficulty from 1-9, but it doesn't seem to make any difference whatsoever when you play. In fact, nothing you do makes much difference, but we'll come to that later.
Killer Caverns is graphically primitive, even for the time. The treasure chest is literally a red block, the caverns have flat, purple ceilings containing pencils of varying length, and Harold himself looks like the logo for a courier service. There is very little sound, save for an occasional hiss made by one of the cavern's traps.
I think these are spiders. They could also conceivably be crabs or defective wigs.
There are only two controls: one for moving left and one for moving right. Harold seems incapable of jumping as well as basic human reasoning. From the starting location next to the treasure-bearing well, you move left and keep going in the hope of stumbling over a bit of ladder. There is no route selection, you just repeatedly go from right to left.
Some screens are empty, but most contain some kind of horrifying, deadly problem you need to get past. These are:
• Spiders on the roof that randomly lower themselves
• A deadly jet of steam that randomly appears
• A set of spikes that randomly fall from the ceiling
• A giant blue snake/worm thing that randomly pops up from the floor
• A flying scorpion that randomly floats around the screen making comical noises, as if it's propelled by flatulence
You will notice that each obstacle has the word "randomly" in its description, and therein lies the absolute downfall of the game. Every danger appears and disappears entirely at random, meaning it's impossible to time your run past them. You may as well just hold left and hope, as trying to assert any control over your character is totally pointless. You've heard the phrase "more luck than judgement"? Well Killer Caverns is all luck and no judgement. It may as well be a coin-tossing simulator.
Farty the Floating Scorpion in action. Heaven help us.
There's also precious little variety in the caverns you run through. I could only find the five obstacles listed above and the occasional piece of ladder inexplicably suspended from the ceiling. You frequently run through the same screen twice in a row, and sometimes three or more times. Occasionally you die immediately on entering a cavern, which could either be due to a bug or extreme bad luck with the random obstacles. Either way it's bad news, as you only have five lives, although depositing an umbrella piece down the well earns you an extra one.
On the plus side, as the game is written in BASIC, it's trivially easy to get more lives. You can just break into the program and change a single variable to give yourself as many lives as you'd like. The downsides to being written in BASIC are that the game is sluggish, the controls are unresponsive, and the collision detection is vague at best. Not that the last point really matters due to the random nature of the game...
Kingseeker Frampt from Dark Souls makes his first video game appearance.
Even in 1983, Killer Caverns was totally unacceptable, especially for what was full price at the time. It looks awful, plays badly, and ultimately there's no point in playing it at all. The final insult is that after the game ends, it asks if you want to play again with a Y/N prompt. Pressing N does nothing, and it simply waits forever for you to press Y. Curse you, Killer Caverns.
Virgin's game releases of the time featured a photo and a mini-interview with the programmer, from which we learn that Killer Caverns was written by a 15-year-old schoolboy called Daryl who played synthesiser in a local band. It's hard to stay angry at him for this game though, as he seems like such a nice guy. If you completed his later Commodore 64 game Cheap Skate, it gave you his home phone number and invited you for a drink if you were ever in Kings Lynn. Plus he went on to program the excellent C64 version of comedy war game North & South, which obviously redeems him.
Here is every single one of Helpless Harold's animation frames. You're welcome.
Virgin only released one other game for the Oric – a strange collection of mini-games called – Them: A Paranoid Fantasy that was actually pretty good.
REVIEW SCORES
Personal Computer Games magazine gave it 1/10, declaring that "This game is so bad in so many respects, it amazes me how Virgin could have released such rubbish!"
other versions
None whatsoever. If you want the authentic Killer Caverns experience, you'll have to get yourself an Oric. (I suggest going for the upgraded Atmos version as it has a cool black and red keyboard.)
# Killjoy
Format: Commodore Amiga 1200
Year of Release: Unreleased (Finished 1996)
Developer: Stuart Ashen
Publisher: Unpublished
Original Price: N/A – Freeware
Warning: This entry is a bit of a cheat as it wasn't released commercially – or at all, in fact – but I am honour-bound to include it as a consequence of the way this book was originally funded. You can blame Alice Broadribb. (And it's only fair that people laugh at my crap attempt at a game since I've been laughing at others' the whole time.)
Back in 1995 I was tinkering with AMOS Professional, a BASIC programming language for the Commodore Amiga. The main program had been included on a magazine cover disk, and I'd managed to find a copy of the associated machine code compiler at a car boot sale. All I'd actually made were a couple of novelty programs to amuse my friend Raymond, but I'd sent them off to the public domain libraries of the time anyway. Bolstered by the success of seeing the names of my programs listed as two tiny lines of text in a magazine, I decided the time was right to make an actual game.
Suit-man is about to shoot. The background and blood spatter continue to look dreadful.
Unfortunately I was painfully aware that whatever I made would have to be extremely simple, as my programming skills were pathetic. I decided to opt for a target shooting game, since all it effectively entailed was having the player click on things with the mouse. Even I could handle that. Unfortunately I still had to deal with my lack of artistic skills when it came to the game's graphics.
Sega's 3D light gun game Virtua Cop 2 was popular at the time, and it made me realise that the graphics could be heavily stylised rather than traditionally drawn. Obviously full 3D was way beyond my abilities, and realistically those of the machine I was writing for, if I wanted the game to run at a decent frame rate. But there were other options. I had recently bought a device called Videomaster AGA that allowed me to import footage from a VHS recorder. A plan formed – I would borrow my dad's creaky Ferguson video camera, film myself arsing around in front of it, transfer the footage to my Amiga, and then draw over every other frame. This rotoscoping technique was rarely used in games at the time, but it worked incredibly well, giving the game a unique look. Sadly, every other aspect of Killjoy was awful.
Everyone you shoot is me. It's like Hunt the Ashens or something.
After the loading message, which I entered as "Loading, please dance" (I thought "Please wait" was boring) the game starts up by telling you how much RAM your computer has free. This is totally useless information from the player's point of view, and it doesn't even help me as the programmer because AMOS manages the memory itself. It may as well tell you the average annual rainfall in Helsinki.
The title screen tells you to shoot things without missing in order to accumulate score, whilst various characters from ZX Spectrum games scroll past. This wasn't really an aesthetic choice – I was just excited that I'd got a Spectrum emulator and ripped a load of graphics from it. A jolly little tune called "Cabbage" plays in the background and in no way matches the feel of the game. Like all other sounds in Killjoy, I took it from somewhere else – in this case I'd found it on a public domain disk somewhere.
My centre part haircut was the height of mid-90s fashion. (No it wasn't.)
So before the game begins, we have irrelevant information, graphics and music. This total lack of cohesive design is a feature of most of my early projects, in which I was overexcited by disparate ideas and threw them all together to the detriment of the overall enterprise.
The game itself is barebones and frankly not much fun. The single view is of an unbelievably poorly drawn road and a building full of windows. (I recall that it was a test background that I never got round to changing.) Featureless but realistically animated characters appear at the windows and shoot into the screen after a few seconds, unless you shoot them first. Other enemies run along the road, but they don't actually shoot or pose any threat; they just serve as a distraction. Occasionally, in a nod to Virtua Cop, people appear very close to the screen and try to slash it with a knife or meat cleaver. Unfortunately the slashing effects are so badly drawn that it looks more like they've been drawn on the screen with a red crayon.
Bang! One life gone. Green-man here is the only character not rotoscoped from my movements – the running animation is taken from Jodie Foster at the very beginning of Silence of the Lambs.
And that's it really. You just have to shoot as many people as possible before you lose all three of your lives. It becomes easy after a bit of practice, but you'll still be killed off by an annoying bug that makes your shots go straight through the melee of attackers about a third of the time. Other exciting programming errors include duplicating corpses and the ability to kill the people who appear in the building by shooting the frame of the window they're in. Also, the game only works on higher specification A1200 computers when it could easily run on the standard A500 machines.
When you do finally succumb to the onslaught of rotoscoped maniacs, the game plays the clichéd soundbite of Hudson from Aliens shouting "Game over, man!" and you're presented with statistics showing how many shots you fired and what percentage of them hit their mark. That's actually one of the few features I'm pleased with, as it adds an extra element to the game – making you try to keep your accuracy at 100%. Or at least you might do if the game was enjoyable in any way.
The Killjoy cast: Suit-man, Shirt-man, Green-man, Hazmat-man.
Killjoy isn't actually as bad as I remembered. It's utter rubbish, of course, but it might actually be possible to enjoy yourself playing it for a minute or so before the bugs and boredom force you to play something else. The sprites still look well animated and are vaguely reminiscent of The Last Express, an excellent PC game released the following year that made heavy use of rotoscoping to much better effect. But everything else about Killjoy is concentrated arse wash.
At one stage, I had plans to make a bonus round where you had to shoot an apple off a person's head while hindered by the targeting crosshair flickering around. I put together a test version, but it simply wasn't any fun so I abandoned it. Many years later, I discovered Hunter for the Atari 8-bit computers is exactly that idea but stretched to fill an entire game. It's amazing to think that only a year previously, people were charging money for something I considered too crap to include with a low-quality freeware title...
All that remains of my next game – a hacking simulator – are these icons. Why are "Mail" and "Upload" written lower down than "Dial" and "Analysis"? RUBBISH.
I finished Killjoy in early March 1996. Before I compiled it properly, a murderer shot dead sixteen primary school children and a teacher in the Scottish town of Dunblane. That made me decide the world didn't need a plotless game where you shoot random people, so Killjoy was never released.
Shortly after, I started to write another game – a kind of hacking simulator set in the early eighties and based on the 8-bit games Hacker and SATCOM. I put together the game's back end but never actually added any content, as the Amiga was on its last legs. Instead I got a PC, and then an internet connection the next year, and I started writing comedy articles instead of substandard games.
REVIEW SCORES
No reviews – the game wasn't released, and freeware games were rarely reviewed at the time anyway.
other versions
None.
# Licence to Kill
Format: Acorn Electron
Year of Release: 1987
Developer: Simon Guest & J. Hamblett
Publisher: Alternative Software
Original Price: 1.99 pounds
Before I delve into the well of fetid bum rot that is Licence to Kill, I need to make it clear that it has nothing to do with the James Bond film of the same name. That was released two years later, and the tie-in game wasn't released for the Electron. Here ends the public service message.
Another entry on the list of old budget games that couldn't decide what they were called, the cover of this game proclaims the title to be Licence to Kill, but the actual in-game text calls it Licenced to Kill. I'm going with the name on the case because it seems more official, and it's one less letter to type.
Fun fact: You do not have to be facing enemies to hit them. This is not a good game.
On loading, Licence to Kill presents you with 27 seconds of a black screen with occasional fart noises. The noises seem to be gunshot effects for the target logo that eventually appears and gets riddled with bullet holes. So far, so weird.
You are then given an amazingly long list of instructions for a budget game. The plot revolves around you being a top secret agent who must infiltrate a factory that has been taken over by a "neonasty organisation" to recover a valuable prototype. There are various digs at the ZX Spectrum in the names used – the factories are owned by "Sink-Lair" and the villains are known as the "Surclives", references to Sinclair Research and its founder Sir Clive. Even the prototype is called the "C7 3/4" which pokes fun at Sinclair's ill-fated electric tricycle, the C5.
Our hero stands impassively, accepting that his imminent death is unavoidable.
In order to retrieve the prototype, you need to get access codes from six different computers whilst collecting cassettes, keys and a disk. Enemy robots will hinder your mission by trying to murder you, but you're armed with an electromagnetic screwdriver which makes them teleport away when you prod them with it.
Got all that? Excellent! Now to start the game and wish you were doing almost anything else.
This is what happens when you climb the ladder. Not pictured: deep regret for playing this game at all.
The title screen is a hideous slab of green with black bars and an ugly custom font plastered on it. The title music seems to consist mostly of randomised, discordant beeping. A thin strip near the top of the screen has some text scrolling in it. You start the game and discover that the thin strip is the whole of the play area.
It's like you lost the keys to your house and are having to play the game looking through the letterbox. Amazingly, Licence to Kill uses only 12.5% of the available screen area for gameplay. There isn't even a lot of status information shown on the rest of the screen – it's nearly all empty!
This is the high score table with default entries! Because we've seen quite enough of the in-game graphics.
The graphics are about as basic as you can get. The almost featureless main character has two frames of walking animation and a frame for jabbing with his screwdriver... and that's the lot. The enemies are just palette swaps of the main character. The floor looks like a rope made out of unravelled Christmas jumpers. And the only background features are red doors, each of which is marked with a swastika. So rather than the game being set in a robot-infested factory as the instructions state, it actually seems to be set in a Nazi base of some kind.
You start off on the 32nd level of the astonishingly tall "factory" next to a ladder, which you can use to climb down to any of the other 31 floors. Each floor appears identical. You move right and your character shuffles along at high speed, a shrieking bleep accompanying every single step he takes.
Every frame of animation for the main character. I reckon that's a knife and not an "electromagnetic screwdriver".
After a few seconds, the enemies appear and rush towards you from both in front and behind. You press the return key for a screw-driver jab, and chances are you instantly die. This is be-cause the stabbing animation only appears for a tiny fraction of a second and doesn't seem to work all the time, and the enemies jolt along the screen so fast you can't time the attack properly. Actually hitting an enemy is largely down to blind luck – and when you do manage it, they sometimes just teleport right next to you anyway.
By employing super-human patience I was able to actually run a fair distance along several of the levels, but I encountered absolutely nothing except for background doors that are just for show. The levels seem to go on forever, and at no stage did I see anything to pick up or any computers to interact with for codes. I had a look online, and nobody else who played the game seems to have either. Are the instructions mentioning non-existent features and the game is actually a sham, with nothing to actually do? Or is it just so insanely difficult that nobody has ever got far enough to find anything?
I actually hate Licence to Kill. I have pretty neutral feelings about most of the games in this book and mostly think of them as amusing curiosities. But there's something about the sheer disdain this game seems to have for the player – and by extension the buyer – that makes me want to punch it right in the tape spool. It's painfully difficult, as progression is based more on blind luck than skill. The insultingly small letterbox that the game plays in is utterly unnecessary. Most of the game's described features don't actually seem to exist – or might as well not exist. The stated plot seems to have no bearing on the game, which actually seems to be about infiltrating a Nazi base armed with a knife. The high score table plays an off-key version of the cancan. And worst of all, it's called Licence to Kill but features no killing, just forcibly teleporting androids. This game hates me and I hate it right back.
It's amazing that a game this primitive and dreadful was released so late in the Electron's life. If the cassette inlay didn't clearly state the copyright date as 1987, I'd have thought it was a bad mail-order title from 1983.
Alternative Software released a slew of budget games across most of the 8-bit computer formats. Many of them were poor, to the extent that two of them are featured in this book. The development dream team of Guest & Hamblett also made incompetent Breakout clone Spheroids (AKA Round Ones) and the horrifying, flickery mess Indoor Soccer, making them the equivalent of war criminals in the Electron world.
REVIEW SCORES
No known reviews. I imagine the staff of Electron User magazine hid in the basement for a week when they heard it was being released. A wise choice.
other versions
None. I am pleased to report that all other platforms remained free of Licence to Kill.
# THE STATE OF THE INDUSTRY
Ste Pickford is a veteran games designer, graphic artist, and half of the Pickford Bros with his brother John. The Pickfords have worked on over 36 games since 1984 and were responsible for many successful, critically acclaimed budget games including 180, Feud, and Zub and Amaurote, as well as full price releases such as Glider Rider and Plok! Here's some insight into the industry that spawned the terrible games in this book, from someone who made good ones...
Beautiful loading screen for Feud on the Amstrad CPC.
My insight into the industry comes largely from my time working at Binary Design Limited which was a fairly large place (at least by the standards of the time).
It was actually a pretty professionally run place in many ways, probably ahead of its time as a proper, work-for-hire development studio in the mid-80s, which I don't think was especially common. There were maybe a couple of other places around the country similar to Binary Design, making games for budget developers like Mastertronic, but I think bedroom coders – amateur teams, essentially – made a good chunk of budget games. It was a weird mix. About half of budget games were made by teenagers in their bedrooms, and the other half were made at reasonably professional, large studios with several teams and multiple projects on the go at any one time.
The brilliant darts game 180 for the Spectrum. I played it so much that I became dart-perfect.
I'm not sure you'd be able to tell by playing the games which were made by professional studios and which were made by amateurs at home. We weren't necessarily making better games, but we were probably making them more quickly. I guess the budget publishers weren't getting enough games sent in on spec, so they had to commission more to satisfy the market.
Interestingly, at Binary Design we also developed full price games for Quicksilva and some other publishers. There was absolutely no difference in how we developed full price or budget games. I don't know if the money was any better (the boss never shared that information), but in terms of deadlines, which team was given the gig, how much effort we put in, etc., full price and budget games got exactly the same treatment.
Strategy and action collide in Death Wake, much like the aircraft and bullets seen here.
The full price publishers generally had a clearer idea of what type of genre they wanted (a flight simulator, future sport, etc.), whereas Mastertronic were more hands-off and just wanted it on time, but neither were very strong on judging quality or playability. That was really down to us. All that publishers were really bothered about was if a game was late or if there were serious bugs.
We (the development team) were really the only ones who cared about the quality of the games. The reason we were always late was because we were determined to make our games good, if we could. We took some pride in our work, we wanted players to like the games and we wanted good reviews. I don't recall any publisher caring about how a game would review while it was in development, although they were pleased with good reviews after release.
In school I became so enamoured of the Zub character that I drew comic strips about him for my friend Phil. I hope he doesn't still have them.
Binary Design definitely wasn't a tiny operation. They were about as big as development studios got in those days, and may well have been the biggest in the UK at the time. They just developed a lot of games for budget publishers.
When I started at Binary Design, the setup was five "teams", each of which consisted of an island of three desks pushed together in a large, open plan office. One of each team's desks was home to the ZX Spectrum programmer, one to the C64 programmer, and one to the Amstrad CPC programmer. All three members of the team would be writing the same game, each for their respective platforms (other conversions, like MSX or Atari were handled by freelancers). One of the three would be the designated lead programmer, which usually meant they designed the game as well. Depending on the game and the relative skill of the programmers, the lead would either write the game and the other two programmers convert the code, or they'd each write essentially separate versions of the same game better suited to their platform. Sometimes the ZX Spectrum and Amstrad programmers would write the game together, sharing code (each guy writing different Z80 "subroutines" shared between both versions), and the C64 programmer would write something different (6502 code, using C64 specific hardware sprites and scrolling, which couldn't be shared).
Plok! The Exploding Man for the Super Nintendo. Ste currently draws a comic about the character.
Music and sound were handled by a separate department comprising one musician (David Whittaker when I started – my line manager), and two or three graphic artists. We would provide sprites and backgrounds and loading screens for each of the five projects and their three versions, on an ad hoc basis. Mainly it was who asked first, or who seemed most in need. At one point our boss tried to introduce a "graphic request form" system, in which programmers had to submit forms listing a sprite or tile or something they needed, and we had to draw whatever was on the form at the top of the list, but that didn't work very well. It was easier to talk to the teams and judge for ourselves what was needed and in what order.
Deadlines were always an issue, though – we never felt we had long enough. My brother's very first project (Death Wake for Quicksilva) was given eight weeks. He was a new employee and didn't even know machine code at the time, so he was learning assembler while developing the game. He took 12 weeks and was in some trouble for being so late. Generally I think we had around 16 weeks for most games (and it was the same for budget or full price), but we always took a few weeks longer and were always slightly in trouble for being late.
The Pickfords also made Wizards & Warriors 3 for the NES. I'm only mentioning this so I can show this amusing sprite.
We would be scheduled to have, say, half a day allocated to getting the main character moving (this was in Zub on the Spectrum that John was programming). John spent half a day getting it working, but it didn't feel quite right. It wasn't enjoyable to simply run and jump. So John spent the rest of the day tweaking the feel of the jump and the movement. He might alter the speed of animation, or I might tweak the pixels in a frame of animation or add a new frame; then John would alter the strength of gravity and maybe the speed of movement, or add an extra delay before taking off from a crouch, etc. John would play it and tweak it until he was happy. All told I think the running and jumping in Zub took two days. John was then in trouble for making the game one and a half days late as only half a day had been allocated to main character movement. This pattern repeated itself over the development of the whole game (and every other game we worked on) – the boss's main focus was finishing on time, and our main focus wasmaking the game good.
When the game was finished, two weeks late, we were in trouble for "costing the company money", but very often our games went on to sell really well, bring in royalties, and (I'm certain) help the company secure future work. The games made by some of the other teams that were on time were often the most forgettable games that nobody cared about and didn't sell. So we used to argue that we were actually the ones making the company money. There was always tension between us and the boss, though, about being good or being on time.
In Feud, two brothers attempt to murder each other with magic.The Pickford Bros assure me it is not autobiographical.
As the 80s progressed, the industry began to change. The biggest shift was the switch to 16-bit. That was a massive transition, essentially increasing the number of artists needed on a team. With the 8-bit games, we had about three artists servicing 15 programmers (ok, that was five projects with three versions each, so some of the graphics were shared between games). With the 16-bit stuff, however, it got closer to one artist per programmer on each project, and more in some cases.
Toward the very end of the 80s, the consoles started to appear. We got in with Nintendo stuff earlier than most, so we switched from 16-bit to NES development around '88, whereas it was probably early 90s for most other British studios.
The switch to console was MASSIVE. Basically, we had to make games that were genuinely good – that £40 price tag meant the game had to offer a lot more value than a £1.99 game – and we had to make games that were bug-free. We scoffed at first – it was impossible to make bug-free games – but that was the requirement, and we did it, by and large. Console development was a big, big step up in professionalism.
## Which of your budget games are you most proud of?
I'd say Feud. That was the first project where John designed the game but wasn't the programmer. We actually sold the design to the company, with the map I drew being part of the game design, rather than something created during development. So this was our first experience of being game designers rather than game developers, and of designing a game before development started. The project was a success as well (on Spectrum and Amstrad at least), and it was a game where the actual design of it mattered and worked. As well as doing the 8-bit graphics, I also got to do the Amiga graphics, which was my first taste of 16-bit graphics work. I have extra fond memories of it for that reason.
Valhalla spoils the ultimate ending to the Avengers movies.
## What was the most disappointing game you ever paid money for?
Probably something big. There were loads of games that promised epic experiences but failed to deliver. Maybe Valhalla? I was expecting some epic adventure, and all I got was a buggy mess.
Ste is still making video games and drawing comic strips. He can be found at www.zee-3.com/pickfordbros/ and on Twitter at @stepickford
# Los Angeles SWAT
Format: Amstrad CPC
Year of Release: 1987
Developer: Beechnut Creative Software
Publisher: Entertainment USA (Mastertronic)
Original Price: 1.99 pounds
## Guest entry
from "Guru" Larry Bundy Jr, a British gaming television presenter who likes nothing more than to talk about obscure old video games in a humorous manner.
If this were any more macho it would be made of raw beef.
One of the weekly highlights for me as a child of the 80s was going with my parents to the newly built Tesco hypermarket in Watford for our big weekly shop. It was a huge, awe-inspiring building which (back then) was made to look like a converted village-barn-come-town-hall, complete with fake clock tower.
Halfway through our serial zigzagging of the many consumable-laden corridors, we came across an aisle presenting a vast collection of budget games for home computers. There were countless boxed cassettes, each pegged onto the wall in their own individual blister packs, and each one covered in exciting hand-drawn artwork, designed to separate young Johnny from his hard-earned pocket money.
An all-action shot showing a granny falling apart and a SWAT team member shooting at a colleague.
Upon one of these many visits, one game's artwork in particular caught my eye – that of a tough-looking riot cop, all in black, with mirrored shades and baseball cap, and sporting a rather fetching Burt Reynolds-esque moustache. Police cars and vans sped in front of him as he brandished an assault rifle so bloomin' huge he could take out a tank with it. So to my easily impressionable seven-year-old brain, it looked like the ultimate in awesomeness. Only a ninja dual wielding UZIs attached to nunchucks could possibly top it!
That game was Los Angeles SWAT. So I kissed goodbye my £1.99 and anticipated the excitement in my imminent future during my ride home from the supermarket.
Head inflation is a rare side effect of a gunshot wound, yet it happens all the time in L.A. SWAT!
Now, Los Angeles SWAT, or L.A. SWAT as everyone called it (the 80s loved its acronyms), is essentially a knock-off of Konami's arcade game Jail Break. You play a tough-as-nails riot cop, accompanied by two other officers (acting as your second and third lives) in a top-down, vertically scrolling shoot 'em up. You take on hordes of baseball bat-wielding gang members and roof-based snipers, all whilst avoiding innocent grannies and burnt-out vehicles in the riot-stricken streets of L.A.
Our hero is smashed into a bloody pulp as two clones salute each other.
Maybe it was a political statement on the militarization of police forces in the USA, or maybe it was just an excuse to make the game not look like a complete rip-off of Commando. It was a reasonably entertaining arcade style shooter and played essentially the same across all formats... Well, all except the Amstrad CPC version. Guess which computer I had as a child?
To call the Amstrad version "crap" is an insult to excrement. After ten minutes of loading, you're treated to one of the laziest title images in history – a mostly blank screen with nothing on it aside from a poorly cropped image of the Jaguar car company logo in the top left corner and the words "L.A. SWAT" in blocky italics. And things go downhill from there.
This is what happens when you complete level one. It's not a great incentive.
For starters, the programmer decided that he couldn't be bothered to program in the snipers or any audio whatsoever. There is only one enemy type in the game, and he resembles a Lego version of Daniel Stern's burglar character from Home Alone. He constantly spawns multiple clones of himself while viciously wielding an extremely in-timidating stick of liquorice.
Now Mr Stern is a feisty fellow. He will not only have seven or eight clones of himself on screen at the same time, but another will immediately take the place of one you killed the femtosecond he disappears, ultimately making killing them completely pointless – especially considering the main way to gain points in L.A. SWAT is to simply hold up on the joystick.
Luckily, the hordes of Daniels are easy to kill, as a single bullet from your rifle will cause his body to literally explode through his own eyeballs (yes, seriously). But, if he manages to break through your awkward, 30 degree angled firing lines, he will brutally murder you... and I mean brutally. Seriously, your corpse is just a pile of blood, bone and goo after he's finished with you!
But to be honest, the only legitimate danger is from the random grenades that the multiple clones occasionally throw in your direction. If they hit you, then confusingly they turn you into a dying Daniel Stern due to the game loading up the wrong death animation.
Speaking of which, the game is full of graphical glitches. For instance, it appears that the programmer at some point tried to code in the enemy snipers, but gave up halfway through. Their bullets do actually appear randomly on-screen, floating in the middle of the street, but they can't hurt you and the animation has them travelling away from you...
To top it all off, it takes less than a minute to beat the entire game as the single street you traverse just repeats forever. It may sometimes last longer, but that's solely due to the enemies getting themselves stuck in upturned cars and you taking an extra few precious seconds to run around and find the optimal angle to kill them.
So why was the Amstrad port of L.A. SWAT so bad? Well, it all seems to come down to Mastertronic wanting to port the game to all systems. American developer Sculptured Software, the original creators of the game, worked on the majority of the ports. But as the ZX Spectrum and the Amstrad CPC were British computers, those conversions was contracted out to an obscure and inexperienced local developer by the name of Beechnut Creative Software.
Beechnut must have been an extremely small company, as according to Google Maps, their place of operations was a terraced house on a council estate in Suffolk. Not only did Mastertronic never hire them again, but the only other Amstrad title they ever worked on was the judo simulator Uchi Mata. That scored 61% in Amtix magazine's review of the game, which said, "UCHI MATA is a pathetic piece of programming on what could have been a decent game."
Larry can be found at youtube.com/larry
and on Twitter at
@LarryBundyJr
REVIEW SCORES
None known. It's almost as if Mastertronic didn't send any copies out for review!
other versions
The Commodore 64 and Atari 8-bit versions are simple, slightly crude budget games that you could have some fun playing on a rainy afternoon. A very short rainy afternoon. The Spectrum version is a hideously ugly, jerky mess, but still far better than the diabolical Amstrad release.
# Show-Jump
Format: Dragon 32
Year of Release: 1985
Developer: Unknown
Publisher: Computerware
Original Price: 6.50 pounds
If you were making a video game about showjumping, to the extent of naming it after the activity, you'd at least look up how it was spelled, wouldn't you? Maybe the author had a load of spare hyphens lying around that needed to get used up.
Sadly this lack of basic effort leaks through into the whole game. Such were the joys of the mail-order industry for the more obscure computer formats in the 80s – you could release any old tat as long as the description was tempting.
This is the puissance course, which means there is a big wall at the end. Or several, in this game.
Show-Jump is a painfully basic attempt to simulate a complicated equestrian event. The screen is split into eight horizontal strips, with the very top showing the number of faults and the rest showing a side view of the course. Your rider starts at the top left and when he reaches the right-hand side of the screen, he teleports to the left-hand side of the next strip down, which I believe rarely happens at actual show jumping events. Perhaps each segment represents the view from a different, super-ultra-widescreen television camera positioned equally along the course?
Your horse and rider are represented by a handful of dark blue pixels that look more like a St Bernard dog with a desk tidy on its back. There are only two frames of animation, and jumping involves the horse taking a short flight, complete with gradual take-off and landing. Fences are red sticks, and water hazards resemble unmade beds with garish duvet covers. Sound is limited to an ear-splitting bell at the start of a race, popping noises for the horse's hoof steps and some beeps if you hit an obstacle.
Tragedy strikes at the equestrian meet as a horse devolves into some kind of crab monster between jumps.
Gameplay is extremely simple. First you select one of the game's nine courses. Then you can control the horse's speed and make it jump, and that's your lot. The faster the horse goes, the further it leaps, so you need to slow down if there isn't much space between obstacles or you will land on them. But it's harder to time jumps the slower you're travelling, so the game is mostly about managing speed.
And here the game breaks its leg and has to be taken out of the paddock and shot. You can't actually tell how fast the horse is travelling as it has no discernible effect until you jump. The accelerate and decelerate controls don't seem to work effectively either, so you have no fine control over something you desperately need them for. It's frustrating as the jump control is extremely responsive and the collision detection seems spot on. I'm not saying that Show-Jump would be a good game if you could gauge speed, but it would at least be playable for a minute or two.
Fail to jump a hurdle and, understandably, your horse refuses to run headfirst into it.
The simplicity of the gameplay is vaguely reminiscent of the "endless runner" genre of mobile games such as Canabalt, but lacking the finesse and compulsion that made those open-ended games so successful. (And it's also almost impossible to play effectively. Let's not forget that.)
There is one commendable feature in the game: when you clip an obstacle, it gets the top taken off at the height you hit it. A single nice touch in a field of garbage.
All the frames of animation used in Show-Jump. I believe there was no motion capture involved.
No developer is credited for Show-Jump, so I can only assume that it was made in-house at Computerware by ninjas and ghosts. They only released a few games for the Dragon 32, mostly based on existing games like Scrabble and Blockbusters, and they're all much better than Show-Jump.
REVIEW SCORES
Dragon User magazine gave it 1/5 and described it as "boring" – a damning insult for any game.
other versions
None. Phew.
# Surprise Surprise
Format: Amstrad CPC (464 Only)
Year of Release: 1986
Developer: Unknown
Publisher: Central Solutions Ltd
Original Price: 1.99 pounds
It is midnight. A hill overlooks the city. A dark figure stands atop it, gazing down at the lights below. A cold wind whips at its cloak but it does not seem to feel it. A small misshapen creature scrabbles to the hilltop, fear etched into its distorted features. The dark figure does not look away from the city as it begins to speak in a low, rasping voice devoid of any positive emotion.
"The plans have finally reached fruition. Soon these people will know true suffering."
The figure falls silent. Terrified, the creature next to him speaks hesitantly. "Master... Is it time?"
This is from the game's intro sequence. Apparently that's a mansion.
The dark figure turns towards the creature. Under its cowl, its face is a paper-white mask of evil – so twisted by years of seething hatred that it is barely recognisable as human. Its mouth contorts into a terrifying mirthless grin as it spits out the words, "Yes. Release Surprise Surprise for the Amstrad CPC."
Surprise Surprise is a rare thing – a game that seems to have been actively designed to frustrate and annoy the player to the point of illness. On loading you're presented with a headache-inducing mess of flashing colours, random beeps and randomly generated lines. The result is that your screen looks like it has been smashed, something you'll have the urge to do in real life if you continue and actually play the game.
This is every single frame of animation for the main character.
The cassette inlay reveals a simple plot. You've been invited to a banquet in a 100-room mansion, but on entering you have to find four "clues" to reveal the banqueting hall. Also the mansion is full of lethal, giant fruit that flies around everywhere. Yet rather than realise your host is a complete maniac and leave immediately, you decide to take up the challenge! I don't know what's on offer at the banquet, but it must be better than Turkey Twizzlers.
Surprise Surprise is absolutely hideous from the second you take control. The first thing you notice is the main character's ludicrous walking animations – moving left and right resembles a bizarre shuffle, and vertical movement involves his whole body staying rigid while his feet repeatedly dislocate themselves. In a strange design choice, his hair is only visible when he walks upwards.
A red blob falls into some random pixels. Or possibly an apple falls onto the rainbow road to Asgard. Who can tell?
Then you try playing the game, and any remaining hope you may have had for a fun experience evaporates into a cloud of pure hatred. Your character has a seemingly random walk speed: it starts off insanely sluggish in the first room and is even slower in others, to the extent that some screens can take an entire minute to cross. In order to travel from one room to another you have to align yourself precisely with the door gaps or nothing happens, and the alignment isn't precisely based on what's visible which adds an extra layer of annoyance.
Add these points to dodgy collision detection and it can be almost impossible to avoid the enemies that float around the mansion. That is a shame, as if you touch any of them at any point, it is INSTANTLY game over. There are no lives and no continues. This game can incite levels of frustration so extreme that they can cause nosebleeds.
I apparently found a clue in this dead end! It took 34 seconds to walk to the bottom and then back up again. I hate this game.
But it's the sound that really pushes Surprise Surprise beyond the realms of normal annoyance to somewhere the mind of man should never go. Constantly playing in the background is a hideous cacophony of random bleepy percussion noises. It's like something designed to break the will of captured soldiers that was banned under the third Geneva Convention. And as you've probably guessed, there is no option to turn it off.
As for actually progressing through the game, I only found one of the elusive "clues." Upon walking to the bottom of a weird, brown corridor, the screen flashed and the inevitable Game Over screen appeared. I had apparently been awarded one point out of an available five. Any attempts to take another route through the house led to instant death at the hands of the almost unavoidable enemies. I am a patient man, but this game is actually painful to play.
Our hero impersonates Eminem whilst being hassled by some giant floating limes near the very worst lamp Ikea sells.
The cover art is interesting because it shows a suit of armour shooting lightning from its hand, which has nothing to do with the game whatsoever. This attempt to hide the true nature of the game could possibly explain why it's called Surprise Surprise, as buyers were doubtless surprised by the hideous truth of their purchase. Or maybe the name was supposed to cash in on the television series Surprise Surprise! which was popular at the time.
When a game requires more patience than skill to progress, then its fundamental design is flawed. Surprise Surprise goes way beyond this to a point where it almost seems actively designed to cause the player discomfort. It is a grotesque mockery of an entertainment product.
The writer of the game remained anonymous, presumably so he or she could more easily escape with the money whilst laughing hysterically. Central Solutions Ltd only released two other Amstrad games – a terrible shoot 'em up called Barchou and the dull text adventure Mansion. They released a slew of other text adventures for the Spectrum, some well-regarded, but they never made the jump to the Amstrad.
REVIEW SCORES
Amstrad Action magazine awarded Surprise Surprise 10% and recommended that the reader buy a top of the line Amstrad CPC6128, simply because the game doesn't work on that model. And whilst I don't usually mention internet reviews, I'm going to give the last word to "Ritchardo" from his cpczone.emuunlim.org piece that gives the game zero out of ten: "I'm almost tempted to give it marks for the sheer bloody cheek of releasing this in the first place."
other versions
None. Thank heaven for small mercies.
# THE MOST DISAPPOINTING GAME I EVER BOUGHT
by Steve Benway, a retro gaming collector who plays games badly so you can see what they look like
Uranians
Format: Acorn Electron
Year of Release: 1986
Developer: S. Howitt
Publisher: Bug-Byte
Original Price: 2.99 pounds
I was, and still am, a fan of single screen vertical shooters, so when I saw the screen shots on the back of the Uranians cassette case, with lots of descending aliens, a mother ship at the top, and what looked like a really nice glowing effect, I was excited. Something like Phoenix, I thought. Pushing the system to the limit of its capabilities, I thought. Er... not quite.
After the typical five minutes of loading from tape, I hit "play", and the very first thing that happened was the big mother ship dropped a super-fast bomb which landed a quarter of the way across the screen from me. "Hah! Missed!" would be a reasonable reaction to such a lame attack, except the bomb created an explosion that filled a third of the bottom of the screen. Half a second of game-play... I hadn't even fired, and I'd already lost my first life.
It wasn't all bad. The movement of my ship was fast and responsive, though I'm guessing they used all the CPU cycles to do that, as the aliens' movement was predictable but jerky in a way that made them hard to shoot.
So that early death was just a bad start, you might wonder? Nope. The mother ship proceeded to dump those super-fast bombs with super-wide explosions on a regular basis, and even if they didn't kill you, the explosion would stay in place for around five to ten seconds, leaving you no room to move and allowing the aliens to pick you off.
That just leaves the impressive glowing effect of the graphics, shown in the screen grabs on the sleeve. Yeah, right. They'd just taken a photo of a TV screen, and the glow was from the screen.
Uranians? From Uranus? Yeah... I would say so.
I felt cheated and pretty bloody furious about it. The game was only £2.99, but as a young pup just out of school and suffering the exploitation of what was laughably called the Youth Training Scheme, I couldn't afford to just throw money away. However five minutes playing Uranians did make me want to throw my computer out of the window.
It didn't really change my attitude to buying games, though. I learned not to trust what was written or pictured on the case, but the problem was the Electron wasn't as common as the Spectrum or Commodore 64. As a result, the games were harder to find, and sometimes you just had to take what you could get. The sad truth is I was prepared to settle for really crappy games over no games at all.
Steve can be found on YouTube at <https://www.youtube.com/user/SteveBenway> and on Twitter at @SteveBenway
FACT!
There's also a BBC Micro version which has much nicer music, but it is so fast it's almost uncontrollable.
# SQIJ!
Format: ZX Spectrum
Year of Release: 1987
Developer: Jason Creighton
Publisher: The Power House
Original Price: 1.99 pounds
This is it. This is the worst game in this book. If anyone ever tells you that the worst commercially released game ever is E.T. for the Atari 2600 or Big Rigs: Over the Road Racing for PC, show them this. In fact, I'm not even sure this is technically a game. It was sold as a game, certainly, but it doesn't actually work as one.
SQIJ! is a conversion of aCommodore 64 game in which a mutant bird called "Sqij" lives in a post-apocalyptic world where food is running out. He must search some caves to find the parts of the Enertree, which will provide an infinite supply of future comestibles. However, the Spectrum version seems to focus on an immobile piece of folded paper sitting on the floor.
This was all there was to SQIJ! For any buyers who didn't understand the game's code well enough to fix the caps lock problem. Which was about 99% of them.
After starting SQIJ! you are presented with what appears to be a huge origami bird stuck between two scribbles in a dark cave. The scribbles, which look like they've been drawn by a three-year-old girl with her mind on something else, slowly flicker up and down. Your score increases. And that's it forever.
None of the controls listed in the instructions work. No buttons do anything. That's what your £1.99 got you in 1987 – a piece of paper wedged between some flickering infant's scrawl while a number increases.
After moving Sqij about a bit, the screen is a mess of virtual bird droppings as the graphics corrupt.
The problem is the game's code forces caps lock to stay on, but it then only accepts lower case key inputs. Apparently "playtesting" and "quality control" were terms totally missing in whatever alien language The Power House understood. And not only did they release the game in this state, they released it twice – first on its own, and then as part of a compilation.
However! Due to the monstrous, cosmic-level ineptitude of the programming, the BREAK key has not been disabled, so you can dive right into the source code and alter it at whim after pressing a single button. Also, the memory contains the full binaries for Laser Basic, the language the game was programmed in, meaning it effectively contains a pirate copy of a £14.99 utility. This is why testing a game before putting it on shelves and charging people for it is a good idea. So, by stopping the program and switching off caps lock in the memory (That's POKE 23658,0 if you want to try this at home) you can actually play SQIJ!
The start of the source code. Notice that line 1 exists solely to point to line 2. A ridiculous redundancy. Now notice that line 2 doesn't exist.
But then things get even worse. Animation is entirely limited to a small spasm on the row of dots representing Sqij's wing. There is no sound other than a few random beeps when the game loads. The instructions list eight control keys, but only four actually do anything, and they are the ones that move you around the screen. Sqij flickers and jerks in a direction if you hold the key down long enough. The scribble enemies move at a glacial pace and stop moving when you do. Graphic glitches are rife – as you move, you leave weird trails and can actually tear parts off the scribbles if you go near them. And ultimately playing the game is futile as any attempt to leave the middle of the screen bounces poor Sqij back and costs him ten energy points. It doesn't matter if you're near an enemy or not; there's no escape.
One odd thing is that when I first played the game on an emulator years ago, I somehow managed to go straight to the exits on each side of the screen (and through the enemies if I recall correctly). One didn't do anything, but going near the other crashed the game. I've not been able to replicate this through emulation or on original hardware, which is heartbreaking, as it means I've spent ages playing SQIJ! when I could have been doing anything else.
A scan of my copy of SQIJ! Yes, I paid money for it. Pity me.
Of course SQIJ! isn't the only game to have been released broken, bug-ridden and incomplete. C-Tech's Krazy Kong for the Spectrum was so infamously poor that Computer and Video Games magazine dedicated an entire page to readers' complaints about it. But SQIJ! is the most egregious example I've come across.
By far the best thing about the game is the cover art, which is a shame as it may have enticed people to buy it. The Power House often reused existing art, and this striking, dynamic image of a mutant bat by Tim White is a beautiful example. It was painted for the cover of the 1975 sci-fi novel Under a Calculating Star by John Morressy, and it has been used for multiple books since. The screenshots shown on the back of the cassette were from the Commodore 64 version with a note saying "Screen shots may vary from your version", presumably in order to hide the visual horror of the actual version you were buying.
The game over screen, adding insult to already substantial injury.
And SQIJ! just doesn't stop giving! At the time of release, The Power House were adding free audio tracks to their cassettes after the game data. They were promoting the music of a band called H.E.X. (House Electronic Xperience). Presumably they were connected to them in some way. The song on the SQIJ! tape is a repetitive, five minute funk track with semi-audible vocals that sounds like it was recorded on an old tape recorder in a bathroom. There's no title given, but from what I can make out of the lyrics, it's called something like Swimming Against the Tide of the Time.
So what the hell does SQIJ! mean anyway? Professional video gaming man Larry Bundy Jr suggested to me that it's a corruption of squigeon, a colloquial term for a pigeon. As the game stars a bird, I think that's by far the most likely explanation. It annoys me that there's no U after the Q though, as the English language doesn't work like that.
The Power House included digitised photos of programmers in their cassette inlays. Mr Creighton does not appear to be amused.
SQIJ! was written by Jason Creighton, who actually supplied an explanation for the game's startling lack of quality on the Spectrum 2.0 review website. Apparently he was contractually obligated by The Power House to produce the game, but after he fell out with a member of staff, he didn't want to deliver it. After avoiding the issue for a while, he wrote a deliberately terrible game in 40 hours to get them off his back, understanding that they would reject it. But as we all know, they happily duplicated it and sent it off to shops instead.
He also claimed that the caps lock error wasn't in the original game, and that it's possibly caused by modern computers emulating the Spectrum's hardware. I can debunk that immediately – I've played an original copy of the game on both a 48K+ and a 128K+2, and the caps lock error absolutely is present. Maybe it wasn't in the version he sent to The Power House and they added it? Seems unlikely as I very much doubt they paid any attention to it after checking that it loaded up, or they would never have released it...
The Commodore 64 version. Looks like a prototype of Angry Birds.
A look at the source code for the game reveals not only a frightening number of internal variables that don't do anything, but a message to be displayed if the impossible happens and the game is completed. It reads: "WELL DONE OLD BEAN!! YOU'VE DONE IT. BUT FOR ME IT MEANS ANOTHER 2 MONTHS IN A DARK DANK BEDROOM (WHICH BADLY NEEDS DECORATING) WRITEING A FOLLOW UP. OH WELL. NEVER MIND. BYE FOR NOW." The glamourous world of the bedroom coder hasn't changed much in 30 years.
Although almost unknown at the time, SQIJ! has gone on to garner infamy in the Spectrum community. The annual comp.sys.sinclair crap games competition, where people write deliberately awful Spectrum games, is currently hosted at sqij.co.uk. There could be no more fitting tribute.
REVIEW SCORES
No known reviews.
other versions
Commodore 64: This original version is predictably completely different. It's a smooth, well-animated exploration game with heavy shoot 'em up elements. The bad news is that it's frustrating rubbish – your energy drains away so quickly that most games last less than a minute, and most deaths are caused by getting caught on the background when you enter a new screen. The music is nice, though.
Commodore 16: Wow. This conversion could be an entry into this book on its own merits... or lack thereof. Similar to the C64 version and just as smooth, the positives end there. It's insanely fast, Sqij looks like an apple, every screen has the same weird chain of portraits flying around it, you can't kill anything so your bullets are useless, and there's no sound. Not as frustrating as the C64 version, but worse as a game.
# Trench
Format: BBC Micro
Year of Release: 1983
Developer: Unknown
Publisher: Virgin Games
Original Price: 7.99 pounds
The climactic Death Star trench battle in Star Wars is one of the most iconic sequences in cinema. Everyone remembers the exhilaration of watching Luke Skywalker skim along the battle station's surface as half of his friends blew up around him, then seeing him turn off his targeting computer because he heard a dead man's voice. The makers of Trench were obviously fans too, as they shamelessly ripped it off for this game.
Trench doesn't attempt to hide its influences. It specifically refers to "the Empire's Death Star" and "your X-wing fighter" in the instructions, although oddly it refers to TIE fighters as "alien guard ships." The setup is exactly as you would expect – you have to fly along a trench and then shoot an exhaust port the size of a womp rat to blow up the Death Star.
A laser blast narrowly misses the X-wing fighter! Not that the player had any say in the matter.
First impressions are extremely positive. The game starts with a rear view of your fighter flying into the trench as laser blasts hit the walls around you. In the background are constant whooshing noises and the pew-pew of the lasers. Then a siren-like sound starts as a TIE fighter comes flying towards you – it's genuinely exciting as you feel like you've been thrown into the middle of the action, yet it's still easy to take stock of what's going on around you. Then one of the lasers hits you and it's instantly game over, even though you've only been playing for a few seconds. Surprised, you wonder what happened. You start the game again and your second impressions are an awful lot less positive. The hideous, Grand Canyon-sized flaws in the game design become obvious as soon as you fully get your bearings. The first flaw is a disappointment – despite there being a button for "shoot", you cannot attack the TIE fighters. You only have a single shot saved for the exhaust port at the end.
The second flaw utterly cripples the game: the lasers that shoot into the trench appear instantly and at random in the rough area your ship is in. There is zero indication of where they're coming from and as such they are literally impossible to dodge. All you can do is move around and hope that one doesn't appear on top of you, meaning the game is down to luck rather than skill. And, of course, you have no extra lives, so the slightest hit ends the game immediately.
And that's it – the game is over. And to think they painted that TIE fighter red for nothing.
Other exciting ways to die include hitting one of the TIE fighters that jerk towards you or moving to the extreme edges of the screen where you hit the trench walls. Even travelling to the very top of the screen is enough to end the game, as apparently going "out of trench" invokes an immediate death penalty.
If the Trench gods are on your side, you may survive the short flight to the exhaust point. Here the game switches to a first-person view, showing the exhaust port as a 3D environment made up of a few lines. It runs at about three frames a second, so to say control at this point is sluggish would possibly be the biggest understatement of the century so far. You have to position the tiny port – which inexplicably doesn't get larger the closer you get to it – right in the centre of your targeting reticule before you fire. Your ship is glacially slow in this stage, so it takes ages to line up, and you can only just get a shot in before you smack into the trench wall in front of you. Hit it dead on and – you've guessed it! – you still continue onwards and smack into the wall. The "Game Over" message states, "You have destroyed the Empire's Death Star, but at the loss of your own life." I suppose it may be possible to escape in the handful of movement frames left, but I've not come close to working out how.
Whoops. Sorry everyone!
Trench is one of the most frustrating games I've ever played. But if that irritation isn't enough for you, the difficulty level can be cranked up, which increases the frequency of the laser blasts and thus the likelihood of instantly losing the game due to circumstances utterly beyond your control.
No, Mister Copyright Lawyer. That's definitely not an X-wing fighter. Not at all.
REVIEW SCORES
None. The only reference I could find to Trench anywhere in a magazine was an advert selling it in January 1984, which is why I've assumed a release date of sometime in 1983.
other versions
None. Just play Death Star Interceptor on the ZX Spectrum instead, as it takes the same basic idea, but the outcome is actually based on some measure of skill rather than blind luck.
# THE MOST DISAPPOINTING GAME I EVER BOUGHT
by Violet Berlin, who made TV shows about games in the nineties and the norties, and is now a scriptwriter for games & other interactive media
Castlevania II: Simon's Quest
Format: Nintendo Entertainment System
Year of Release: 1987 (1990 UK)
Developer: Konami
Publisher: Konami
Original Price: Approx. 34.99 pounds
I loved the first Castlevania on NES. Sooo much. I went hours and hours saying "just one more go", unable to stop playing, faint from hunger, and staying up all night.
Then Castlevania II came out. Reviewers loved its genre-breaking boldness – it introduced RPG elements and cryptic clues. Amazing! Except that the clues were too cryptic, or even non-existent in some puzzles, and I now know that subtleties lost in the English translation were partly to blame.
Castlevania II was a closed book to me. Or, rather, it was an exciting book that wouldn't open. Today you can just go on the net and find a walkthrough. Not so in those days. I was the only person I knew who played video games, so I was out in the cold with this one.
Reading about Castlevania II now, with hindsight, it is acknowledged that it didn't give proper clues, and without a walkthrough, it was almost impossible to know what to do. Apparently there was one in Nintendo Power magazine back in the day, but I didn't see it.
So even though Castlevania II had great promise, it was actually a mean trick... an impossible game that the reviewers probably got help with. The screen I was stuck on is still burnt into my memory, and I didn't play any Castlevania games after that.
You can find Violet on Twitter at @VioletBerlin
FACT!
The most infamously opaque puzzle in Castlevania II involves the following two clues: "HIT DEBORAH CLIFF WITH YOUR HEAD TO MAKE A HOLE" and "WAIT FOR A SOUL WITH A RED CRYSTAL ON DEBORAH CLIFF". What you actually have to do is kneel down in a specific place after equipping yourself with a red crystal and wait a few seconds, at which point a tornado takes you further into the game. Unbelievable. The infinitely clearer Japanese version of the second clue states "PRESENT THE RED CRYSTAL IN FRONT OF DEBORAH'S CLIFF AND WAIT FOR THE WIND", which implies that the translation was completed by a partially concussed nitwit.
# ULTRA SUPER REFUND ADVENTURE TURBO REVIVAL CHAMPIONSHIP EDITION EX PLUS ALPHA
## A text adventure for very all ages
# 1
It is 1987. You bought a copy of AIRBORNE RANGER for the COMMODORE 64 but the tape does not work. You are DISAPPOINTED.
You are in your bedroom. You have a RECEIPT and a NON-WORKING CASSETTE.
What now...?
> RETURN THE GAME TO THE SHOP
> PRAY TO HACIN, GOD OF LOADING ERRORS
NO CHEATING!
Please go back and choose a path
# 2
You walk along the HIGH STREET towards the shop you bought AIRBORNE RANGER from. You pass a NEWSAGENTS.
What now...?
> STOP OFF AND BUY A BOTTLE OF FIZZY DRINK
> CONTINUE TO THE GAME SHOP
NO CHEATING!
Please go back and choose a path
# 3
You light INCENSE and intone the sacred words "SHIFT/RUN STOP" that open a direct channel to HACIN. His HOLY VISAGE fades into view above your bed.
You tell HACIN of your woes, but he is ANGRY. He says that your FEALTY is in question as you have occasionally used your BIG TOE to press play on your DATASETTE - a grave SIN.
Before you can respond he shoots a STRING OF RIGHTEOUS FLAME from his SACRED NOSTRILS and you are burned alive.
You are DEAD. THE END.
NO CHEATING!
Please go back and choose a path
# 4
You enter the NEWSAGENTS. You survey a REFRIDGERATOR full of FIZZY DRINKS. You choose a bottle of CORONA ORANGEADE, as it is a long defunct brand that poses no potential LEGAL PROBLEMS if used in this TEXT ADVENTURE.
You REMINISCE about the CORONA MAN, a driver who used to deliver CORONA drinks directly to your house. Although the service still exists in 1987, it is becoming UNCOMMON due to broad changes in the SHOPPING HABITS of contemporary consumers.
You also REMINISCE about their ADVERTISING CAMPAIGN based around anthropomorphic BUBBLES passing a "fizzical" examination before they were deemed WORTHY to appear in the drinks.
Unfortunately your REMINISCING has resulted in more TEXT in this entry than anticipated, and your BRAIN reacts violently to the surfeit of POINTLESS CAPITALISATION that this text parser uses. You fall to the floor TWITCHING violently as your CEREBELLUM haemorrhages. BLOOD streams from your NOSE. The NEWSAGENT calls an ambulance but is too late.
You are DEAD. THE END.
NO CHEATING!
Please go back and choose a path
# 5
You enter SMITHSON MICROS, the independent VIDEO GAME SHOP you bought AIRBORNE RANGER from. It smells like a WRESTLER'S ARMPIT.
JON SMITHSON, the shop owner, greets you as you enter.
What now...?
> ATTEMPT TO RETURN THE GAME
> HUM THE SONG "THE ONLY WAY IS UP"
NO CHEATING!
Please go back and choose a path
# 6
You give JON SMITHSON the RECEIPT and NON-WORKING CASSETTE. He apologises and explains that he has no other copies of AIRBORNE RANGER in stock.
What now...?
> ASK FOR A CASH REFUND
> EXCHANGE THE GAME FOR ANOTHER OF EQUAL VALUE
NO CHEATING!
Please go back and choose a path
# 7
You begin to hum the song "THE ONLY WAY IS UP" by YAZZ AND THE PLASTIC POPULATION. Unfortunately it was not released until 1988, and this ANACHRONISTIC EVENT causes a rip in the SPACE-TIME CONTINUUM.
The very FABRIC OF EXISTENCE tears asunder and all of PHYSICAL REALITY collapses in on itself, forming a SINGULARITY that will serve as a COSMIC EGG for the birth of a new UNIVERSE.
You are DEAD. THE END.
NO CHEATING!
Please go back and choose a path
# 8
You receive £14.99 in cash from JON SMITHSON and return home even more DISAPPOINTED than before.
Unfortunately he pays you back partially in FILTHY COINS, which are covered in VICIOUS GERMS. You contract multiple forms of INFLUENZA simultaneously and DIE within 48 hours.
You are DEAD. THE END.
NO CHEATING!
Please go back and choose a path
# 9
You look over the shelves for a suitable REPLACEMENT GAME. You are tempted by two different titles.
The first is KNIGHT GAMES 2, a sequel to your favourite MEDIEVAL FIGHTING GAME. The second is KNIGHT ORC, a TEXT ADVENTURE with cool box art.
What now...?
> CHOOSE KNIGHT GAMES 2
> CHOOSE KNIGHT ORC
NO CHEATING!
Please go back and choose a path
# 10
You take KNIGHT GAMES 2 back home and load it up.
You reel in HORROR as you discover that the game bears no RESEMBLANCE to its predecessor - it is inexplicably a SIMPLISTIC ACTION GAME set in the year 3002. Enraged beyond RATIONAL THOUGHT, you hurl the box at the wall. As it comes to rest you notice the PRICE LABEL.
KNIGHT GAMES 2 only cost £9.99, but you paid £14.99 for AIRBORNE RANGER. Not only have you ended up with a NAFF GAME, but JON SMITHSON has ripped you off. Your anger builds to such a level that your ENTIRE HEAD explodes violently.
You are DEAD. THE END.
NO CHEATING!
Please go back and choose a path
# 11
You take KNIGHT ORC back home and load it up.
You SMILE SMUGLY as you discover the game is an excellent SPRAWLING ADVENTURE set across three distinct scenarios. You have CHOSEN WISELY and overcome all obstacles in your path to achieve the BEST POSSIBLE OUTCOME.
Then you SUDDENLY DIE for no reason whatsoever.
You are DEAD. THE END.
# Acknowledgements
I would like to offer thanks and appreciation to:
• Mike Cook, without whom this book would not exist.
• The team at Unbound for all their work and believing in this book in the first place.
• ChinnyHill10 for kindly checking that I hadn't messed up the technical details of the Amstrad CPC.
• Sarah Watts for her useful advice on equestrian matters.
• Brad Taylor, who independently confirmed my research into Sam Coupé games only for none of the information to be used... yet.
• The unknown army of people who scan old video game magazines and upload them to the Internet.
• People who watch my YouTube videos, as without them I'd have nothing. And that would be rubbish.
# INDEX
Albino Lego models
Alien chasing an inner tube
Amuse my friend Raymond
Black waffles
Bonus eyeballs
Coffee-addled businessman
Concentrated arse wash
Cosmic-level ineptitude
Dangerously barefoot skateboarder
Daniel Stern's burglar character
Dead man's voice
Defective wigs
Dog with head-mounted helicopter blades
Drugged bees
Eight horizontal strips
Extraterrestrial idiots
Freak-obsessed sociologist
Frog-headed child
Grand Canyon-sized flaws
Greedy Human Kind
Hair gel attack
Head stuck in the ceiling
Hideous graphical errors
Incomprehensible mess
Insult to excrement
Kings Lynn
Laser powered umbrella
Lethal giant fruit
Mentally incapacitated by paint fumes
Occasional fart noises
Off-key version of the Can-Can
Old tape recorder in a bathroom
Paper-white mask of evil
POINTS DOUBLE
Purple sloth
Sock-faced elk
Strategy Alpha
Unmade beds
# Terrible Names You've Probably Never Heard Of
Unbound is a new kind of publishing house. Our books are funded directly by readers. This was a very popular idea during the late eighteenth and early nineteenth centuries. Now we have revived it for the internet age. It allows authors to write the books they really want to write and readers to support the writing they would most like to see published.
The names listed below are of readers who have pledged their support and made this book happen. If you'd like to join them, visit: www.unbound.co.uk.
A frankly absurdly large amount of tat
A tiny Asian man with 17 Welsh sex slaves
"An Excellent Bryan Goldsmith"
AnthonyGiants AnthonyGiants
Akwa
BADMAN 2
The Baryshnikov Twins
Big Hairy Marty
Brandon and Becky
[CITATION NEEDED]
Dom and Faye
GameGlitchGuy G3
Geoffrey, The Meownarch of Kittenia
[INSERT NAME HERE]
Jonathan May, loves Hailey, Buddy, and Mishu
Lara S and Lissy H
Mackenzie & Yivo
Michael Kitch and Sam Clements
Most evil bastard
R M.
Vicky and Craig
Jack Abbott
Loren Abbott
Markel Abel
Adrian Acosta
Jake Adams
Peter Adams
Ronni Adams
Slater Adams
Terry Adams
Anakin Adcock
John Adlington
Angela Adrian
Aaliyah Agar
Joshua Agar
Anthony Aggett
Michael Agostinelli
Alice Ahn
Simon Aitken
Neil Aitken
Kim Akerø
David Alasow
Robert Alavoine
Oskar "Shamelessly asking if you ever used a BBS?" Albinsson
António Albuquerque
Adam Alby
Cody Alcina
Jaber Al-Eidan
Andréa Alexander
Andrew "imnotanerd" Scott Ali
Ediz Ali
Brian Allan
James Allan
Greg Allen
Paul Allen
Jim Alm
Mariah Almeida
Robert Altoft
Jose Alvarez
Vasco Alves
Matthew Amann
Emma Amfelt
Arman "Eyebro" Amin
Mike Amos
Justin Anastasio
Brad Anderson
Craig "Fox" Anderson
Stephanie Anderson
Virginia Anderson
Will Anderson
Cayden Andrews
Chris Andrews
Frankie Andrews
Tova Äng
Christian Ankerstjerne
Alexander Answine
David Anthony
Omari "Techandtrains101" Antony
Oskari Anttalainen
Drake Anubis
Nathan Applegarth
Phil Arber
Peter Arbuthnot
Guillem Arias
Alex Aris
Chris Arlott
Chris Armitage
Tom Armstrong
Dan Arries
Elliot Ash
Elizabeth Ashford
Dominic Ashman
Jason Ashmore
Tharglet Asimis
Magnus Asplund
Hannah Atkins
Nick Atkins
Michael Atkinson
Troy Atkinson
Tom Austin
Paul Auton
Jessica Ayako
Michael Ayling
Lady Azkadelia
Collin Bachman
Nicholas Backhouse
Erica Bäcklund
Calyb Badger
Jordan Badger
Doctor Bag PhD
Lewis Bage
James Bagg
Richard Baggaley
Paul Baggett
Andrew Bailey
Chris Bailey
Logan Bailey
Michael Bailey
Richard J Bailey
Richard Bairwell
Connor Baker
Josh Baker
Matthew Baker
Mike Baker
Vyvyen Baker
Dustin Baldus
Joe Baldwin
Stephen Baldwin
Jamie Balfour
Christopher Ball
Mark Ball
Matthew Ball
Kyle Ballagher
Robin Ballard
Toby Balshaw
Russ Bamber
Andrew Banas
Jack Bannerman
Broderic Banta
Adam Barbery
Jennifer Barden
Andre Bardin
Nik "TFk" Barham
Toby Barham
Matthew Barhorst
Andrius Barkauskas
Ryan Barkham
Riyad Barmania
Patrick Barnes
Tony Barnett
Jakob Barnstorf
Danielle Barr
Emma Barratt
Dane Barrett
Darrell Barrett
Joe Barrett
James Barry
Elliot Bartram
Jeremy Baruffa
Arnold Bashkevits
Paul Bastin
Jean Batzloff
Gavin Bauer
Daniel Baxendale
Chris Baxter
Chelsi Beale
Sheree Beasley
Fraser Beattie
Connor Beck
Greg Beck
Joseph F. Becker
John Beckett
Richard Beckett
Matthew Beckly
Michael Bedra
Daniel Beeley
Robyn Behan
Michael Behle
Keir Beigel
Aaron Bekir
Ole Bekkelund
Adrian Belcher
Andrew Bell
David Bell
Erik Bell
Mark Bell
Michael Bell
Philip Bell
Paul Bellamy
Christopher Belt
Garry Benfold
Kristoffer Bengtsson
Charles Bennett
Jon Bennett
Scott Bennett
Stan Bennett
Alex Bentley
Boris Bentley
Joe Bentley
Jon Bentley
Jared Berga
Lars Berge
Sven Berghuijs
Robert P. Bergman
CJ Berrisford
Michael Berry
Patrick Berry
Sam Berry
Simon Berry
Tim Berry
Koen Bertels
Leonardo Bertinelli
Chris Beshansky
Tim Best
Owain Bestley
Tom Betts
Kent Bevan
Sam Bevan
Sabrina Bewey
Christopher Bezzina
Braeden Bice
Eric Bickerdyke
Marcel Bienert
Jordan Bigness
Matthew Billany
Sophie Billing
David Bilous
Charlotte Birch
Jordan Bird
David Birdsall
Alexander Birk
Nicholas Birlie
Aidan Bishop
Scott Bishop
Isaac Bishop-Ponte
Joshua Bitzer
Jostein Bjørge
Guy Black
Robin Black
Tryston Black
Zayne Black
Robert Blackburn
Tom Blackburn
Craig S. Blackie
Alex Blackmon
Hugo Blair
Emily Blance
Andrew Blane
Elana Blane
Stephen Blane
Thomas Blindbaek
Jonathan Bloom
Nathan Bloomfield
Jürgen Bloß
Martyn Blundell
Alan Blyth
Kim Blyth
Tabitha Bodin
Philipp Boehme
Ed Boff
Bartek Bok
Steve Bolsover
Graeme Bolton
Jason Bonar
Jack Daniel Bond
Wilf Bond
Nicolai Bonde
David Bone
Anthony Bonica
Cees Bood
Anthony Booth
James Booth
Kevin Booth
Matt Booth
Robert Booth
Tim Boring
Victoria Borisova
Reese Borowiak
James Borrett
Scott Boughton
Hakim Boukellif
Alan Boulais
Chris Boulton
James Bouma
Joel Bourassa
William Bourgeois
Antoine Bourget
George Bourne
Nicola Bourne
Mackinnon Bowden
James Bowen
Drew Bower
Bodhi Bowers
Adam Bowes
Luke Bowes
Joth Bowgett
James Bowman
Munroe Stephen Stanley
Box-Cameron
Jacob Boyce
Bethany Boyd
David Boyd
Sean Frederick Boynton
Jacob Bracken
Graham Bradbury
Donya Bradshaw
James Bradshaw
Mark Bradshaw - (QuantumParadox)
Owen Brady
Paul Braiden
Christopher Brailsford
Dave Brain
William Brall
Tyler Bramley
Ewan Brammall
Kristen Brand
Michael Brand
Lee Brandon
Claus Just Brandstrup
Asbjørn Brask
Alex Breach
Derek Brealey
Martin Brear
Joshua Breazeale
Jamie Breeze
William Breeze
Mike Brent
Tom Brent
Simon William Brett
Wyatt Brewer
Dino Brewster
Alex Bricault
Roy Brickey
Ian Bridge
Billy Bridgeman
Timothy Bridges
Mat Brignall
William Brittain
Alice Broadribb
Johan Brockstedt
Louis Bromilow
Martin Brook
Matt Brook
Sam Brookes
Tim Brookes
Chris Brooks
Shaun "Dave" Brooks
Josh Broom
Brendan Brothers
Adam Brough
Ryan "madspy" Browell
Andrew Brown
Antony Brown
Austen Brown
Carl Brown
Dan M Brown
Ethan Macnair Brown
Gary Brown
George Brown
Graham Brown
Kevin Brown
Louise Brown
Stuart Brown
Theodore Brown
Zachary Brown
Carly Browne
Olly Browning
Phil Bruce-Moore
Carine Brunet
Max Bruton
Steve Bryce
Michael Buchan (Squeeowl)
Robert Buchan
Rosie Buck
Kevin Bucknall
Hendri Budi
David Budziszewski
Lars Bull
Sam Bull
Matthew Bulley
Andrew Bullock
Stuart Bullock
Stephen Bunclark
Kirk Bunston
Antonio M. Buonomo
Ian Matthew Burch
Martin C Burchett
Wes Burden
Ethan Burge
Calum Burgess
Matthew Burke
Alex Burnett
Andrew Burnett
Ross Burnett
Stephanie Burnette
Daniel Burridge
Kyle Burrows
Peter Burrows
Grant Burt
Richard Burton
Joe Bussert
Ben Butcher - JedForces
Anthony Butirro
Lee Butler
Alicia Butteriss
Robert Butterworth
Alan Byrne
Elizabeth Byrne
Thomas Byrne
Scott Byrne-Fraser
Kale Cabbage
Alejandro Cabrera
Stephen Caile
Pete Cain
Liam Caldwell
Aaron Calhoun
Ryan Callaghan
Tim Callaghan
Robert Callister
Craig Cameron
Scott "Young Scott" Cameron
Harry Campbell
Andy & Joy Candler
Rachel Cann
Daniel Capaldi
Rob Caporetto
Mark Carbonaro
Dane Carless
Philip Carlson
Rachel Carn
Manuel Gomez Carnero
Gavin S Carpenter
Louise Carpenter
Mark Carr
Matthew Carr
Nicholas Carr
David J. Carreiro
Tom Carrick
Bryan Carroll
David Carruthers
Stuart Carruthers
Seth Carson
Dan Carter
Laurie Carter
Alex Cartwright
Alice Casey
Karla Castillo
Mark Caswell
Caution Cat
Tenshi Cat
Corey Catalano
Gregory Cathcart
Richard Caywood
Josh (Yimyams) Chablis
Jean-Baptiste Chabrier
Barnaby Chambers
Gary Chambers
Scott Chambers
Tom Chamley
Chris Chan
Kai Chance
Ben Chandler
Edward Chapman
Harry Chapman
James Chapman
Jordan Charles
Sam Charleston
Ben Charlesworth
Rohan Charlseworth
Rory Charlesworth
Cameron Charlton
Philip Charlton
Steven Charlton
Alexander Chase
Tom Chatham
Tom Chatt
James Chatterton
Isaiah Chavez
Jon Cheng
Joseph Cherrett
Alexander Blake Cheskis
Alex Chesnut
Jordan Chew
Chloe Cheyne
Joseph Chiappa
Luke Childs
Ameya Chilekar
David Chipres
Andy Chirnside
Johannes Christ
Rasmus Mejer Christensen
Gordon Chung
Richard Churchill
Steven M. F. X. Cimprich
Daniel Clackson
Reed Clanton
Ben Clark
Em Clark
James Clark
Kieran Clark
Lewis Clark
Matthew Clark
McKay Clark
Ben Clarke
Iwan Clarke
Kieran Clarke
Matthew "DK" Clarke
Scott Clarke
Steven Clarke
Toby Claus
Joe Clausen
Brennan Clay
Joe Clay
David Clearwater
Tom Cleaver
Lachlan Clement
Scott Clements
Sean Clements
Jordan Cleverley
Josh Cliff
Robert Cliffe
Shane Cloherty
Josh Close
Jessica Clossey
Stuart Clough
Garrett Coakley
Nick Coakley
Richard Cobbett
Jay Cochran
Andrew Coggin
Macauley Coggins
Thomas Cohen
Maxime Cohin
Mario Coiro
Darren Colclough
Benjamin Cole
Christine Cole
Rhiannon Coleman
Nathan Collen
Shaun Collier
Christopher Collingridge
James Collins
Timothy Collins
Murray Colpman
Lily-May Colson
Ben Condon
Callum Connah
Rory Conneely
Christopher Connor
M. Conrace
Evan Conrod
Ryan Constantin
Freaky Constantina
Fatim Conteh
Conall W M Conway
Ashley Cook
Caleb Cook
Jamie Cook
Jessie Cook
Nicholas Cook
Ollie Cook
Sam Cook
Andrew Cooke
Jack Cooper
James Cooper
Joe Cooper
Neil Cooper
Richard Cooper
Richard W Cooper
Taylor Cooper
Tim Cooper
Zachary Cooper
Mike Coopland
Mark Cope
Michael Coppolino
Paul Corkindale
Michael Cormier
Brenton Costan
Alec Costan
Andrew Costin
Amanda Cournoyer
Aaron Coville
Matthew Cowan
Jack Coward
Scott Cowie
Eleri Cowlyn
Daniel Cox
Kieran Cox
Leon Cox
Lewis Cox
Matthew Alexander Cox
Sam Coy
Kit Coyne
Rebecca Crabb
Danielle Crain
Elizabeth Crampin
Matthew Crane
James Cranwell
Mike Crawford
Joel Cresswell
Kane Crichton
Bram Crielaard
Philip Crisp
Magnus Criwall
Kyle Crocker
Mihai Catalin Croicu
Mark Crook
Matthew Crook
Mark Crosby
Terry Crosher
Alex Crossley
Rob Crossley
Johnston Crothers
Ben Crowe
Adam Crowell
Matt Crowhurst
Richard Crowther
Aaron Crutchley
Gabriel Cruz
Christopher Csabon
Sanya Culp
Jake Culshaw
John Culverhouse
Curtis Cummings
Luke Cummins
Mallory Currier
James Curry
Simon Curry
Tom Curtis
Kelsey Custodio
Chris Cutts
Sarah Louise Cutts
Daniel D'Abate
Peter Daisley
Sandy Dakers
Sebastian Dalby
David Dalcino
Laura Dale
Stuart Dales
Daniel Daley
Dave Daniels
Thomas Lee Darby
Julian Daugaard
Craig Daveson
Daragh Davey
Colin Davidson
Sam Davidson
Adam Davies
Kyea Davies
Mark Davies
Matthew Davies
Paul "Wid3boy" Davies
Stu & Lindz Davies
Tony Davies
Adam Davis
Alex Davis
Jacob "Davistoa" Davis
Michael Davis
Morgan "Mo" Davis
Sam Davis
Adrian Davison
Allan Davison
Richard Davison
Samuel Dawes
Kayleigh Dawson
Mark Dawson
Harry de Carle
Danny De Casto
Dik de Jong
Cas de Rooij
Martin Dean
Shaban Jonathan Dean
Tobias Dean
Elliot Deans
Devin Debenport
Aaron Deicmanis
Jürgen Deinlein
Kayla and Zachary Del Rio
Niall Delaney
Stephen DeLay
Chris DelGobbo
Lee Dellbridge
Joe Demartino
Adam Demmon
Sophia & Joe Dempsey
Mark Dempster
Jack Denham
Thomas Obi Denham
Jenny Denholm
Christopher Denk
Matthew Denning
Kyle Dennis
Matthew Dent
Jonathan Denton
Wyatt Denues
Corey Derbyshire
Ryan Dermody
Ian Derrick
Tim Dettmar
Sebastian Deußer
Devjock Devjock
Lukas DeVries
Félix Dewaleyne
Corey DeWalt
Emily Diamond
Nathan Dibley
Stuart Anderson Dick
Miranda Dickinson
Stuart Dickinson
Jens Dietrich
Kevyn Dietz
Gabriel DiGennaro
Brendon Robert Dillon
Jude Dillon
Jonny Dimaline
Matthew Dimmick
Simon Dimmock
Thomas "Dimmock" Johnson
Sean DiMuzio
Sasha Distan
Thom Divine
Adam Dixon
Jono Dixon
Sarah Dixon
James Dobson
Terry Doel
Adam Doheny
Chris Doig
Sebastian Domagala
Jack Domenici
Jacob Donaghy
Ethan Donnachie
Kevin Donnellon
Amy Donnelly
Claire Baker Donnelly
Robert Donovan
Christian Doran
Sarah Dorrington
Jack Dorris
Anthony D'Orsi
Christopher Dostal
Aaron Doughty of Amigos Podcast
Joshua Dowding
Craig Downer
Thomas Downes
Andrew Doyle
Connor Doyle
Hannah Doyle
Jean-Raphaël Doyon
Thomas Drake
Laurent Dreikaus
Nicholas Drew
Thomas Drinan
Kirill Dronov
Colin Drum
Christopher Dudley
Cormac Duffy
Sean Dugan
Eric "Carrot" Skylar Duncan
John Duncan
Alex Dunn
Michael Dunn
Richard Dunn
Ryan Dunn
Scott Dunn
Vivienne Dunstan
Steven Duong
Andrew Durney
Hog Duske
Neil Dutton
Gary DuVall
Graeme Dyas
Rainer Dybevick
Doug Dysart
Liam Earley
Logan Eason
Peter East
Beverley Eastwood
Owen Eastwood
Josh Eaton
Will Eaton
Tom Eatwell
Daniel Eccleston
Richard Eckley
James Edge
Pete Edge
Timothy Edmonds
Christian Edwards
Edward Edwards
John Edwards - "An Excellent Bloke"
John Edwards
Kelman Edwards
Stephen Edwards
Tom Edwards
David Eggleton
Harry Egre
Nathan Ehrlich
Jake Ehuan
Jack Eisenmann
Adam Eisenstein
Greg Ekstrom
Dominick Elio
Aidan Ellams
Matthew Ellerington
Addam Ellington-Lewis
Thomas Ellinson
Ariel Elliott
Daniel Elliott
Chris Ellis
David Ellis
Morgan Ellis
Paul Ellis
Peyton Ellis
Richard Ellis
Sadie Ellis
David Ellwood
Scott Elrick
Rob Wagner Else
Timothy Elsy
Vidar Viking Elvigen
Galen Embry
Harry Emmott
Marshall Eng
Marius Engen
Paul England
Edward Englund
EpicLPer EpicLPer
Wolfgang Christopher Arispe Ervin
Matthew Etherington
Ryan Etherington
Alex Evans
Calum Evans
Daniel Evans
Edward Evans
Euan Euan
Graham Evans
Morgan Evans
Neil Evans
Paul Evans
Stuart Evans
Terry Evans
Harry Evely
Matthew Evert
Patrick Evison
Duncan Ewart
Paul Fadness
Benjamin Faiers
Chris Faiers
Sapphire Fairhurst
Robert Falb
Paul Fallon
Edwin Falter
Thomas Faltermeier
Antoine Fantys
Jacob Farrimond
Daniel Fawcett
James Fellows
Paddy Fellows
Christopher Femalè
Matt Ferguson
Daniel Fern
Erik Fernsund
David (mightyferret) Ferries
Thomas Ferry
Heather-Louise Fewins
Robert Fiddis
Chris Field
James Fielden
Richard Fielding
Lia Filippone
Casey Finder
Bret Finley
Luke Finnegan
Nicola R. Fiorelli
Joe Firman
Nick Firth
Andrew Fisher
Joseph Fishlock
Austin Fitch
Richard Fitzjohn
Michael Flack
V. Flack
Adam Flaxman
Katya M R P Fleming
Jack Fletcher
Josh Fletcher
Cameron Gazorpazorp fleuchar
Joseph Flint
Jorge Flores
Matthew Floyd
Jake Floyd-Eve
Dean Flukes
Peter Fodor
Paul Fogarty
Marc Fokkert
Emily Forbes
Adam Ford
Christopher Ford
Steve Ford
David Fornuff
Mike Forrest
Jamie Forsyth
William Forsyth
Emma Foster
John Foster
Stacey Foster
Geoffrey Fountain
Allan Fouracre
Vincent Fournier
Ben Fox
Josh Fox
Tim Foxall
Sebastian Fraatz
Kelsey Frame
Dan France
Philip France
Josh Francis
Lorenzo Francis
Monika Francis
Andrew Franklin
Samuel Franklin
Thomas Franklin
Finlay Franks
Aaron Franz
David Franzkoch
Joshua Fraser
Lachlan Fraser
Stuart "Felix" Fraser
Cameron Fray
Jens Fredriksson
Jeremy Free
Mike Freeman
Games Freezer
Max Freshour
Colby Friend
Theo Friess
Þór Friggjarkind
Carl Frill
Garry Fromont
Torey Frost
James Fry
Ian Fuller
Robert Fultz
Karsing Fung
Garry Furey
Justin Furlong
Axel Furzer
Cameron Gable
John Gabriel
Charlie Gadd
Matthias Gaebel
Sam Gain
Joseph Gaiser
James Gale
Shaun Gale
Anna Gales
Jake Patrick Gallagher
Rachael Galley
Mark Gamble
GameNeek GameNeek
Nicholas Gammans
Liam Francis Gannon
Ian Garcia
Barry Gardiner
Jonny Gardiner
Jordan Gardiner
Robert Gardiner
Ed Gardner
Steve "Xevian" Gare
Mike Garland
Ian Garner
William Garrard
Billy Garratt-John
Michael "Mikki" Garry
Daniel "Lord-Ashford" Garton
Edward Gaudion
Ashley Gaul
Dmitriy Gavryushkin
David Gaynor
Melanie Geer
Alex Geeves
Mariah Geiger
Andrew Gelhard
Max Gent
Daniel Geoghan
Nils Georgii
Jack Gerard
Michael Gernoth
Sebastian Gerstl
Jan Geselle
Sol Getcheffsky
Marius Ghita
Harry Gibb
Leon Gibb
Douglas Gibbons
Mark Gibbons
Scott Gibbs
Frederick Gibson
Carl Gietl
Andrew Gilbert
Christopher Gilbert
Neil Gilbert
Peter Thomas Gildersleve
Ben Gill
Travis Gillett
Isaiah Gillette
Billy Giorgio
Adam Girling
Nigel Henryk Girouard
Jon Gjelle
Lewis Glaister
Ed Glaser
James Glass
David Glover
James Glover
David Glover-Aoki
Jack Gloyens
Adam Glynn
Danny Godál
Peter Godden
Jose Godoi
Steve Godrich
Killian Goetowski
Christopher Goldasz
David Gometz
Dennis Gooden
Sean Goodliffe
Max Goodman
Andrew Goodro
Dan Goodwin
James Goral
Zack Gordon
Vijay Kumar Goswami
Tim Goss
Tom Gothorp
Ben Gough (Terrum)
Chris "Chairs" Gough
Alex Gould
Archie Gould
Gemma Gould
Andrew Goulding
Jack Gowrie
Nick Grabau
Jamie Graham
Tim Grainger
Callum Grant
Joe Grant
Xiola Granville
Joanne Grason
Troy Grauel
Jon Graves
Adam Gray
Callum Gray
Joshua Gray
Matt Greaves
Ben Green
Chris Green
Mark Green
Spencer Green
Walter Green
Rachael Greenfield
James E Greenhorn
Mark Greenwood
Wayne "Greeny" Greenwood
Mikkel Gregersen
Phoebe Greggor
Micheal Gregory
Harry Gregory
Stuart Greig
Matthew Greig
Mark Griffin
Nathan Griffin
Phillip Griffin
Mike Griffiths
Christopher Grimshaw
Jai Grimshaw
Frank Grisi
Edward John Gizzi
Brett Grocke
William Groom
Andrew Grover
Tom Groves
John Grun
Shauni Grund
Simon Grundy
Antoni Guest
Fu Gui
Chris Guler
Andrew Gurcsik
Mike Gurval
Catalina Gutierrez
Benjamin Guy
Carl Guyton
Davis Gysin
James Habermann
Jenny Hackett
Tre Had
Russell Haddock
Reece Hagan
Joshua Hagon-Fenton
Evan SirFucknut Haines
Ilja Häkkinen
Ed Hale
Thomas Hale
Simon Hales
Graham Hall
Jarrett Hall
Rhiannon Davies Hall
Kelvin Ham
Ben Hames
Steven Hamilton
Philip Hamling
Andreas Schack Hammann
Katie Hammer
Sam Hampshire
Stephen Hampshire
Youssef and Yara Hamway
Ashley Hancock
Christopher Hancock
Emma Hancock
Kieran Hancock
Richard Hancock
Matt Hancock
Robert Hancock
Doug "TestZero" Hancox
Steven Hand
Jason Handy
Bryan Hanes
Matthew Hanley
Stephanie Hanmer
Christian Hansen
Joe Hanson
Matthew Harbour
Martin Harder
Leonard Hardiman
Will Harding
Michael Hardy
Phillip Hardy
Jason Hargrave
Jake Hargreaves
Nathaniel Harley
Ryan Harms
David Harries
Brad Harriger
Calum Harris
Emma-Lea Harris
Kyle Harris
Nicholas Harris
Sam Harris
Samantha Harris
Bradley Harrison
Michael Harrison
Tyler Harrison
Richard Harseno
Bob Hart
Jonny Hart
Adam Hartley
Marcus Hartwig
Ben Harvey
Caitlin Harvey
Lucy-Jane Harvey
Mike Harvey
Sam Harvey
Symi Harvey
Jamie Hasted
Aaron Hastings
Ådne Haugen
James Hauser
Lee Danger Hawken
Adam Hawkes
Chris Hawkins
Luke Hawkins
Ruffian Hawkins
John Haworth
Günter Haydinger
Anthony Hayes
Joe "Chef Sexcellence" Haynes
Thomas Haynes
Michael Hayward
Martin Hdbrg
Efan Headford
Tony Heald
Brian Christopher Healy
Connor Heard
Cameron Heide
Joseph Heimbecher
Rob Hein
Harry Hein-Hartmann
Daniel Heinrich
Heikki Heiska
Olli Heiskanen
Arnt Helge Helland
Mark Hellewell
Jake Helliwell
Patrick David Helm
Luke Helyer
Jacob Hemmerich
Ian Hemming
J Hemphill
Ryan Hemsley
Morton Hender
Thomas Henderson
Oliver Henkel
Benjamin Hennig
Fin Hennigan
Andrew Henry
Archie Henry
Paul Henry
Anthony Herana
Craig Heritage
Robert D. Hermann
Serena Householder Hernandez
Seb Heron
Tyrone Hesbrook
Alex Hesford
Elizabeth Hesketh
Robbie Hess
Joakim Dominic Hetland
Andy Hewitt
Joe Hewitt
James Heydecker
Henry Hibbs
Stan Hickinbottom
Alex Higgins
Marlon Montel Higgins
Richard Higgs
Anthony Highton
Luke Hill
Samuel Hill
Yannick Hill
Keiran Hillcoat
Dennis Hillmann
Ethan "Batman" Hilton
Michael Hilton
Stephan Hilzendegen
Daniel Hinchcliffe
Matthew Hine
Adam Hirst
Alex Hiscox
Jonathan Hoban
Adam Hobson
Samuel Hobson
Joshua Hodgkinson
Martin Hodgson
Matthew Hodkinson
Gunnar "Crazy_Borg" Hoffmann
Sean Hogan
Tom Hogan
Dean "Oh Bother" Hogarty
James Hogg
Harrison Hoggarth
Jacob Holdcroft
Scott Holder
Jordan "Thornbush42" Holloway
Mariel Holm
Dan Holmes
Ian Holmes
Michael Holmlund
Byron Holton
Steven Holtz
Calvin Holtzclaw
Sam Homand
Elizabeth Homer
Mark Honeyborne
Chris Honeyman
Shaun Hoolahan
Mark Hooton
Joey Hopkins
Austin Hoppes
Jordan Hoppes
Jeffrey Hordon
Taylor Horn
Rachele Horsfield
Zöe Horsham
Robert Horvath
Paul Hott
Luke Hough
Jacob Hougie
David Howard
Louise Howard
Ralph Howard
Drew Howell
Adam Howes
Paul Howes
Samuel Howitt
Yuyang Huang
Benjamin Hubbard
Caleb Hubble
Jett Hudjik
Connor Hudson
Shannon Hudson
Steven Hudson
Wayne Hudson
Daniel Huffman
Daniel Hughes
Dave Hughes
Jim Hughes
Kara Hughes
Kyle Hughes
Rebecca Hughes
Folko Hülsebusch
Joshua Humphrey
Chris Humphreys
Troy Hungerford
Arron Hunnisett
Bryan Hunt
Liam Hunt
Palex James Hunt
Walter John Hunt
Ben Hunter
Jeremy Huntink
Alex Hurding
Sean Hurley
Calvin Hurndell
Simon Hurst
Dale Hurton
Damian Hustyn
Francis Hutchinson
Rob Hutchinson
John Huxley
James Hynes
Jack James Iball
Daniel Ibbertson
Hristo Ignatov
Nicole Imber
Dylan Imeneo
Tobias "Rotzetool" Immel
Paul Immerzeel
John Imray
Eric Ingland
Karl Inglott
Carla M. Iovino
Alexander Iris
Jason Irving
Sara "Blufrog" Isakova
Goemon Ishikawa
Mohammed Issa
Jesper Ivarsson
Biliby Iwai
James Jackman
Luke Jackson
Luke Jackson
Tom Jackson
Oli Jacobs
Rowan Jacobs
Paul Jacobson
Justen Jagger
Ben Jakobek
Tuulia Jalava
Andy James
Bonnie James
Edward James
Greg James
Matt James
Hunter James
Marcus James
Thea Jamieson
Usman "Grey Butter" Jamil
Andrew Janosi
Lucia Janousek
Eddy Jansson
Felix Bonney Jarman
Michael Jarrett
Cheis Jarrett
Jimmy Jarshaw
Harry Jarvis
Russell Jarvis
Joshua Jasper
Tom Jasper
Jedrzej Jawor
Mike Jeavons
David Jelfs
Tony Jenkins
Rhys Jenkins
Wayne Jenkins
Jack Jenkinson
Parker Jensen
Dustin Jethro
Andrew Jewell
Espen Johannesen
Runa Johannsdottir
Kim Johansson
Brian Johnson
Charles Johnson
Chris "Chika" Johnson
Chris Johnson
Daryl Johnston
David "NFi" Johnson
Edward Johnson
Gram Johnson
Hayley Johnson
Kevin Johnson
Matthew Johnson
Oliver Johnson
Ryan Johnson
Louis Johnston
Nikki Johnston
Andreas Jokiel
Jon Jon
Ashley Jones
Cat Jones
Dean Jones
Gareth Jones
Jai Jones
Joachim Jones
Joel Jones
Jonathan Jones
Julie Iler Jones
Luke Jones
Martin Jones
Nicholas Jones
Oliver Jones
Phil Jones
Samuel M. Jones
Weeaboo Jones
Will Jones
Zachary David Jones
Victor Jonsson
Wes Jordan
Darren Joseph
Colin Josey
David Jozwiak
James Judd
Spencer Julian
Ged Jurga
Kah-Hoe K
Jürgen Kadlec (DC the cyBerfoxy)
Samuel "Sambomacho" Kadoche
James Kael
Sarah Kage
Geoffrey Kahler
Ossi Kajo
Alesja Kalinikova
Michele Kalva
Dennis Alexander Kanabey
ZH Kane
Arjun Shivanand Kannan
Kevin Karan
Artem Karapetyan
Jussi Karjalainen
Martin Karlsson
Alexander "Xan" Kashev
Alex Kassa
Kevin Katz
Philip Kaufmann
Adam Kavan
James/제임스 Kavanagh
Anders Kavla
James Kay
Stephen Kay
Matthew Keany
Kathleen Keating
Tom Keen
David Keenan
Kim Keeton
Scott Keith
Tobias Kelle
David Keller
Chris Kelley
Declan Kelly
Mark Kelly
Ryan Kelly
Joe Kemsley
Tayler Kemsley
Andrew Kennedy
Christina Kennedy
Ash Kenyon
Stefan Keranov
Nick Kerins
Fraser Kerr (OfficialPirateFraser)
Jamie Kerr
Daniel Kerrigan
Amanda Kersshaw
Jae Kerwood
Patrick Ketaner
Ryan Ketteridge
Melissa Keursten
Kevin Kevane
Ian Kho
Khashayar Khoshrou
Wilf Kieran
Brandon Kiesling
Joanne Kilgour
Callum Kill
Peter Kimball-Evans
Andy Kimberley
Adrian Kind
Anton Kindestam
Daniel King
Ms. Gary Alexandria King
Iain King
Kevin King
Robert Kinns
Matthew Kirk
Ryan Kirkhoff
Jamie Kirkland
Luke Kirkpatrick
Chris Kirman
Parfyon Kirshnit
Simone Kirwan
Andre Kishimoto
Paul Kitching
Matt Kiteley
Fabian Klaetke
Adam Klassen
Michał Klaus
Benjamin Kleinfelter
Alex Kleinschmidt
Joe Klesczewski
Brian Kmak
Howard Knibbs
Paul Knibbs
Charlie Knight
James Knight
John Knight
Aaron Knight
Neil Knight
James Knill
Jared Knisely
Raphael Knott
Eldon Ko
Tony Koeffler
Stefan Koengeter
Thomas Kohl
Stefan "Chapi" Köhler
Tat Sing Kong
Dennis Konttaniemi
Janne Mikael Korhonen
Nikke Kostiainen
Manuel Kovats
Tim Kowalik
Sebastian Kozłowski
Jan Krause
Tjalfe Krause
Doug Krauss
Jens Krebs
Tobias Hernvig Kristensen
Zach Kromer
Matthew Kubicki
Zachary Kuhn
Mart Kuldkepp
Michael Kuligowski
Joseph Kuntz
Teemu Kurki
Jake Küssmaul
Sascha Kutzmann
Johan Kvande
Rachel L. Wedekind
Joshua Laber
Jessica Lach
Sam Ladner
Harmohn Laehri
Ville "jipostus" Lahtinen
Josh Lake
Chris Lakowicz
Lex Lamprey
Alexander Lane
Keith Lane
Alex Lang
George Langdon
Thomas Langford
Reece Langham
Markus Långström
Anne Lanham
Dominic Laoutaris-Brown
Nick LaPointe
Brian Largent
David Larkin
Alannah Larsen
Charlotte Larson
Emil Larsson
Elin Larsson
Pelle Larsson
Rowena Lashley
Jed Lath
Sam Lavin
Andrew Law
Keith Lawler
Jack Lawlor
David Lawrence
Lindsey Lawrence
Harry Lawrence
Saul Lawrence
Kris Lawton
Nicholas Lawton
Graham Layfield
Katie Leach
Kevin Leah
Alexander Leake
Darren Lean
Daniel Learmouth
Quentin LeBeau
Michel LeBlanc
Thomas LeBlanc
Jay Ledger
Alice Lee
Andy Lee
Corin Lee
Dennis Lee
Kris Lee
Matt Lee
Neil Lee
Richard Lee
Robert Leech
Rhys Leeke
Thomas Lees
James Lees
Zane Leff
Ryan LeGrand
Steven Leicester
Ian Leighly
Pentti Leino
Matthew Lennon
Brad Leonard
Janne Lepistö
Serena Leppanen
Alyssa Lerner
Stephan Lesch
Joseph Leslie
Dan Lesser
Jonathan Lester
Sam Leswisse
Alexander Lever
Adam Levitt
Bex Lewis
Bob Lewis
Christopher Lewis
Dan Lewis
Jacob Lewis
Kev Lewis
Matthew Lewis
Owen Lewis
Peter Lewis
Rhiannon Lewis
Ross Lewis
Sebastian Lewis
Carys Lewis-Watson
Francesco Lezi
Alex Lightfoot
Antti Juhani Liimatta
Stefan Lindfors
Ronald E. Lindhé
Fredrik Lindroth
Kristofer Lindsjö
Alexander Andrew Linton
George Lipyeat
Gunnar van Lit
Adam Little
Edward Little
Augustine Lloyd
Chi Lo
Kingston Lo
Brian Lobertini
Kristin Lockhart
Jamie Lockyer
Daz Lodge
Ryan & Bailie Loebs
Aaron Loessberg-Zahl
Arran Logan
Joseph Logan
Brandon Long
James Longley
Karl Johan Lõhmus
Dom Loraine
Maffiiee Lord
Moritz Lorey
Andrew Loughran
João Pedro H. G. Loureiro
Jon Lovegrove
James Loveridge
Ryan Low
Jenny Lowe
Jim Lowe
Stephen Lowe
Ruairi Lowery
Alexander Lowson
James Lowther
Anthony Lucas
Rob Lucas
Albert Lucia
Louis Luck
Nick Ludgate
Frank Ludlow
Stephen Ludlow
Andreas Lundgren
Steven Luo
Baustin Lux
Michael Lynch
Stephen Lynch
David Lyons
Korben Mabbs
Tamara Macadam
Sean MacBean
Angus Macdonald
Myles MacDonald
Nick Macey
George Machin
Hamish Mackay
Martin Macken
Ted Mackey
Curtis Mackie
Michael MacKinnon
Shawn MacRae
Katlin Maddox
John Madigan
Andrew Maeer
Robert Maehl
Patrick Magee
Venkat Mahadevan
Jehad Maher
Luke Robert James Main
Nathan Mainville
Robert Mair
Juho Majaniemi
Harrison Makepeace
Neil Malcolm
Nicholas Malthouse
Giorgio Malvone
Christopher "Chris" Man
Mike Manger
Zak Manley
Richard Manning
Hunter Manson
Per-Axel Mansson
Ian Marchant
Philip Marien
Thomas Mariucci
Joseph & Scarlett Markham
Iggy Markos
Richard Marr
Alan Marriott
Conor "Ronoc Mars" Marshall
Ethan Marshall
Helen Marshall
Philip Marshall
Rhys Marshall
Spencer Martell
Danny Martin
Graeme Martin
Kevin Martin
Law Martin
Robert Martin
Tim Martin
Tom A Martin
Stephen Martyn-Johns
Joe Marvin
Eric S Marynowski
Zak Mason
Kyle Massey
Michael Massey
Samantha Massey
Richee Mathwin
Lizzy Matterson
Colin Matthews
Lawrie Matthews
Daryl Mattinson
Whyle Mauriello
Christopher Mauro
Douglas Mawson
Matthew May
Paul May
Andreas Mayerhofer
Felix Mayfield
Maz Maz
Jacob Mc.
Paul McAteer
Chris McBride
Bernie McBurnface
Daniel McCabe
Stephen McCabe
Melissa Mccafferty
Kenneth Ellis McCall
James-Lachlan McCallum
Alice McCane
Matthew McCarroll
Paul McCarron
Jamie McCauley
Benjamin "Wile Man" McClune
Alasdair McCluskey
Kar McConnachie
Joey McConnell-Farber
Jonni McConville
William Mac McCorcle
Rachel McCormack
Matthew McCoy
Jack McCracken
Coire McCrystall
Kevin Paul McCullagh
Julie-Anne McCutcheon
Aaron McD
Robert McDaniel
Niall McDermott
Charlotte McDonald
Mark McDonald
Samantha McDonald
Thomas Mcdonald
Felix McDougle
John McElroy
Patrick McElwee
Liam McFarlane
Butterroac McFliggleblobb'n
Ross McGarvey
Conor McGhee
Raymond McGinty
Lee McGookin
Andrew McGregor
Niall McGuinness
Claire McHale
Elizabeth McIntivey
Andrew McIntyre
Logan McIntyre
Ian McIvor
Peter McKane
Sean Mckay
Erin Mckelvey
Darren McKenzie
Scott Mckerral
Theo McKinnon
John McLear
Bruce McLennan
Graham McLeod
Maranda McLeod and Mitch Crosby
Jennifer McLester
David McLintock
Hamish McMahon
Kevin McMullan
Craig Mcmurtry
Alex McNair
Henry McNamara
Amy McNeil
G. McNeil
Jamie McNeil
Alan McNeill
Cameron McPherson
Jason McPherson
Craig McSeveney
Nicholas McTaggart
Ryan McVicar
Daniel Mead
Eric Meadows
Jordan Meakin
Catherine Mearns
Dana Meddings
David Medina
Lukasz Medza
Chris Meeder
Jordan Meehan
Charles Meekins
Alexander Meijs
Tiffany Meldau
Ben Melluish
Dan Melluish
Andrew Melnick
Rev. Dr. Tomas Mendez
Uncle Mentuss
Nader Meradji
Ciaran Merrifield
Theodore Merrill
John Mestemacher
Ben Metcalf
Dan Michael
Kyriakos Michail
Abigail Michaud
Evan Michelsen
Connor Michie
Adam Campbell Milne
D. Mills
Danny Mills
Harris W. Miller
Ian Miller
Jack Miller
Kay Miller
Laura Mills
Luke Miller
Nathan Mills
Scott Miller
Theo Minetos
Francisco Martínez Miranda
Nicholas Ryan Misturak
Bryan Mitchell
Callum Mitchell
Chris Mitchell
James Mitchell
Ross Mitchell
Hayley Mitrano
Christian Mittelstädt
Manuel Mizelli
Glenn Moase
Harrison Moenster
Daniel Moffatt
Kristoffer "Alctors" Mogensen
Hollie Moir
Neil Moir
Chloe Monaghan
David Monid
Simon Monk
Gonzalo Paolo Carrasco Montanares
Paul "Monty" Montgomery
Robert Montgomery
Taylor Montoya
Gabriel Moody
Jordan Mooney
Andrew Moore
Arthur Moore
Daniel Moore
Dimitri Moore
Richard Moore
William Moore
Jonathon Moran
Rachel Moran
Johan Moremalm
Carl Morgan
Jamie Morgan
Tim Morgan
Dominic Morley
Chris Morris
Dan Morris
Elijah Morris
Grace Morris
Richie Morris
Drew Morrison
Grant Morrison
Harry Morrow
Aaron Morton
The Mother
Andreas Mottl
Sarah Mouhajer
Will Mower (ProfSquirrel_)
MrBrick MrBrick
Laura Muehlbauer
Wayne Muff
Darren "Weebl" Muir
Mike Müllejans
Maike Muller
James Mulvale
Jason Mumford
Joseph Mumford
Rose Mundie
Charlie Munns
Shanneen Murphy
Miranda Murphy
Patrick Fisher Murphy
Sarah Murphy
Daniel Murray
Ewen Murray
Andy Murrell
Joseph Murse
Shalott Muse
Kacper Musialkowski
John Mylan
Sindri Myr
Michaela Nachtigall
Benoit Nadeau
Phillip Naeser
Adam Nail
Billy Naing
Andrew Nairn
John Nash
Mark Nation
Michael Neal
Stuart Neal
Alexander Ruben Neave
Chuck Neely
Ivo Nelissen
Dylan Nelson
Michael Nelson
Shaun Nelson
Darrow Nemecek-Gulack
Absurd Nerd
Trevor Neubeck
Aaron Neville
Matty "Cirno" Newell
Elliot Newman
Kate Newman ㋡
Stu Newnham
Rob Newstead
Alexander Newton
Tony Nguyen
Natalie Nicholas
Dan Nicholls
Robert Nicholson
Ed Nickel
Chris Nicklin
Alexander Nicolas
Martin Walberg Nicolaysen
Gerard Nieborg
Derek Nielsen
J Nielsen
Simon "FischOderAal" Nienhaus
Alice Nietgen
Marie-Jose Nieuwkoop
Va Nilla
Joel Nilsson
Mark "Fawlkes" Nisbet
Michael Nisbet
Sam Nissen
Finlay Niven
Dan Nixon
Cain Noble-Davies
Nathaniel Noda
David Noddle
Antonia Noel-Buxton
Mitch Noon
Rebecca Noonan
Matti Nordström
Colin Norris
Joshua Norris
Bryana Norstedt
Matt North
Steve Northcott
James Norton
Kirk Norton
Andrew Nosler
Jens Nøstvik
Carsten Nottebohm
David "Twisted" Nottingham
Patrick Novak
Elizabeth Nuhfer
Adie Nunn
Andy Oakley
Loz Oakley
Joanna Oakley
Anthony Robert O'Brien
Mike Obrien
Peter O' Brien
Eileen O'Byrne-Hudson
Oliver Ockenden
Dan O'Connor
Darkūūmbāus Ocoorime
Ivan Odintsoff
Marc Ó'Dubhlinn
Britt Oertel
Liam O'Flynn
David O'Grady
Jack O'Keeffe
Iver Oknes
Rose Oldershaw
Ronan O Leary
Joshua Oliva
Adam Olivari
oliver oliver
Brian K. Olsen
Ben Olson
Cameron T. Olson
Erik Olson
Par Olsson
DJ Omnifusion
Mark O'Neill
Garry O'Neill
Cormac O'Neill
Ted O'Quilley
Michael Ordidge
Alex Orman
Jeff Orr
Ryan Mark Orrell
James Osey
Paul Osman
Maciej Ostaszewski
Daniel Österby
Andreas Filskov Kirk Østergaard
Carsten Otte
Paige Overbury
Danny Owen
Scott Owens
Sam Owens
Alastair Meengamer Oxby
Andrew Oxford
Sean Oxspring
Hakan Özalp
Frank P.
Kirstie "Kujatus" Parr
Sergio P Pereira
Hazel Page
Steven Page
Matt Pagliaro
Markus Pahl
Stelle Luna Star Paige
Daniel Palfrey
Daniel Palm
Alan Palmer
Ty Palmer
Gunnar Pálsson
Arjen Pander
Nep Pangilinan
Kostas Papadakis
Stelios Papanastasiou
Austin Paquette
Lucas Pardue
Ryan Parish
Allan Parker
Jamie Parker
Josh Parker
Robert Parker
Cassie Parkes
Graham Parks
Jacob Parley
David Parr
Jon Parry
Karl Parry
anthony parsons
Martin Partridge
Jacqueline Pasco
Anthony Pascone
Brian S Paskin
Patrick Pastolero
Kiran Patel
Mark Patelunas
Mark Paterson
Terence Paterson
James Paton
Patrick Patrick
William Paxton
Kyle J Peace
Andrew Peak
Emily Peak
Jay Pear
Ayase-Lewis Pearce
Gareth Pearce
Nick Pearce
Iain Pearson
William George Peckham
Katharina Alberta Pedersen
Erica Pegg
Ruben Pender
John Penney
Laurent Pépin-Julien
Jacob Peplinski
Elena Pereira
Richard Perrins
Sam "Graphikal" Persaud
Peskeh Peskeh
Carl Peters
Dan Peters
Thomas Petersen
Eric Peterson
Joshua Peterson
Simon Peterson
Joe Petner
Jon Petrusev
Sebastian Pettersson
Sten Jørgen Pettersen
Matt Petts
Devin Philipps
Frederick Phillips
Jamie A S Phillips
Jon Phillips
Thomas Phillips
Connor Philpott
Severin Pick
Elliott Pickett
Dixie Pickles
Jon Pidduck
Fingal Pierce
Ross Pigrum
Mateusz Pikora
Adam Pilborough
James Pilcher
Holly Pilgrim
Ben Pinkerton
Simon Pinkerton
Gemma Pinney
Laura Pinnick
Harry Pipes
David John Pires
Jacob Pitcock
Valentino Pizzi
Michael Plasket
Jeremy Platt
Haydn Plumb
Chris Plumridge
Mark Pocock
Mathew Poehlman
Callum Pogson
Michael Polcari
Daniel Polcari
Gabriel Pollard
Alastair Pollitt
Dean Poole
Ivan Popov
Amir Porat
Ian Port
Chris Porter
Lewis Porter
Matthew Porter
Steven Porter
Thomas Porter
Tim Porter
Juan Postel
Aidan Potter
Daniel Potter
Jon Potter
William Potts
Ewen Pountney
Alan Pow
Matt Powell
Aaron Powers
Adrian Powici
Mats Powlowski
Samantha Poynter
Jurate Pozeraite
John Pratt
Kieran Pratt
Matt Preiss
Ethan Prendergast
Michael Pressburg
Bobby Lee Price
Callum Price
Cameron Price
Ian Price
Lee Price
Thomas Price
Sam Pridige
Alex Pringle
Dan Proença
Steffen Seth Prohn
Mitchell Proud
Max Pruce
Patrick Prudlik
Kevin Pryke
Michael Cody Przeslica
Edward Puckering
Brent Puet
Matthew Pull
Jillian Pullara
Dan Punter
Justin Puopolo
Jas Purewal
Tim Purt
Tyler Puryear
Aaron Puzey
Huan Quayle
Zachary Quick
Jamie Quinlan
Jeremy Quinn
Daniel Quinones
Kevin Rademacher
Olivia Radford
Andrew Radlett
Angus Rae
Nicholas Ragan
Mikko Rajanen
Matan Ram
Eric G. Ramirez
Sarah Ramsay
Bobby Rank
Nath Raspin
David Ratcliffe
Rae Raven
Luke Raymond
William "Elliot" Rayner
Christina Razzi
Gordon Ream
Blainy RedCat
Ashley Reed
Owen Reed
Gaz Rees
Jamie Rees
Joshua Reeson
Samuel Reeve
Jay Reichman
Craig Reid
Shannon Reid
Craig Reilly
Liam Reilly
David Reinhardt
Thibaut Renaux
james Reuben
Gabe Reyna
John Reynolds
Matthew Reynolds
Josh Rice
The Rt Hon Mr James Marshall Harrison Rich Esq.
Troy Gordon Rich
Craig Richards
Dan Richards
Stephen Richards (RetroUnlim.com)
Ashley Richardson
Justin Richardson
Nick Richardson
Jonah Richcardson
Alex Richmond
Jake Emile Richmond
James E Richmond
Lisa Richmond
Liam Riddell
Sam Riddell
Chris Rider
Jonathan Rigby
Daniel Riley
Aidan Riley
Nicholas Ring
Christopher Ringe
Zachary Rippe
Jess M. Rivera
Jon-Carlos Rivera
Christopher Rivett
Martin Rix
Ian Robb
Cynthia Roberson
Andy Roberts
Benjamin Roberts
Harry Roberts
Iain "Chumpyman" Roberts
Kelly Roberts
Louis D Roberts
Rhys Roberts
Russell Roberts
Stacy Roberts
Stuart Roberts
Gary Roberts (Related)
Steven Roberts (Related)
James Robertson
Corey Robillard
Aaron Robinson
Alexander James Robinson
Jack Robinson
Jacob Robinson, Happy Birthday!
Jason Robinson
Paul Robinson
Scott Robinson
Zachary Robinson
Lara Robinson-Hoyer
John Roblin
Thomas Robson
Paddy Roche
Paul Roche
Jackson Roché
Gregory Rockcliffe-Smith
Iain Rockliffe
Lee Rodger
Shaun Rodger
Harry Rodgers
Andrew Rodland
Stian Rødland
Marek Rogalski
Adam Rogers
Kole Rogers (The Dark and Mysterious)
The Rohe Brothers
Andrew Rohl
Victor Portela Romero
George Ronksley
David Rose
Joshua Rosebrough
Lea Roselli
Scott Rosevear
Andrew Scoundrel Ross
Jack Ross
Cory Roth
David Rourke
Chris Rowland
Mark Rowley
Stephen Rowley
James "Llama Likes Gaming" Rowsell @CoolJWR100
Joey Rucker
Will Rucker
Brad Rudacille
Maxi Rüdiger
Jonny Ruff
Lukas Russell
Johan Rutberg
Toni Ruža
Alex Ryan
Kian Ronan Ashton Ryan
Megan Ryan
Sam Ryan
Sean Ryan
Justin Rybinskì
Iikka Ryynänen
TJ Saari
Sam Sackett
Phil Sadler
John Sadowski
Johan Saf
Matthew Sager
Aaron Saine
Salvador R. Salcido
Ramon Saldivar
Sarah Sale
Jeremy Salisbury
Keenan Salla
Rikki Salmon
Calum Salmond
Colin Salvona
Ivan Sanchez
Tammy Sandeen
Hugh Sandeman
James Danger Sanders
Scott Sanderson
Isak Roald Sandvik
Michael Santos
Mark Sargent
Alex Sarll
Callum Sarracino
Rosaria Sasso
Martin Saul
Alexander Saunders
Alix Saunders, the Magnificent & Spectacular (Asauz)
Neil Sawell
Adam Sawyers
Tomás Scaiola
Dave Scammell
Matthew Schacht
William Scharmach
Oliver Schawohl
John Scheinler
Kevin Schepler
Lucas Scheuenstuhl
Michael Schiciano
Michael Schlechta
xeetsh (Max Schmitt)
Eliza Schnabel
Austin Scholl
Andrew Schonenberger
Andreas Schouten
Alex Schramke
Michael Schultz
Daniel Schulz
Tristan Schulze
Jonathan Schuman
Alex Scott
Austin Scott
Hamish Scott
Jenny Scott
Kayleigh Scott
Mitchell Scott
Philip Scott
Robert Scott
Tim Scott
Katie Scrivener
Paul Scullion
seagull (www.seagull.io)
Owen Searfoss
Jack Seaton
Paul Sebert
Jonas Segura
Claudiu Selar
Liam Self
Terho Selin
Mica Sellers
Dell Selter
Ben Jammin Semple
Chaz Serir
Dylan Servilla
Steven Serzant
Matthias Seul
Oliver Shackleton
Mehdi shahmehdi327
Roger Shanks
Ethan Sharon
Christopher Sharp
Paul Sharp
James Shaw
John Shawler of Amigos Podcast
¯°·._.• Ʈɨʍǿţh¥ ρąţяɨȼЌ ȿɦƹƹɦ¥ •._.·°¯
Sean Shelley
Matt Shepherd
Gary Sheppard aka Dominoid
Kelvin Sherman
Grant Shipcott
Shared Shirts
Stephen Shiu
Pasha Shmuylovich
Jaime Shuminski
Jon Shute
James Shuter
Kaspar Shyjka
Emily Siddle
Jonathan Siddle
Dave & Holly Siederer
Matt Sieker
Matthew Sigmond
Maiju Siltaniemi
Jorge "punkmaniac" Silva
Duste Silverfin
Dan Silvester
Kieron Sim
Mark Simister
Paul Simkowski
Andrew Simmonds
David Simmonite
Henrik Simonsen
Verity Simpson
Daniel Simpson
Joe Simpson
Lauren Simpson
Louise Simpson
Michael Simpson
Ryan Simpson
Adam Sims
Cord Sims
Iain Sinclair
Alexander Singler
Daniel Singleton
Antti Sirviö
Charles Skeavington
Steven Skelly
Søren Skov
Richard Skrei
Misty Skylight
Dave Slater
Mollie Slater
Stephen Slatky
Ben Slee
Joshua Sloane
Eva Slusher
James Slusher, Jr.
Alexander Smakman
Jimmy Smallman
Alexander Smith
Andrew Smith
Anthony J Smith
Benjamin James Smith
Christopher Smith
Colin Smith
Daniel Smith
Dean Smith
Emma Smith
Hazel Smith
Jessica Smith
Joel Smith
Josh Smith
Joshua Smith
Isaac Smith
Ryan Smith
Scott Smith
Simon Smith
Stuart Smith
Robert Smith
Sam Smith
Steve Smith
Zaq Smith
Leon Smulders
Michael Smythe
Charley Snape
Natalie May Snook
Susan Snow and Justin Waskiewicz
Ryan Snyder
Markel Soikes
Stian Solli
Alexandra Solomon
David Somers
Aleanne Sommer
Ian Soon
Stuart Sopko
Mario Sorgente
Matthew "ReplayRetro" Sorrell
Natasha Soutar
Chloe Spencer
Izaak Spencer
James Spencer
Samuel Spencer
Sean Spencer
Rick Spermon
Ellis Spice
Joel Spicer
Liam Spinage
Jamie Spong
Aaron Sporer
Mark Sprusen
Marcus Spry
John Squyers
Alasdair J. Stainer
Ashley Stancill
Gabrielle Stanley-Sims
Dan Stanton
Rusty Stark
Andrew Steele
Sam Steele
Casper Steen
Matvei Stefarov
Emily Stell
David Stelling
Jens-Ejnar Stephansen
Nick Stephens
Robert E. Stephenson
Callum Steven
Alec Stevens
Hannah Stevens
Jason Stevens
Lee Stevens
Andrew Stevenson
Robert Spencer Stewart
U.E. Callum T. Stewart
Isaac Stidham
Kieran Still
Matthew Stobbs
Sam Stockdale
Kevin Stock-Kitzerow
Matthew Stogdon
Michael Stokes
Sondre Stølen
Curits Stollery
James Stone
Connor Storr
Dan Stott
Joshua Stough
Katie Stowell
Samuel Stracey
Robert Straub
Michael Strawson
Kevin Street
Matthew Streuli
Ulf Strömberg
Daniel Stuart
Will Stubbs
Wong Su Jun
Matthew Suconick
Antti-Jussi Suksi
Kent Sullivan
Alex Summers
Lee Summers
Paul Summers
Sean Suprenant
Tim Suter
Graham Sutherland
Scott Sutherland
Matt "Echo" Sutton
James Sutton
John Sutton
Wilhelm Svenselius
Lucy Swan
Liam Swann
C.J. Sweatt
Lewis Sweeney
Kevin Swidzinski
Lyndon Swift
Stephen Swift
Jennifer Swindells
Stephen Swires
David Symmons
Leah Elizabeth Szpak
Marc T
Ryan Tabbner (Turnip)
Nulani t'Acraya
Gábor Waitforit Takács
Timo Takalo
Luke Takoto Burns-Luckhurst
Aidan Talbot
Ben Talbot
Zak Talbot
Toni Tammisalo
Ian Tanswell
Ashley Tasker (Ashlo122)
Tuomas Taskila
Ezra Tassone
Allen Tate
Kayleigh Tate
Jose Taveras
Chris Taylor
Christopher "Ceryndrion" Taylor
David Taylor
Duncan Taylor
Grant Taylor
Hannah Taylor
James Taylor
Joel Taylor
Kat Taylor
Lee Taylor
Matt Mallory Taylor
Maxwell Taylor
Peter J. L. Taylor
Ross Taylor
Stuart Taylor
Glyn Tebbutt
Harry Tedeschi
Finn Tempo
John Testa
Matt Tester
Leonie Texier
Morgan The Bloodedge
Daniela Thelen
Sian Thirkettle
Theresa Thirkill
William Thode
Daniel "Soup" Thomas
Emily Thomas
Garan Thomas
James Thomas
Randy Thomet
Benjamin George James Leaver Thompson
Daniel Thompson
Derek Thomson
Jack Thompson
James Thompson
Isaac Thompson
Katherine-Louvain Thompson
Katie Thompson
Lewis Thompson
Naomi Thompson
Tyler Thompson
Robert Thomson
Alex Thorn
Benjamin Thornton
Brandon Thornton
Raphael Thoulouze
Ben Thrussell
Kyle Thurman
Chris Thursfield
Matthew Thwaites
Daniel Tighe
Sophie Tillbrook
Owen Tilling
Jamy Timmermans
Hans Timmers
Alex Tindall
Ben "the bespectacled" Tindall
Michael Tindall
Ted Tinker
matthias tirednsore
Douglas Titchmarsh
Joann Tober
Matt Tobin
Jake Todd
Tom Todd
Andrew Todhunter
Ville Toivanen
Nathan Tokala
Charles Toler
William Tomkinson
Paul Tomlin
Calvin Tomlinson
Charlie Tomlinson
Will Tommo
Johann-Mattias Toom
Dan Tootill
Rob Toplis
Mark Topp
Niko Torkkel
Espen Torseth
Ryan Townsend
Adam Towsey
Dave Toyne
Matt Trafford
Miika Tranberg
Richard Tranter
Ross Tregaskis
Lowell Treude
Leonardo Trevas
Hollie Tribbeck
Daniel Tribe
Joe Trigg
John T. Trigonis
Stuart Trotter
William Truong
Jon Truran
Hector Ttofa
Matt Tucker
James Tudhope (Tuddy)
Will Tudor
Zoltan Tudos
Peter Malcolm Tullett
Faye Tunnicliff
Andrew Turcich
James Turner
Josh Turner
Matt Turner
Sean Turner
Shareef Turner
Alex Turnpenny
Jess Turpin
Richard Twyman
Jeffrey McClain Tyson
Joseph Ullmann
Kay Are Ulvestad
Josh Underdown
Percy Underwood
Lloyd Unruh
Ryan Unruh
Connor Unsworth
Darek V.-J.
Aiden Vaines
Mika Väinölä
Marcello Valastro
Ernesto Francisco Arias Valverde
Carlos Gutiérrez Valerio
Estevan Valle
Michael Vallender
Martijn van Antwerpen
Werner Van Campenhout
Remco van den Heuvel
Jeroen van der Velden
Yves Van Hoof
Misja van Laatum
Davy Van Obbergen
Isaac Van Ristell
Wouter Vander Waeren
Alan Vanhoven
Luke Varley
Ruben Varne
Daven Vasishtan
Alex Vaughan
James Stuart Vaughan
Christopher Veach
Leo Veloz
Mark Vent
Colin Venters
Tatiana Ventura
Timothy Verheyn Jr.
BjøRn Vermöhlen
Robin Verschoren
Paco Verschut
Dylan Veysey
Harry Vigers
Markus Vikmanis
Mark Vincent
Jernej Virag
Frankie Viturello
Jose Vizcaino
Daniel von Oesen
Emily VonSydow
Yury Voronin
George Vosper
Jamie Voss
vpolp vpolp
Crystal Vu
Steven Vuong
Benjamin Waas
Alexander Waddell
Adam Wade
Evan Wagoner
Neal Wahlfield
Bradley Wainwright
Emilia Wake
Daniel Wakefield
Barry Wakenshaw
Thomas Waldo
Josh Walker
Paul Walker
Thomas Walker
Trevor Walker
Ryan Walker (nine3hundred)
Matthew "J Wall" Wallace
Michael Elton Wallace
Sam Wallace
Robb Wallace
Thomas Wallace
Jono Wallcraft
Julien Wallet-Houget
Mark Wallis
Matthew Wallis
Mathew Walls
Simon Xavier Walmsley
Jorge Walsh
Kieran Walsh
Jared Walske
Eric Walstrom
David Walter
Mark Walton
Benjamin Walton
Daren Walz
Thomas Wampler
Marcus Wan
Mark Wane
Peter Waples
Hannah Ward
John Ward
Lawrence Ward
Steven Ward
Ellie Ware
Marc Warner
Stu Warner
Timmo Warner
David Warren
Ben Warrender
David Warrington
Joshua Washburn
Cody S. Watkins
Dominic Watling
Marc Watson
Neil "poonab" Watson
Ryan Watson
Thomas Watson
Stewart Watters
Bethany Webb
Christopher Webb
Dylan Webb
Richard Webb
Björn Weber
Ben Webster
Russell Elliott Webster
Thomas Webster
Oscar Weckström
Oliver Wedgwood
Michael Weeks
Max Wegner
Bryan Weights
Ewan Weir
Stewart Weir
Russell Welfare
Joey Weller
Todd Weller
Kristofer Wells
Kyle Wells
Reese Wells
Robert Wells
Robert "Weaselspoon" Wells
Tom Wells
Rhys Welsby
Sean Welsh
Stephen Welsh
David Wendt Jr.
Jens Wengman
Tanner Wenzel
Roland Wenzel
Adam Wesley
Willem Wesseldijk
Callum West
Ryan West
Andrew Westgate
Chris Weston
Samantha Westwood
Elizabeth Wetton
Joseph Wharmby
Andy Whatman
Callum Wheatley
Mark Wheeler
Nicholas Wheeler
Phoebe Wheeler
Flynn Whelan
Paul Whelan
Steve Whipp
Nathan Whipps
Russell Whiskin
Katie Whitby
Marc Whitcombe
Alicia White
Grant White
Jason White
Skylar White
Stephen White
Richard Whitechest
Anthony Whiteley
Douglas Whiteside
Dani Whitford
Ben Whiting
Sam Whiting
David Whitney
David Whitten
Pete Whitton
Luke Wholey
David Whyld
Tom Whyte
Matthew Wieker
Keith Wiggins
Hannah Wigmore
Wout "Tenshi" Wijker
Pekka Wikman
Travis Wikoff
Gavin Wilcock
Nicola Wilcox
Rhys Wilcox
Jake Wiles
Timothy Wiles
Dominic Wiley
Stephen Wilkicki II
Ben Wilkinson
Kai Arne Willerud
Andrew Williams
Brenden Williams
Calvin Williams
Caylen Williams
Dafydd Williams
Damien Williams
Dave Williams
Giles Williams
Glyn Williams
Harry Williams
Holly Williams
Jamie Williams
Matthew Williams
Michael Williams
Mike Williams
Olivia Williams
Simon Williams
Tom Williams
Tristan Williams
Jake Williamson
Katie Williamson
Sean Williamson
Steve Williamson
Adam Willighan
Nikolas Willingham
Andrew Wilson
Bob Wilson
Frank Wilson
Lorna Wilson
Martin Wilson
Mat Wilson
Nicholas Wilson
Robert Wilson
Ruairidh Wilson
Steven Wilson
Joe Wilson-Palmer
Peter Wiltshire
Jessica Winch
Josh Windus
Michael Winn
Chris Winter
Adam Witney
Billy Witton
Joel Woelke
Auld Wolf
James Wolfe
Sasha Wolf-Powers
Gregory Wolking
Wojciech Wołoszczak
Martin Wolters
Joel Womack
Pete Wonnacott
Andrew Wood
Ben Wood
Edward Wood
Sarah Wood
Yvette Wood
David Woodley
Andrew Woodrup
Joanna Woodworth
Nathan Wookey
Katie Woolford
peter woolford
Christian-Philipp Worring
John Worster
Thomas Worster
Eddy Worthington
Thomas Wren
Alexander Wright
Dakota Wright
David William Wright
Glen Wright
Jeffrey Wright
Matthew Wright
Samuel Wright
Mikko Wrightson
Peter Wroot
Kenny Wu
Zak Wyeth
Jonathan Wynter
Tré X
Krista Yabe
David Yarnold
Ben Yates
Peter Yates
William Yates
Oladapo Yeku
Timo Yli-Rosti
Joanne York
Anthony Young
David Young
Jonny Young
Scott Young
Tim Young
Zac Youngdale
Amy "AutumnSounds" Yue
David Yuill-Kirkwood
Alec Z
Efrain Zamora
zard1 zard1
Christoph Zeitz
Jackson Zellmer
Alex Zevenbergen
Rui "John Money" Zhi
Greg Ziegler
Jakub Ziemkiewicz
Nick Zignauskas
Jeremy Zitnik
Walter Zollinger
Elric Zufan
Bart Zuidgeest. Someone You've Probably Never Heard Of. Also someone whose last name you'll find unpronounceable if you're not Dutch. You know, this text box seems to go on forever. I wonder how long I can make my name. Maybe get the entire book in here...
Ϩᴧᴜᴢ ソウザ
WagicalGale
AfxTwn
Federati
Eelface
CorranJP
JamesCAP
David.J.Bosworth
Alejandro
Drennor
DunKology
HiP.P
Robbo
Jimpan666
JojoYoungWolfieHachiVicLeafaKurtisSha
Kikoskia
Logi8ear
Maxamorph
Nigel
Odyssic
Earfolds
Figgy
Skelig
Rywern
UncheckedCrowd
Sliferjam
Spiderish
cooldude
Lurch666
DiamondPigman
GtBFilms
PartyMarty
Will3001
# This edition first published in 2015
Unbound
6th Floor, Mutual House, 70 Conduit Street, London W1S 2GF
www.unbound.co.uk
All rights reserved
© Stuart Ashen, 2015
The right of Stuart Ashen to be identified as the author of this work has been asserted in accordance with Section 77 of the Copyright, Designs and Patents Act 1988. No part of this publication may be copied, reproduced, stored in a retrieval system, or transmitted, in any form or by any means without the prior permission of the publisher, nor be otherwise circulated in any form of binding or cover other than that in which it is published and without a similar condition being imposed on the subsequent purchaser.
Text Design by Friederike Huber
Art direction by Friederike Huber
A CIP record for this book is available from the British Library
ISBN 978-1-78352-256-9(trade hbk)
ISBN 978-1-78352-266-8 (ebook)
ISBN 978-1-78352-257-6 (limited edition)
# Terrible Old Games You Probably Never Heard Of – Table of Contents
1. Hall of Fame
2. Unbound
3. Letter from Unbound
4. Contents
5. About this Author
6. Dedication
7. Superfriends List
8. Introduction
9. Alien Raiders
10. Alien Sidestep
11. Battle Probe
12. Interview: Alan Boiston
13. Bionic Granny
14. Car Race
15. Count Duckula 2
16. Interview: Jeff Minter
17. Crazy Kong
18. Dangerous Streets
19. Graffiti Man
20. Interview: Mentski
21. Button Press 3000
22. Highlander
23. Hunter
24. Interview: Paul Rose AKA Mr Biffo
25. Killer Caverns
26. Killjoy
27. Licence to Kill
28. The State of the Industry
29. Los Angeles SWAT
30. Show-Jump
31. Surprise Surprise
32. Interview: Steve Benway
33. SQIJ
34. Trench
35. Interview: Violet Berlin
36. ULTRA SUPER REFUND ADVENTURE TURBO REVIVAL CHAMPIONSHIP EDITION EX PLUS ALPHA
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
37. Acknowledgements
38. Index
39. Terrible Names You've Never Heard Of
40. Copyright
1. Cover
2. Letter From Unbound
3. ToC
4. Copyright
5. Introduction
6. Acknowledgements
7. Dedication
8. Index
Copyright (C) 2015 Stuart Ashens
| {
"redpajama_set_name": "RedPajamaBook"
} | 1,576 |
{"url":"https:\/\/alexschroeder.ch\/wiki?action=browse;diff=2;id=2011-03-08_More_Character_Shortcuts","text":"# 2011-03-08 More Character Shortcuts\n\nLast edit\n\nChanged:\n\n< A bit over a year ago I wrote my first draft of the [[2009-12-14 Character Generation Shortcuts|Character Generation Shortcuts]] fold old school D&D with four backgrounds each for fighters, wizards and clerics. In a way I wanted to show that I didn't need thieves, rangers and paladins -- I wanted to model these classes using a base class with some appropriate background and equipment -- and I wanted to speed up character creation by avoiding rolling for starting gold and shopping for equipment. Half a year later I [[2010-06-24 Character Genration Shortcuts PDF|increased the number of backgrounds to eight]] and used it in a convention game I ran, but I still missed backgrounds for demihumans. The following is a list of four backgrounds each.\n\nto\n\n> A bit over a year ago I wrote my first draft of the [[2009-12-14 Character Generation Shortcuts|Character Generation Shortcuts]] fold old school D&D with four backgrounds each for fighters, wizards and clerics. In a way I wanted to show that I didn't need thieves, rangers and paladins -- I wanted to model these classes using a base class with some appropriate background and equipment -- and I wanted to speed up character creation by avoiding rolling for starting gold and shopping for equipment. Half a year later I [[2010-06-24 Character Generation Shortcuts PDF|increased the number of backgrounds to eight]] and used it in a convention game I ran, but I still missed backgrounds for demihumans. The following is a list of four backgrounds each.\n\nChanged:\n\n< We'll see about adding more entries and revising the [[2011-03-15 Character Genration Shortcuts PDF|PDF]] when I have some extra time. :)\n\nto\n\n> We'll see about adding more entries and revising the [[2011-03-15 Character Generation Shortcuts PDF|PDF]] when I have some extra time. :)\n\nA bit over a year ago I wrote my first draft of the Character Generation Shortcuts fold old school D&D with four backgrounds each for fighters, wizards and clerics. In a way I wanted to show that I didn\u2019t need thieves, rangers and paladins \u2013 I wanted to model these classes using a base class with some appropriate background and equipment \u2013 and I wanted to speed up character creation by avoiding rolling for starting gold and shopping for equipment. Half a year later I increased the number of backgrounds to eight and used it in a convention game I ran, but I still missed backgrounds for demihumans. The following is a list of four backgrounds each.\n\n1d4Elf Dwarf Halfling\n1you are a woodland hunter; you own an elven longbow with twenty arrows and a curved dagger decorated with silver runes; the lore masters have taught you the spell sleep to keep you safe while alone in the wilderness you are a miner but it was dangerous work for little gain; you own a canary bird in a wooden cage, a small pony to carry your load, a lantern, studded leather armor and a heavy pick you are a shepherd; you own a sling, a dagger, a woolen cloak, and a ferocious dog that will defend you in combat\n2you are a student of ancient lore; you own a ceremonial elven longsword in the old tradition and a set of chain mail; the lore masters have taught you the spell read languages to help your studies you are a gem cutter by trade but decided to go looking for the real thing; you own gleaming chain mail, a beautiful two-handed sword and a jewel encrusted girdle handed to you from your father you are a gardener; you own a hammer and a sling and some ill-fitting goblin leather armor\n3you are a spell singer; you own an elegant elven longsword, a dagger, leather armor, a wooden shield, a lyre and a silver flute; you have learned the spell charm person to keep you safe in human lands you are berserker with warding tattoos covering every inch of your skin; you own a two-handed dwarven battle axe inscribed with old runes of death and destruction and battered scale armor you are a scout and have travelled the wilderness; you own leather armor, a shield, a short sword and a sling\n4you are a fae knight; you own a white horse, a white steel plate armor, a shield, a lance, a long sword, a mace; your master taught you the spell protection from evil before sending out into the world you are rune warrior and a defender of the realm; you own the finest dwarven plate armor, a heavy shield engraved with runes of protection and an axe.you are a bored landowner but left your siblings in charge of it all; you own a short sword, a shield, light dwarven chain mail and a sling\n\nWe\u2019ll see about adding more entries and revising the PDF when I have some extra time.\n\nTags:\n\nDifference between revision 14 and current revision\n\nSummary: $\\[gravatar:.*$\\]\\n? \u2192\n\nDeleted:\n\nDeleted:\n\n< [[gravatar:http:\/\/blog.mausdompteur.de Harald:fd33438f1aeed32f19760834a93da0f5]]\n\nDeleted:\n\n< [[gravatar: AlexSchroeder:e33b88db6bc04e1c93db25c702baea28]]\n\nDeleted:\n\nDeleted:\n\n< [[gravatar: AlexSchroeder:e33b88db6bc04e1c93db25c702baea28]]\n\nDeleted:\n\nDeleted:\n\n< [[gravatar: AlexSchroeder:e33b88db6bc04e1c93db25c702baea28]]\n\nTypical \u2013 if you are elf, you can be awesome things like a hunter, spell singer, or fae knight, and if you are dwarf, you could be a rune warrior or berserker. But if you are a halfling, you probably used to be a gardener\n\nLooks like Alex got a whiff of \u201cimplicit setting\u201d here \u2026\n\nHarald 2011-03-08 19:54 UTC\n\nAbsolutely. One roll life-path, baby!\n\nActually, I\u2019d love to brainstorm some more:\n\n; Elf: a sea elf with trident, net, bow, longsword; a moon elf with a horse, a member of the wild hunt, a horn, a bow, a scimitar, a wolf hound companion; a shadow elf from a far realm, an illusionist with a spider companion and a dagger; a dark elf that lived under the hill, a member of the winter court, a forger of rings (lame easter egg?)\n\n; Halflings: a crazy naked ferocious halfling cannibal; an escaped slave, broken by years spent in the darkness deep underground; maybe something crazy like a windling \u2013 those halflings that were picked up and blown across half the world by the five great storms; a fool that was sent on adventure by a wizard (lame easter egg?)\n\n; Dwarf: Any ideas?\n\nDwarf - beardless outcast, apprentice brewmaster, grizzled campaigner (fought against orcs and goblins) Halfing - deputy shiriff\n\nNice! There\u2019s also the Thief to think of\u2026 Cutpurse, burglar, harlequin or clown, dancer, rat catcher, assassin, contortionist (too much circus?), spy.\n\n1d4Elf Dwarf Halfling\n5you are a sea elf; you own a trident, a net, a longbow and a longsword; the captain of your first ship has taught you the sleep spell you are a surface merchant; you own a suit of chain mail armor, a shield, a hammer, a donkey, a cart, 200 gp in trade goods, and three gems worth 50 gp each you are a crazy naked halfling cannibal; you own a dagger, a femur bone usable as a club and a lot of blue body paint\n6you are a moon elf and belong to the wild hunt; you own a horse, a horn, a longbow, a scimitar, a silver dagger and a wolf hound companion that will attack anything that flees; the lore masters have taught you the spell detect magic to aid you in your raids you are an escaped slave, broken by years spent in the darkness deep in a kobold mine; you own a pick axe, ill-fitting goblin armor, a serrated goblin dagger and a wooden shield\n7you are a shadow elf from a far realm with a fist-sized spider companion; you own a billowing shadow cloak, studded leather armor, a black shield, a scimitar and a curved dagger; you have studied the spell hold portalyou are a brewmaster\n8you are a dark elf from under the mountain and a member of the winter court, you own elegant flowing robes, a silver diadem worth 100 gp, a scimitar engraved with silver runes of banishment; you have studied the light spell you are a grizzled campaigner from the goblin wars, you own plate mail, a polearm (halberd), a hand axe, and a dagger\n\nAlexSchroeder 2011-03-09 17:51 UTC\n\nGaah, need some dwarven background inspiration. Perhaps I should look at some Warhammer careers.\n\nAlexSchroeder 2011-03-14 17:21 UTC\n\nA dwarf criminal, his beard shaved off and his face branded, fled to the surface and surviving as a ruffian. Leather armor, club or axe, dagger.\n\nWhat about an apprentice smith? Seems like an obvious one. Nice hammer or axe, decent armor, some gold.","date":"2016-05-06 05:37:49","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\": 0.1980074644088745, \"perplexity\": 10472.507754317237}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-18\/segments\/1461861727712.42\/warc\/CC-MAIN-20160428164207-00202-ip-10-239-7-51.ec2.internal.warc.gz\"}"} | null | null |
Movers and shakers: new faces at Anderson & Garland and Chiswick among the latest arts and antiques appointments
Movers and shakers: new faces at Anderson & Garland and Chiswick Auctions among the latest arts and antiques appointments
Our latest look at new roles across the art and antiques trade as the new season begins.
Laura Chesters
Former Sotheby's, Henry Spencer & Sons and Tennants valuer Nigel Smith has joined Anderson & Garland's valuation team. He will be running the Asian & European Ceramics and Glass departments. Managing Director Julian Thomson said: "Nigel is a hugely knowledgeable valuer and a great all-rounder. His experience will really help with the firms' expansion plans."
New departments
Chiswick Auctions' has hired another 12 new starters taking the firm to a headcount of 80 including the opening of two new departments – arms, armour and militaria, and photography. For more on the Chiswick expansion story read the report in our latest issue.
Bonhams auction house has promoted Nima Sagharchi to the newly created post of director of Middle Eastern, Islamic and South Asian art. He was previously Bonhams' head of modern and contemporary Middle Eastern art.
Art recruiter D.R.A.W Recruitment has opened a new office in Berlin. The firm said there has been a rising number of art businesses in Germany, Austria and Switzerland and it plans to take advantage of this growth. The office is run by general manager Lisa Bosse.
Bonhams launches fashion and handbags auctions in Knightsbridge
Matthew Girling assumes global role at Bonhams
Bonhams promote Yip to UK board
Bonhams aim to raise Contemporary art sales with new appointment
New head of furniture for Bonhams | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,053 |
import React, { useMemo } from 'react';
import { styled, t } from '@superset-ui/core';
import { Column } from 'react-table';
import debounce from 'lodash/debounce';
import { Input } from 'src/common/components';
import {
BOOL_FALSE_DISPLAY,
BOOL_TRUE_DISPLAY,
SLOW_DEBOUNCE,
} from 'src/constants';
import Button from 'src/components/Button';
import {
applyFormattingToTabularData,
prepareCopyToClipboardTabularData,
} from 'src/utils/common';
import CopyToClipboard from 'src/components/CopyToClipboard';
import RowCountLabel from 'src/explore/components/RowCountLabel';
export const CopyButton = styled(Button)`
font-size: ${({ theme }) => theme.typography.sizes.s}px;
// needed to override button's first-of-type margin: 0
&& {
margin: 0 ${({ theme }) => theme.gridUnit * 2}px;
}
i {
padding: 0 ${({ theme }) => theme.gridUnit}px;
}
`;
const CopyNode = (
<CopyButton buttonSize="xsmall">
<i className="fa fa-clipboard" />
</CopyButton>
);
export const CopyToClipboardButton = ({
data,
}: {
data?: Record<string, any>;
}) => (
<CopyToClipboard
text={data ? prepareCopyToClipboardTabularData(data) : ''}
wrapped={false}
copyNode={CopyNode}
/>
);
export const FilterInput = ({
onChangeHandler,
}: {
onChangeHandler(filterText: string): void;
}) => {
const debouncedChangeHandler = debounce(onChangeHandler, SLOW_DEBOUNCE);
return (
<Input
placeholder={t('Search')}
onChange={(event: any) => {
const filterText = event.target.value;
debouncedChangeHandler(filterText);
}}
/>
);
};
export const RowCount = ({
data,
loading,
}: {
data?: Record<string, any>[];
loading: boolean;
}) => (
<RowCountLabel
rowcount={data?.length ?? 0}
loading={loading}
suffix={t('rows retrieved')}
/>
);
export const useFilteredTableData = (
filterText: string,
data?: Record<string, any>[],
) =>
useMemo(() => {
if (!data?.length) {
return [];
}
const formattedData = applyFormattingToTabularData(data);
return formattedData.filter((row: Record<string, any>) =>
Object.values(row).some(value =>
value?.toString().toLowerCase().includes(filterText.toLowerCase()),
),
);
}, [data, filterText]);
export const useTableColumns = (
data?: Record<string, any>[],
moreConfigs?: { [key: string]: Partial<Column> },
) =>
useMemo(
() =>
data?.length
? Object.keys(data[0]).map(
key =>
({
accessor: row => row[key],
Header: key,
Cell: ({ value }) => {
if (value === true) {
return BOOL_TRUE_DISPLAY;
}
if (value === false) {
return BOOL_FALSE_DISPLAY;
}
return String(value);
},
...moreConfigs?.[key],
} as Column),
)
: [],
[data, moreConfigs],
);
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,170 |
\section{introduction}
Magnetic layered materials, due to their reduced dimensionality, have exceptional physical properties and potential applications in spintronics~\cite{novoselov20162d,geim2013van,deng2018gate}.
Recently, Fe$_{3-x}$GeTe$_2$ has attracted much attention as a magnetic van der Waals layered material with a wide range of interesting properties~\cite{deiseroth2006fe3gete2,chen2013magnetic,verchenko2015ferromagnetic,leon2016magnetic,may2016magnetic,zhu2016electronic,zhuang2016strong,liu2017critical,yi2016competing,nguyen2018visualization,zhang2018emergence}.
Spin-polarized scanning tunneling microscope measurements have demonstrated the existence of skyrmionic bubbles in Fe$_{3-x}$GeTe$_2$~\cite{nguyen2018visualization}. This has been confirmed in a series of follow-up studies~\cite{ding2019observation,wang2019direct,park2019observation,wu2019n,you2019angular}.
In addition, several other intriguing physical properties have been discovered in Fe$_{3-x}$GeTe$_2$ , such as a large anomalous Hall current induced by topological nodal lines~\cite{kim2018large}, Kondo lattice behavior~\cite{zhang2018emergence}, giant tunneling magnetoresistance~\cite{song2018giant} and current-driven magnetization switching~\cite{wang2019current}.
It is noteworthy that the magnetic ordering temperature can be controlled by Fe occupancy~\cite{may2016magnetic} and gating~\cite{deng2018gate}.
Furthermore, these materials have been cleaved to the monolayer limit where magnetic order persists and gating has been demonstrated to tune the Curie temperature order in exfoliated crystals~\cite{Fei2018, Deng2018}.
As shown in Fig. $\text{\ref{fig:structure}}$, Fe$_{3}$GeTe$_2$ consists of a triangular layer of planar FeGe (with iron atoms
labeled Fe-II) sandwiched between two triangular layers of buckling FeTe (with iron atoms labeled Fe-I). The Fe$_{3}$GeTe$_2$ ``sandwiches'' are weakly bound to each other via van der Waals interactions. Interestingly it has been found that there can be large amounts of Fe-II vacancies in the FeGe layer up to 30\% ~\cite{verchenko2015ferromagnetic,may2016magnetic}.
\begin{figure}[!htb]
\includegraphics[width=1.0\columnwidth]{figure1}\caption{\label{fig:structure} Interlayer magnetic couplings between two layers in Fe$_{3-x}$GeTe$_2$. (a) FM (b) AFM.}
\end{figure}
Bulk Fe$_{3-x}$GeTe$_2$ has been reported to be a van der Waals magnetic material with a relatively high magnetic ordering temperature and large easy-axis anisotropy~\cite{deiseroth2006fe3gete2,chen2013magnetic}. Importantly, however, both the magnetic ordering temperature ($140 \;{\rm K} < T_c < 230 \;{\rm K}$) and magnetic anisotropy are reduced with increasing concentration of Fe-II vacancies~\cite{may2016magnetic}. Early on it was concluded that Fe$_{3-x}$GeTe$_2$ has an interlayer ferromagnetic (FM) ordering as shown in Fig. $\text{\ref{fig:structure}}$(a) based on magnetization measurements~\cite{deiseroth2006fe3gete2,chen2013magnetic,verchenko2015ferromagnetic,leon2016magnetic,may2016magnetic,zhu2016electronic,zhuang2016strong,liu2017critical}. Also the temperature dependence of several neutron diffraction peaks are consistent with FM ordering with the moments aligned along the $c$-axis~\cite{may2016magnetic}. However, it was found that when using a lower magnetic field, the magnetic susceptibility of Fe$_{3-x}$GeTe$_2$ suggest antiferromagnetic (AFM) ordering between the layers ( Fig. $\text{\ref{fig:structure}}$ (b)) instead of the FM ordering.~\cite{yi2016competing}. In particular, the temperature dependence of the magnetization shows a kink around a characteristic temperature $T^{*}$ below the ordering temperature $T_c$, with $T^{*}\sim150$ K and $T_c\sim210$ K for the samples used in Ref.~\cite{yi2016competing}. In addition the zero-field cooled (ZFC) magnetization curve goes very close to zero as the temperature goes to zero when using an external magnetic field parallel to the easy axis. Furthermore it was concluded from AC susceptibility measurements and magnetic force microscopy that in the temperature range between $T^{*}$ and $T_c$ the system enters a second more complex magnetic phase~\cite{yi2016competing}. To further support this scenario it was shown from Density Functional Theory (DFT) that at zero temperature the AFM interlayer ordering has a lower energy than the FM one~\cite{yi2016competing}.
A recent theoretical study ~\cite{jang2019origin} concluded that while undoped Fe$_{3}$GeTe$_2$ has an AFM interlayer ordering, the ground state of hole-doped Fe$_{3-x}$GeTe$_2$ ($0.11<x<0.36$) should have an interlayer FM ordering. The interlayer magnetic ordering controls inversion symmetry and time-reversal symmetry, which in turn controls many physical properties
such as the topology, giant magnetoresistance, second harmonic generation and piezo electricity~\cite{Li2019MnBi2Te4,klein2018probing,Sun2019CrI3SHG}.
Therefore it is important to resolve the interlayer magnetic ordering in Fe$_{3-x}$GeTe$_2$.
Understanding the interlayer coupling in Fe$_{3-x}$GeTe$_2$ may also help researchers to understand the magnetism in related metallic ferromagnets, notably Fe$_{5-x}$Ge$_2$Te$_2$~\cite{ Jothi2019} and Fe$_{5-x}$GeTe$_2$~\cite{Stahl2018,May2019_ACSNano, May2019_PRM}, the latter of which has a Curie temperature over 300K.
In our work, a series of experimental and theoretical methods has been employed to study the interlayer magnetic ordering of Fe$_{3-x}$GeTe$_2$. This includes neutron diffraction, scanning tunneling microscopy (STM) around Fe-II vacancies, spin-polarized STM measurements across step-edges and Density Functional Theory (DFT) calculations. Our results indicate that Fe$_{3-x}$GeTe$_2$ is ferromagnetically ordered between the layers. In order to reach agreement of the theoretical results with the experimental observations we have found that the DFT+U method is needed to
treat the local Coulomb interactions among the Fe-d orbitals.
\section{Methods}
\textit{Neutron diffraction experiments and samples}
Neutron scattering was performed on a 5 gram powder sample of composition Fe$_{2.9}$GeTe$_2$ and a single crystal sample of concentration Fe$_{2.76}$GeTe$_2$ with dimensions up to 10 mm. The preparation and characterization of these samples are described in Ref.~\cite{may2016magnetic}. The powder sample was loaded into a cylindrical Al can and measured on the HB-2A neutron diffractometer at the High Flux Isotope Reactor (HFIR), ORNL ~\cite{calder2018}. A constant wavelength of 2.41 \AA{} was selected from the 113 reflection of a vertically focusing Ge monochromator. The pre-mono, pre-sample and pre-detector collimation was open-21'-12'. Measurements were performed in the range 5 to 130 degrees. Single crystal elastic measurements were performed on the HB-3 triple axis instrument at HFIR using a PG(002) monochromator and analyzer with a fixed energy of 14.7 meV. The collimation was 48'-40'-40'-120' for pre-mono, pre-sample, pre-analyzer and pre-detector. We note that the neutron beam is larger than the samples. We also note that the samples used for neutron scattering in this study correspond to some of the samples used in the previous literature. Specifically, the powder sample was measured in Ref. ~\cite{may2016magnetic} and the single crystal was the one discussed in Ref. ~\cite{yi2016competing}.
\textit{Scanning tunneling microscope and samples}
STM and spin-polarized STM was performed using a variable-temperature Omicron STM instrument. The sample was grown using the chemical vapor transport method as described in the Ref. ~\cite{nguyen2018visualization}. A single crystal of Fe$_{3-x}$GeTe$_2$ was cleaved \textit{in situ} in an ultrahigh vacuum at room temperature and then transferred to STM for measuring at 120 K. The atomic-resolution topographic image was acquired using a tungsten tip. Etched ferromagnetic nickel tips were prepared for spin-polarized STM measurements as in our previous reports~\cite{nguyen2018visualization,park2017}. d$I$/d$V$ maps were obtained using a lock-in technique with ac modulation of 1 kHz and 30 mV.
\textit{Theoretical methods.} DFT~\cite{hohenberg1964inhomogeneous} within the projected augmented wave method~\cite{kresse1996efficient,kresse1999ultrasoft} has been employed, as implemented in the Vienna \textit{ab initio} simulation package. The generalized gradient approximation of Perdew, Burke and Ernzerhof was used for the electron exchange-correlation functional~\cite{perdew1996generalized}. To account for the strong intra-atomic interactions two types of DFT+U approximation schemes were used ~\cite{dudarev1998electron, liechtenstein1995prb}. Also approximate van der Waals corrections have been added to treat the interactions between the layered structures, according to the optB86b-vdW method~\cite{klimevs2009chemical,klimevs2011van}. The in-plane and out-of-plane lattice constants $a=3.991$ \AA{} and $c=16.336$ \AA{}, the space group and the initial atomic positions were taken from X-ray diffraction~\cite{deiseroth2006fe3gete2}. The relaxation of the atom positions was performed by the conjugate gradient scheme until the maximum force on each atom was less than 1 meV\AA$^{-1}$, and the total energy was converged to $10^{-7}$ eV. The energy cutoff of the plane waves was chosen as 520 eV. To simulate the effects of Fe-II vacancies three type of supercells have been considered in which the in-plane lattice vectors have been extended, while keeping the out-of-plane lattice vectors fixed. These supercells are depicted in the supplement~\cite{supp}. The k-point grid used for the normal cell, the $\sqrt{3}\times\sqrt{3}$, $2\times2$ and $4\times1$ supercells were $12\times12\times3$, $7\times7\times3$, $5\times5\times3$ and $3\times12\times3$, respectively. To perform the STM simulations a vacuum of $\sim20$ \AA{} was inserted. To simplify the STM simulations, the atomic positions were taken to be those corresponding to the bulk supercells. The STM simulations have been performed with the P4VASP software~\cite{p4vasp} using the constant current mode. Atomic images were produced with the VESTA program~\cite{vesta}.
\section{Results}
\begin{figure}[!htb]
\includegraphics[width=1.0\columnwidth]{figure2}\caption{\label{fig:neutron}(a) Neutron powder diffraction at 60 K on Fe$_{2.9}$GeTe$_2$. (b) Single crystal measurements at the (003) reflection for temperatures of 5 K, 60 K, 165 K, 200 K and 220 K on Fe$_{2.76}$GeTe$_2$.}
\end{figure}
First, to investigate the possibility of interlayer AFM, neutron diffraction experiments were performed as shown in Fig. \ref{fig:neutron}. As we can see from the neutron diffraction in Fig. \ref{fig:neutron}(a) there are no Bragg peaks associated with AFM ordering at (001) and (003). These measurements were performed at 60 K which is well below $T^{*}\sim150$ K for which the kink was observed in the magnetization measurements of Fe$_{3-x}$GeTe$_2$ ~\cite{yi2016competing}. In addition the (003) refection in Fig. \ref{fig:neutron}(b) shows no significant temperature dependence in going from above the magnetic transition at 220 K down to 5 K. These results show there is no interlayer AFM long range order in Fe$_{3-x}$GeTe$_2$.
\begin{figure}[!htb]
\includegraphics[width=1.0\columnwidth]{figure3}\caption{\label{fig:sp-stm}
(a) STM topographic image of a stepped area with a line profile across the step (inset) (sample bias $V_{s}=-0.1$ V, tunneling current $I= 50$ pA) (b) The corresponding spin-polarized differential conductance (d$I$/d$V$) map which shows no contrast between two terraces.}
\end{figure}
In order to further study the possibility of interlayer AFM order we performed spin-polarized STM measurements across a large number of step-edges. A typical example is shown in Fig $\text{\ref{fig:sp-stm}}$. The height of a stepped layer is measured to be about 0.7 nm as shown in Fig $\text{\ref{fig:sp-stm}}$(a), which is roughly consistent with the half of lattice constant in $c$-axis ($\sim 0.8$ nm). Importantly, the map of d$I$/d$V$ at bias -0.1 V as shown in Fig $\text{\ref{fig:sp-stm}}$(b) shows no spin-polarized contrast between the two terraces. This is also confirmed by the d$I$/d$V$ maps at biases -0.5 V, -0.2 V and 0.2 V shown in the supplement~\cite{supp}. On the other hand, using the same STM tip, we were able to resolve magnetic domains in Fe$_{3-x}$GeTe$_2$ ~\cite{supp}. We note that no contrast in spin-polarized STM does not necessarily imply the same magnetic configuration. It could also be that the spin-polarized STM is not sensitive enough to detect a difference. Nevertheless, the spin-polarized STM observation is consistent with the neutron scattering measurements discussed above, which show no evidence for AFM coupling between the layers.
\begin{table}[!htb]
\begin{tabular}{|c|c|c|c|c|}
\hline
\multirow{2}{*}{U(eV)} & \multicolumn{4}{c|}{ Energy difference $E_{FM}-E_{AFM}$ (meV)} \\
\cline{2-5}
& $1\times1$ cell & $\sqrt{3}\times\sqrt{3}$ cell & $2\times2$ cell & $4\times 1$ cell \\
\hline
0 & 22.4 & 16.0 & -5.0 & 35.0 \\
\hline
1 & -31.6 & -47.3 & -97.6 & -84.2 \\
\hline
2 & -45.9 & -51.1 & -112.4 & -116.8 \\
\hline
3 & -59.4 & -85.6 & -101.7 & -72.4 \\
\hline
4 & -41.1 & -91.1 & -188.1 & -176.8 \\
\hline
\end{tabular}\caption{\label{tab:energy}The total energy difference per cell between interlayer FM and AFM ordering in the normal cell without Fe-II vacancies and the single Fe-II vacancy $\sqrt{3}\times\sqrt{3}$, $2\times2$ and $4\times1$ supercells defined in the supplement~\cite{supp}, with the Hubbard U parameter increasing from 0 to 4 eV.}
\end{table}
Following the experimental results, we performed first-principle calculations to investigate the interlayer magnetic coupling in Fe$_{3-x}$GeTe$_2$. Several reports~\cite{zhang2018emergence,zhu2016electronic,xu2020spectroscopic} have suggested that correlations in Fe$_{3-x}$GeTe$_2$ play an important role. Given that Fe is a 3d transition metal this is a reasonable assertion. The simplest approach to treat local Coulomb interactions beyond DFT is via the so-called DFT+U method in which the Hubbard U parameter quantifies the local Coulomb repulsion among the Fe-d orbitals. To this end we first consider the DFT+U scheme implemented by Dudarev {\it et al} ~\cite{dudarev1998electron}. Tab. ~\ref{tab:energy} shows the energy difference between the interlayer FM and AFM configurations as a function of U. The second column corresponds to the Fe$_3$GeTe$_2$ normal cell without Fe-II vacancies. When $U=0$ eV, the energy difference between FM and AFM configuration for the normal cell without vacancies is $22.4$ meV, which is consistent with the DFT without U calculation reported in Ref. ~\cite{yi2016competing}. However, as we increase U from 0 to 4 eV, the energy difference $E_{FM}-E_{AFM}$ gives negative values as shown in the second column of Table $\text{\ref{tab:energy}}$. The negative energy difference for the listed finite U values show that the ground state of Fe$_3$GeTe$_2$ has an interlayer FM ordering for the case without vacancies, consistent with the experimental observations. When using the DFT+U scheme implemented by Liechtenstein {\it et al} ~\cite{liechtenstein1995prb}, the same conclusion is reached.~\cite{supp}
In Ref. ~\cite{jang2019origin} it has been concluded that Fe-II vacancies are responsible for inducing the ferromagnetism in Fe$_{3-x}$GeTe$_2$. To study the effect of Fe-II vacancies we considered the $\sqrt{3}\times\sqrt{3}$, $2\times2$ and $4\times1$ single Fe-II vacancy supercells defined in the supplement~\cite{supp}. Tab. ~\ref{tab:energy} shows the total energy of the FM configuration per supercell relative to that of the AFM configuration for these various supercells. Let us first focus on the $U=0$ results. Just like in Ref. ~\cite{jang2019origin} we find that for the $2\times2$ supercell the Fe-II vacancy flips the FM configuration from being energetically unfavorable to favorable. However, for the $\sqrt{3}\times\sqrt{3}$ and $4\times 1$ supercells we find that the Fe-II vacancies don't reduce the total energy of the FM configuration relative to that of the AFM configuration enough to stabalize it. Therefore it seems we cannot draw a simple conclusion about the influence of Fe-II vacancies on the stability of the FM and AFM configurations. On the other hand, we see from Tab. ~\ref{tab:energy} that for all the listed finite values of U the FM configuration has the lowest energy in all the three supercells, in agreement with the experimental observations.
\begin{figure}[!htb]
\includegraphics[width=1.0\columnwidth]{figure4}\caption{\label{fig:stm}(a) Experimental STM image of Fe$_{3-x}$GeTe$_2$ (tunneling current $I= 100$ pA) and theoretical DFT+U STM simulation of a $\sqrt{3}\times\sqrt{3}$ single Fe-II vacancy supercell for (b) the AFM solution with U=0 and (c) the FM solution with $U=4$ eV. In both experiment and simulation the bias $V_{s}=-0.5$ V is used.}
\end{figure}
Finally we find that the DFT+U approximation is also more consistent with recent STM experiments compared to plain DFT. Naturally, Fe$_{3-x}$GeTe$_2$ is Te terminated, so the STM tip is probing the local electronic structure above the Te atoms. The Te atoms in turn are located directly above the Fe-II atoms. In Ref. ~\cite{nguyen2018visualization} it had been shown that the STM intensities above the Fe-II vacancies is darker than those above the Fe-II atoms. In Fig.$\text{\ref{fig:stm}}$(a) a similar experimental STM image is presented that shows the same effect. To simulate the STM around Fe-II vacancies we perform DFT+U calculations on a $\sqrt{3}\times\sqrt{3}$ supercell with a single Fe vacancy in it. Fig.$\text{\ref{fig:stm}}$(c) shows that the contrast seen in STM is reproduced by the FM solution for $U=4$eV, because the STM intensity above the Fe-II vacancy is lower compared to the sites that are above the Fe-II atoms. On the other hand the STM simulation based on the AFM solution for $U=0$, shown in Fig.$\text{\ref{fig:stm}}$(b), has the opposite contrast: the STM intensity is bright/dark above the Fe-II vacancies/atoms. In other words, the STM simulation based on DFT without U corrections qualitatively disagrees with the STM experiments. In the supplement we demonstrate the same conclusion for the $2\times2$ and $4\times1$ single Fe-II vacancy supercells~\cite{supp}.
To better understand the origin of the STM contrast above the Fe-II vacancies and Fe-II atoms we analyzed the relaxed positions and local density of states of the Te atoms that are located directly above the Fe-II atoms. For all the considered Fe-II vacancy supercells and values of the Hubbard U, in both the FM and AFM configuration, the Te heights above the Fe-II vacancies are lower than the Te heights above the Fe-II atoms~\cite{supp}. So even for the AFM DFT case without a Hubbard U correction we find that the Te height above the Fe-II vacancy is lowered despite the fact that the STM intensity above these Te atoms is raised. This suggest that the origin of the contrast in the STM is electronic in nature instead of structural. To study the electronic contributions to the STM intensity we consider the local density of states (DOS) of the Te-$p$ orbitals integrated between the bias voltage of -0.5 eV used in the STM experiment and the Fermi energy. For all three supercells we find that for the AFM DFT simulation without a Hubbard U correction the integrated DOS of the Te-$p$ orbitals above the Fe-II vacancies is higher than the integrated DOS of the Te-$p$ orbitals above the Fe-II atoms. For the FM DFT+U simulations with $U=4$ eV this is reversed ~\cite{supp}. This further confirms that indeed the contrast in the STM simulations is driven by changes in the local electronic structure.
\section{Discussion}
In our work we find that the interlayer magnetic coupling in Fe$_{3-x}$GeTe$_2$ is FM and that in order to capture this theoretically, Hubbard U corrections need to be included within DFT. This conclusion is consistent with some earlier studies that highlight the importance of correlation effects in Fe$_{3-x}$GeTe$_2$ ~\cite{zhang2018emergence,zhu2016electronic,xu2020spectroscopic}. While we have focused on the interlayer magnetic coupling in our study, our conclusion that local Coulomb interactions play an important role in Fe$_{3-x}$GeTe$_2$ will help understanding the properties of this system in general.
One question that remains unanswered is why the DFT calculations show that upon including a Hubbard U correction, Fe$_{3-x}$GeTe$_2$ undergoes an AFM to FM transition. More generally this ties to the question what the nature is of the FM interlayer coupling. In the van der Waals system CrI$_3$ it has been concluded that the interlayer magnetic coupling is controlled by the super-superexchange mechanism ~\cite{nikil2018CrI3}. However, unlike CrI$_3$, Fe$_{3-x}$GeTe$_2$ is metallic. In particular, the in-plane as well as the out-of-plane resistivity does not show activation behavior as a function of temperature. ~\cite{kim2018large}. At the same time there have been several reports with evidence for the presence of local moments in Fe$_{3-x}$GeTe$_2$ ~\cite{zhang2018emergence,zhu2016electronic,xu2020spectroscopic, calder2019prb}. One possibility is that within pure DFT the AFM is driven by nesting conditions in the out-of-plane band structure and that within DFT+U a FM exchange mechanism based on local moments becomes dominant. Since the AFM coupling occurs between layers within the unit cell, the nesting properties cannot directly be analyzed from the band structure. Instead one can compute the Lindhard function to study a spin-wave density scenario as was done for example for the case of intra-unitcell AFM in RuO$_2$~\cite{berlijn2017RuO2}. We leave such an endeavor for future studies.
Another question is how the magnetization measurements can be interpreted given that there is no AFM in Fe$_{3-x}$GeTe$_2$. Specifically in Ref.~\cite{yi2016competing} it has been shown that the ZFC magnetization curve for low magnetic fields along the easy axis is very close to zero at low temperatures. This is indicative of AFM~\cite{Kittel}. Furthermore, the magnetization curves display a kink around a characteristic temperature $T^{*}$ that is below the magnetic ordering temperature $T_c$. In Ref. ~\cite{cktian2019domainwall} these findings in the magnetization measurements have been reproduced. However, the authors of Ref. ~\cite{cktian2019domainwall} argue that domain-wall pinning is a more likely explanation for the observed behavior than AFM. After cooling Fe$_{3-x}$GeTe$_2$ in zero external field it contains an equal number of domains parallel and anti-parallel to the easy axis. Then if the magnetic fields and the temperatures are too low, the walls between these domains remain pinned and the induced magnetization stays negligible. The kink at $T^{*}$ is interpreted in Ref. ~\cite{cktian2019domainwall} as the temperature at which the domain walls depin. Magnetic force microscopy measurements have shown that the magnetic domains evolve from a branching structure at $T_c$ to a bubble structure at $T^{*}$ and remain constant at lower temperatures~\cite{yi2016competing}. It would be interesting to see if in future studies these observations can be understood within a domain-wall depinning scenario.
\section{Conclusions}
Using neutron diffraction, scanning tunneling microscopy, spin-polarized STM and DFT+U based total energy calculations and STM simulations we have studied the question whether the magnetic interlayer ordering in Fe$_{3-x}$GeTe$_2$ is FM or AFM. Based on our experimental results and the previous results in the literature we conclude that Fe$_{3-x}$GeTe$_2$ is FM. The resolution of the out-of-plane magnetic order is important given that it controls the time-reversal and inversion symmetry and therefore many physical properties such as the topology, second harmonic generation and piezo electricity to mention but a few. To theoretically reproduce the experimental observations we have learned that it is necessary to include Hubbard U corrections beyond pure DFT. This conclusion derived from the interlayer magnetic coupling will help understanding the electronic and magnetic properties of Fe$_{3-x}$GeTe$_2$ in general.
\begin{acknowledgments}
We thank R. Fishman for valuable discussions. This research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility. We used resources of the Compute and Data Environment for Science (CADES) at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. In addition we used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. DOE under Contract No. DE-AC02-05CH11231. This research used resources at the High Flux Isotope Reactor, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. Sample synthesis (A.F.M.) was supported by the U. S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.
This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,181 |
Home/Sports/Indian women's hockey team loses 2-3 to Argentina in a thrilling contest
Indian women's hockey team loses 2-3 to Argentina in a thrilling contest
markwilliamsJanuary 27, 2021
The goals of Sharmira (34th) and Gurgit Cowl (40th) gave India a lead after the host scored in the 25th minute via Mikaela Retegi, while Argentina scored Augustina Gorzerani in the final quarter. Granat Maria (57th) wins on Tuesday with 50th).
India's defense was strong on Tuesday. Twitter / @ TheHockeyIndia
Buenos Aires: The Indian women's hockey team fought bravely before losing 2-3 to World No. 2 Argentina in a thrilling match here.
"We're close to winning, but for opponents like Argentina, we need to stay focused until the final Hooters. The main point of the match is to stay consistent for all four quarters. "Chief coach Sjoerd Marijne said. As I said in the release of Hockey India.
Argentina put India on its hind legs early in the match and scored a penalty corner (PC) in the 6th minute, but Indian goalkeeper Savita made a great save to avoid the danger.
Argentina continued to seek opportunities throughout the second quarter, creating PCs in the 21st and 23rd minutes, but India's defense maintained the fort.
It was Retegi who took the 1-0 lead of the home team in the 25th minute and quickly changed the goal.
After a 10-minute half-time break, India returned strongly to the game, playing in a disciplined structure, filling the 25-yard mark gap and making Argentina unable to easily enter the circle.
Meanwhile, the forward line aimed for the goal, and in the 34th minute Navjot Kaur set up a young forward Sharmila and succeeded in striking. Argentina won the PC in the 38th minute, but India managed to keep the home team 1-1.
In the 40th minute, India's only drug flicker, Grugit, scored a strong goal and set an important 2 to 1 lead.
In the next few minutes, both India and Argentina traded PCs respectively, but couldn't convert. It was the penalty stroke that was finally given to Argentina in the 50th minute that changed the course of the game.
"After winning the 2-1 lead, we were in some situations where we were able to calm down and try to widen the goal gap by scoring more scores," Marijne said. I did.
"For a team like Argentina, you have to lead beyond your goal to ensure victory, or you'll catch up. These are valuable lessons for us and this is the next game. I want to improve it, "he says. Added.
Find the latest and upcoming tech gadgets online with Tech2 Gadgets. Get tech news, gadget reviews and ratings. Popular gadgets for laptops, tablets, mobile specifications, features, prices, comparisons and more.
Source link Indian women's hockey team loses 2-3 to Argentina in a thrilling contest | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,190 |
\section{}
Let us consider the $SU(2)_L\times SU(2)_R$ linear sigma model in order
to describe the hadronic system close to the chiral phase transition
\cite{linear}. All the arguments presented below will only depend on the
smallness of the chiral condensate and the $\sigma$-mass. Therefore, we will
consider the system only in the hadronic phase -- possibly close to the chiral
phase transition temperature-- and ignore effects from deconfinement.
We furthermore assume that the axial $U_A(1)$ symmetry is not restored at the
temperatures under considerations, which is supported by recent lattice
calculations \cite{Laer}.
The linear sigma model includes isotriplet pseudoscalars ($\pi^a$), the pions,
and the isosinglet scalar ($\sigma$).
They form a $({1\over2},{1\over2})$ representation of
$SU(2)_L\times SU(2)_R$, and are grouped into
\begin{equation}
\Phi={1\over2}
(\sigma{\bf 1} +i\mbox{\boldmath$\tau$}\cdot\mbox{\boldmath$\pi$}),
\end{equation}
where ${\bf 1}$ is the $2\times 2$ unit matrix and
the $\mbox{\boldmath$\tau$}$'s are the Pauli spin matrices.
We furthermore include vector $(\mbox{\boldmath $\rho$}^\mu)$
and axial-vector $(\mbox{\boldmath $a$}_1^\mu)$ mesons as gauge fields
and the total Lagrangian is
given by \cite{lvector,pisarski}
\begin{eqnarray}
{\cal L}_{eff}&=& {\rm Tr}D_\mu\Phi^* D^\mu\Phi
+ \mu^2 {\rm Tr}\,(\Phi^*\Phi)
- \lambda\, {\rm Tr}\,(\Phi^*\Phi)^2
\nonumber\\[2pt]
&&-{1\over4}{\rm Tr}(F_{L\,\mu\nu}F_L^{\mu\nu}
+F_{R\,\mu\nu}F_R^{\mu\nu})
\nonumber\\[2pt]
&&+{1\over2}m_0^2\,{\rm Tr}\,(A_{L\,\mu}A_L^\mu+A_{R\,\mu}A_R^\mu)
\nonumber\\[2pt]
&&-h{\rm Tr}(\Phi),
\end{eqnarray}
where
$A_{L}^\mu=(\mbox{\boldmath $\rho$}^\mu+\mbox{\boldmath $a$}_1^\mu)
\cdot\mbox{\boldmath$\tau$}/2$,
$A_{R}^\mu=(\mbox{\boldmath $\rho$}^\mu-\mbox{\boldmath $a$}_1^\mu)
\cdot\mbox{\boldmath$\tau$}/2$ and
\begin{equation}
D^\mu\phi=\partial^\mu\phi+ig A_L^\mu\phi-ig \phi A_R^\mu.
\end{equation}
The last term is responsible for the explicit breaking of chiral symmetry due
to the small but finite mass of the light quarks.
$\mu$, $\lambda$, $g$, and $h$ are constants which are inferred by fitting
the pion decay constant, the vector meson decay width, the sigma meson mass
as well as the mass of the pion.
In the broken phase, at low temperatures, the scalar field has a
non-vanishing vacuum expectation value,
$\langle\sigma\rangle\equiv\sigma_0
=(\mu^2/\lambda)^{1/2}$,
which plays the role of the
order parameter of the chiral phase transition. After redefining the field
$\sigma\to\sigma+\sigma_0$, one obtains massless Goldstone boson,
$m_\pi=0$, and a massive scalar meson, $m_\sigma=\sqrt{2\lambda}\sigma_0$
in the chiral limit, $h=0$. The degeneracy between vector and axial-vector
meson
masses is also broken due to the finite expectation value of the
$\sigma$-field;
$m_\rho^2=m_0^2$ and $m_{a_1}^2=m_0^2+g^2\sigma_0^2$.
Because of the spontaneous breaking of chiral symmetry, the derivative of the
pion field contributes to the axial current and, therefore, the pion and axial
vector field mix.
To obtain physical fields we redefine the axial gauge fields as
\begin{equation}
\mbox{\boldmath $a$}_1^\mu\to \mbox{\boldmath $a$}_1^\mu-{\chi\over Z}
\biggl( \partial^\mu\mbox{\boldmath$\pi$}
-ig[\mbox{\boldmath$\rho$}^\mu,\mbox{\boldmath$\pi$}]\biggr),
\end{equation}
where $\chi=g\sigma_0/(g^2\sigma_0^2+m_0^2)$. $Z$ is the pion wave function
renormalization constant and given by
\begin{equation}
Z^2=1-{g^2\sigma_0^2\over (g^2\sigma_0^2+m_0^2)}.
\end{equation}
In the broken phase we have a strong decay channel for the
scalar meson into two pions, namely
\begin{equation}
{\cal L}_{\sigma\pi\pi}=
-{\lambda\sigma_0\over Z^2}
\sigma\mbox{\boldmath $\pi$}^2
+{g\chi\over Z^2}\left[\partial_\mu\sigma\mbox{\boldmath $\pi$}\cdot
\partial^\mu \mbox{\boldmath $\pi$}
-(1-g\sigma_0\chi)\sigma\partial^\mu \mbox{\boldmath $\pi$}\cdot
\partial^\mu \mbox{\boldmath $\pi$}\right]
\end{equation}
where the parameter $\lambda$ is determined by the sigma meson mass.
It assumes a value of 21.4 (7.62) for $m_\sigma\sim 1$ GeV (0.6 GeV).
With this coupling the
resulting width is $\Gamma_{\sigma\pi\pi}\simeq 800\,(600) \>\rm MeV$.
In the chirally symmetric phase, the expectation value of the $\sigma$-field
vanishes, $\sigma_0=0$. In this case, the $\sigma$-meson and
the pions as well as the vector- and axial-vector fields
form a degenerate chiral multiplet, respectively.
As a consequence the decay of the $\sigma$-meson into two pions is
kinematically forbidden. Also the vector and axial-vector current-current
correlators
will be identical, a property which persists at finite temperature
\cite{pisarski}.
Moreover, the coupling constants among the mesons will be modified
in the symmetric phase since they depend on the strength of the scalar
condensate.
In the chirally symmetric phase we have
\begin{eqnarray}
{\cal L}_{\pi\pi\rho} &\rightarrow& g\mbox{\boldmath $\rho$}^\mu\cdot
(\mbox{\boldmath $\pi$}\times
\partial_\mu\mbox{\boldmath $\pi$}),
\nonumber\\[2pt]
{\cal L}_{\pi\pi\sigma} &\rightarrow & 0,
\nonumber\\[2pt]
{\cal L}_{\pi\rho a_1} &\rightarrow & 0,
\nonumber\\[2pt]
{\cal L}_{\pi\sigma a_1} &\rightarrow& -g\mbox{\boldmath $a$}_1^\mu\cdot
(\sigma\partial_\mu\mbox{\boldmath $\pi$}
-\partial_\mu\sigma\mbox{\boldmath $\pi$}).
\label{coupl}
\end{eqnarray}
We can see that the coupling of
$\sigma$ meson to two pions vanishes, that is,
the decay channel for scalar mesons into two pions is completely closed.
Also the $\pi-\rho-a_1$ coupling vanishes in the chirally symmetric phase.
Only vector and axial vector mesons decay into two pions, and pion and
scalar meson, respectively.
Since the couplings are proportional to the scalar
condensate, they become already negligible once one gets
close enough to $T_\chi$
{\em without} actually restoring chiral symmetry.
The dependence of the coupling constants on
the chiral condensate leads to interesting consequences related to the chiral
phase transition. For example the thermal
photon production in hadronic matter would be affected considerably. The
dominating production channel is believed to be the reaction
$\pi\rho\to a_1\to\pi\gamma$ \cite{song}
which is due to the interaction
\begin{equation}
{\cal L}_{a_1\rho\pi}=-{g\over Z}\chi\biggl[
(\partial_\mu \mbox{\boldmath $\rho$}_\nu
-\partial_\nu \mbox{\boldmath $\rho$}_\mu)\cdot
\partial^\mu\mbox{\boldmath $\pi$}\times
\mbox{\boldmath $a$}_1^\nu
+(\partial_\mu \mbox{\boldmath $a$}_{1\,\nu}
-\partial_\nu \mbox{\boldmath $a$}_{1\,\mu})\cdot
\partial^\mu\mbox{\boldmath $\rho$}^\nu\times
\mbox{\boldmath $\pi$}\biggr]
\end{equation}
assuming vector meson dominance.
This reaction is shut off in the symmetric phase since
$Z\to 1$ and $\chi\to 0$ as the condensate ($\sigma_0$) vanishes, implying
a suppression of the photon production in the chirally symmetric phase \cite
{song_photon}.
\section{}
In this section we study the consequences of the chiral phase transition
related to the chemical equilibration of pions.
To this end we will calculate the chemical equilibration times in the broken as
well as in the chirally symmetric phase. Thermodynamic equilibration
is driven by the multiple collisions among the particles in the system.
When the collision rate is fast compared to the lifetime of the hadronic
system thermodynamic equilibrium can be reached.
In both phases, broken as well as symmetric, thermal, i.e. kinetic
equilibration of pions
is governed by elastic two-body collisions, $\pi\pi\rightleftharpoons\pi\pi$.
At temperatures $T > 100 \, \rm MeV$, this reaction is dominated by the strong
p-wave isovector ($\rho$) channel. Since the coupling to the $\rho$-meson is
not changed in the symmetric phase (see eq. (\ref{coupl}) ),
this reaction will be equally strong in both phases. In addition, in the
symmetric phase, the s-wave scattering will be considerably stronger than in
the broken phase where these reactions are small due to the Goldstone nature
of the pions.
It has been shown that already in the broken phase
elastic collisions are frequent enough
for pions to maintain thermal equilibrium even at low temperatures
\cite{thermal}. Since there are the additional s-wave interactions in the
symmetric phase, it is safe to assume that kinetic equilibrium will be
maintained in both phases to a very good approximation.
Chemical
equilibration, on the other hand involves inelastic processes
which only contribute in the next to leading order of the low energy expansion.
As we shall see in the following, the disappearance of some of the couplings
(\ref{coupl}) in
the symmetric phase will lead to quite different chemical equilibration
conditions from these in the broken phase.
\subsection{In symmetric phase}
{\it (i)} $\pi\pi\rightleftharpoons\pi\pi\pi\pi$
\noindent
Chemical equilibrium is caused by the various inelastic, particle-number
changing reaction.
Contrary to the broken phase, we have strong s-wave
$\pi\pi\rightleftharpoons\pi\pi\pi\pi$ interactions in the symmetric phase
as shown in Fig.~\ref{feyn_pppp}.
This reaction leads to an {\em absolute} chemical
equilibrium of pions in medium which is defined by $\mu_\pi=0$
\footnote{For a definition of the meaning of a pion chemical equilibrium
in the context of heavy ion collisions see ref. \cite{chemical}.}.
The chemical relaxation time is given by \cite{chemical}
\begin{equation}
{1\over\tau_{ch}}={4\over n_\pi^0} I_0(\pi\pi\leftrightarrow\pi\pi\pi\pi; T)
\end{equation}
where $n_\pi^0$ is the pion density at equilibrium and
\begin{eqnarray}
I_0(\pi\pi\leftrightarrow\pi\pi\pi\pi; T)&=& {\cal S} \,
\int{d^3p_1\over (2\pi)^3 2E_1}\int{d^3p_2\over (2\pi)^3 2E_2}
\cdots\int{d^3p_6 \over (2\pi)^3 2E_6}
\nonumber\\[4pt]
&&
\times \,\, (2\pi)^4\delta^{(4)}(p_1 + p_2 - p_{3} - \cdots-p_6)
\nonumber\\[4pt]
&&
\times \sum_{1,2,\ldots,5,6}\vert{\cal M}
(\pi_1\pi_2\leftrightarrow\pi_3\cdots\pi_6 )
\vert^2 e^{-(E_1+E_2)/T}.
\label{izero}
\end{eqnarray}
Here $\cal S$ indicates the symmetric factors. Here, and throughout this paper,
we use the Boltzmann limit of the Bose-Einstein quantum statistics.
The calculation has been done ignoring
the interference terms among the six different diagrams \cite{japan}.
At a temperature $T = 180 \, \rm MeV$ we find for the chemical relaxation
time $\tau_{ch}= 2.8 \, \rm fm$
corresponding to the couplings $\lambda =21.4 $ ($m_{\sigma} = 1 \, \rm GeV$).
Since the cross section is proportional to
$\lambda^4$ the results strongly depend on the values of $\lambda$.
From the result we can see that it might be possible for pions to
achieve an {\em absolute}
chemical equilibrium with $\mu_\pi=0$ near the symmetry restored phase for
large values of $\lambda$. However, the value, of the coupling $\lambda$
depends on the assumed value of the mass of the $\sigma$ meson, which is not
well determined. Furthermore, higher order thermal effect may
renormalize the value of $\lambda$. Therefore, we cannot make any definite
statements about the possibility of an absolute chemical equilibrium in the
symmetric phase.
There are also inelastic reactions involving vector and axial vector
mesons such as $\pi\pi\rightleftharpoons a_1 a_1$ or $\pi\pi\rightleftharpoons
\rho\rho$. These reactions, which would drive the system to an
absolute chemical equilibrium ($\mu_\pi\to 0$), however, turn out to be as
slow as in the broken phase, $\tau_{ch}\sim 7 \rm\>fm/c$
at $T=180\rm\> MeV$ \cite{chemical}.
\bigskip
{\it (ii)} $\pi\pi\rightleftharpoons\sigma\sigma$
\noindent
Next there is the reactions $\pi\pi\rightleftharpoons\sigma\sigma$
(Fig.~\ref{feyn_ppss}). Processes involving the exchange of an
axial vector meson (Fig.~\ref{feyn_ppss}.a and \ref{feyn_ppss}.b) as well the
the direct coupling of two pions to two sigma mesons
(Fig.~\ref{feyn_ppss}.c) contribute. The latter is given by
\begin{equation}
{\cal L}_{\pi\pi\sigma\sigma}=
{\lambda\over 2Z^2}\sigma^2\mbox{\boldmath $\pi$}^2
+{g^2\chi^2\over 2Z^2}\sigma^2(\partial_\mu\mbox{\boldmath $\pi$})^2.
\end{equation}
These reactions lead to {\em relative} chemical equilibrium for which
$\mu_\pi=\mu_\sigma$ but $\mu_\pi$ need not to be zero.
The {\em relative} chemical relaxation time is given by \cite{chemical}
\begin{equation}
{1\over\tau_{ch}}=4I_0(\pi\pi\rightleftharpoons\sigma\sigma; T)
\left({1\over 3 n_\pi^0} + {1\over n_\sigma^0}\right)
\end{equation}
where $I_0(\pi\pi\rightleftharpoons\sigma\sigma; T)$ is given by the similar
form as that of Eq.~\ref{izero} for the reaction
$\pi\pi\rightleftharpoons\sigma\sigma$.
In the calculation of the scattering amplitude
we introduce a form factor for the vertex
involving the exchange of axial vector meson, given by
\begin{equation}
F={\Lambda^2-m_{a_1}\over \Lambda^2-t}
\end{equation}
where we use the values of $\Lambda=1.7 \,\rm GeV$.
The results for the relaxation time are shown in Fig.~\ref{t_symmetry1}
as a function of temperature assuming that the degenerate masses of the
scalar and vector mesons are $m_\pi=m_\sigma=140\,\rm MeV$
and $m_\rho=m_{a_1}=770\,{\rm MeV}$.
Two different values of the $\lambda=$21.4 and 7.62
are considered corresponding to
$m_\sigma=$1 GeV and 0.6 GeV respectively.
We can see that the relaxation time is about 0.3 $\sim$ 0.6 fm at $T=180$ MeV
which is much shorter than the effective size of the hot matter,
$R=2\sim 3 \,\rm fm$ \cite{chemical}.
This implies that
pions will reach {\em relative} chemical equilibrium with
respect to the reaction
$\pi\pi\rightleftharpoons\sigma\sigma$ with $\mu_\pi=\mu_\sigma$ in the
chirally symmetric phase.
In order to take into account thermal corrections to the effective mass of
the mesons \cite{pisarski}
we also show the chemical relaxation times for
$m_\pi=m_\sigma=220\, \rm MeV$ and $m_\rho=m_{a_1}=980 \,\rm MeV$
in Fig. \ref{t_symmetry2}.
In this case the reaction times are considerably slower but it is still
possible to reach chemical equilibrium near the critical temperature, which
is $T_\chi\approx 220 \,\rm MeV$ in this model.
In addition, there are the decays and formation of the vector meson, which are
according to eq. (\ref{coupl}), $\rho\rightleftharpoons\pi\pi$,
$a_1\rightleftharpoons\pi\sigma$. Notice, that in the symmetric phase
the $a_1$ could not decay into $\pi \rho$. These decays are fast and will lead
to a relative chemical equilibrium characterized by $\mu_\rho=2\mu_\pi$ and
$\mu_{a_1}=\mu_\pi+\mu_\sigma$. Taking into account the relative equilibrium
between pions and the $\sigma$ meson, we arrive at the following chemical
equilibration conditions in the symmetric phase:
$\mu_\pi = \mu_\sigma$, $\mu_\rho=2\mu_\pi$, $\mu_{a_1}=2 \mu_\pi$
\subsection{In broken phase}
Recently \cite{chemical}, we have shown that pions can easily reach a
{\em relative}
chemical equilibrium with the $\rho$-mesons while the reaction times
leading to
a {\em absolute} chemical
equilibrium, i.e. $\mu_\pi = 0$ are too long to be effective at temperatures
$T<160 \, \rm MeV$.
For the reactions involving scalar mesons we expect a
{\em relative} chemical equilibrium of
pions with the $\sigma$-mesons through the
reaction $\sigma\rightleftharpoons\pi\pi$,
since the decay width of $\sigma\to\pi\pi$ is very large.
Assuming {\em relative} chemical
equilibrium between pions and scalar mesons
the reaction $\pi\pi\rightleftharpoons\sigma\sigma$
is effectively identical to the reaction
$\pi\pi\rightleftharpoons\pi\pi\pi\pi$ and, thus, leads to
{\em absolute} chemical equilibrium.
The same reaction channel has been considered in the symmetric phase and shown
to be very fast. In broken phase the dominant contribution comes
from the pion
exchange diagrams as shown in Fig.~(\ref{feyn_ppss}.d) and
(\ref{feyn_ppss}.e).
However, the leading contribution
proportional to $\lambda^4$ is canceled by the diagrams with four pions as in
Fig.~\ref{feyn_pppp} and
the result is very similar to that obtained in chiral perturbation theory
\cite{goity}, which is $\tau_{ch} \simeq 200 \, \rm fm$.
In the broken phase at a temperature of about $T\sim 160$ MeV, therefore,
a {\em relative} chemical equilibrium is maintained and it is characterized by
$\mu_{\sigma} = 2 \mu_\pi$, $\mu_{\rho} = 2 \mu_\pi$, $\mu_{a_1} = 3 \mu_\pi$.
This is different from the conditions in the symmetric phase.
\section{}
Finally, we study observable consequence of the different chemical
relaxation conditions in the broken and symmetric phase.
In the symmetric phase, $m_\pi = m_\sigma$ and $\mu_\pi = \mu_\sigma=\mu$.
Therefore,
we will have as many $\sigma$ mesons as one third of
pions,
\begin{equation}
N_\sigma=\frac{1}{3}N_\pi=\frac{1}{3}
\biggl(N_{\pi^+}(T,\mu)+N_{\pi^-}(T,\mu)+N_{\pi^0}(T,\mu)\biggr)
\end{equation}
Similar for the vector mesons we have
$m_{a_1} = m_\rho$ and $\mu_{a_1} = 2 \mu_\pi =
\mu_\rho$.
Thus there are
as many $a_1$ mesons as $\rho$ mesons in the symmetric phase.
In the broken phase, on the other hand, we have
$\mu_\sigma=2\mu_\pi=2\mu$ and $m_\sigma \gg m_\pi$ and, therefore,
\begin{equation}
N_\sigma\sim e^{-m_\sigma/T}\ll N_\pi,
\end{equation}
as long as $\mu_\pi \ll m_\sigma$.
For the vector and axial vector mesons the chemical equilibrium conditions are
$\mu_\rho=2\mu_\pi$, $\mu_{a_1}=\mu_\pi+\mu_\rho=\mu_\pi+\mu_\sigma=3\mu_\pi$.
Given the same chemical potential in both phases, there will be
more sigma mesons and axial vector mesons in chirally symmetric phase
than in the broken phase simply due to the mass difference.
This abundance can be observed in the final state pion number,
if all inelastic channels, except
the decay process, $\sigma\rightleftharpoons\pi\pi$,
$a_1\rightleftharpoons\pi\rho$, are inactive as the system passes through
the broken phase.
For a simple estimate
we assume a chirally symmetric phase at the early stage of
the hot matter with $\mu_\pi=0$.
Since all resonances decay into pions the observed
pion number will be
\begin{eqnarray}
\bar N_\pi(T_f) &=& N_\pi(T_h)+2N_\sigma(T_h)+\cdots\cr
&\approx& {5\over3} N_\pi(T_h)+\cdots.
\end{eqnarray}
where we use the fact that $N_\sigma={1\over3}N_\pi$. Here we do not show
the contribution from $a_1$ mesons explicitly since $N_{a_1}\ll N_\pi$.
$T_h$ is either the hadronization temperature or initial temperature of the
hot hadronic matter and $T_f$ is the freeze-out temperature.
Alternatively, let us assume that there is no chirally symmetric phase at the
initial stage of hot hadronic matter.
Since the number of sigma mesons is almost negligible
the observed pion number will be
\begin{equation}
\bar N_\pi(T_f) \approx N_\pi(T_h)+\cdots.
\end{equation}
When there is a chirally symmetric phase initially,
thus, we have about 1.6 times more thermal pions.
However, this result will be modified when there are pion number
changing reactions in the system at low temperatures.
In our previous work \cite{chemical}, we have shown that the reaction rates
for the pion number changing processes will depend on the pion chemical
potential as well as temperature.
If we assume a chirally symmetric phase
initially, which then turns into a phase of broken symmetry where the mass of
the $\sigma$-meson is large, the number of
$\sigma$-mesons will be oversaturated.
These $\sigma$-mesons will rapidly decay leading to a finite chemical potential
for the pions. Similarly, since the mass of the $a_1$ mesons increases as
chiral symmetry gets broken, they also will be oversaturated leading to an
additional increase of the pion chemical potential.
To estimate the induced pion chemical potential we assume
that the chiral condensate instantly build up at $T=T_\chi$ and $\mu_\pi=0$
initially.
Since the effective number of pions should be constant at temperatures both
slightly above ($T=T_\chi^+$) and below ($T=T_\chi^-$) the critical
temperature, we have
\begin{equation}
\bar N_\pi(T_\chi^+,\mu_\pi=0)=\bar N_\pi(T_\chi^-,\mu_\pi)
\end{equation}
where $\bar N_\pi(T)=N_\pi+2N_\sigma+2N_\rho+3N_{a_1}$.
From this we have $\mu_\pi=55\sim 66$ MeV at $T_\chi=160\sim 200$ MeV,
respectively.
If $T_\chi\sim 160$ MeV the chemical relaxation time of pions, with
$\mu_\pi=55$ MeV, will be about 3 fm and is comparable to the
effective size of the hot hadronic system \cite{chemical}.
If the chiral phase transition occurs at higher temperature than $T=160$ MeV
pion number changing processes will be active and the number of pions will be
reduced. Thus we expect less pions than that obtained when we
completely neglect the pion number changing
processes as long as $T_\chi>160\>\rm MeV$.
\section{}
In summary, we have studied the chemical equilibration conditions of pions
in hot hadronic matter assuming chiral symmetry restoration.
The chirally symmetric phase is described with
light scalar mesons which are degenerate with pions, and with
degenerate vector and axial-vector mesons.
In the symmetric phase a {\em relative}
chemical equilibrium among the particles will be established rapidly, leading
to $\mu_\sigma = \mu_\pi $ and $\mu_\rho = 2 \mu_\pi = \mu_{a_1}$.
The number of scalar mesons is then given by one third of
the total number of pions at the given temperature.
This is quite different from the situation encountered in the broken
phase, where $\mu_\sigma = 2 \mu_\pi$ and $\mu_{a_1} = 3 \mu_\pi$.
This difference in chemical equilibration conditions of pions
might lead to the excess of pions at freeze-out.
As temperature decreases and the symmetry is broken
scalar mesons become heavier and decay into two pions. Also $a_1$ mesons decay
into three pions.
The number of observed pions will be given by the number of pions plus
contributions from the resonance decay.
When we include the scalar and $a_1$ meson contributions to observed pions,
we have $\sim 1.6$ times more pions
compared to the case when there is no chiral phase transition.
This, however, can only be observed, if the chiral transition temperature
is not too high, $T_{\chi} \leq 160$ MeV. Otherwise, pion number changing
processes in the broken phase will absorb the excess obtained from the chiral
phase transition.
Finally, let us conclude by pointing out that an analysis of the particle
abundances measured at SPS-energy heavy ion collisions found an excess of pions
by a factor of 1.6 over the expected thermal value \cite{gadiz}.
However, a different analysis based on the same data, does not find such an
excess of pions \cite{stachel}.
\bigskip
This work supported by the Director, Office of Energy Research, Office of High
Energy and Nuclear Physics, Division of Nuclear Physics, Division of Nuclear
Sciences, of the U. S. Department of Energy under Contract No.
DE-AC03-76SF00098.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,886 |
Q: Split Location into City, State Code and Country in Panda I would like to know to split a location column into a few new columns such as city, state code and country in pandas.
From this:
'Location': {0: 'Warszawa, Poland',
1: 'San Francisco, CA, United States',
2: 'Los Angeles, CA, United States',
3: 'Sunnyvale, CA, United States',
4: 'Sunnyvale, CA, United States',
5: 'San Francisco, CA, United States',
6: 'Sunnyvale, CA, United States',
7: 'Kraków, Poland',
8: 'Shanghai, China',
9: 'Mountain View, CA, United States',
10: 'Boulder, CO, United States',
11: 'Boulder, CO, United States',
12: 'Xinyi District, Taiwan',
13: 'Tel Aviv-Yafo, Israel',
14: 'Wrocław, Poland',
15: 'Singapore'}
To this:
'Country': {0: 'Poland',
1: 'United States',
2: 'United States',
3: 'United States',
4: 'United States',
5: 'United States',
6: 'United States',
7: 'Poland',
8: 'China',
9: 'United States',
10: 'United States',
11: 'United States',
12: 'Taiwan',
13: 'Israel',
14: 'Poland',
15: 'Singapore'}
Thanks.
A: I am not sure if its the best method, others please comment or suggest a better method.
I tried to split the data, but the challenge is that foreign countries have only city and country name and the entries from US have City, Sate and Country. Hence, I was not able to split it with one method. Below are two methods which I employed to split the data and then you have to figure out how to merge into one dataframe.
b = pd.DataFrame ({'Location': {0: 'Warszawa, Poland',
1: 'San Francisco, CA, United States',
2: 'Los Angeles, CA, United States',
3: 'Sunnyvale, CA, United States',
4: 'Sunnyvale, CA, United States',
5: 'San Francisco, CA, United States',
6: 'Sunnyvale, CA, United States',
7: 'Kraków, Poland',
8: 'Shanghai, China',
9: 'Mountain View, CA, United States',
10: 'Boulder, CO, United States',
11: 'Boulder, CO, United States',
12: 'Xinyi District, Taiwan',
13: 'Tel Aviv-Yafo, Israel',
14: 'Wrocław, Poland',
15: 'Singapore'}})
c[['City', 'Country']] = b['Location'].str.split(',', n=1, expand=True) # This splits the data into city and Country. So this works very well for Foriegn address or data with just city and country.
Out put is:
City Country
0 Warszawa Poland
1 San Francisco CA, United States
2 Los Angeles CA, United States
3 Sunnyvale CA, United States
4 Sunnyvale CA, United States
5 San Francisco CA, United States
6 Sunnyvale CA, United States
7 Kraków Poland
8 Shanghai China
Second method is:
regex = r'(?P<City>[^,]+)\s*,\s*(?P<State>[^\s]+)\s+(?P<Country>[^,]+)'
df=b['Location'].str.extract(regex)
df # This splits the data into City, State and Country, so it works well for US address.
Output is :
City State Country
0 NaN NaN NaN
1 San Francisco CA, United States
2 Los Angeles CA, United States
3 Sunnyvale CA, United States
4 Sunnyvale CA, United States
5 San Francisco CA, United States
6 Sunnyvale CA, United States
7 NaN NaN NaN
A: $ ipython
Python 3.6.8 |Anaconda custom (64-bit)| (default, Feb 21 2019, 18:30:04) [MSC v.1916 64 bit (AMD64)]
Type 'copyright', 'credits' or 'license' for more information
IPython 7.5.0 -- An enhanced Interactive Python. Type '?' for help.
In [1]: d = {'Location': {0: 'Warszawa, Poland',
...: 1: 'San Francisco, CA, United States',
...: 2: 'Los Angeles, CA, United States',
...: 3: 'Sunnyvale, CA, United States',
...: 4: 'Sunnyvale, CA, United States',
...: 5: 'San Francisco, CA, United States',
...: 6: 'Sunnyvale, CA, United States',
...: 7: 'Kraków, Poland',
...: 8: 'Shanghai, China',
...: 9: 'Mountain View, CA, United States',
...: 10: 'Boulder, CO, United States',
...: 11: 'Boulder, CO, United States',
...: 12: 'Xinyi District, Taiwan',
...: 13: 'Tel Aviv-Yafo, Israel',
...: 14: 'Wrocław, Poland',
...: 15: 'Singapore'}}
In [2]: import pandas as pd
...: df = pd.DataFrame.from_dict(d)
...: df
Out[2]:
Location
0 Warszawa, Poland
1 San Francisco, CA, United States
2 Los Angeles, CA, United States
3 Sunnyvale, CA, United States
4 Sunnyvale, CA, United States
5 San Francisco, CA, United States
6 Sunnyvale, CA, United States
7 Kraków, Poland
8 Shanghai, China
9 Mountain View, CA, United States
10 Boulder, CO, United States
11 Boulder, CO, United States
12 Xinyi District, Taiwan
13 Tel Aviv-Yafo, Israel
14 Wrocław, Poland
15 Singapore
In [3]: df['Country'] = df['Location'].str.split(',').apply(lambda x: x[-1])
...: df
Out[3]:
Location Country
0 Warszawa, Poland Poland
1 San Francisco, CA, United States United States
2 Los Angeles, CA, United States United States
3 Sunnyvale, CA, United States United States
4 Sunnyvale, CA, United States United States
5 San Francisco, CA, United States United States
6 Sunnyvale, CA, United States United States
7 Kraków, Poland Poland
8 Shanghai, China China
9 Mountain View, CA, United States United States
10 Boulder, CO, United States United States
11 Boulder, CO, United States United States
12 Xinyi District, Taiwan Taiwan
13 Tel Aviv-Yafo, Israel Israel
14 Wrocław, Poland Poland
15 Singapore Singapore
In [4]: df['Country'].to_dict()
Out[4]:
{0: ' Poland',
1: ' United States',
2: ' United States',
3: ' United States',
4: ' United States',
5: ' United States',
6: ' United States',
7: ' Poland',
8: ' China',
9: ' United States',
10: ' United States',
11: ' United States',
12: ' Taiwan',
13: ' Israel',
14: ' Poland',
15: 'Singapore'}
A: This is little more refined and does the same job, and can be fit in one line of code.
b['City'] = b['Location'].str.split(',').apply(lambda x: x[0])
b['Country'] = b['Location'].str.split(',').apply(lambda x: x[-1])
b
The output:
Location City Country
0 Warszawa, Poland Warszawa Poland
1 San Francisco, CA, United States San Francisco United States
2 Los Angeles, CA, United States Los Angeles United States
3 Sunnyvale, CA, United States Sunnyvale United States
4 Sunnyvale, CA, United States Sunnyvale United States
5 San Francisco, CA, United States San Francisco United States
6 Sunnyvale, CA, United States Sunnyvale United States
7 Kraków, Poland Kraków Poland
8 Shanghai, China Shanghai China
This is the one line version, however I am having trouble to have them in two different columns. Something wrong here, I am not able to find it out.
b['City', 'Country']= pd.DataFrame (b['Location'].str.split(',').apply(lambda x:( x[0], x[-1])))
(City, Country)
0 (Warszawa, Poland)
1 (San Francisco, United States)
2 (Los Angeles, United States)
3 (Sunnyvale, United States)
4 (Sunnyvale, United States)
5 (San Francisco, United States)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,492 |
\section{Introduction}
We consider the worst-case convergence of the gradient and Newton methods (with or without exact linesearch, and with possibly inexact search directions)
for certain smooth and strongly convex functions.
Our analysis is computer-assisted and relies on semidefinite programming performance estimation problems, as introduced by Drori and Teboulle \cite{drori2014}.
As a result, we develop a set of tools that may be used to design or analyse a wide range of interior point algorithms. Our analysis
is in fact an extension of the worst-case analysis of the gradient method in \cite{Klerk_Glineur_Taylor_2016}, combined with the
fact that Newton's method may be viewed as a gradient method with respect to a suitable local (intrinsic) inner product.
This is similar in spirit to
recent analysis by Li et al \cite{Li_et_al_2016} of inexact proximal Newton methods for self-concordant
functions, but our approach is different.
As an illustration of the tools we develop, we show how one may give a rigorous analysis of a recent interior point method by
Abernethy and Hazan \cite{Abernethy_Hazan_2015}, where
the search direction is approximated through sampling. This particular method has sparked much recent interest, since it demonstrates the
links between simulated annealing and interior point methods. However, a rigorous analysis of the method is not given in \cite{Abernethy_Hazan_2015}, and we supply crucial
details that are missing in \cite{Abernethy_Hazan_2015}.
Polynomial-time complexity of certain simulated annealing methods for
convex optimization was first shown by Kalai and Vempala \cite{Kalai-Vempala 2006}, and the link with interior point methods
casts light on their result.
\section{Preliminaries}
Throughout $f$ denotes a differentiable convex function with convex domain $D_f \subset \mathbb{R}^n$.
We will indicate additional assumptions on $f$ as needed. We will mostly use the notation from the book by Renegar \cite{Renegar2001a}, for easy reference.
\subsection{Gradients and Hessians}
In what follows we fix a reference inner product $\langle \cdot,\cdot\rangle$ on $\mathbb{R}^n$ with induced norm $\|\cdot\|$.
\begin{definition}[Gradient of differentiable $f$]
\label{def:gradient}
The gradient of $f$ at $x \in D_f$ with respect to $\langle \cdot , \cdot \rangle$
is the unique vector $g(x)$ such that
\[
\lim_{\| \Delta x\| \rightarrow 0} \frac{f(x+\Delta x) - f(x) - \langle g(x) , \Delta x \rangle }{\|\Delta x\|} = 0.
\]
\end{definition}
Note that $g(x)$ depends on the reference inner product. If $\langle \cdot,\cdot\rangle$ is the Euclidean dot product then
$g({x}) = \nabla f({x}) = \left[\frac{\partial f({x})}{\partial x_i}\right]_{i=1,\ldots,n.}$
If $B:\mathbb{R}^n \rightarrow \mathbb{R}^n$ is a self-adjoint positive definite linear operator, we may define a
new inner product in terms of the reference inner product as follows:
$\langle \cdot,\cdot\rangle_B$ via $\langle {x}, {y}\rangle_{B} = \langle {x}, B{y}\rangle$ $\forall x,y \in \mathbb{R}^n$.
(Recall that all inner products in $\mathbb{R}^n$ arise in this way.)
If we change the inner product in this way, then the gradient changes as follows:
\[
\langle \cdot, \cdot \rangle \rightarrow \langle \cdot, \cdot \rangle_{B} \Rightarrow g({x}) \rightarrow B^{-1} g({x}).
\]
Thus one always has $g(x) = B^{-1} \nabla f(x)$ for some positive definite $B$, that depends on the choice of reference inner product.
If $f$ is twice differentiable, we define its Hessian as follows.
\begin{definition}[Second derivative of twice differentiable $f$]
\label{def:hessian}
The second derivative (or Hessian) of $f$ at $x$ is defined as the (unique) linear
operator $H(x)$ that satisfies
\[
\lim_{\|\Delta x\| \rightarrow 0} \frac{\|g(x+\Delta x) - g(x)-H(x)\Delta x\|}{\|\Delta x\|} = 0.
\]
\end{definition}
The second derivative also depends on the reference inner product, since $g(x)$ does.
Recall that $H(x)$ is self-adjoint with respect to the reference inner product if $f$ is twice continuously differentiable.
Assuming that $H(x)$ is positive definite and self-adjoint at a given $x$, define the intrinsic (w.r.t. $f$ at $x$) inner product
\[
\langle u,v\rangle_{x} := \langle u,v\rangle_{H(x)} \equiv \langle
u,H(x)v\rangle.
\]
The definition is {\em independent of the reference inner product}
$\langle \cdot, \cdot \rangle$, e.g. without loss of generality we may set the reference inner product to be the Euclidean one, to obtain:
\[
\langle u,v\rangle_{x} = u^{\sf T} \nabla^2f(x)v,
\]
where $\nabla^2f(x) = \left(\frac{\partial^2 f(x)}{\partial x_i\partial x_j}\right)$ is the usual $n\times n$
Hessian matrix of second partial derivatives at $x$. (The Hessian matrix is obtained by writing $H(x)$ as a matrix in the standard basis, when the
reference inner product is the Euclidean inner product.)
The induced norm for the intrinsic inner product is denoted by: $\|u\|_x = \sqrt{\langle u,u\rangle_{x}}$.
For the intrinsic inner product
\[\langle u,v\rangle_{x} := \langle u,v\rangle_{H(x)},
\]
the gradient at $y$ is denoted by $g_x(y) := H(x)^{-1}g(y)$, and
the Hessian at $y$ by $H_x(y):=H(x)^{-1}H(y)$.
\subsection{Fundamental theorem of calculus}
In what follows, we will recall coordinate-free versions of the fundamental theorem
of calculus. Our review follows Renegar \cite{Renegar2001a}, and all proofs may be found there.
\begin{theorem}[Theorem 1.5.1 in \cite{Renegar2001a}]
\label{thm:151}
If $x,y \in D_f$, then
\[
f(y) - f(x) = \int_0^1 \langle g(x + t(y-x)), y-x\rangle dt.
\]
\end{theorem}
Next, we recall the definition of a vector-valued integral.
\begin{definition}
Let $t \mapsto v(t) \in \mathbb{R}^n$ where $t \in [a,b]$.
Then $u$ is the integral of $v$ if
\[
\langle u,w\rangle = \int_a^b \langle v(t),w\rangle \; dt \mbox{ for all } w \in \mathbb{R}^n.
\]
\end{definition}
Note that this definition is in fact independent of the reference inner product.
We will use the following bound on norms of vector-values integrals.
\begin{theorem}[Proposition 1.5.4 in \cite{Renegar2001a}]
\label{prop:154}
Let $t \mapsto v(t) \in \mathbb{R}^n$ where $t \in [a,b]$.
If $v$ is integrable, then
\[
\left\|\int_a^b v(t)dt \right\| \le \int_a^b \|v(t)\|dt.
\]
\end{theorem}
Finally, we will will require the following version of the fundamental theorem for gradients.
\begin{theorem}[Theorem 1.5.6 in \cite{Renegar2001a}]
\label{thm:156}
If $x,y \in D_f$, then
\[
g(y)-g(x) = \int_0^1 H(x+t(y-x))(y-x)dt.
\]
\end{theorem}
\subsection{Inexact gradient and Newton methods}
The minimizer of $f$
is denoted by $x_*$.
We consider approximate gradients ${d}_i \approx g(x_i)$ at a given iterate $x_i$ $(i=0,1,\ldots)$; to be precise we assume the following for a given $\varepsilon \ge 0$:
\begin{equation}
\label{eq:error}
\|d_i-g({x}_i)\| \le \varepsilon\|g({x}_i) \| \quad i = 0,1,\ldots
\end{equation}
Note that $\varepsilon = 0$ yields the gradient, i.e.\ $d_i = g(x_i)$.
\begin{center}
{\small \fbox{
\parbox{0.7\textwidth}{
\textbf{Inexact gradient descent method}
\begin{itemize}
\item[] \textbf{Input:} $f:\mathbb{R}^n\rightarrow \mathbb{R}$, ${x}_0\in \mathbb{R}^n$, ${0\le \varepsilon < 1}$.\\[-0.2cm]
\item[] \textbf{for} $i=0,1,\ldots$ \\ [-0.2cm]
\item[]\hspace{1cm} Select any ${d}_i$ that satisfies \eqref{eq:error}; \\ [-0.2cm]
\item[]\hspace{1cm} {Choose a step length $\gamma > 0$} \\ [-0.2cm]
\item[]
\hspace{1cm} {${x}_{i+1}={x}_i-\gamma {d}_i$} \\ [-0.2cm]
\end{itemize}
}}}
\end{center}
We will consider two ways of choosing the step length $\gamma$:
\begin{enumerate}
\item
Exact line search:
$\gamma=\text{argmin}_{\gamma \in \mathbb{R}}f\left({x}_i-\gamma {d}_i\right)$;
\item
Fixed step length: $\gamma$ takes the same value at each iteration, and this value is known beforehand.
\end{enumerate}
We note once more that, at iteration $i$, we obtain the Newton direction by using the $\langle \cdot,\cdot \rangle_{x_i}$ inner product.
Similarly, by using an inner product $\langle \cdot,\cdot\rangle_{B}$ for some positive definite, self-adjoint operator $B$, we obtain
the direction $-B^{-1}g(x_i)$, which is of the type used in quasi-Newton methods. Finally, the Euclidean dot product
yields the familiar steepest descent direction $-\nabla f(x_i)$.
\section{Classes of convex functions}
In this section we review two classes of convex functions, namely smooth, strongly convex functions and self-concordant functions.
We also show that, in a certain sense, the latter class may be seen as a special case of the former.
\subsection{Convex functions}
Recall that a differentiable function $f$
is convex on on open convex set $D \subset \mathbb{R}^n$ if and only if
\begin{equation}
\label{convex_f}
f(y) \ge f(x) + \langle g(x),y-x\rangle \quad \forall x,y \in D.
\end{equation}
Also recall that a twice continuously differentiable function is convex on $D$ if and only if $H(x) \succeq 0$ for all $x \in D$.
\subsection{Smooth strongly convex functions}
A differentiable function $f$ with $D_f = \mathbb{R}^n$ is called $L$-smooth and $\mu$-strongly convex if it satisfies the following two properties:
\begin{itemize}
\item[(a)] {\bf $L$-smoothness}: there exists some $L>0$ such that $\frac{1}{L}\norm{ g(u) - g(v)}\leq \norm{u-v}$
holds for all pairs $u,v$ and corresponding gradients $g(u), g(v)$.
\item[(b)] {\bf $\mu$-strong convexity}: there exists some $\mu>0$ such that the function $x \mapsto f(x)-\frac{\mu}{2}\|{x}\|^2$ is convex.
\end{itemize}
The class of such functions is denoted by $\mathcal{F}_{\mu,L}(\mathbb{R}^n)$.
Note that this function class is defined in terms of the reference inner product and its induced norm.
In particular, it is not invariant under a change of inner product: under a change of inner product a smooth, strongly convex function
remains smooth, strongly convex, but the parameters $\mu$ and $L$ depend on the inner product.
If $D\subseteq \mathbb{R}^n$ is an open, convex set, then we denote the set of functions that satisfy properties (a) and (b) on $D$ by $\mathcal{F}_{\mu,L}(D)$.
\begin{lemma} Let $D$ be an open convex set and $f:D\rightarrow \mathbb{R}^d$ be twice continuously differentiable. The following statements are equivalent:
\label{lemm:Lsmooth}
\begin{itemize}
\item[(a)] $f$ is convex and $L$-smooth on $D$,
\item[(b)] $0\preceq H(x) \preceq L I$ $\;\forall x\in D$,
\item[(c)] $\langle{g(y)-g(x)},{y-x}\rangle \geq \frac{1}{L}\normsq{g(y)-g(x)}$ $\;\forall x,y\in D$.
\end{itemize}
\end{lemma}
\begin{proof}
$(a)\Rightarrow(b)$:
First of all, convexity of $f$ is equivalent to $H(x) \succeq 0$ for all $x \in D$.
If $f$ is also $L$-smooth of $D$, then $\|g(x)-g(y)\| \le L\|x-y\|$ for all $x,y \in D$.
By the definition of the Hessian one has that, for any $\epsilon >0$, there is a $\delta >0$ such that
\[
\|g(y)-g(x)-H(x)(y-x)\| \le \epsilon \|y-x\|
\]
if $\|y-x\| \le \delta$. This implies
\begin{eqnarray*}
\| H(x)(y-x)\| &\le& \epsilon \|y-x\| + \|g(y)-g(x)\| \quad \mbox{(triangle inequality)} \\
&\le& \epsilon \|y-x\| + L\|y-x\| \quad \mbox{($L$-smoothness)}.
\end{eqnarray*}
Thus we have
\[
\frac{\| H(x)(y-x)\|}{\|y-x\|} \le \epsilon + L,
\]
which in turn implies
\[
\|H(x)\| = \max_{\|v\| = 1} \|H(x)v\| \le L,
\]
since $\epsilon \ge 0$ was arbitrary. Finally we use the fact that, since $H(x)$ is self-adjoint and positive semidefinite,
$\|H(x)\|$ equals the largest eigenvalue of $H(x)$, so $\|H(x)\| \le L$ is the same as $H(x) \preceq L I$.
$(b)\Rightarrow(c)$:
If $\|H(x)\| \le L$, then $H(x) - \frac{1}{L}H^2(x) \succeq 0$ for all $x \in D$, and Theorem \ref{thm:156} implies
\begin{eqnarray*}
\langle g(y)-g(x),y-x\rangle &=& \left\langle y-x,\int_0^1 H(x+t(y-x))(y-x)dt\right\rangle \\
&=& \int_0^1\langle y-x, H(x+t(y-x))(y-x)\rangle dt \\
&\ge & \int_0^1\langle y-x, \frac{1}{L}H^2(x+t(y-x))(y-x)\rangle dt \\
&=& \frac{1}{L} \int_0^1 \| H(x+t(y-x))(y-x)\|^2 dt \\
&\ge & \frac{1}{L} \left(\int_0^1 \| H(x+t(y-x))(y-x)\| dt\right)^2 \quad \mbox{(Jensen inequality)} \\
& \ge & \frac{1}{L} \left\|\int_0^1 H(x+t(y-x))(y-x) dt\right\|^2 \quad \mbox{(Theorem \ref{prop:154})}\\
&=& \frac{1}{L}\|g(y)-g(x)\|^2 \quad \mbox{(Theorem \ref{thm:156})}.
\end{eqnarray*}
$(c)\Rightarrow(a)$:
Condition $(c)$, together with the Cauchy-Schwartz inequality, immediately imply $L$-smoothness.
To show convexity, note that, by Theorem \ref{thm:151},
\begin{eqnarray*}
f(y) - f(x) -\langle g(x),y-x\rangle &=& \int_0^1 \frac{1}{t}\langle g(x + t(y-x))-g(x), t(y-x)\rangle dt \\
&\ge& \int_0^1 \frac{1}{tL}\| g(x + t(y-x))-g(x)\|^2 dt \ge 0, \\
\end{eqnarray*}
where the first inequality is from condition $(c)$. Thus we obtain the convexity inequality \eqref{convex_f}.
\end{proof}
The last Lemma allows us to derive the following necessary and sufficient conditions for membership of $\mathcal{F}_{\mu,L}(D)$.
The condition $(d)$ below will be used extensively in the proofs that follow.
\begin{theorem}
\label{thm:mu_L_H}
Let $D$ be an open convex set and $f:D\rightarrow \mathbb{R}^d$ be twice continuously differentiable. The following statements are equivalent:
\begin{itemize}
\item[(a)] $f$ is $\mu$-strongly convex and $L$-smooth on $D$, i.e.\ $f \in \mathcal{F}_{\mu,L}(D)$,
\item[(b)] $\mu I\preceq H(x) \preceq L I$ $\forall x\in D$,
\item[(c)] $f(x)-\frac{\mu}{2}\normsq{x}$ is convex and $(L-\mu)$-smooth on $D$,
\item[(d)] for all $x,y\in D$ we have
\begin{equation}
\label{gradient inequality}
\langle{g(x)-g(y)},{x-y}\rangle\geq \frac{1}{1-\frac{\mu}{L}} \left(\frac{1}{L}\normsq{g(y)-g(x)}+\mu\normsq{x-y}
-2\frac{\mu}{L}\langle{g(x)-g(y)},{x-y}\rangle\right).
\end{equation}
\end{itemize}
\end{theorem}
\begin{proof}
The equivalences $(a)\Leftrightarrow (b)\Leftrightarrow(c)$ follow directly from Lemma \ref{lemm:Lsmooth} and the relevant definitions.
$(c)\Leftrightarrow(d)$: Requiring $h(x)=f(x)-\frac{\mu}{2}\normsq{x}$ to be convex and $(L-\mu)$-smooth on $D$ can equivalently be formulated as requiring $h$ to satisfy
\[\langle{g_h(x)-g_h(y)},{x-y}\rangle \geq \frac{1}{L-\mu}\normsq{g_h(y)-g_h(x)}\] for all $x,y\in D$, where $g_h$ is the gradient of $h$. Equivalently:
\begin{align*}
(L-\mu)\left[\langle{g_f(x)-g_f(y)},{x-y}\rangle-\mu \normsq{x-y}\right]\geq &\normsq{g_f(y)-g_f(x)}+\mu^2\normsq{x-y}-2\mu\langle{g_f(y)-g_f(x)},{y-x}\rangle,
\end{align*}
which is exactly condition $(d)$ in the statement of the theorem.
\end{proof}
We note once more that the spectrum of the Hessian is not invariant under change in inner product, thus the values $\mu$ and $L$ are
intrinsically linked to the reference inner product. If $D = \mathbb{R}^n$, a stronger condition than condition $(d)$ in the last theorem holds, namely
\begin{equation}
\label{eq:FmuL}
f(y)-f(x) - \langle{g(x)},{y-x}\rangle \geq \frac{1}{2(1-\frac{\mu}{L})} \left(\frac{1}{L}\normsq{g(y)-g(x)}+\mu\normsq{x-y}-2\frac{\mu}{L}\langle{g(x)-g(y)},{x-y}\rangle\right).
\end{equation}
\subsection{Self-concordance}
Self-concordant functions are special convex functions
introduced by Nesterov and Nemirovski \cite{int:Nesterov5}, that play a certral role in the analysis of interior point algorithms.
We will use the (slightly) more general definition by Renegar \cite{Renegar2001a}.
\begin{definition}[Self-concordant functional]
Let $B_x(x,1)$ be the open unit ball centered at $x$ for the $\|\cdot\|_x$ norm. Then
$f$ is called self-concordant if:
\begin{enumerate}
\item
For all $x \in D_f$ one has $B_x(x,1) \subseteq D_f$;
\item
For all $y \in B_x(x,1)$ one has
\[
1 - \|y-x\|_x \le \frac{\|v\|_y}{\|v\|_x} \le \frac{1}{1 - \|y-x\|_x} \mbox{ for all } v \neq 0.
\]
\end{enumerate}
\end{definition}
A subclass of self-concordant functions, that play a key role in interior point analysis, are the so-called self-concordant barriers.
\begin{definition}[Self-concordant barrier]
A self-concordant function $f$ is called a $\vartheta$-self-concordant barrier
if there is a finite value $\vartheta \ge 1$ given by
\[
\vartheta := \sup_{x\in D_f} \|g_x(x)\|_x^2.
\]
\end{definition}
A self-concordant barrier tends to $\infty$ as $x$ approaches the boundary of $D_f$, hence the name.
\medskip
An equivalent characterization of self-concordance is as follows.
\begin{theorem}[Theorem 2.2.1 in \cite{Renegar2001a}]
\label{thm:alt def sc}
Assume $f$ such that for all $x \in D_f$ one has $B_x(x,1) \subseteq D_f$.
Then $f$ is self-concordant if, and only if, for all $x \in D_f$ and $y \in B_x(x,1)$:
\[
\|H_x(y)\|_x, \|H_x(y)^{-1}\|_x \le \frac{1}{(1 - \|y-x\|_x)^2}
\]
or, equivalently
\[
\|I-H_x(y)\|_x, \|I-H_x(y)^{-1}\|_x \le \frac{1}{(1 - \|y-x\|_x)^2}-1.
\]
\end{theorem}
This alternative characterization allows us to establish the following link between
self-concordant and $L$-smooth, $\mu$-strictly convex functions.
\begin{theorem}
\label{thm:sc_vs_FmuL}
Assume $f:D_f \rightarrow \mathbb{R}$ is self-concordant, $x \in D_f$, and $\delta < 1$.
If
\[
D = \left\{y \; | \; \|x-y\|_x <\delta \right\} = B_x(x,\delta),
\]
then $f \in F_{\mu,L}(D)$ with
\[
\mu = (1-\delta)^2, \; L = \frac{1}{(1-\delta)^2}.
\]
\end{theorem}
\proof
By Theorem \ref{thm:alt def sc}, the spectrum of $H_x(y)$ is contained in the interval
$\left[(1 - \|y-x\|_x)^2,\frac{1}{(1 - \|y-x\|_x)^2}\right]$, which in turn is contained
in the interval $\left[(1 - \delta)^2,\frac{1}{(1 - \delta)^2}\right]$ for all $y \in B_x(x,\delta)$.
Theorem \ref{thm:mu_L_H} now yields the required result.
\qed
\section{Performance estimation problems}
Performance estimation problems, as introduced by Drori and Teboulle \cite{drori2014}, are semidefinite programming (SDP) problems that
bound the worst-case performance of certain iterative optimization algorithms. Essentially, the goal is to find the
objective function from a given function class, that exhibits the worst-case behavior for a given iterative algorithm.
In what follows we list the SDP performance estimation problems that we will use.
The performance estimation problems have variables that correspond to (unknown) iterates $x_0$ and $x_1$, the minimizer $x_*$, as well
as the gradients and function values at these points, namely $g_i$ ($i \in \{*,0,1\})$) correspond to $g(x_i)$ ($i \in \{*,0,1\})$), and
$f_i$ ($i \in \{*,0,1\})$) correspond to $f(x_i)$ ($i \in \{*,0,1\})$). We may assume $x_* = g_* = 0$ and $f_* = 0$ without loss of generality.
The objective is to find the maximum (worst-case) value of either
$f_1 - f_*$, $\|g_1\|$, or $\|x_1-x_*\|$. Note again that the norm may be any induced norm on $\mathbb{R}^n$.
\subsection{Performance estimation with exact line search}
\begin{itemize}
\item
Parameters: $L \ge \mu > 0$, $R > 0$;
\item
Variables:
$\left\{({x}_i,{g}_i,f_i) \right\}_{i\in S}$ $\;\; (S = \{*,0,1\})$.
\end{itemize}
\subsubsection*{Worst-case function value}
\begin{equation}
\label{pep:els_f}
\left.
\begin{array}{rll}
\max \ &f_1-f_* &\\
\mbox{s.t. } &
f_i - f_j - \langle{{g}_j},{{x}_i-{x}_j}\rangle \geq \frac{1}{2(1-\mu/L)}\left( \frac{1}{L}\norm{{g}_i-{g}_j}^2+ \mu \norm{{x}_i-{x}_j}^2 - 2\frac{\mu}{L} \langle{{g}_j-{g}_i},{{x}_j-{x}_i}\rangle\right) & \forall i,j \in S\\
& {g}_* = {0} &\\
&\langle {x}_{1}-{x}_0, {g}_1\rangle = 0 &\\
& \langle{g}_0 , {g}_1\rangle \le \varepsilon \|g_0\|\|g_1\| &\\
&f_0-f_* \leq R & \\
\end{array}
\right\}
\end{equation}
The first constraint corresponds to
\eqref{eq:FmuL}, and models the necessary condition for $f \in {\mathcal{F}}_{\mu,L}(\mathbb{R}^n)$.
The second constraint corresponds to the fact that the gradient is zero at a minimizer. The third constraint
is the well-known property of exact line search,
while the fourth constraint is satisfied
if the approximate gradient condition \eqref{eq:error} holds.
Finally, the fifth constraint ensures that the problem is bounded.
Note that the resulting problem may be written as an SDP problem, with $4\times 4$ matrix variable given
by the Gram matrix of the vectors $x_0,x_1,g_0,g_1$ with respect to the reference inner product.
In particular the fourth contraint may be written as the linear matrix inequality:
\begin{equation}
\label{noisy lmi}
\left(
\begin{array}{cc}
\varepsilon \|{g}_0\|^2 & \langle{g}_0, {g}_1\rangle\\
\langle{g}_0, {g}_1\rangle & \varepsilon \|{g}_1\|^2 \\
\end{array}
\right)
\succeq 0.
\end{equation}
Also note that the optimal value of the resulting SDP problem is independent of the inner product.
The SDP problem \eqref{pep:els_f} was first studied in \cite{Klerk_Glineur_Taylor_2016}.
\subsubsection*{Worst-case gradient norm}
The second variant of performance estimation is to find the worst case convergence of the gradient norm.
\begin{equation}
\label{pep:els_g}
\left.
\begin{array}{rll}
\max \ &\|g_1\|^2 &\\
\mbox{s.t. } &
{\langle{g_i-g_j},{x_i-x_j}\rangle\geq \frac{1}{1-\frac{\mu}{L}}\left(\frac{1}{L}\|{g_i-g_j}\|^2+\mu\|{x_i-x_j}\|^2-2\frac{\mu}{L}\langle{g_i-g_j},{x_i-x_j}\rangle\right)} & \forall i,j \in S\\
& {g}_* = {0} &\\
&\langle {x}_{1}-{x}_0, {g}_1\rangle = 0 &\\
& \langle{g}_0 , {g}_1\rangle \le \varepsilon \|g_0\|\|g_1\| &\\
&\|g_0\|^2 \leq R & \\
\end{array}
\right\}
\end{equation}
\subsubsection*{Worst-case distance to optimality}
The third variant of performance estimation is to find the worst case convergence of the distance to optimality.
\begin{equation}
\label{pep:els_x}
\left.
\begin{array}{rll}
\max \ &\|x_1-x_*\|^2 &\\
\mbox{s.t. } &
{\langle{g_i-g_j},{x_i-x_j}\rangle\geq \frac{1}{1-\frac{\mu}{L}}\left(\frac{1}{L}\|{g_i-g_j}\|^2+\mu\|{x_i-x_j}\|^2-2\frac{\mu}{L}\langle{g_i-g_j},{x_i-x_j}\rangle\right)} & \forall i,j \in S\\
& {g}_* = {0} &\\
&\langle {x}_{1}-{x}_0, {g}_1\rangle = 0 &\\
& \langle{g}_0 , {g}_1\rangle \le \varepsilon \|g_0\|\|g_1\| &\\
&\|x_0\|^2 \leq R & \\
\end{array}
\right\}
\end{equation}
In what follows we will give upper bounds on the optimal values of these performance estimation SDP problems.
\subsection{PEP with fixed step sizes}
For fixed step sizes, the performance estimation problems \eqref{pep:els_f}, \eqref{pep:els_g}, and \eqref{pep:els_x}
change as follows:
\begin{itemize}
\item
for given step size $\gamma > 0$, the condition $x_1 = x_0 - \gamma d$ is used to eliminate $x_1$,
where $d$ is the approximate gradient at $x_0$.
\item
The condition
$
\normsq{d-g_0}\leq \varepsilon^2\normsq{g_0}
$
is added, that corresponds to \eqref{eq:error}, and $\langle{g}_0 , {g}_1\rangle \le \varepsilon \|g_0\|\|g_1\|$ is omitted.
\end{itemize}
\section{Error bounds from performance estimation}
The optimal values of the performance estimation problems in the last section give
bounds on the worst-case convergence rate of the gradient method.
\subsection{PEP with exact line search}
\begin{theorem}
\label{thm:ELS improvements}
Consider the inexact gradient method with exact line search applied to some $f \in \mathcal{F}_{\mu,L}(\mathbb{R}^n)$.
If $\kappa := \frac{\mu}{L}$ and $\varepsilon \in \left[0, \frac{2\sqrt{\kappa}}{1+\kappa}\right]$, one has
\begin{eqnarray*}
{f(x_1)} - f(x_*)&\le & \left(\frac{1-\kappa +\varepsilon(1-\kappa)}{1+\kappa +\varepsilon(1-\kappa)}\right)^2 ({f(x_0)}-f(x_*)), \\
\|g(x_1)\| &\le & \left(\varepsilon+ \sqrt{1-{\varepsilon}^2}\frac{1-\kappa}{2\sqrt{\kappa}}\right)\|{g(x_0)}\|, \\
\|{x_1-x_*}\| & \le & \left(\varepsilon+ \sqrt{1-{\varepsilon}^2}\frac{1-\kappa}{2\sqrt{\kappa}}\right)\|{x_0-x_*}\|. \\
\end{eqnarray*}
\end{theorem}
\proof
The three inequalities in the statement of the theorem follow
from corresponding upper bounds on the optimal values of the SDP performance estimation problems \eqref{pep:els_f}, \eqref{pep:els_g}, and \eqref{pep:els_x}, respectively.
The first of the SDP performance estimation problems, namely \eqref{pep:els_f}, is exactly the same as the one in \cite{Klerk_Glineur_Taylor_2016} (see (8) there).
The first inequality therefore follows from
Theorem 1.2 in \cite{Klerk_Glineur_Taylor_2016}.
It remains to demonstrate suitable upper bounds on the SDP performance estimation problems \eqref{pep:els_g}, and \eqref{pep:els_x}.
This is done by aggregating the constraints of these respective SDP problems by using suitable (Lagrange) multipliers.\footnote{The
multipliers used in the proof were obtained by solving the SDP problems
\eqref{pep:els_g} and \eqref{pep:els_x} numerically for different values of $\mu$, $L$ and $R$, and subsequently
guessing the correct analytical expressions of the multipliers by looking at the optimal solution of the dual SDP problem.
The correctness of these expressions for the multipliers is verified in the proof. Thus the performance estimation problems were only used to
find the proof of Theorem \ref{thm:ELS improvements}, and play no role in the proof itself.}
To this end, consider the following constraints from \eqref{pep:els_g} and their associated multipliers:
\begin{align*}
&{\langle{g_0-g_1},{x_0-x_1}\rangle\geq \frac{1}{1-\frac{\mu}{L}}\left(\frac{1}{L}\|{g_0-g_1}\|^2+\mu\|{x_1-x_0}\|^2-2\frac{\mu}{L}\langle{g_0-g_1},{x_0-x_1}\rangle\right)} &&:{(L-\mu)}\lambda,\\
&\langle{g_1},{x_1-x_0}\rangle\leq 0 && :L+\mu,\\
&\begin{pmatrix}
\epsilon ||g_0||^2 & \langle{g_0},{g_1}\rangle\\
\langle{g_0},{g_1}\rangle & \epsilon ||g_1||^2
\end{pmatrix}\succeq 0 &&:S,
\end{align*}
with $S=\begin{pmatrix}
s_{11} & s_{12}\\ s_{12} & s_{22}
\end{pmatrix},$ and:
\begin{align*}
&\lambda=\frac{2 \varepsilon \sqrt{\kappa}}{\sqrt{1 - {\varepsilon}^2} \left(1 - \kappa\right)} + 1,
& \\
&s_{11}=\frac{3 \varepsilon}{2} - \frac{\varepsilon \left(\kappa + \frac{1}{\kappa}\right)}{4} + \frac{1-\kappa}{2 \sqrt{\kappa(1 - {\varepsilon}^2)}} - \frac{{\varepsilon}^2 \left(1 - \kappa\right)}{\sqrt{\kappa(1 - {\varepsilon}^2)}},
&\\
&s_{22}= \frac{2 \sqrt{\kappa(1 - {\varepsilon}^2)}-\varepsilon \left(1 - \kappa\right)}{\left(1-{\varepsilon}^2\right) \left(1 - \kappa\right) + 2 \varepsilon \sqrt{\kappa(1 - {\varepsilon}^2)}}, &
\\
&s_{21}=
\frac{\varepsilon\, \left(1 - \kappa\right)}{2 \sqrt{\kappa(1 - {\varepsilon}^2)}} - 1.&
\end{align*}
{Assuming the corresponding multipliers are of appropriate signs (see discussion below), the proof consists in reformulating the following weighted sum of the previous inequalities (the validity of this inequality follows from the signs of the multipliers):
\begin{equation}\label{eq:weightedsum_grad}
\begin{aligned}
0\geq &(L-\mu)\lambda\left[\frac{1}{1-\frac{\mu}{L}}\left(\frac{1}{L}\|{g_0-g_1}\|^2+\mu\|{x_1-x_0}\|^2-2\frac{\mu}{L}\langle{g_0-g_1},{x_0-x_1}\rangle\right)-\langle{g_0-g_1},{x_0-x_1}\rangle\right]\\&+(L+\mu)\left[\langle{g_1},{x_1-x_0}\rangle\right]-\mathrm{Trace}\left(\begin{pmatrix}
s_{11} & s_{12} \\ s_{12} & s_{22}
\end{pmatrix}\begin{pmatrix}
\epsilon ||g_0||^2 & \langle{g_0},{g_1}\rangle\\
\langle{g_0},{g_1}\rangle & \epsilon ||g_1||^2
\end{pmatrix} \right).
\end{aligned}
\end{equation}To this end, we first show that all multipliers are nonnegative; that is, $(L-\mu)\lambda\geq 0$, $L+\mu\geq 0$ and $S\succeq 0$. The nonnegativity of the first two is clear from their expressions (sum of nonnegative terms). Concerning $S$, let us note that $s_{22}\geq 0\Leftrightarrow \varepsilon\in\left[\frac{-2\sqrt{\kappa}}{1+\kappa},\frac{2\sqrt{\kappa}}{1+\kappa}\right]$.}
When $\varepsilon < \frac{2\sqrt{\kappa}}{1+\kappa}$, $s_{22}$ ensures that there exists a positive eigenvalue for $S$, since $s_{22}>0$.
In order to prove that both eigenvalues of $S$ are nonnegative, one may verify:
\begin{equation*}
\det S=s_{11}s_{22}-s_{21}^2=0.
\end{equation*}
{Therefore, one eigenvalue of $S$ is positive and the other one is zero when $\varepsilon < \frac{2\sqrt{\kappa}}{1+\kappa}$, and in the simpler case $\varepsilon = \frac{2\sqrt{\kappa}}{1+\kappa}$, we have $S=0$, and hence the inequality~\eqref{eq:weightedsum_grad} is valid.}
{Reformulating the valid inequality~\eqref{eq:weightedsum_grad} yields:}
\begin{align*}
\|{g_1}\|^2\leq &\left(\varepsilon+ \sqrt{1-{\varepsilon}^2}\frac{1-\kappa}{2\sqrt{\kappa}}\right)^2 \|{g_0}\|^2\\
&-\kappa \frac{2 \varepsilon \sqrt{\kappa}+(1-\kappa)\sqrt{1-\varepsilon^2} }{(1-\kappa)\sqrt{1-\varepsilon^2}}
\normsq{\frac{\varepsilon (1+\kappa)}{\sqrt{\kappa} \left(\sqrt{1-\varepsilon^2}(1-\kappa) +2 \varepsilon \sqrt{\kappa}\right)}g_1
-\frac{1+\kappa}{2 \kappa}g_0 +L(x_0-x_1)},\\
\leq &\left(\varepsilon+ \sqrt{1-{\varepsilon}^2}\frac{1-\kappa}{2\sqrt{\kappa}}\right)^2 \|{g_0}\|^2,
\end{align*}
where the last inequality follows from the sign of the coefficient:
\[\kappa \frac{2 \varepsilon \sqrt{\kappa}+(1-\kappa)\sqrt{1-\varepsilon^2} }{(1-\kappa)\sqrt{1-\varepsilon^2}}\geq 0.\]
Next, we prove the exact same guarantee as for the gradient norm, but in the case of distance to optimality $\|{x_1-x_*}\|^2$.
Let us consider the following constraints from \eqref{pep:els_x} with associated multipliers:
\begin{align*}
&{\frac{1}{1-\frac{\mu}{L}}\left(\frac{1}{L}\|{g_0}\|^2+\mu\|{x_0-x_*}\|^2-2\frac{\mu}{L}\langle{g_0},{x_0-x_*}\rangle\right)+\langle{g_0},{x_*-x_0}\rangle\leq 0} &&:\lambda_{0},\\
&{\frac{1}{1-\frac{\mu}{L}}\left(\frac{1}{L}\|{g_1}\|^2+\mu\|{x_1-x_*}\|^2-2\frac{\mu}{L}\langle{g_1},{x_1-x_*}\rangle\right)+\langle{g_1},{x_*-x_1}\rangle\leq 0} &&:\lambda_{1}, \\
&{\langle{g_1},{x_1-x_0}\rangle\leq 0} && :{\lambda_2},\\
&\begin{pmatrix}
\epsilon ||g_0||^2 & \langle{g_0},{g_1}\rangle\\
\inner{g_0}{g_1} & \epsilon ||g_1||^2
\end{pmatrix}\succeq 0 &&:S,
\end{align*}
with $S=\begin{pmatrix}
s_{11} & s_{12}\\ s_{12} & s_{22}
\end{pmatrix},$ and:
\begin{align*}
&\lambda_{0}=\frac{1-\kappa}{\mu}\left[1-2\varepsilon^2+\frac{\varepsilon\sqrt{1-\varepsilon^2}}{2\sqrt{\kappa}(1-\kappa)}(-1-\kappa^2+6\kappa)\right],\\
&\lambda_1=\frac{1}{\mu}-\frac{1}{L},\\
& {\lambda_2}=\frac{1}{\mu}+\frac{1}{L},\\
&L\mu s_{11}=\frac{3 \varepsilon}{2} - \frac{\varepsilon \left(\kappa + \frac{1}{\kappa}\right)}{4} + \frac{1-\kappa}{2 \sqrt{\kappa(1 - {\varepsilon}^2)}} - \frac{{\varepsilon}^2 \left(1 - \kappa\right)}{\sqrt{\kappa(1 - {\varepsilon}^2)}},
&\\
&L\mu s_{22}= \frac{2 \sqrt{\kappa(1 - {\varepsilon}^2)}-\varepsilon \left(1 - \kappa\right)}{\left(1-{\varepsilon}^2\right) \left(1 - \kappa\right) + 2 \varepsilon \sqrt{\kappa(1 - {\varepsilon}^2)}}, &
\\
&L\mu s_{21}=
\frac{\varepsilon\, \left(1 - \kappa\right)}{2 \sqrt{\kappa(1 - {\varepsilon}^2)}} - 1.&
\end{align*}
{As in the case of the gradient norm, we proceed by reformulating the weighted sum of the constraints. For doing that, we first check nonnegativity of the weights $\lambda_0,\lambda_1,\lambda_2\geq 0$ and $S\succeq 0$.}
{As in the previous case}, $s_{22}\geq 0\Leftrightarrow \varepsilon\in\left[\frac{-2\sqrt{\kappa}}{1+\kappa},\frac{2\sqrt{\kappa}}{1+\kappa}\right].$
We therefore only need to check the sign of $\lambda_0$ in order to have the desired results (the $S\succeq 0$ requirement is the same as for the convergence in gradient norm, and the others are {easily} verified).
Concerning $\lambda_0$, we have
\[ \lambda_0\geq 0 \Leftrightarrow \frac{\kappa-1}{\kappa+1} \leq \varepsilon\leq \frac{2\sqrt{\kappa}}{\kappa+1},\] with $\frac{\kappa-1}{\kappa+1} \leq 0$, {and hence $\lambda_0\geq 0$ in the region of interest}.
Aggregating the constraints with {the corresponding} multipliers yields:
\begin{align*}
\|{x_1-x_*}\|^2\leq &\left(\varepsilon+\sqrt{1-\varepsilon^2}\frac{1-\kappa}{2\sqrt{\kappa}}\right)^2 \|{x_0-x_*}\|^2 \\ &- \frac{2 \varepsilon \sqrt{\left(1-\varepsilon^2\right) \kappa}+\left(1-\varepsilon^2\right) (1-\kappa)}{\kappa(1-\kappa)}\times\\ &\normsq{\left(1-\frac{\varepsilon (1-\kappa)}{2 \sqrt{\left(1-\varepsilon^2\right) \kappa}}\right) \frac{g_0}{L} -\frac{1+\kappa}{2}(x_0-x_*)+\frac{1-\kappa}{2 \varepsilon \sqrt{\left(1-\varepsilon^2\right) \kappa}+\left(1-\varepsilon^2\right) (1-\kappa)}\frac{g_1}{L}},\\
\leq &\left(\varepsilon+\sqrt{1-\varepsilon^2}\frac{1-\kappa}{2\sqrt{\kappa}}\right)^2 \|{x_0-x_*}\|^2,
\end{align*}
{where the last inequality follows from the sign of the coefficient
\[ \frac{2 \varepsilon \sqrt{\left(1-\varepsilon^2\right) \kappa}+\left(1-\varepsilon^2\right) (1-\kappa)}{\kappa(1-\kappa)}\geq 0.\]
This completes the proof.}
\qed
One has the following variation on Theorem \ref{thm:ELS improvements} that deals with the case where $f \in \mathcal{F}_{\mu,L}(D)$ for some open convex set $D \subset \mathbb{R}^n$.
\begin{theorem}
\label{thm:ELS improvements D}
Consider the inexact gradient method with exact line search applied to some $f \in \mathcal{F}_{\mu,L}(D)$ where $D \subset \mathbb{R}^n$ is open and convex,
from a starting point $x_0 \in D$. Assume that $\left\{x \in \mathbb{R}^n \; | \; f(x) \le f(x_0)\right\} \subset D$.
If $\kappa := \frac{\mu}{L}$ and $\varepsilon \in \left[0, \frac{2\sqrt{\kappa}}{1+\kappa}\right]$, one has
\begin{eqnarray*}
\|g(x_1)\| &\le & \left(\varepsilon+ \sqrt{1-{\varepsilon}^2}\frac{1-\kappa}{2\sqrt{\kappa}}\right)\|{g(x_0)}\|, \\
\|{x_1-x_*}\| & \le & \left(\varepsilon+ \sqrt{1-{\varepsilon}^2}\frac{1-\kappa}{2\sqrt{\kappa}}\right)\|{x_0-x_*}\|. \\
\end{eqnarray*}
\end{theorem}
\proof
The proof follows from the proof of Theorem \ref{thm:ELS improvements} after the following observations:
\begin{enumerate}
\item
The proof of the last two inequalities in Theorem \ref{thm:ELS improvements} only relies on the inequality \eqref{gradient inequality},
which holds for any open, convex $D \subset \mathbb{R}^n$, i.e.\ not only for $D = \mathbb{R}^n$, by Theorem \ref{thm:mu_L_H}.
\item
By the assumption on the level set of $f$, exact line search yields a point $x_1 \in D$, as required.
\end{enumerate}
\qed
Note that the first inequality in Theorem \ref{thm:ELS improvements} (convergence in
function value) does not extend readily to all convex $D$, since its proof requires the inequality \eqref{eq:FmuL}.
\subsection{PEP with fixed step sizes}
We now state a result that is similar to Theorem \ref{thm:ELS improvements}, but deals with fixed step lengths in stead of exact line search.
\begin{theorem}
\label{thm:FS improvements}
Consider the inexact gradient method with fixed step length $\gamma$ applied to some $f \in \mathcal{F}_{\mu,L}(\mathbb{R}^n)$.
If $\varepsilon\leq \frac{2\mu}{L+\mu}$, and $\gamma \in \left[0, \frac{2\mu-\varepsilon(L+\mu)}{(1-\varepsilon)\mu(L+\mu)}\right]$, one has
\begin{eqnarray*}
f(x_1)-f(x_*) &\le & (1-(1-\varepsilon)\mu\gamma)^2(f(x_0)-f(x_*)), \\
\|g(x_1)\| &\le & (1-(1-\varepsilon)\mu\gamma) \norm{g_0}, \\
\|{x_1-x_*}\| & \le & (1-(1-\varepsilon)\mu\gamma) \norm{x_0-x_*}. \\
\end{eqnarray*}
\end{theorem}
\proof
The proof is similar to that of Theorem \ref{thm:ELS improvements}, and is sketched in the appendix. \qed
\medskip
Note that, if $\gamma = \frac{2\mu-\varepsilon(L+\mu)}{(1-\varepsilon)\mu(L+\mu)}$, the factor $(1-(1-\varepsilon)\mu\gamma)$ that appears in the inequalities in Theorem \ref{thm:FS improvements} reduces to
\[
1-(1-\varepsilon)\mu\gamma = \frac{1-\kappa}{1+\kappa} + \varepsilon,
\]
where $\kappa = \mu/L$ as before.
Next, we again consider a variant constrained to an open, convex set $D \subset \mathbb{R}^n$.
\begin{theorem}
\label{Cor:F mu L error bounds D}
Assume $f \in \mathcal{F}_{\mu,L}(D)$ for some open convex set $D$. Let $x_0 \in D$ so that $B(x_0,2\|x_0-x_*\|) \subset D$.
If $x_1 = x_0 - \gamma d$, with $\|d - g(x_0)\| \le \varepsilon\|g(x_0)\|$, $\varepsilon \le \frac{2\kappa}{1+\kappa}$, and
\[
\gamma = \frac{2\mu-\varepsilon(L+\mu)}{(1-\varepsilon)\mu(L+\mu)},
\]
then
\begin{eqnarray*}
\|g_{x_0}(x_1)\|_{x_0} &\le & \left(\frac{1-\kappa}{1+\kappa}+\varepsilon\right)\|{g_{x_0}(x_0)}\|_{x_0},\\
\|{x_1-x_*}\|_{x_0} & \le & \left(\frac{1-\kappa}{1+\kappa}+\varepsilon\right)\|{x_0-x_*}\|_{x_0}, \\
\end{eqnarray*}
where $\kappa= \mu/L$.
\end{theorem}
\proof
Note that the result follows from the proof of Theorem \ref{thm:FS improvements}, provided that $x_1 \in D$.
In other words, we need to show that the condition $x_1 \in D$ is redundant. This follows from:
\begin{eqnarray*}
\|x_1-x_0\|_{x_0} &\le & \|x_1-x_*\|_{x_0} + \|x_*-x_0\|_{x_0} \quad\mbox{ (triangle inequality)} \\
& \le & \left(\frac{1-\kappa}{1+\kappa}+\varepsilon\right)\|{x_0-x_*}\|_{x_0} + \|x_*-x_0\|_{x_0} \quad\mbox{ (by Theorem \ref{thm:FS improvements})}\\
&\le& 2\|x_*-x_0\|_{x_0} \quad\mbox{ (by $\varepsilon \le \frac{2\kappa}{1+\kappa}$)}, \\
\end{eqnarray*}
which implies $x_1 \in D$ due to the assumption $B(x_0,2\|x_0-x_*\|) \subset D$. \qed
\section{Implications for Newton's method for self-concordant $f$}
Theorem \ref{Cor:F mu L error bounds D} has interesting implications when minimizing a self-concordant function $f$ with minimizer $x_*$ by
Newton's method.
The implications become clear when fixing a point $x_0 \in D_f$, and using the inner product $\langle \cdot,\cdot \rangle_{x_0}$.
Then the gradient at $x_0$ becomes $g_{x_0}(x_0) = H_{x_0}^{-1}(x_0)(g(x_0))$, which is minus the Newton direction at $x_0$.
We will consider approximate Newton directions in the sense of \eqref{eq:error}, i.e.\ directions $-d$ that satisfy
$\|d-g_{x_0}(x_0)\|_{x_0} \le \varepsilon \|g_{x_0}(x_0)\|_{x_0}$, where $\varepsilon >0$ is given.
We only state results for the fixed step-length case, for later use. Similar results may be derived when using exact line search.
\begin{corollary}
\label{Cor:SC error bounds FS}
Assume $f$ is self-concordant with minimizer $x_*$. Let $0< \delta < 1$ be given and $x_0 \in D_f$ so that $\|x_0-x_*\|_{x_0} \le \frac{1}{2}\delta$.
If If $x_1 = x_0 -\gamma d$, where $\|d-g_{x_0}(x_0)\|_{x_0} \le \varepsilon \|g_{x_0}(x_0)\|_{x_0}$ with $\varepsilon \le \frac{2(1-\delta)^4}{1+ (1-\delta)^4}$, and
\[
\gamma = \frac{2(1-\delta)^4 - \varepsilon(1+(1-\delta)^4)}{(1-\varepsilon)(1-\delta)^2((1-\delta)^4 + 1)},
\]
then
\begin{eqnarray*}
\|g_{x_0}(x_1)\|_{x_0} &\le & \left(\frac{1-\kappa_\delta}{1+\kappa_\delta}+\varepsilon\right)\|{g_{x_0}(x_0)}\|_{x_0},\\
\|{x_1-x_*}\|_{x_0} & \le & \left(\frac{1-\kappa_\delta}{1+\kappa_\delta}+\varepsilon\right)\|{x_0-x_*}\|_{x_0}, \\
\end{eqnarray*}
where $\kappa_\delta = (1-\delta)^4$.
\end{corollary}
\proof
By Theorem \ref{thm:sc_vs_FmuL}, if we fix the inner product $\langle \cdot,\cdot\rangle_{x_0}$, then $ f \in \mathcal{F}_{\mu,L}(B_{x_0}(x_0,\delta))$ with
\begin{equation}
\label{eq:mu L delta}
\mu = (1-\delta)^2, \; L = \frac{1}{(1-\delta)^2}.
\end{equation}
As a consequence $\kappa_\delta := \kappa = \mu/L = (1-\delta)^4$. (We use the notation $\kappa = \kappa_\delta$ to emphasize that
$\kappa$ depends on $\delta$ (only).)
The required result now follows from Theorem \ref{Cor:F mu L error bounds D}.
\qed
\medskip
We note that, for $\varepsilon = 0$, the inequalities imply convergence whenever $\kappa_\delta > (6-\sqrt{32})/2$, which is satisfied if $\delta \le 0.3564$.
\medskip
A final, but important observation is that the results in Corollary \ref{Cor:SC error bounds FS} remain
valid if we use the $\langle\cdot,\cdot\rangle_{x_*}$ inner product, as opposed to $\langle\cdot,\cdot\rangle_{x_0}$.
This implies that we (approximately) use the direction $-g_{x_*}(x_0) = -H^{-1}(x_*)g(x_0)$.
Such a direction may seem to be of no practical use, since $x_*$ is not known, but in the
next section we will analyze an interior point method that uses precisely such search directions.
For easy reference, we therefore state the worst-case convergence result when using the $\langle\cdot,\cdot\rangle_{x_*}$ inner product.
\begin{corollary}
\label{Cor:SC error bounds FS2}
Assume $f$ is self-concordant with minimizer $x_*$. Let $0< \delta < 1$ be given and $x_0 \in D_f$ so that $\|x_0-x_*\|_{x_*} \le \frac{1}{2} \delta$.
If $x_1 = x_0 -\gamma d$, where $\|d-g_{x_*}(x_0)\|_{x_*} \le \varepsilon \|g_{x_*}(x_0)\|_{x_*}$ with $\varepsilon \le \frac{2(1-\delta)^4}{1+ (1-\delta)^4}$, and step length
\[
\gamma = \frac{2(1-\delta)^4 - \varepsilon(1+(1-\delta)^4)}{(1-\varepsilon)(1-\delta)^2((1-\delta)^4 + 1)},
\]
then
\begin{eqnarray*}
\|g_{x_0}(x_1)\|_{x_*} &\le & \left(\frac{1-\kappa_\delta}{1+\kappa_\delta}+\varepsilon\right)\|{g_{x_0}(x_0)}\|_{x_*},\\
\|{x_1-x_*}\|_{x_*} & \le & \left(\frac{1-\kappa_\delta}{1+\kappa_\delta}+\varepsilon\right)\|{x_0-x_*}\|_{x_*}, \\
\end{eqnarray*}
where $\kappa_\delta = (1-\delta)^4$.
\end{corollary}
\section{Analysis of the method of Abernathy-Hazan}
Given a convex body $\mathcal{K}\subset \mathbb{R}^n$ and a vector $\hat\theta \in \mathbb{R}^n$, the Abernathy and Hazan \cite{Abernethy_Hazan_2015} describe an interior point method to solve the convex optimization problem
\begin{equation}
\label{prob:convex}
\min_{x \in \mathcal{K}} \hat \theta^{\sf T} x,
\end{equation}
if one only has access to a membership oracle for $\mathcal{K}$. This method has generated much recent interest, since it is formally equivalent to
a simulated annealing algorithm, and may be implemented by only sampling from $\mathcal{K}$. The interior point method in question
used the so-called entropic (self-concordant) barrier function, introduced by Bubeck and Eldan \cite{Bubeck_Eldan_2014}, and we first review the necessary background.
\subsection{Background on the entropic barrier method}
The following discussion is condensed from \cite{Abernethy_Hazan_2015}.
The method is best described by considering the Boltzman probability distribution on $\mathcal{K}$:
\[
P_\theta(x) := \exp(- \theta^\top x - A(\theta)) \quad \text{ where } \quad A(\theta) := \ln \int_K \exp(-\theta^\top x')dx',
\]
where $\theta = \eta \hat \theta$ for some fixed parameter $\eta > 0$. We write $X \sim P_\theta$ if the random variable $X$ takes values in $\mathcal{K}$
according to the Boltzman probability distribution on $\mathcal{K}$ with density $P_\theta$.
The convex function $A(\cdot)$ is known as the \emph{log partition function}, and has derivatives:
\begin{eqnarray*}
\nabla A(\theta) & = & - \mathbb{E}_{X \sim P_\theta}[X] \\
\nabla^2 A(\theta) & = & \mathbb{E}_{X \sim P_\theta}[(X - \mathbb{E}_{X \sim P_\theta}[X])(X - \mathbb{E}_{X \sim P_\theta}[X])^\top].
\end{eqnarray*}
The Fenchel conjugate of $A(\theta)$ is
\[
A^*(x) := \sup_{\theta \in \mathbb{R}^n} \theta^\top x - A(\theta).
\]
The domain of $A^*(\cdot)$ is precisely the space of gradients of $A(\cdot)$, and this is the set $\text{int}(-\mathcal{K})$.
The following key result shows that $A^*$ provides a self-concordant barrier for the set $\mathcal{K}$.
\begin{theorem}[Bubeck-Eldan \cite{Bubeck_Eldan_2014}]
The function $x \mapsto A^*(-x)$ is a $\vartheta$-self-concordant barrier function on $\mathcal{K}$ with $\vartheta \leq n(1 + o(1))$.
\end{theorem}
The function $x \mapsto A^*(-x)$ is denoted by $A^*_{-}(\cdot)$ and called the {entropic barrier} for $\mathcal{K}$.
At every step of the associated interior point method, one wishes to minimize (approximately) a self-concordant function of the
form
\begin{equation}
\label{def:f}
f(x) = \eta\hat\theta^\top x + A^*_{-}(x).
\end{equation}
Subsequently the value of $\eta$ is increased, and the process is repeated.
In keeping with our earlier notation, we denote the minimizer of $f$ on $\mathcal{K}$ by $x_*$. Thus $x_*$ is the point on the central path corresponding to
the parameter $\eta$.
We also assume a current iterate $x_0 \in \mbox{int}(\mathcal{K})$ is available
so that $\|x_* -x_0\|_{x_*} = \frac{1}{2}\delta < \frac{1}{2}$.
Abernathy and Hazan \cite[Appendix C]{Abernethy_Hazan_2015} propose to use the following direction to minimize $f$:
\begin{equation}
\label{eq:search direction Hazan}
-d = -\nabla^2 f (x_*)^{-1}\nabla f(x_0).
\end{equation}
The underlying idea is that $\nabla^2 f (x_*)^{-1}$ may be approximated to any given accuracy through sampling, based on the following result.
\begin{lemma}[\cite{Bubeck_Eldan_2014}]
\label{thm:Hessian sampling}
One has
\[
\nabla^2 f (x_*)^{-1} = \nabla^2 A(\theta) = \mathbb{E}_{X \sim P_\theta}[(X - \mathbb{E}_{X \sim P_\theta}[X])(X - \mathbb{E}_{X \sim P_\theta}[X])^\top],
\]
where $\theta = \eta \hat \theta$.
\end{lemma}
The proof follows immediately from the relationship between the hessians of a convex function and its conjugate, as given in \cite{Crouzeix_1977}.
Thus we may approximate $\nabla^2 f (x_*)^{-1}$ by an empirical covariance matrix as follows.
If $X_i \sim P_\theta$ $(i = 1,\ldots,N)$ are i.i.d., then we define the
associated estimator of the covariance matrix of the $X_i$'s as
\begin{equation}
\label{empirical covariance}
\hat\Sigma := \frac{1}{N}\sum_{i=1}^N (X_i - \bar X)(X_i - \bar X)^\top \quad \mbox{ where } \bar X = \frac{1}{N} \sum_{i=1}^N X_i.
\end{equation}
The estimator $\hat \Sigma$ is known as the empirical covariance matrix, and it may be observed by sampling $X \sim P_\theta$.
This may be done efficiently:
for example, Lov\'asz and Vempala \cite{Lovasz_Vempala_2007} showed that one may sample (approximately) from log-concave distributions on compact bodies in polynomial time,
by using the Markov-chain Monte-Carlo sampling method called hit-and-run, introduced by Smith \cite{Smith 1984}.
The following concentration result (i.e.\ error bound) is known for the
empirical covariance matrix.
\begin{theorem}[cf.\ Theorems 4.1 and 4.2 in \cite{Adamczak_et_al_2010}]
Assume $\epsilon \in (0,1)$ and $X_i \sim P_\theta$ $(i = 1,\ldots,N)$ are i.i.d.\, and $\hat \Sigma$ is the empirical covariance
matrix in \eqref{empirical covariance}.
Then there exists a $C(\epsilon) > 0$ (depending only on $\epsilon$), so that for $N \ge C(\epsilon)n$,
the following holds with overwhelming probability:
\begin{eqnarray}
(1-\epsilon) y^\top \hat\Sigma y &\le & y^\top\Sigma y \le (1+\epsilon) y^\top \hat\Sigma y \quad\quad\quad\quad \; \forall y \in \mathbb{R}^n \label{isotropy1}\\
(1-\epsilon) y^\top \hat\Sigma^{-1} y & \le & y^\top\Sigma^{-1}y \le (1+\epsilon) y^\top \hat\Sigma^{-1} y \quad\quad \forall y \in \mathbb{R}^n \label{isotropy2}
\end{eqnarray}
where
\begin{equation}
\label{eq:sigma}
\Sigma = \mathbb{E}_{X \sim P_\theta}[(X - \mathbb{E}_{X \sim P_\theta}[X])(X - \mathbb{E}_{X \sim P_\theta}[X])^\top
\end{equation}
is the covariance matrix.
\end{theorem}
The phrase overwhelming probability in the theorem refers to the fact that the probability goes to $1$ as $n$ goes to infinity.
The exact details of hit-and-run sampling are outside the scope of this paper. For simplicity, we will therefore assume, in what follows,
the availability of an approximate covariance matrix $\hat\Sigma $ that satisfies \eqref{isotropy1} and \eqref{isotropy2}.
\subsection{Analysis of the approximate direction}
We can now show that an approximation of the search direction of Habernathy-Hazan \eqref{eq:search direction Hazan} satisfies
our `approximate negative gradient' condition \eqref{eq:error}.
\begin{theorem}
\label{thm:approximate direction}
Let $\epsilon > 0$ be given, the covariance matrix $\Sigma$ as in \eqref{eq:sigma}, and a symmetric matrix $\hat \Sigma$ that
approximates $\Sigma$ as in \eqref{isotropy1} and \eqref{isotropy2}. Further, let $f$ be as in \eqref{def:f} with minimizer $x_*$
on a given convex body $\mathcal{K}$.
Then the direction $-d = - \hat \Sigma \nabla f(x_0)$ at $x_0 \in \mathcal{K}$ satisfies
\[
\|\nabla^2 f(x_*)^{-1}\nabla f(x_0) - d\|_{x_*} \le \sqrt{\frac{2\epsilon}{1-\epsilon}}\| \|\nabla^2 f(x_*)^{-1}\nabla f(x_0)\|_{x_*}.
\]
In other words, one has
$\|g_{x_*}(x_0) - d\|_{x_*} \le \varepsilon \|g_{x_*}(x_0) \|_{x_*}$ where $\varepsilon = \sqrt{\frac{2\epsilon}{1-\epsilon}}$, i.e.\ condition \eqref{eq:error}
holds for the inner product $\langle \cdot,\cdot\rangle_{x_*}$,
when the reference inner product $\langle \cdot,\cdot\rangle$ is the Euclidean dot product.
\end{theorem}
\proof
We fix the reference inner product $\langle \cdot,\cdot\rangle$ as the Euclidean dot product,
so that $H(x_*) = \nabla^2 f(x_*) = \Sigma^{-1}$ and $g(x_0) = \nabla f(x_0)$.
One has
\begin{eqnarray*}
\|H^{-1}(x_*)g(x_0) - d\|^2_{x_*} & = & \langle H^{-1}(x_*)g(x_0) - \hat \Sigma g(x_0), H^{-1}(x_*)g(x_0) - \hat \Sigma g(x_0)\rangle_{x_*} \\
& = & \langle H^{-1}(x_*)g(x_0) - \hat \Sigma g(x_0), g(x_0) - H(x_*)\hat \Sigma g(x_0)]\rangle \\
& = & g(x_0)^\top H^{-1}(x_*)g(x_0) - 2g(x_0)^\top \hat \Sigma g(x_0) + [\hat \Sigma g(x_0)]^\top H(x_*)[\hat \Sigma g(x_0)] \\
& \le & (1+\epsilon)g(x_0)^\top \hat \Sigma g(x_0) - 2g(x_0)^\top \hat \Sigma g(x_0) + (1+\epsilon)[\hat \Sigma g(x_0)]^\top \hat \Sigma^{-1}[\hat \Sigma g(x_0)] \\
& = & 2\epsilon \cdot g(x_0)^\top \hat \Sigma g(x_0),
\end{eqnarray*}
where the inequality is from \eqref{isotropy1} and \eqref{isotropy2}. Finally, using \eqref{isotropy1} once more, one obtains
\begin{eqnarray*}
\|H^{-1}(x_*)g(x_0) - d\|^2_{x_*} &\le& \frac{2\epsilon}{1-\epsilon} g(x_0)^\top H^{-1}(x_*) g(x_0) \\
&= & \frac{2\epsilon}{1-\epsilon}\|g_{x_*}(x_0)\|^2_{x_*},
\end{eqnarray*}
as required. \qed
We need to consider another variant of the search direction in \eqref{eq:search direction Hazan},
since $\nabla f(x_0)$ will not be available exactly in general. Indeed, one can only obtain $\nabla f(x_0)$ approximately via the relation
\[
\nabla f(x_0) = \eta \hat \theta + \nabla A^*_{-}(x_0) = \eta \hat \theta + \arg\max_{\theta \in \mathbb{R}^n} \left[-\theta^\top x_0 - A(\theta)\right],
\]
where the last equality follows from the relationship between first derivatives of conjugate functions.
Thus $\nabla f(x_0)$ may be approximated by solving an unconstrained concave maximization problem in $\theta$ approximately, and,
for this purpose, one may use the derivatives of
$A(\theta)$ as given above.
In particular, we will assume that we have available a $\tilde g(x_0) \approx \nabla f(x_0)$ in the sense that
\begin{equation}
\| \tilde g_{x_*}(x_0) - g_{x_*}(x_0)\|_{x_*} \le \epsilon' \|g_{x_*}(x_0)\|_{x_*},
\label{eq:tilde g}
\end{equation}
where $\tilde g_{x_*}(x_0) := \Sigma \tilde g(x_0)$, $g_{x_*}(x_0) = \Sigma \nabla f(x_0)$ as before, and $\epsilon' > 0$ is given.
Thus we will consider the search direction
\begin{equation}
-\tilde d := -\hat \Sigma \tilde g(x_0) \approx -\Sigma \nabla f(x_0).
\label{eq:tilde d}
\end{equation}
\begin{corollary}
Under the assumptions of Theorem \ref{thm:approximate direction}, define for a given $\epsilon' > 0$, the direction
$-\tilde d$ at $x_0 \in D_f$ as in \eqref{eq:tilde d}, where $\tilde g(x_0) \approx \nabla f(x_0)$ satisfies \eqref{eq:tilde g}.
Then one has
\[
\|\tilde d - g_{x_*}(x_0)\|_{x_*} \le \left(\epsilon'\cdot \sqrt{\frac{1+\epsilon}{1-\epsilon}}+\sqrt{\frac{2\epsilon}{1-\epsilon}}\right)\|g_{x_*}(x_0)\|_{x_*}.
\]
In other words, one has
$\|g_{x_*}(x_0) - \tilde d\|_{x_*} \le \varepsilon \|g_{x_*}(x_0) \|_{x_*}$ where $\varepsilon = \epsilon'\cdot \sqrt{\frac{1+\epsilon}{1-\epsilon}}+\sqrt{\frac{2\epsilon}{1-\epsilon}}$, i.e.\ condition \eqref{eq:error}
holds for the inner product $\langle \cdot,\cdot\rangle_{x_*}$,
when the reference inner product $\langle \cdot,\cdot\rangle$ is the Euclidean dot product.
\end{corollary}
\proof
Recall, the notation $d = \hat \Sigma \nabla f(x_0)$ from Theorem \ref{thm:approximate direction}, and note that, by definition,
\begin{eqnarray*}
\| \tilde d - d\|^2_{x_*} &=& \|\hat \Sigma\left(\tilde g(x_0)-g(x_0) \right)\|_{x_*}^2 \\
&=& \langle \hat \Sigma(\tilde g(x_0)-g(x_0), \Sigma^{-1}\hat \Sigma(\tilde g(x_0)-g(x_0)\rangle \\
&\le& (1+\epsilon)(\tilde g(x_0)-g(x_0))^\top \hat \Sigma (\tilde g(x_0)-g(x_0)) \quad\quad\mbox{ (by \eqref{isotropy2})} \\
&\le& \left(\frac{1+\epsilon}{1-\epsilon}\right)\|\tilde g_{x_*}(x_0)-g_{x_*}(x_0)\|^2_{x_*} \quad\quad\quad\quad\quad\quad\mbox{ (by \eqref{isotropy1})}\\
&\le & (\epsilon')^2\cdot \frac{1+\epsilon}{1-\epsilon}\|g_{x_*}(x_0)\|^2_{x_*} \quad\quad\quad\quad\quad\mbox{ (by \eqref{eq:tilde g})}.
\end{eqnarray*}
To complete the proof now only requires the triangle inequality,
\[
\|g_{x_*}(x_0)-\tilde d\|_{x_*} \le \|g_{x_*}(x_0)- d\|_{x_*} + \|d-\tilde d\|_{x_*},
\]
as well as the inequality from Theorem \ref{thm:approximate direction}.
\qed
\subsection{Complexity of a short-step interior point method}
We now sketch how to bound the worst-case iteration complexity of a short-step interior point method using the
entropic barrier, that is similar to the algorithm outlined in \cite[Algorithm 3 and Appendix C]{Abernethy_Hazan_2015}.
In particular, is uses the search direction \eqref{eq:tilde d}, described above.
The key observation is that one may analyse the complexity of interior point methods by only analysing
the progress during one iteration; see e.g.\ \cite[\S2.4]{Renegar2001a}. Thus our analysis of the previous section may be applied readily.
In what follows we need to modify our previous notation slightly to account for the
changing value of the parameter $\eta$ in the interior point algorithm.
In particular, we will denote the point on the central path corresponding to a given $\eta > 0$, by $x(\eta)$ (as opposed to $x_*$). In other words,
\[
x(\eta) = \arg\min_{x \in \mathcal{K}} \eta\hat\theta^\top x + A^*_{-}(x).
\]
We may now state the short-step, interior point method that we will analyse as Algorithm \ref{alg}.
\begin{center}
\begin{algorithm}[H]
\KwData{Tolerances: $\epsilon,\epsilon',\bar\epsilon >0$;
Proximity to central path parameter: $\delta \in (0,1)$;
Entropic barrier parameter: $1 \le \vartheta \le n+o(1)$; Objective vector $\hat \theta \in \mathbb{R}^n$; an $x_0\in \mathcal{K}$ and $\eta_0 >0$ such that
$\|x_0- x(\eta_0)\|_{x(\eta_0)} \le \frac{1}{2}\delta$.}
\KwResult{$\bar \epsilon$-optimal solution to $\min_{x\in \mathcal{K}} \hat \theta^\top x$}
$\varepsilon = \epsilon'\cdot \sqrt{\frac{1+\epsilon}{1-\epsilon}}+\sqrt{\frac{2\epsilon}{1-\epsilon}}$\;
Fixed step length: $\gamma = \frac{2(1-\delta)^4 - \varepsilon(1+(1-\delta)^4)}{(1-\varepsilon)(1-\delta)^2((1-\delta)^4 + 1)}$\;
Iteration: $k=0$\;
\While{$\frac{\vartheta}{\eta_k} > \bar\epsilon$}{
Compute $\hat \Sigma$ that satisfies \eqref{isotropy1} and \eqref{isotropy2}\;
Compute $\tilde g(x_k)$ that satisfies \eqref{eq:tilde g}\;
$\tilde d = \hat \Sigma \tilde g(x_k)$\;
$x_{k+1} = x_k - \gamma \tilde d$\;
$\eta_{k+1} = \left(1+ \frac{1}{16\sqrt{\vartheta}}\right)\eta_k$\;
$k \leftarrow k+1$\;
}
\caption{Short-step interior point method using the
entropic barrier \label{alg}}
\end{algorithm}
\end{center}
We will show the following worst-case iteration complexity result.
\begin{theorem}
Consider Algorithm \ref{alg} with the following input parameter settings:
$
\epsilon > 0$, and $\epsilon' >0$ any values such that $\varepsilon =
\epsilon'\cdot \sqrt{\frac{1+\epsilon}{1-\epsilon}}+\sqrt{\frac{2\epsilon}{1-\epsilon}} \le \frac{1}{32}$, and $\delta = \frac{1}{4}$.
If the algorithm is initialized with
an $x_0\in \mathcal{K}$ and $\eta_0 >0$ such that
$\|(x_0)- x(\eta_0)\|_{x(\eta_0)} \le \frac{1}{2}\delta$, then it terminates
after at most
\[
k =\left\lceil 20\sqrt{\vartheta}\ln\left(\frac{\vartheta}{\eta_0 \bar\epsilon}\right) \right\rceil
\]
iterations. The result is an $x_k \in \mathcal{K}$ such that
\[
\hat \theta^\top x_k - \min_{x\in \mathcal{K}} \hat \theta^\top x \le \bar \epsilon.
\]
\end{theorem}
\proof
The proof follows the usual lines of analysis of short-step interior point methods; in particular we will repeatedly refer to
Renegar \cite[\S2.4]{Renegar2001a}.
We only need to show that, at the start of each iteration $k$, one has
\[
\|x_k- x(\eta_k)\|_{x(\eta_k)} \le \frac{1}{2}\delta.
\]
Since, on the central path one has $ \hat \theta^\top x(\eta) - \min_{x\in \mathcal{K}} \hat \theta^\top x \le \vartheta/\eta$, the required result will
then follow in the usual way (following the proof of relation (2.18) in \cite[p.\ 47]{Renegar2001a}).
Without loss of generality we therefore only consider the first iteration, with a given
$x_0\in \mathcal{K}$ and $\eta_0 >0$ such that
$\|x_0- x(\eta_0)\|_{x(\eta_0)} \le \frac{1}{2}\delta$, and proceed to show that
$\|x_1- x(\eta_1)\|_{x(\eta_1)} \le \frac{1}{2}\delta$.
First, we bound the difference between the successive `target' points on the central path, namely $x(\eta_0)$ and $x(\eta_1)$, where
$\eta_1 = \left(1+ \frac{k}{\sqrt{\vartheta}}\right)\eta_0$ with $k = 1/16$. By the same argument as in \cite[p.\ 46]{Renegar2001a}, one obtains:
\begin{eqnarray*}
\|x(\eta_1) - x(\eta_0)\|_{x(\eta_0)} &\le& k + \frac{3k^2}{(1-k)^3}\\
&\le& 0.0767 \mbox{ for $k = 1/16$}.
\end{eqnarray*}
Moreover, by Corollary \ref{Cor:SC error bounds FS2},
\begin{eqnarray*}
\|{x_1-x(\eta_0)}\|_{x(\eta_0)} &\le& \left(\frac{1-(1-\delta)^4}{1+(1-\delta)^4}+\varepsilon\right)\|{x_0-x(\eta_0})\|_{x(\eta_0)} \\
&\le & 0.1596\cdot \frac{1}{2} \delta \le 0.02.
\end{eqnarray*}
Using the triangle inequality,
\begin{eqnarray*}
\|{x_1-x(\eta_1)}\|_{x(\eta_0)} &\le& \|{x_1-x(\eta_0)}\|_{x(\eta_0)} + \|{x(\eta_1)-x(\eta_0)}\|_{x(\eta_0)} \\
& \le & 0.02 + 0.0767 = 0.0967.
\end{eqnarray*}
Finally, by the definition of self-concordance, one has
\[
\|{x_1-x(\eta_1)}\|_{x(\eta_1)} \le \frac{\|{x_1-x(\eta_1)}\|_{x(\eta_0)}}{1-\|{x(\eta_0)-x(\eta_1)}\|_{x(\eta_0)}} \le \frac{0.0967}{1-0.0767} \le 0.1047 < \frac{1}{2}\delta,
\]
as required. \qed
\section{Concluding remarks}
An unresolved question in our analysis is to understand the class of functions where the following inequality
holds
\[
f(y)-f(x) - \langle{g(x)},{y-x}\rangle \geq \frac{1}{L}\normsq{g(y)-g(x)}
\]
for all $x,y$ in a given open convex set $D$, where $L>0$ is fixed.
In particular, does it hold for all $f \in \mathcal{F}_{0,L}(D)$?
A recent, related result by Azagra and Mudarra \cite{Azagra_Mudara_2017}, shows that, if $f$ satisfies
this inequality on a given subset of $\mathbb{R}^n$,
then $f$ has an extension to some $\tilde f \in \mathcal{F}_{0,L}(\mathbb{R}^n)$, in the sense that the values and
gradients of $f$ and $\tilde f$ coincide on the given subset.
This implies that if a function satisfies inequality \eqref{eq:FmuL} on some subset of
$\mathbb{R}^n$, then it has an extension to $\mathcal{F}_{\mu,L}(\mathbb{R}^n)$.
It is not clear though, if any $f \in \mathcal{F}_{\mu,L}(D)$, for given open convex $D$, has an extension to $\mathcal{F}_{\mu,L}(\mathbb{R}^n)$.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,131 |
James City County .org
Home | Clerk | Sheriff | Fire | Court | Community College | Schools | Library | History
Department of Health | Hospitals | Humane Society | Airport | Parks | Fair | Real Estate | Business Directory
James City County was formally created in 1634 as James City Shire by order of King Charles I. Originally, it was first settled by the English colonists in 1607 at Jamestown. James City County is considered one of only five original shires of the Virginia Colony to still be extant today in essentially the same political form.
In 1632 Middle Plantation was established as a fortress in the ongoing conflicts with Native Americans. It became the site of the College of William and Mary in 1693 and became the location of the capital in 1699 after Jamestown was burned (again) in 1698. Shortly thereafter, Middle Plantation was renamed Williamsburg in honor of King William III of England. The capital was moved to Richmond in 1780 at the outset of the American Revolution. The Battle of Green Spring was fought in the county just a short time before the British surrender at Yorktown. (Green Spring Plantation was the former home of Royal Governor William Berkeley).
During the American Civil War, the Battle of Williamsburg was waged in York and James City County during the Peninsula Campaign in 1862. After the War, Collis P. Huntington extended the new Chesapeake and Ohio Railway through the county to reach new coal piers he had built at at Newport News on Hampton Roads. Railroad stations were established at Diascund, Toano, Norge, Kelton, Williamsburg, and Grove. In Williamsburg, the temporary tracks initially laid ran down the middle of Duke of Gloucester Street.
Williamsburg became an independent city from the county in 1884, after a change in the Virginia constitution in 1871. Williamsburg and James City County share a combined school system, courts, and some constitutional officers. Beginning in the early 20th century, preservation and restoration efforts resulted in a major increase in tourism to the county and surrounding area. Attractions developed included Colonial Williamsburg, Jamestown Settlement, the Colonial Parkway, Carter's Grove Plantation, and Busch Gardens. At the turn of the 21st century, new archaeological work was underway at Jamestown and nearby Green Spring Plantation, with the promise of new historical discoveries.
Add Your Website/About Us
©1997-2019 All Rights Reserved | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,887 |
Q: Multiple Markdown FIle Selection in Reveal I am using Reveal.js for my lectures. It works great loading an external markdown file at runtime. Is there a way to set up one master index.html file that allows me to select which external file to load? What I have in mind would be like a table of contents, but each topic would be a separate markdown file. I suspect javascript would be the way to do this, but while I am capable (not expert) with HTML and CSS, I can't write a line of javascript (I can copy, paste and load).
Google was not my friend.
A: This was bugging me, too, and so I decided to see if I could Google-search and splice my way through this.
The basic Reveal.js div looks like this:
<body>
<div class="reveal">
<!-- Any section element inside of this container is displayed as a slide -->
<div class="slides">
<section data-markdown="somefile" data-separator="^\n\n\n" data-vertical="^\n\n" data-notes="^Note:">
</section>
</div>
</div>
<script src="reveal.js/lib/js/head.min.js"></script>
<script src="reveal.js/js/reveal.min.js"></script>
<script>
// Full list of configuration options available here:
// https://github.com/hakimel/reveal.js#configuration
Reveal.initialize({
. . .
});
</script>
</body>
Simple Way (Manual Entry of Entire Filename)
We can dynamically set an attribute, e.g. the data-markdown field in the <section> element with JavaScript. There are two small snags here: we have to do it after the element is created, but before Reveal.js does its entire initialization, otherwise the state of the DOM and Reveal.js's internal state will get out of alignment. This is easy enough (only showing the changed section):
<!-- Any section element inside of this container is displayed as a slide -->
<div class="slides">
<section id="presentation" data-separator="^\n\n\n" data-vertical="^\n\n" data-notes="^Note:">
</section>
<script type="text/javascript">
document.getElementById("presentation").setAttribute("data-markdown",prompt("Filename:","default-filename.md"));
</script>
When you load the page, you get a small alert/prompt where you enter the full filename (relative to the web server root). If you do like I do and use python -m'SimpleHTTPServer to run a local webserver directly in the directory with the all the slides, then this isn't too bad.
Complicated Way (File Chooser Dialog)
The simple way is a nice start, but it isn't quite as convenient as a fully graphical chooser. Luckily, it turns out that we can do that, too. The hard part here is that we have to run the file chooser after the page is fully loaded and rendered, which means we have to do something to get Reveal.js's state lined back up with the DOM. There's a sync() method in the API that's supposed to be useful for just such situations, but it doesn't work here for some reason. Instead, we delay Reveal.js's full initialization until we've set the external Markdown file:
<body>
<!-- Choose file button -->
<input type="file" id="external_md" name="markdown" >
<div class="reveal">
<!-- Any section element inside of this container is displayed as a slide -->
<div class="slides">
<section id="presentation" data-separator="^\n\n\n" data-vertical="^\n\n" data-notes="^Note:">
</section>
<script type="text/javascript">
function selectFile(evt) {
// the file chooser actually returns a list
// (in case you enabled multiple selection)
file = evt.target.files[0].name;
document.getElementById("presentation").setAttribute("data-markdown",file);
// now it's time to init!
delayed_init();
// remove file selector button
fileSelector = document.getElementById("external_md");
fileSelector.parentNode.removeChild(fileSelector);
}
document.getElementById('external_md').addEventListener('change',selectFile,false);
</script>
</div>
</div>
<script src="reveal.js/lib/js/head.min.js"></script>
<script src="reveal.js/js/reveal.min.js"></script>
<script>
// we have to wrap the init function both to delay it and to make it
// easier to call later, all without moving big blocks of code around
function delayed_init(){
// Full list of configuration options available here:
// https://github.com/hakimel/reveal.js#configuration
Reveal.initialize({
. . .
});
}
</script>
</body>
That are three change areas:
1. Addition of an <input> element to drive the file chooser.
2. Extra Javascript in the middle.
3. Wrapping the call to Reveal.initialize() with a dummy function to delay initialization.
All of this worked for me with the current release of Reveal.js (9cf7de54b8f). Please note that I keep all of the Reveal.js stuff in a subfolder reveal.js, so you may need to adjust the paths above accordingly.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,065 |
# PRAISE FOR PETE EGOSCUE AND PAIN FREE
**"Shows how we can break the circuit of pain and naturally heal one of the most significant disabilities of our times."**
**—Deepak Chopra, author of _The Path of Love_ and _The Seven Spiritual Laws of Success_**
**"Born from the genius of Pete Egoscue, the simple and effective routines in _Pain Free_ are the cutting edge of physical therapy."**
**—Anthony Robbins, author of _Awaken the Giant Within_ and _Unlimited Power_**
**"Pete Egoscue teaches you practical, powerful 'motioncises'—motion exercises that will become your own best exercise therapist."**
**—Harold Bloomfield, M.D., author of _How to Heal Depression_**
PAIN FREE AT YOUR PC
A Bantam Book / November 1999
All rights reserved.
Copyright © 1999 by Pete Egoscue
Photos copyright © The Egoscue Method
Line drawings by Wendy Wray
No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. For information address: Bantam Books.
Library of Congress Cataloging-in-Publication Data
Egoscue, Pete
Pain free at your PC / Pete Egoscue, with Roger Gittines. p. cm.
eISBN: 978-0-307-48931-9
1. Microcomputers—Health aspects. 2. Pain—Prevention.
I. Gittines, Roger. II. Title.
RC95.V53E36 1999 99-26664
613.6′2—dc21
Bantam Books are published by Bantam Books, a division of Random House, Inc. Its trademark, consisting of the words "Bantam Books" and the portrayal of a rooster, is Registered in U.S. Patent and Trademark Office and in other countries. Marca Registrada. Bantam Books, 1540 Broadway, New York, New York 10036.
v3.1
# CONTENTS
_Cover_
_Title Page_
_Copyright_
**List of Illustrations**
[**One** THE PC—FROM PAINFUL TO PAIN FREE
_Blaming the PC and repetitive motion isn't the answer_](Egos_9780307489319_epub_c01_r1.htm)
[**Two** MUSCLE MATTERS
_The design of the human body is rugged enough to withstand nearly anything—except lack of motion_](Egos_9780307489319_epub_c02_r1.htm)
[**Three** THE BIG SQUEEZE
_Skeletal misalignment hurts with or without a PC_](Egos_9780307489319_epub_c03_r1.htm)
[**Four** THREE CURVES AND YOU WALK
_The spine's shape determines the shape of your health_](Egos_9780307489319_epub_c04_r1.htm)
[**Five** FIVE E-CISE PIECES
_An introduction to E-cise therapy_](Egos_9780307489319_epub_c05_r1.htm)
[**Six** E-CISES FOR THOSE IN PAIN
_Hurting and in a hurry_](Egos_9780307489319_epub_c06_r1.htm)
[**Seven** E-CISE MENU FOR OCCASIONAL COMPUTER USERS
_A little just-in-time therapy_](Egos_9780307489319_epub_c07_r1.htm)
[**Eight** E-CISE MENU FOR MODERATE COMPUTER USERS
_Ramping up the right way_](Egos_9780307489319_epub_c08_r1.htm)
[**Nine** E-CISE MENU FOR POWER PC USERS
_Wired, worried, and what to do about it_](Egos_9780307489319_epub_c09_r1.htm)
[**Ten** OTHER SYMPTOMS, OTHER CHOICES
_Feeling no pain_](Egos_9780307489319_epub_c10_r1.htm)
[**Eleven** BREAKING THE PATTERNS OF PAIN
_How to avoid being locked in a motionless box_](Egos_9780307489319_epub_c11_r1.htm)
[**Twelve** JUST THE FAQS
_Move your body, not the keyboard or monitor_](Egos_9780307489319_epub_c12_r1.htm)
[**Thirteen** DESPERATE MEASURES—SURGERY, DRUGS, AND ERGONOMICS—DON'T WORK
_A billion dollars of good intentions gone bad_](Egos_9780307489319_epub_c13_r1.htm)
**Acknowledgments**
_Other Books by This Author_
_About the Authors_
As for all my books, I provide a disclaimer with a difference. Instead of the usual "The following material is not intended as a substitute for the advice of a physician," followed by a recommendation that you consult a doctor before following the program that's being offered and a disclaimer of legal responsibility should there be adverse consequences, I take another approach. Don't read this book if you feel you need the protection of a disclaimer and its counsel. I'm serious. Health care must start with personal responsibility. This vital role should not be delegated to any expert. Yours is the ultimate judgment. Any disclaimer that suggests otherwise does a great disservice.
# List of Illustrations
## Chapter 3
Figure 3.1: The human musculoskeletal grid.
Figure 3.2(a): The grid as the musculoskeletal superstructure.
Figure 3.2(b): Side view of the superstructure.
Figure 3.3: The grid shows individual range of motion.
Figure 3.4: Variation in solid lines and grid demonstrate how IROM and DROM are at odds and produce dysfunction.
Figure 3.5: Side view of musculoskeletal dysfunction with functional DROM superimposed.
Figure 3.6: Side view of joint misalignment.
## Chapter 4
Figure 4.1: The S-curve of the spine.
Figure 4.2: Side view of spine and pelvis.
Figure 4.3: A rounded and dysfunctional spinal posture.
Figure 4.4: Hips in neutral position.
Figure 4.5: Hips in flexion.
Figure 4.6: Proper skeletal alignment in a seated position.
Figure 4.7: The wrist arch flattens as the hip and spine go into flexion.
Figure 4.8: Loss of the wrist arch increases tension while operating a mouse.
Figure 4.9: Erect posture eliminates wrist tension.
Figure 4.10: The skeletal structure of the hand.
## Chapter 6
Figure 6.1: Gravity Drop
Figure 6.2: Sitting Knee Pillow Squeezes
Figure 6.3: Static Wall
Figure 6.4: Sitting Floor
Figure 6.5(a, b): Pelvic Tilts
Figure 6.6(a, b): Hip Crossover
Figure 6.7(a, b, c): Three-Position Toe Raises
Figure 6.8(a, b): Sitting Cats and Dogs
## Chapter 7
Figure 7.1(a, b): Arm Circles
Figure 7.2(a, b): Elbow Curls
Figure 7.3: Foot Circles and Point Flexes
Figure 7.4: Sitting Floor Twist
Figure 7.5(a, b): Cats and Dogs
Figure 7.6: Kneeling Groin Stretch
Figure 7.7: Upper Spinal Floor Twist
Figure 7.8(a, b): Downward Dog
Figure 7.9: Air Bench
Figure 7.10: Standing Chair Stretch
Figure 7.11: Sitting Overhead Extension
Figure 7.12: Standing Quad Stretch
Figure 7.13(a, b): Sitting Cats and Dogs
Figure 7.14: Sitting in Extension
## Chapter 8
Figure 8.1: Forearm Stretch
Figure 8.2(a, b, c): Wall Clock
Figure 8.3: Static Back
Figure 8.4(a, b): Pullovers in Static Back
Figure 8.5: Pullover Presses in Static Back
Figure 8.6: Cobra on Elbows
Figure 8.7: Supine Groin Stretch
Figure 8.8(a, b): Elbow Curls in Extension
Figure 8.9: Sitting Assisted Hip Lift
Figure 8.10(a, b, c): Three-Position Toe Raises
## Chapter 9
Figure 9.1: Abdominal Contractions in Static Back
Figure 9.2: Abductor Presses in Static Back
Figure 9.3: Standing Overhead Extension
Figure 9.4: Static Wall with Pullbacks
Figure 9.5: Static Extension Position
Figure 9.6: Supine Groin Progressive
Figure 9.7(a, b): Sitting Arm Circles
Figure 9.8: Sitting Hip Flexor Lifts
Figure 9.9: Sitting Chair Twist
## Chapter 11
Figure 11.1: A treadmill workout that is not working out.
Figure 11.2: Functional skeletal alignment on the treadmill is important.
Figure 11.3: Weight machines and musculoskeletal dysfunctions are a bad combination.
Figure 11.4: Weight machines will not unduly stress properly aligned joints.
Figure 11.5: Hip and back flexion are detriments on stationary bikes.
Figure 11.6: A stationary bike delivers full benefits to a functional rider.
Figure 11.7(a, b, c): Standing Spread Foot Forward Bend
## Chapter 12
Figure 12.1: _The Thinker_ goes digital.
## Chapter 13
Figure 13.1: A knight on-line and in-line.
#
**"The true source of chronic musculoskeletal pain is rarely the site of the pain.... If your wrist hurts while you are pointing and clicking with a mouse, the pain probably has nothing to do with the device."**
" _It's a deal. Let's shake on it_."
" _I can't, my wrist hurts_."
" _Hah! I told you that was going to happen_."
" _I know, but my career's golden. I'm on the cutting edge_."
" _Cutting edge? High-tech hell is more like it_."
" _I'm going to try a wrist splint. I've got a shinbone of a musk ox I can use_."
" _Try getting another job. Your wrist is always going to hurt. Humans weren't designed to swing a hammer all day. Your basic rock was good enough_."
Musk ox? Hammer? A quick visit to a Pleistocene valley startup? Sorry for the cheap trick, but it probably worked. I know _you_ saw right through me, but many other readers thought I was referring to that dreaded public health menace, the personal computer—wrecker of wrists, despoiler of eyesight, inflamer of elbows, cricker of necks, and begetter of headaches.
And now I am in more trouble because it may seem like I'm being unsympathetic to people experiencing agonizing pain. But on that charge, as someone who's spent almost every day of nearly the last thirty years helping those suffering from chronic musculoskeletal pain, I plead not guilty. Millions of men, women, and children are hurting. The sleepless nights are real, as is the inability to tie shoelaces and the struggle to surmount the wall of pain that stands in the way of pointing and clicking with a mouse or tapping the space bar of a keyboard with a thumb. Likewise, the stiff necks and nauseating headaches destroy productivity and any sense of a job well done.
No, I'm deeply sympathetic to those in chronic pain. I've been there myself, and my search for a cure to relieve my pain led to the formulation of a therapeutic method, the Egoscue Method, that is now known worldwide as a remarkably successful alternative to drastic drug and surgical treatments or gimmicky "ergonomic" solutions that do more harm than good.
My point about the PC and the hammer is this: Just as it would be wrong to blame the hammer for the aches and pains that beset workers from the era of the caveman to the cabinetmaker, the coal miner to the carpenter, it's a mistake to think that the personal computer is responsible for the variety of conditions that are being labeled "computer pain syndrome."
The term is as inapt as _hammer pain syndrome, fountain pen pain syndrome_ , or _microscope pain syndrome_. These are tools, not diseases. We've flourished as toolmakers and tool users—our tools are blameless. Certainly, accidents happen on the job. Safety must always be a priority, although it frequently isn't. But to treat a tool—any tool, high tech or low—as the source of an epidemic is something new and profoundly disturbing.
**_Whatever pain you may be feeling, it is not caused by your PC. And it cannot be cured by reinventing the PC or the way you use it_.** There is a remedy, though, and that's what this book is all about.
_Pain Free at Your PC_ challenges conventional wisdom with what I regard to be the most persuasive and conclusive body of evidence—the human body. Being pain free at your PC is as natural and attainable as a pain-free night's sleep or a pain-free day of hard work. Our hands and wrists are inherently strong enough to operate a keyboard and a mouse for hours on end. Human necks, heads, and eyes can take the stress and strain too.
So what's the problem? Why is the federal government describing repetitive stress injuries (RSIs) as a workplace "epidemic"?
Why is the incidence of carpal tunnel syndrome (CTS) and other forms of chronic pain associated with computer use rising dramatically?
Why are we quick to blame this valuable new tool?
The answer is that a search for the _cause_ of computer-related pain has veered off course and locked onto the _effect_ instead. Let me filter this predicament through an observation I made early in my career as a therapist: **The true source of chronic musculoskeletal pain is rarely the site of the pain**. That means if your wrist hurts while you are pointing and clicking with a mouse, the pain probably has nothing to do with the device, and everything to do with muscular weakness, skeletal misalignment, and structural (joint) instability elsewhere in the body. Those conditions can be reversed without drastic measures— _and you can do it yourself_.
I've also learned that muscular weakness, skeletal misalignment, and structural instability usually _precede_ the onset of pain that is attributed to accidents, overuse, or aging. That's right, precede. And that means we're ignoring the real cause of the pain when we tinker with the PC or the mouse, replace the chair, brace the wrist, or surgically remove the transverse carpal ligament (the usual CTS surgical procedure). The symptoms may abate temporarily because peripheral conditions have changed, but the pain usually returns or shifts to another spot. We're better off retracing our steps to correct—here's the chorus again—muscular weakness, skeletal misalignment, and structural instability. Just call them _dysfunctions_ to save time.
## Remembering to Forget
It's easy to draw the wrong conclusion about PCs when cause and effect get jumbled around. The PC seems to be placing an inordinate demand on our physical functions by asking us to move our fingers, hands, wrists, and arms again and again. And that's true. But it's only because we come to the PC expecting to use muscles and joints that were drained of much of their strength and flexibility long before Bill Gates made his first billion dollars. As modern specialists, we are now using special tools under special conditions. In itself that's no problem. Amnesia is the problem. We forget that our bodies evolved in service to the all-purpose, multifaceted work and lifestyles of a species of magnificent generalists. By remembering where we came from and who we are, we can forget the pain.
The musculoskeletal system is a virtual historical textbook chronicling the varied and demanding everyday movements required of humankind for millions of years. Look at it. Look at yourself. The erect spine and the rugged shoulders, the solid hips and the hard-driving knees, the sturdy ankles, tough feet, and clever hands are all chapters of a success story about creatures who could not keep still.
As an exercise therapist, when I "read" the text, I see an integrated, balanced unit of muscles and joints that must be fed or refueled _in its entirety_ by motion. Although the world has changed, the musculoskeletal system remains the same—still magnificent, still a generalist after all those years. Our specialized work, however, restricts and limits motion to the relatively few muscles and joints that are directly involved. Even our recreational activity is specialized. Relatively few muscles work and play; all the rest languish.
Surgery, drugs, and ergonomic redesign do not address this fundamental source of chronic musculoskeletal pain.
Hardworking fingers, wrists, and hands cannot be isolated from nonworking (or minimally working) hips, knees, ankles, and their supporting musculature without painful consequences. The necessary mechanical and muscular interaction is lost. As a result, our integrated bodies are _disintegrating_ and being deconditioned—not by the PC but by the TV, the CD, the RV, and all the other "A to E-Z" accoutrements of modern living. Our bodies are in trouble before we even sit down at the computer keyboard. Overall lack of motion and highly restricted specialized motion are the culprits. I'll explain the phenomenon in the remainder of this chapter and in chapters 2 and . After addressing the whys, the book will focus on what—what you can do about it quickly and easily.
And that's both good and bad news. Good because there is a solution; bad in that it requires a personal commitment to make small but significant changes in the way you live and work. Frankly, it's probably a bad idea to acknowledge this downside. Many people are turned off by the notion that they won't be able to buy good health just like any other product. Surgery, painkilling drugs, and products like ergonomic keyboards, wrist braces, and special desk chairs hold the promise of a quick fix. As dedicated consumers, we tend to believe we can purchase nearly anything that's needed ready-made and right off the shelf. Unfortunately, the human body doesn't work that way.
Did I use the word _unfortunately_? Actually, this is an entirely fortunate situation. Bones, joints, muscles, tendons, and ligaments maintain and sustain themselves on the go. All we have to do is _go_ and keep going. The changes in your work and lifestyle that this book promotes are designed to take the stops out.
## E-Therapy
As I do at my Egoscue Method Clinic in Del Mar, California, this book offers a program of "no sweat" E-cises—shorthand for Egoscue-cises, but the term could well be "Easy-cises." The body's musculoskeletal system doesn't require heavy workouts to function properly. That's why I refer to E-cises as "No Sweats," since you'll be able to do them in your office dressed in business clothes, and many can be performed sitting down with little interruption to your work routine.
These E-cises are culled from the hundreds I've devised from scratch based on a close study of human motion requirements. Many are also adapted from yoga positions, posture-enhancement routines, or classic therapeutic movements. Each one provides stimulation to specific muscle groups, joints, and functions that are not being used adequately or that are being abused by skeletal misalignment.
The results speak for themselves. In 1998 more than a thousand repetitive stress injury sufferers came to the clinic for treatment. In addition, I've worked with world-class professional and amateur athletes striving for peak performance, accident victims determined to recover, elderly people fighting to maintain their quality of life, and those with severe workplace injuries and disabilities who refuse to give up. We haven't used drugs or surgery. Our success rate is around 94 percent. The few disappointments came from a client's unwillingness or inability to commit to spending as little as twenty minutes a day doing specific E-cises.
## The Common Cadence of Different Drummers
Most people who visit the clinic or take part in our home video therapy program have one thing in common—chronic pain. I assume the same is true for my readers. If not, and you're being proactive, you've also come to the right place. I'm glad you did. Pain or no pain, it's important to understand that almost all of us were born with the same musculoskeletal design. The difference—why one person has agonizing pain, a second some tightness, and a third no overt symptoms at all—is caused by what we do or don't do with that design. In that way everybody is, in fact, different: different jobs, different lifestyles, different hobbies, and different interests. At first those differences seem to make a consistent therapeutic response to chronic pain impossible. But the universal design of the body saves the day. Over the last twenty-five years, the E-cise programs that this book offers have been proven effective in helping people get back to using their body's musculoskeletal system in accordance with that basic design. They amount to tutorials. Weakened, disengaged muscles literally forget how and when to move according to design. The E-cises give them a quick refresher course.
You'll notice that in many cases the E-cises do not directly target the site of the pain symptom. The focus may be on the shoulders or hips rather than a sore neck or wrist. Why? Hit the "back button" on the browser and return to my first observation, a page or three ago: The body is so carefully balanced and functionally interrelated that the place where we feel the pain is usually a long way from its source. This is particularly true of the hands and wrists.
To see what I mean, clench your fist. Do it a couple of times. Clench and relax. Feel movement in your forearm, elbow, and shoulder? Good. That's where the prime muscular movers are located in order to keep the hands and wrists compact and flexible. The muscles themselves are elongated; their tendons are among the longest in the body. The arrangement allows for both a powerful grasp and fine joint articulation in the fingers. Otherwise, our hands would be crude and cumbersome.
The E-cises in _Pain Free at Your PC_ reflect this principle of anatomy: The site of the pain and the source of the problem are often not the same. If that strikes you as repetitious, better get used to it. You'll read it several more times.
The immediate purpose of the E-cise program is to reengage and strengthen muscles that aren't being adequately sustained by your physical activities away from the PC. At the same time, they restore lost skeletal alignment that sets in when key functions are disrupted. It's pointless to "buff" muscles that are not doing their jobs properly or to struggle to reduce inflammation in the wrist when the source of the problem is the elbow or shoulder. Pain, stiffness, and swelling are symptoms. E-cises treat root causes and thereby eliminate both the symptom and the dysfunctions they generate. In addition they produce an increase in energy, strength, and your sense of well-being.
Since long before _Gray's Anatomy_ was published in 1858, medical researchers have known that muscles lose strength and proper function when they are not used. It's pure supply and demand. The supply and effectiveness of muscle power grows in direct proportion to the demands we make on those muscles. In the pages ahead, I will point to the reasons why fewer and fewer muscles and the functions they support are being regularly used, and why there is a growing muscular-demand deficit. The E-cises in chapters 6 through are intended to fill the gap and balance supply and demand.
Throughout this book I will challenge misconceptions about the way the body's muscles and joints work. One prevailing myth is that overuse or repetitive use of muscles and joints is dangerous. By now I hope you are beginning to realize that the opposite is the case. In almost every instance, underuse is central to the "Painful PC."
Underuse is happening head to toe. It's happening to computer users and concert pianists, football players and financiers; to the fit and flabby, to the young and old. Knees are blowing, hips are crumbling, lumbar disks are rupturing. For PC users, the front line, the primary hurting zone, involves the hands and wrists. Again, it's caused by underuse. The joints and muscles of this zone have been left to fend for themselves by allied muscles and joints that are supposed to be interactively supporting and assisting the job of finger flexing and extending, thumb waggling, gripping, grabbing, and stretching. Some muscles and joints are working like crazy, while others are in an it's-crazy-to-work mode.
By misdiagnosing this as overuse, the prescription then becomes one that is based on promoting underuse. Lock the wrist, back, or neck in a brace; stop using a keyboard; get a new job that doesn't require a computer. The effective remedy is use—proper use.
Another myth is that ergonomic gadgets can provide "workarounds" to patch the body's weak spots. These workarounds are actually masking dysfunctions and making the body weaker and more unstable. That's not what ergonomic experts intended, but that's what's happening.
And the third myth is that high technology supplants muscle power. A computer—the kind we use today, anyway—is a hand tool, and like any hand tool, be it a hammer or a pair of scissors, it makes specific demands on the body, far more than we realize. To respond to that demand, the musculoskeletal design must be intact and functional, which includes skeletal alignment, joint flexibility, and muscular strength. For most of us those requirements are not being met but can be with a little effort. That's our objective here.
My job is to help you achieve it. There's no reason that the sons and daughters of miners, millers, bridge-builders, and bricklayers should meet their match in the form of a computer keyboard, mouse, and video display terminal. Let's remember and renew our pain-free physical heritage as magnificent generalists, and leave the magnificent PC to evolve like any other useful tool.
#
**"For modern men and women, primary muscles from head to foot are disengaging.... There is stress, friction, and breakdown."**
My work has given me enormous respect for the intricate yet fundamentally simple resilience of the human body. From spry old ladies to strapping young athletes and agile kids, I've closely examined the musculoskeletal system and how its rugged design allows us to function in direct response to the demands of harsh, unforgiving environments—even the harsh, unforgiving environment of a software programmer's cubicle at three o'clock in the morning.
Our earliest ancestors didn't go to work in cubicles—work came to them on all fours, in all four seasons, and from four points of the compass. The musculoskeletal system we inherited is proof of that. The body's arrangement of muscles, bones, joints, and nerves enables a hungry man to reach over his head to pluck ripe apples or to bend down to dig through the snow and into the earth for edible roots. He can run from danger, climb a tree, and throw a spear (and make the weapon with his own hands as well).
Did I say _he_? I may use the masculine pronoun from time to time, but _she_ is just as capable. Male or female, our distant ancestors _embodied_ lives of motion.
Consequently, there is no fixed limit on our stretching, bending, climbing, or running. The reason for that is the almost constant demand for motion that came humankind's way from an always-challenging environment. In short we were designed to do what we can do—move—and do it over and over again, depending only on individual strength and stamina. Simple fatigue and exhaustion, not pain or musculoskeletal damage, are the natural circuit breakers. We are designed to rest or go to sleep, and return to work—return to movement—refreshed _and_ stronger.
**PLANET GYM**
**Our ancestors "worked out" constantly. The issue wasn't staying in shape—they wanted to stay alive. The human body's musculoskeletal functions evolved in a motion-rich environment. No matter where they were—prairie, desert, mountains, seacoast—men and women were required by necessity to keep moving. The enemy was inactivity. Like sharks that constantly swim to breathe, we move to build and retain muscular and skeletal functions**.
Think about that. With time off to recharge, along with adequate food and water, our human apple-picker, root-grubber, or spear-thrower made the Energizer Bunny look like roadkill. Motion is the price we pay for muscle. The more we use muscles, the more they strengthen. So do the joints. Our _batteries_ are designed to run up rather than run down. In terms of evolution, it is the adaptable who survive. This musculoskeletal amplitude is one of the mainstays of human adaptability. Without it we wouldn't have lasted for more than a few centuries. The first drought or plague of locusts would have done us in.
Luckily, though, we have a nearly flawless musculoskeletal system. Nearly. The flaw is that our environment is no longer harsh and unforgiving. We tamed it by eliminating most of the constant working motion. And before you shout hurrah, let me point out that that's what's causing your wrist to hurt or those other symptoms attributed to "computer pain syndrome." The correct term should be "environmental pain syndrome." If motion is the price of muscles, pain is the price of lack of motion _and_ muscle. The computer is not guilty!
## Home on the Range
Muscles don't need to be bulging and rippling and hamlike to be strong; true strength is a matter of tone, accessibility, and function. Are they fully capable of responding when you need them? The test is their ability to meet your requirements. It's not a matter of conquering Mount Everest. If you are a postal worker, can you walk your route without a struggle? If you are a pizza-delivery person, can you climb a steep set of stairs? If you are a researcher, can you operate a computer keyboard? If not, it doesn't matter who you are or what you do, without this readily available underlying muscle strength, your health is doomed to be weak.
Being pain free at your PC or any other tool is all about strength, motion, and health. It comes in one package.
A few pages earlier, I noted that we are designed to do what we can do, and do it over and over again. The reverse is true too—we cannot do what we cannot do. By that I mean we can't live upside down, fly under our own power, swivel our heads 360 degrees, survive without food, water, or oxygen, and so on. There are limits, rules, requirements. As a species, we have known this for several million years and have rarely violated the design limits of the body except by accident or sheer folly. In either of those events, the consequences are instantaneous and drastic. The offender either stops what he or she is doing or perishes.
Do you think there's a bit of evolutionary logic involved here? Seems likely to me.
By establishing what our bodies can't do, we form an instinctive awareness of our range of motion—what we can do. We know that we can stretch, bend at the waist and knees, rotate the torso to the left and right, grasp and release with the fingers and hands, and—well, you get the picture. A picture of motion. We start this process as infants. It's both no big deal, and a very big deal.
But this picture of motion (and muscle) is misleading because we feel it more than we see it; over time it's more a product of remembrance than reality. We remember that we can twist and turn and stretch, but when we do not frequently call on our muscles to perform those actions, they lose the ability to respond. Initially—perhaps years go by—this escapes our attention. Yet the memory of our full range of motion is there, and when we do call on it, confident of an instant response, the answer is pain.
Let me tell you why. The hitch with range of motion—ROM—is that it comes in two forms, design range of motion—DROM—and individual range of motion—IROM. Think of the first as what the body is capable of doing, and the second as what the individual actually does with his or her bones, joints, muscles, and nerves. There is an enormous disparity. For instance, many people hardly ever reach straight up over their heads. The function is there as part of DROM, but IROM is not utilizing it. Over time this function becomes increasingly inaccessible.
Almost all of us—there are very, very few exceptions accounted for by rare birth defects—started out with the same design range of motion once we got past infancy and toddlerhood. Aside from size and some minor bone surface variations, all the musculoskeletal parts are the same and operate in an identical manner. This forms the platform or foundation for the familiar functions like stretching and bending that I've been discussing. If you'll stand up, I will demonstrate what I mean.
**DROM AND IROM**
**Design range of motion—DROM—is like the specs for a car's mechanical systems or any structural design. There are established parameters for muscular contraction and the articulation of joints. Bone size may vary from individual to individual, but the basic configuration and surface characteristics of all femurs (thigh bones), for instance, are the same. Almost everyone starts with the standard equipment package**.
**Individual range of motion—IROM—however, amounts to arbitrarily assuming that mechanical specs are totally elastic. Why bother replacing the passenger-side shock absorbers if no one sits on that side? Why not block half the radiator to warm the car faster in the winter? IROM does the same, albeit unconsciously, by favoring the right knee over the left, or freezing the shoulders in a rounded, stooped posture. These IROM alterations to the body's _mechanism_ produce a net loss of strength, flexibility, and function**.
Up? Good. Now sit down again, please.
What happened? Let me guess. You stood by using a hand to push off from the desk or arms of the chair. It's also likely that you leaned forward, bending at your waist and letting your head drop forward until gravity sort of tugged you out of the chair waiting for your knees to engage. And in the process most of your weight was transferred to one hip and leg.
These contortions are characteristic of human design range of motion in only one crude way. You got to your feet. You were able to access enough DROM—the platform—to improvise your way out of the chair by using individual range of motion—a variety of shortcuts and inventive ploys, like that business with your head. Don't feel bad. Many people do the same thing. Their knee joints are not engaging, but their hips are, which means that their head must act as a counterweight to open the knee joint wide enough to lock and bear weight and to move into semivertical alignment with the hips. The head is doing what weak knee and thigh muscles, thwarted by overly strong hip muscles, cannot.
It's very ingenious. The knee was not specifically designed to be bailed out by one's head, neck, and shoulders, but design range of motion allows for wide tolerances, another reason why we are so adaptable. But the repeated improvisation becomes a mixed-up pattern of a few healthy functions and dysfunctional aberrations. This is what I mean by individual range of motion, and why I am determined to help reestablish your _full design range of motion_.
DROM is there—you're just not using most of it.
I want you to be able to stand up without head fakes and hand tricks. Rising to one's feet, weight balanced equally between them, shoulders and head back, knees and hips in neutral—and look, Ma, no hands!—are the characteristics of a fully functional design range of motion. Without access to DROM, none of us can expect to swing a hammer or use a computer keyboard without pain.
Am I saying that the ability to stand up without these extra efforts has something to do with operating a computer keyboard?
You bet it does!
## Power Struggle
By and large it is the nature of the environment that each of us inhabits that determines the attributes of our individual range of motion. Until roughly fifty or sixty years ago, the environment was sufficiently untamed that DROM and IROM coincided for most of us. Watch the actors in silent films rise from chairs, walk, and bend. They look strange, but it's not just primitive filmmaking techniques. Their postures are erect and their gait-pattern functions (the way they walk) are engaged, unlike modern men and women, who are exhibiting the symptoms of a slow-motion collapse of their musculoskeletal systems.
_Collapse_ is a strong word, but I mean it. We are losing access to our design range of motion, and with it goes our pain-free birthright. It's not just aesthetics. A sexy slouch may be read as coolly sullen or sophisticated, but slumping shoulders and rounded hips are sending a message in loud and clear body language that something is wrong. Pain may or may not be present. The initial symptoms could be poor concentration, fatigue, or anxiety. It may take sitting at a computer for several hours doing research on a term paper or typing software code before a wrist starts getting stiff. Eventually, IROM and DROM will go to war.
The problem isn't that our bodies are frail or that the demands of operating a PC's keyboard and mouse are too strenuous. What's happening is that we've adopted a lifestyle that cannot automatically maintain the health of our musculoskeletal system by keeping DROM and IROM reasonably compatible. Just as we work to master new software applications, we have to learn how to replace environmental stimulus ourselves. There are easy-to-use techniques for restoring and maintaining DROM that will prevent pain associated with computer use. I'll introduce them to you in chapters 6 through , but first I want to spend a little more time acquainting you with how the human body's hardware functions.
**TAKE A LOAD OFF**
**The mass-produced car, the modern office, power tools, and home labor-saving appliances were invented this century. Each of these breakthroughs replaced muscle power. Cars and offices meant that humans could sit down to travel and work, two activities formerly done mostly on foot. Power tools and home appliances mean that back, shoulder, and arm muscles aren't being used nearly as much. How are these muscles and joints stimulated? Very little. Consequently, they are not strong enough to carry out their primary responsibilities or to fully support other interrelated functions like typing or sitting up straight**.
**MUSCLE HEAD**
**Skeletal muscles tell the bones what to do**.
**Skeletal muscles come in pairs**.
**Skeletal muscles pull (contract) and relax, they don't push**.
**Skeletal muscles have assigned primary tasks**.
**Skeletal muscles never function in isolation**.
**Muscles constitute about 40 percent of the average person's body weight. Bones contribute another 20 percent**.
Many people try to argue with me when I say that muscles tell the bones what to do. They contend that the brain, via nerves, calls the shots. And that's actually half right. The nerves transmit a signal, the muscle tissue contracts, and a bone moves. In due course the muscle's partner contracts and moves the bone back to where it started. The muscle is the middleman. It obeys the message—sometimes. When DROM and IROM are at odds, the message gets garbled, goes to the wrong bones, or is ignored.
This situation isn't a disease. It is a natural state. An inactive muscle loses its capacity to contract. An inefficient organism doesn't waste resources on unused functions. Hence the more inactivity, the more incapacity. Eventually, no matter how much a nerve demands a particular muscular response—move those fingers!—the muscles cannot obey.
That's when individual range of motion kicks in. IROM tries to keep the body moving in spite of muscular incapacity. When the nerve's request to move muscle A is ignored, muscle B, C, or J will be recruited to assist. When I asked you to stand, and if you pushed off from the desk or chair with your hands, the muscles and joints of the hand, wrist, elbow, upper arms, shoulder, and upper back were augmenting or substituting for the muscles of the hips, thighs, and lower back.
**TWO JOBS, TWO MUSCLES**
**Skeletal muscles work in pairs: one flexing, the other extending. (Some do both, but only when they control more than one joint.) In both cases the muscles are contracting. A _flexor_ muscle is pulling two bones toward each other. It then relaxes and an _extensor_ pulls them away. Contract-relax-contract-relax. The best illustration of this action is your elbow. Tuck either the right or left elbow into your side. With the forearm held at a ninety-degree angle to start, without moving your elbow, bring your palm toward your shoulder—that's flexion. Move it back to the original position—that's extension. (Full extension would occur when the elbow joint is wide open and the arm is straight at your side.)**
This muscular _compensation_ , to use the term I prefer, isn't all bad. Compensating muscles allow the body to deal with emergencies or to operate from an awkward position. They get the job done. Even so, doing it over and over again means that the bypassed muscles with the primary assignment get less and less stimulus. They weaken and disengage. The flexion-and-extension pairing is disrupted. There may be full flexion followed by a partial extension; like a hinge, the joint opens but doesn't fully close. The combinations and gradations are almost infinite. Try to imagine the chaos that goes on when several joints are behaving this way while they are attempting to function together. In that simple act of standing up that you did at my request, at least one or both hip joints were staying in flexion and not returning to neutral. Try it again right now.
Up? Look at your feet. If one or both are flared out, it is a symptom of your hip being held in flexion. What can't be seen easily is the contortions that the knees and ankles have undergone in reaction to the dysfunctional movement of the hips. Likewise, the lumbar vertebrae (the vertebrae of the lower back) weren't able to function properly. The effects run straight up the spine and influence how your shoulders, arms, wrists, and hands interact with a computer keyboard.
For modern men and women, primary muscles from head to foot are disengaging to an alarming degree. Secondary muscles are being recruited to do work that they are unsuited for. There is stress, friction, and breakdown. How do I know? I can see it. And so can you.
We'll take a closer look in the next chapter. Seeing the problem is the first step to solving it.
#
**"The PC creates the illusion that it's doing all the work. It's simply not true.... Dozens of muscles, joints, and functions are brought into play and kept in play for hours at a time."**
**Figure 3.1 The human musculoskeletal grid**.
Many people who come to my clinic bring envelopes of Xrays. I try not to look at them. Xrays are deceptive, showing symptoms rather than the source of the problem. The best technology for focusing on the problem comes built into the human skull—your two eyes.
Take a look at Figure 3.1. Pretty, isn't she? Or, if you prefer—handsome, isn't he?
I know the illustration looks like a genderless grid, but to me it is the superstructure of a beautiful and functional body. Figures 3.2a and 3.2b will show you what I mean.
Notice how the lines run parallel and form ninety-degree angles exactly at the ankles, knees, hips, and shoulders. Except for the shoulders, those angles are also in vertical alignment, and the only reason for the shoulders being an exception is to account for individual size variation.
**Figure 3.2a**
**Figure 3.2b**
**Front and side view of the musculoskeletal superstructure**
What we're looking at here is intact, fully functional design range of motion. The woman in the next illustration, Figure 3.3, is showing us her individual range of motion. The horizontal lines are no longer parallel, and the ninety-degree angles are not in vertical alignment with the grid. Also, the head seems to have shifted forward and off center. DROM and IROM don't line up.
Figure 3.4 distorts the grid to match the model's musculoskeletal dysfunctions. Figure 3.5 is a side view. See the consequences? The vertical load-bearing capacity of the body achieved by the alignment of the ankle, knee, hip, and shoulders is undermined. In addition the horizontal parallel lines are askew, and with it the balance and stability of the whole structure is radically compromised. Notice the head? It's moved forward of the center line. The support system that was directly under it is gone. The weight is jackknifing the spine forward and down.
**Figure 3.3**
**Figure 3.4**
**Figure 3.5**
**The disparity between the solid lines and the grid show the clash between DROM and IROM that leads to dysfunction and chronic joint and muscle pain**.
Now, in Figure 3.6, we've eliminated the human form and super-imposed both grids. DROM is solid and IROM is dotted. The disparity between the two is pronounced, and therein lies the problem. If our bones do what the muscles tell them, something is wrong with this illustration. The muscles should be telling the bones to stand erect in vertical and horizontal alignment. But the message is not getting through. The major posture muscles of the model are disengaged to various degrees. To stand, she is using IROM to recruit an array of compensating secondary and primary muscles that are producing a dysfunctional misalignment of the body's superstructure.
**Figure 3.6 Side view of joint misalignment**.
The joints that are involved in this IROM are being subjected to stress, friction, extra impact, and lateral twisting. Some muscles are doing extra work, others hardly any at all. Tendons and ligaments are being yanked on and twisted. And cartilage in the joints receives extra wear and tear.
If you were walking down Fifth Avenue in Manhattan and noticed that Rockefeller Center was tilting at the same angle as our model's body, I guarantee that you'd be out of there in a New York minute. Gone! We'd realize instantly that gravity was about to deposit a load of expensive bricks and mortar in the skating rink. But we look at our own body in the mirror and assume that the basic laws of structural engineering don't apply. Gravity affects a misaligned building, but not the human body?
Dream on! The stresses are even worse because the body moves, a building doesn't.
Imagine a giant hand that reaches down, picks up a minivan as it travels along the highway, squeezes, and then sets it back on the road. The minivan continues on, but everything has changed. The relationship and interactions of the components can't possibly remain the same. The tires wear differently, the shock absorbers have been altered, and the drive train is crimped. The giant hand imposed a new design on the minivan, one that's not likely to do much for reliability or resale value.
IROM does the same thing. But instead of being squeezed by a hand, our bodies are being tranquilized by an ever-motionless environment and then crumpled by gravity.
## A Question of Priorities
Roughly speaking, skeletal muscles have three missions: erection, locomotion, and stabilization. I'm not saying that all muscles do all three jobs. Some do, some don't. In general they help us stand upright, walk, run, or make other gross directional movements, and with precise control they move the torso, the lower and upper extremities, and the head. In combination these otherwise-distinct roles work together to provide the necessary finesse to walk, grasp, throw, and—wonder of wonders—operate a computer keyboard and mouse. Locomotion seems to be the precursor to the other two functions. For a newborn infant, the erector and stabilization functions are close to absolute zero. It is only through wiggling and jiggling, flopping and squirming, rolling and crawling that he or she comes to the point of standing up. In the meantime stabilization is jelling as the baby goes from gleefully uncoordinated food disasters to world-class patty-cake. This primitive means of locomotion, sans arms and legs, accesses the posture muscles—the erectors—that will allow her to stand on two feet. (By the way, one of the worst things Mom and Dad can do is hoist the wiggling child to her feet and help her "walk." It's too soon; the posture muscles need to be triggered first.)
What the baby shows us is that musculoskeletal development takes place from the inside out. That's what the contortions in the crib or on the floor are all about. Muscles are arranged in layers, and many of the deepest pairs and groups are responsible for keeping the body erect. Posture muscles maintain their strength and functions like any other muscles—through motion provided by the stimulation of the person's environment. For the baby Mom and Dad are the environment. They tickle, she wiggles. The spinal, hip, and shoulder muscles are stimulated. When she crawls, the same thing happens.
Fully developed structure is lost in the same way. A patient bedridden for a long time can't stand upright, let alone walk. To a lesser extent, the same thing happens to a person stuck at a desk all day. The posture muscles disengage because they aren't being used. With less and less motion being required by the environment, the erectors aren't being stimulated enough to retain their functional capacity. They weaken, and the loss of vertical alignment (I call it "vertical load-bearing") restricts the design range of motion for the load-bearing joints. It's the equivalent of the giant hand squeezing the minivan, but what's being bent is not the axle but our joints.
Because of this restriction and stress, the weakening posture muscles need help. So they recruit other lesser muscles, most of them on the outer periphery of the body, to help keep DROM in a semblance of proper alignment. These recruited muscles are not strong enough or in the right locations to maintain the grid's right angles and parallel lines.
But joint articulation occurs—after a fashion, and at the cost of eventually damaging or destroying the mechanism. In the interest of moving, the body sacrifices proper alignment. Instead of doing one job well, the erector muscles end up doing two jobs poorly: erection _and_ locomotion. It's the lesser evil, seeing that if you can't move, you won't be able to hunt or gather food. But lost alignment interferes with movement, which in turn leads to more lost alignment, even less movement, and so on. Eventually, the body can't stand upright and can't move. The lesser evil has become the maximum threat to survival.
**BALANCING ACT**
**Standing upright on two feet isn't easy. It is a major feat of engineering. Balance is everything. To achieve it, the body's major posture joints, or load joints—the ankles, the knees, the hips, and the shoulders—are stacked one atop the other. There are eight of them in pairs of four on each side of the body. Gravity presses down, and there is vertical load-bearing. Furthermore, to balance the load between two feet, the load joints are in horizontal parallel alignment from left to right**.
Is that an extreme case? But how many times have you heard about "Poor Joe, he's flat on his back in bed because of a ruptured disk"? Trapped at his desk, Joe's posture muscles—the erectors—gradually lost strength. His skeletal alignment deteriorated, and with it came stress on his joints. He had to keep moving, though, so erector functions were borrowed, and peripheral muscles were brought in to help.
At this point Joe wondered if he was developing carpal tunnel syndrome. His wrist started stiffening. But it wasn't because the keyboard was making an unreasonable demand on his hand and wrist. Those functions would have been fine if they hadn't been also recruited to help keep Joe's shoulders and head from jackknifing forward and smashing into the screen. In other words, individual range of motion was in conflict with design range of motion.
Joe was unaware of the danger at first. He didn't notice the symptoms of disengaged posture muscles. His head and shoulder _gradually_ rounded forward. He _gradually_ lost the arch in his lower back. Finally, he felt a _gradual_ tightening in his wrist that _gradually_ started to hurt. Then he bought a wrist brace. (We'll spend more time on braces and other palliatives later in the book, but right now it's enough to know that they are only repositioning the wrist and shifting the stress elsewhere. The pain may go away temporarily, but like Chinese water torture, where the first few drips may go unnoticed, the millionth one causes agony.)
Joe cut back on the number of hours he spent at the keyboard and bought voice-recognition software. He stopped going to the health club and taking walks on the weekends. He could walk all right, but he just didn't feel like it. The worse Joe felt, the less he moved; the less he moved, the worse he felt. Yet at any point, if you asked Joe how he was doing, he'd have shrugged and said, "Fine."
How did Joe end up in the hospital with ruptured disks? He caved in on himself, gradually losing his core muscular strength. Understimulated, Joe's big posture muscles, which are designed to do heavy work, were shut down, and the surface muscles took over. He could move back and forth to the men's room; he could operate his PC. Dutifully, the body contrived to deliver the minimum to keep him moving.
**THE OTHER RSI**
**If you replace the word _repetitive_ with _restricted_ , it's a more accurate label for these common injuries. By limiting movement to just a few of the same moves that occur over and over again, we are creating musculoskeletal imbalances. The few active muscles strengthen, and the inactive ones weaken. But it would be a mistake to adopt solutions that would attempt to get rid of this restricted movement. The only thing wrong with restricted movement is that it is restricted. It should be augmented with a variety of motion that supports related functions. Ergonomic reengineering and gadgetry fail because the solution amounts to replacing a restricted motion that is causing pain with another restricted motion that isn't causing pain—yet. Eventually it will**.
Nevertheless, one day the minimum wasn't enough. Joe's printer was on the floor, and he had to bend over to pick it up and move it. But his weak posture muscles couldn't handle that job. He didn't know that, though. Nor did he suspect that his skeletal misalignment had reached the point that it was severely stressing three of his lumbar disks. Bending over for the printer was the final and _sudden_ straw.
He was still wearing the wrist brace when they admitted him to the emergency room.
Joe followed his individual range of motion down a well-worn path that eventually left him "flat on his back." He became _motionally_ anorexic. His posture muscles were in need of motion, yet he starved them even more. Like many of us, he probably would argue that he moved constantly. But as a result of his life and work style, Joe was moving only a relatively few muscles (even when he worked out at the gym). For the most part, the muscles that he did move were the smaller, peripheral muscles that could not take the wear and tear. Joe's DROM and IROM fought it out, and he lost.
What we are looking for in this book is motion that promotes and provides design range of motion. It's the only way to restore your musculoskeletal platform, and once that happens, there's no reason you can't swing a hammer or pound a keyboard all day long.
## Give and Take
One of the reasons that I deliberately pair hammers and keyboards is that I am still trying to convince you that a PC is a tool. "Yeah, yeah," you're probably thinking, "I work with a PC, so it's a tool." I'm serious. A hammer requires muscle-power. The same goes for a PC's keyboard and mouse. The lack of sweat, blisters, and splinters isn't relevant.
Modern life is very deceptive. We live in such relative luxury that for many of us, "work" seems like it does not require physical effort anymore. Even so-called laborers are using nail guns and power saws. Hold the tool, flip the switch, and let it rip.
Okay. Stop right there. What do you suppose holds the tool? Muscles. But now, instead of fluid hand, wrist, elbow, and shoulder involvement in swinging an old-fashioned hammer, the power tool is being brought to the work and held in position. There's different muscular demand and engagement. Functions that were once involved are being bypassed. A nail gun isn't dainty and light, and carpenters are aware of the physical activity involved (although most of them don't realize that the twinges they feel in their lower back and their neckaches are symptoms of the functions they've lost using a nail gun rather than swinging a hammer). The PC, on the other hand, sits quietly on a stand or desk and creates the illusion that it is doing all the work.
It's simply not true. To operate this high-tech tool, dozens of muscles, joints, and functions are brought into play and kept in play for hours at a time. Typing a single line of the manuscript for this book—about seventy-five keystrokes—took approximately three hundred separate muscular contractions to both flex and extend the fingers of the hand and to abduct and adduct the arms. That's not counting upper-torso movement, arm flexion and extension, and eye muscle activity. Yet we take this muscular demand and engagement for granted. And we should. Our human design range of motion has inspired such confidence that we assume it will always be there when we need it.
However, like Joe's, our individual range of motion isn't up to the job because it has been shaped and determined by the way we live long before we sat down at the keyboard and by what we do away from the keyboard. What DROM giveth, IROM taketh away. It's as if the carpenter went back to swinging a hammer eight hours a day after years of using nothing but the nail gun. The wrist would be flapping, the elbow flying, the shoulder blade sticking out as the body improvised a way to work around inaccessible functions.
The same thing is happening at the PC keyboard. Inside, at the muscular core, there is a vacuum. On the periphery improvisation is running wild. Look around the office at your coworkers. Look in the mirror. Stop the action. Freeze everyone in place. See it?
**ABDUCTION/ADDUCTION**
**_Abduction_ means moving away from a vertical line drawn down the center of the body**.
**_Adduction_ is the opposite function. The movement is toward the vertical center line**.
**On a standard keyboard, when the left hand moves left toward the A-key, the arm is abducting. When the right hand moves left toward the space bar, it is adducting**.
No? What's your posture like as you read this book?
What should be erect and stable postures are slumping.
Hello, Rockefeller Center.
It's becoming increasingly difficult for people to sit up and stand up straight.
Hello, crumpled minivan.
Old-timers used to say, "That boy will be all right once he fills out." The filling out—from the core to the periphery—isn't taking place. As a result, without the capacity for vertical loading, the body is being pulled forward and down by gravity. All work is movement; as the body slumps toward the horizontal, locomotion becomes harder and harder.
Hello, chronic pain.
#
**"People with carpal tunnel syndrome have 'blisters' in their wrists... caused by the adjustments that are made to skeletal misalignment."**
**Figure 4.1 The S-curve of the spine**.
Uh-oh—the spine, centerfold of serious anatomy texts. Don't worry. All you really need to know about the spine is that when it's healthy and functional, it has the shape of an elongated S. Truly, what you see is how you feel. Take a look at Figure 4.1.
The hand and umbrella are props. Focus on that squiggly line to the left—the spinal S-curve. The S seems a little funny at the top, as if somebody stepped on it, but the upper (cervical), middle (thoracic), and lower (lumbar) curves are the important characteristics. They produce a neat balancing act, Figure 4.2, that allows the pelvis to hoist the upper torso and head into a vertical position and keep it there. Instead of a stiff tent pole that would need external support to remain erect, we have a stack of "poker chips"—thirty-three of them—each separated by a semisoft cushion to act as a shock absorber and to provide flexibility.
**Figure 4.2 Side view of spine and pelvis**.
There's a hole drilled into the middle of the chips and cushions, through which the spinal cord travels, branching out here and there to enervate the muscles and organs.
Poker chips? Cushions? Drilled? Hey, I'm trying to keep it simple.
And it is simple. The spine's form follows its function. The individual vertebrae are intended to work together to bear the weight of the skull, the shoulder girdle and upper extremities, and the thoracic skeleton (rib cage) containing the organs of the cardiovascular system; below that the abdominal cavity and the other internal organs hitch a ride. In short, the spine's job is heavy lifting and heavy balancing. This load must be kept aloft while the body twists and turns, runs and walks, stretches, throws, crawls, and dances. At the same time, the spinal column provides a conduit for the main "Information Highway" of the central nervous system and protects it from damage.
**Figure 4.3 A rounded and dysfunctional spinal posture**.
Pretty neat! The secret is the S-curve. By cantilevering and counterbalancing those three curves, the structure achieves dynamic flexibility and strength over a wide range of motion. An Alexander Calder mobile uses the same sort of interaction to glide majestically through space. Calder did it with a welding torch. The human body emerged from a different kind of manufacturing process, with individual components that are sized and shaped to form the S-curve. If you found one in pieces under the Christmas tree, it could be re-created easily like a jigsaw puzzle: _Did anybody see a C-7? No, but I have an L-1_.
Match up the right shapes, and the vertebrae all drop neatly into place, but without ligaments, tendons, and muscles, the jigsaw-puzzle spine would be incomplete. The bones of the spine have practically no overall intrinsic strength of their own. Muscles give us _backbone_. In earlier chapters we discussed how dependent muscles are on motion to contract properly and to perform their assigned functions. Spinal muscles are no exception. Most people who are experiencing chronic pain related to a PC are bringing dysfunctional spinal muscles with them to the computer at work, at school, or to kick back and have some fun at home.
The reason is as plain as day. No, make that as plain as the S-curve. The spine's most vital feature is being replaced by a C. Check out Figure 4.3. The three curves have merged into one. As inactive muscle groups throughout the body lose strength and function, they cannot provide direct or indirect support to the spine. The loss of vertical alignment and load-bearing shows up in a rounded back that throws the head and shoulders forward and rolls the butt back and up. Notice how the vertical arrow on the pelvis in Figure 4.2 has tipped toward the back as the spine rounds in 4.3.
Move forward to sit on the edge of your chair. Pull your head back, and position your feet and thighs a shoulder-width apart. Try to feel the curve in your lower back. Let your stomach muscles relax. If there is someone else around, ask them to tell you when your head and back are in a vertical line. Now sit there, and time how long it takes for you to become uncomfortable. Instantly? Thirty seconds? Two minutes?
We all should be able to sit in that position indefinitely with no discomfort or fidgeting. When you came out of the position, did your shoulders slump and your hips shift back and down as your lower back lost its curve? If so, you went right back into the C-curve. This is a posture of dysfunction. It's the one you use to drive to work in the morning, sit in the coffee shop for a double espresso, attend meetings, watch a movie, veg out in front of the TV—and operate a PC.
Because it doesn't hurt when we drink the espresso, Starbucks is okay; the coffee won't be blamed. When the pain or stiffness occurs in front of the PC, we know what's what: computer pain syndrome. The difference is that we are working with the PC. Work requires muscle-power, and our muscles are taking the day off—the week, month, year, and the rest of our lives. Eventually, lifting the Starbucks cup will hurt too. Even pleasure requires muscle-power.
## A Chain Reaction
Try another experiment. Simply sit in your chair, straighten your back, and then relax it. Do this five or six times. Did you notice that your hips were moving too? If not, place a thumb on each hipbone—the knobs on the right and left sides—and then straighten your back and let it slump a couple of times. Your hipbone knobs will make small arcs. Notice that when you relax, your hips slip back and down into the chair. What's happening is that your hips are going into flexion, which they are designed to do. Basically, when sitting or bending at the waist, the top half of the body is allowed to fold toward the bottom half, with the pelvis acting as a big hinge.
**THE CENTRALITY OF NEUTRALITY**
**In a functional person, going from flexion to extension is like changing the gears in an automobile's manual transmission: The gearshift level passes through neutral before it goes from first gear to second, third, or fourth. Similarly, a muscle takes the joint (any of them, not just the hips) from flexion to neutral, whereupon another muscle takes it from neutral to extension. Neutral, then, is the balance point, where the joint can smoothly open, close, or rotate depending on demand. When the joint is prevented from going into neutral, the body loses balance and vertical alignment because the joint remains locked in either flexion or extension. Try walking without bending your knees. To do it, you're forcing them to stay in extension. The problem is that most people cannot fully relax contracted joint muscles, or, conversely, fully contract relaxed joint muscles. These muscles are either too strong or too weak**.
Think how useful this capability is. We can tie our shoes, weed our garden, and sit in a chair. In fact, since modern men and women spend so much time sitting down, as opposed to tying shoes and weeding the garden, the hip flexors get a lot of use. These muscles are adept at putting us into that flexed, half-folded position and keeping us there for hours at a time. In the process the spine, riding as it does on the pelvis's sacrum, is pulled into flexion as well.
If you recall, flexors are always paired with extensors. In Figure 4.4, the hip flexor and extensor muscles (not shown) are equally matched in strength and function, which puts the hip in a balanced or neutral position, as indicated by the arrow. The spine is also in neutral, as shown by the functional S-curve. But in Figure 4.5, since our hip extensor muscles aren't being used nearly as much, the flexors dominate, and the hip and spine begin to spend more and more time in only one place—not in neutral but in flexion. As a result our hip and spinal extensor muscles weaken and disengage. If you compare the two illustrations and note the arrows, you'll see that in Figure 4.5 the hip is rolling in a counterclockwise direction toward the rear.
**Figure 4.4 Hips in neutral position**.
Hence the spine is deprived of its system of countervailing curves, while at the same time being confronted with the problem of holding the head upright without the benefit of vertical alignment. An upright cervical spine (the upper part of the S) acts as a pedestal for the skull. Tip it over by just a few degrees, and a handful of small muscles in the neck, shoulders, and thoracic back (the middle part of the S) are left to carry the unbalanced load.
Imagine trying to balance an elephant on the tip of a fishing pole. Even if the pole were strong enough to support the weight, once it got out of plumb, Jumbo would be heading south, pronto. Luckily, as the head topples, the powerful hip flexors are at one end of the spine holding on—otherwise the C would resemble an inverted U or worse. But the hip flexors have other important work to do, like helping us walk. This conflict produces enormous stress and strain, along with elaborate muscular contortions and compensation in chain reactions all over the body.
**Figure 4.5 Hips in flexion**.
**HIPS FIRST**
**Head first. No, hips first. What the brain is to the central nervous system, the pelvic girdle is to the musculoskeletal system. All living creatures have brains (more or less); our pelvis is unique. Without it we wouldn't be able to stand fully erect or even to sit down comfortably. Because of its central location, the pelvis is a major player from head to foot**.
Several of the E-cises that I'll be introducing in the next few chapters are designed to help your hips escape from flexion and restore enough extensor function to allow your spine to resume its S-curve. You'll gradually start strengthening and reengaging your underused muscular core.
Many people are perplexed by the idea that therapy focused on the hips can affect hands, wrists, and arms. But the body is a closely integrated unit. A major change in one part of the musculoskeletal system has consequences in every other part of the system. If we can't get the hips out of flexion, the spine's S-curve will never be restored; without the S-curve the head and shoulders remain forward; and that means vertical loading is compromised; and so on, and so on, and so on.
Sound grim? It's not. The body is eager to return to function. In the clinic we often work with individuals who have suffered from joint pain for years, yet after about an hour of E-cise therapy, their pain is gone or significantly diminished. They're amazed. But it's no miracle cure. For one thing, if they return to starving their bodies of motion, their pain will resume. This "motion potion" is so powerful, when delivered to the right places in the right proportions by way of the E-cise program, that the snap-back to good health can seem almost miraculous. Staying with the E-cises keeps the pain at bay. In that way the miracle becomes a matter of routine maintenance.
But let's not get hip happy. I know from experience how hard it is to get the focus off the site of the pain. Most PC users think that they have a problem only in their upper extremities, shoulders, neck, or head. Peter, who came to the clinic a few years ago, was a classic case. His left wrist hurt. Bad. He couldn't use it, which wasn't helpful to a twenty-eight-year-old sales executive in the habit of sending out roughly one hundred e-mails a day to his customers and business team members. You probably know somebody like Peter—or _are_ somebody like Peter: a cell phone in one hand, a notebook computer in the other. We put him on an E-cise program, and when the pain abated, he said, "I wonder if that has anything to do with my back?"
"Your back?" I asked. "This is the first you've mentioned it."
"It's hurt for about a year."
"Does it hurt now?"
He gave me a strange look. "No."
Of course the pain was related. The body is a unit. In Peter's case he was rotating his upper torso to the right and lifting his left shoulder in an attempt to ease the friction in his wrist as he typed at the keyboard. With a rounded spine, that maneuver was creating nerve impingement in the lower back.
Sciatica, another common form of nerve impingement, is also hip-related. Long-distance drivers often experience pain in their low back or buttocks because their hips have settled into flexion enough to interfere with the sciatic nerve root that passes through the area. Many people have learned to raise their shoulder or twist laterally in the seat to relieve the pain. As with Peter, the stress is being transferred up the back toward the shoulders, where the stress is not as immediately noticeable. The next time you're at a highway rest stop, take a look at the drivers emerging from cars who are rubbing their shoulders. What they really should be doing is getting their hips out of flexion.
## The Wrist Taking of Carpal Tunnel Syndrome
The body is acutely sensitive to friction, and that's why, without thinking about it, we twist and turn, make upper body rotations, cock a shoulder, or perform other adjustments. The basis for this response is perfectly logical: a _temporary_ stimulus is provoking _temporary_ misalignment of the body. In turn, to minimize stress, the system is making an appropriate _temporary_ accommodation. The assumption is that the body will return to alignment and balance. But if that doesn't happen, the temporary arrangements become permanent.
If a blister developed on your right heel, you'd probably start favoring your left leg while walking. There'd be a slight limp caused by prematurely transferring weight into the left hip and flexing and extending the knee more forcefully. That's fine. But if the blister never went away, the friction that you were trying to abate in your right heel would be transferred to your hip and knee joints. Eventually, there would be pain and damage to those joints. In all accuracy, you could say, "I have a blister in my hip and a blister in my knee."
People with carpal tunnel syndrome or other computer-related pain symptoms have "blisters" in their wrists. There is friction and stress. These blisters are not caused by using a PC's keyboard or mouse. They are caused by the adjustments that are made to skeletal misalignment. And they are just as visible as a limp. You can see these adjustments in the position of the head, the shoulders, the wrist, and the hands.
In Figure 4.6 the model is seated, which means what? She has lost the use of four of her eight load-bearing joints (knees and ankles). To hold herself in an upright position, she has only her hips and shoulders to work with. In this illustration, no problem—she's fully functional. The head is back and in vertical alignment with the shoulders and hips; her pelvis is strong, and it makes for a stable foundation. But that's not the case in Figure 4.7. And there's another difference between the two illustrations. The functional model's head, shoulder, and hip alignment has affected the position of her wrists (Figure 4.6). There's an arch; with the palm facing down, the wrist is slightly cambered or arched when placed on a flat surface or held in a horizontal position. Do you see that arch in Figure 4.7? It's not there. The elbow has dropped lower as the upper arm's position changed, and the wrist is flat on the desk. Figures 4.8 and 4.9 also show the effect of spine and hip flexion on the wrist position.
**Figure 4.6 Proper skeletal alignment in a seated position**.
Try it yourself. For the moment, ignore the model and sit sideways to a table or desk. Place your forearm on the table, running parallel with your thigh, with your palm down and your upper arm and elbow held at a ninety-degree angle. It doesn't matter whether it's your right or left side. Pull your head and shoulders back as far as you can. Feel the S-curve develop its arch in your lower back? Hold that position, and glance down at your wrist without moving your head position. You should see that now there is a space under the wrist immediately behind the palm of your hand. If there isn't, your head and shoulders are not fully back. Make sure to roll your hips forward and tuck them under to counteract flexion.
**Figure 4.7 The wrist arch flattens as the hips and spine go into flexion**.
**FIRE**
**The body is a furnace. It is always burning. That's what metabolism is all about: the breakdown of molecules to produce energy in the form of heat. Therefore the body is sensitive to temperature variations. It has several mechanisms for responding to excess heat generated by friction. One of them is swelling—appropriately known as "inflammation." Swelling is a simple means of restricting the motion that is producing friction. The fallacy of using anti-inflammatory drugs to reduce swelling is that there is no decrease in the friction**.
Got the arch in your wrist? Now, let go. Slump. Allow your back to round and your head and shoulders to come forward. The arch in your wrist will flatten. If you continue to push your shoulder forward and down, you'll feel a growing strain and pressure in the wrist. Pull back on your shoulder, and the pressure will ease.
Although you've been sitting sideways to the table, this position is similar to operating a mouse or other computer pointing device. In Figure 4.8, the model's back and shoulder flatten her wrist arch, while the mouse levers the hand upward and increases the tension in the wrist; her spine is in a C-curve. But in Figure 4.9, with the S-curve restored, the wrist arch is visible and the wrist tension eases.
Figure 4.10 shows the outline of a hand and the internal bone structure. The fingers or phalanges start at the knuckle of the hand; the metacarpals extend below the knuckles to the wrist, formed by the cluster of eight carpal bones held by ligaments in a transverse arch. It's a relatively small and confined area, isn't it? If you consider the forearm as well as the hand, twenty-nine separate muscles and their tendons share this space. Many of those muscles originate in the forearm, which means that to flex and extend the fingers—each of them has three working joints (the thumb has two)—there isn't much extra room. It's like constant rush-hour traffic getting the tendons threaded through the wrist.
But you know what? In a functional body, there are no fender benders and no gridlock. The tendons and muscles stay in their own lanes. But when skeletal misalignment is present, the traffic in the "carpal tunnel" starts to clog up. That's what you were feeling when I had you roll your shoulder forward until the arch under your wrist flattened.
To experience this in a position more akin to operating a keyboard or mouse, sit forward in a chair with your feet a shoulder-width apart. With your hands palm down on the knees, rest your forearms along the length of the thighs. Ready? Slowly bring your head toward the knees. You'll feel your elbows levering downward on the radius and ulna in the forearm, which are prying upward on the carpal area and squeezing it against the topside of a band of ligaments that encircle the wrist. This is turning your arm bones into levers that are compacting and flattening the carpal area and creating friction on the tendons and nerves that pass through there. Although your thighs are lower than keyboard height, the practical effect is the same in that your hands, wrists, and arms will be typing in a parallel position. In both cases the head, shoulders, and back move forward to create a counterweight at the elbows that transmits upward pressure into the wrists.
**HIP ROLLS TO GO**
**The do-it-yourself examples and E-cises in the book will often ask you to "Roll your hips forward and under." By this I mean for you to take your hips out of flexion and put them into extension. The way to do this is to pull your head and shoulders up and back. You can be either sitting or standing. The upward movement will get your hips to start swinging into position. Now, relax your stomach, and roll your hips forward to create an arch in your back. Don't abruptly snap into this posture, ease into it. Don't worry if it feels stiff or unnatural; that's because your back is used to the flexion-induced C-curve. If there is pain, though, back off the arch until it stops. Hip movement is the key. If your shoulders and head move back without the hips moving forward, you are still in flexion**.
**Figure 4.8 Loss of the wrist arch increases tension while operating a mouse**.
The mouse isn't involved. Not at all. The pressure is coming from your head, shoulders, and back. And it's constant no matter what you are doing with your wrist and hand: pointing and clicking, typing, jotting a note with a pencil, or holding a coffee cup. As with the limp that compensates for the blister in your heel, the body is making adjustments based on the assumption that the loss of vertical alignment is only temporary. In this case the adjustment is squeezing and flattening the carpal tunnel area. It's no big deal really, if it happens occasionally. The alternative would be to stop the fingers from all movement. Such a drastic measure doesn't seem called for. So the body permits hand movement at the cost of extra friction. That's great, until we ask the muscles of the hand to "limp" for hours at a time—chafing tendons and nerves while thousands of flexions and extensions of the fingers are called for. Soon there is enough friction to set our wrists on fire. And it does.
**CTS SYMPTOMS**
**In most cases it really doesn't matter what you call chronic musculoskeletal pain. After all, we're treating the cause, not the symptoms. For the record, carpal tunnel syndrome symptoms are numbness, tingling, or pain in the area of your thumb, index, middle, and ring fingers. The pain is often worse at night than during the daytime. Other medical conditions can cause these symptoms as well. A wide variety of hand, wrist, and arm symptoms go by different designations. Here again there's a tendency to classify and treat conditions according to where the pain happens to occur. An example is Guyon's canal syndrome. It's a lot like carpal tunnel syndrome, except it's a different nerve passing through a different part of the wrist. But it too is caused by skeletal misalignment, muscular weakness, and structural instability. In my view these various syndromes serve only to demoralize people and convince them that they are suffering from some mysterious disease**.
**Figure 4.9 Erect posture eliminates wrist tension**.
In the next chapter we'll start on fire fighting and fire prevention.
**Figure 4.10 The skeletal structure of the hand**.
**NERVE DAMAGE AND CTS**
**The body carefully protects the nervous system from damage. When bones, tendons, or muscles start bumping into nerves, the alarm bells immediately go off in the form of pain. Also activated is the equivalent of a car's airbag to cushion this unwanted contact by creating swelling. Fluid flows into the tissue and puffs it up. Because this process is visible, painful, and constricting, we've devised a way to counteract it—anti-inflammatory drugs. But removing the inflammation does nothing about the impingement. The same goes for braces or other devices that immobilize the wrist. The enforced inactivity will eliminate the friction, and the inflammation will subside. But when the brace is removed, the friction returns. The surgical response is to open the wrist through the palm and cut out a ligament to make more room in the carpal tunnel. But if the misaligned shoulder, back, and head continue to squash the wrist flat, that extra space isn't likely to last long**.
#
**"Every minute spent using a computer is a minute of extremely restricted movement."**
Effective health care is eight parts diplomacy and two parts therapy. An important aspect of the diplomacy is persuading you to take action. If I can't do that, I've failed—and I hate to fail.
This book presents five therapy programs that I've specifically developed for people who use PCs. The backbone of each of them—to choose an appropriate metaphor—is formed by a series of exercises that target specific musculoskeletal dysfunctions or clusters of dysfunctions. These E-cises, as we call them in the clinic, are simple and easy to do on your own. They don't require special equipment beyond a few rolled-up towels, a pillow, a chair, and the like.
To determine which program is best for you, simply calculate the number of hours you spend using a PC. One to three hours a week is my standard for occasional PC users, one hour a day for moderate users, and from one to two hours a day or more—much more—for power PC users.
By dividing the therapeutic process into categories based on how much time you spend working or playing with a PC, I'm bowing to reality. I know all too well that treatment usually starts where and when pain begins. At the same time, there is usually a misleading cause-and-effect motivator: "I'm on my PC ten hours a day, and boy does my wrist hurt!"
Rather than fight this flawed logic, I've decided to go with the flow and link therapy to PC usage. It will allow you to conveniently slot yourself into a relevant category. Does that mean the PC is causing the pain?
I've said it several times already, and to put it diplomatically again—no!
You can use the PC for five minutes a day and still be in agony. Fortunately for Silicon Valley, you probably won't make a cause-and-effect connection to one of their products. The blame will fall—incorrectly—on something else. The toll-taker at the Delaware Memorial Bridge blames his backache on reaching out to the passing cars; the horticulturist at the Arnold Arboretum in Boston says the rose clippers hurt her wrist; the checker at Vons in Del Mar complains that the cash register is wrecking his thumbs. As a diplomat and a therapist, I suggest we just forget about cause and effect and work on a solution instead.
So if you're in musculoskeletal pain right now, or have episodes of pain, you should turn to chapter 6, where there's a program for pain sufferers in every category, no matter how much or how little you use a PC.
If you are not in pain, you'll need to turn to the chapter that corresponds to the amount of time you use the PC. These E-cise programs are purely prevention.
If you are an occasional user, turn to chapter 7; a moderate user, turn to chapter 8. If you fall into either of these categories, you do not rely on the PC as a primary means of livelihood. The occasional user is dabbling in cyberspace, learning the ropes, and perhaps being taught the ropes by their power-user children. The moderate user, however, is in deeper. Those who spend an hour a day on the computer are probably employing it as both a tool and a toy: sending and receiving e-mail, checking company inventory records, or playing a game to unwind in the evening.
Power users should turn to chapter 9. They need the PC to make a living or, if they are students, to make the grades to make a living. They also use the computer for recreation as well as work. And some kids have become power users because they are addicted to the games, chat rooms, and the Internet "mall."
Time is of the essence. Every minute spent using a computer is a minute of extremely restricted movement. This fact alone is what determines which E-cises are deployed for the various categories. Someone who spends hours in front of a computer cannot expend those hours pursuing a wider, more varied range of motion. Higher-impact E-cises with a greater stimulation value are necessary, as a result. On the other hand, occasional and moderate users do not require as forceful an intervention because they are getting stimulation for their muscles and functions from non-PC sources. The whole purpose for all three of these categories is pain prevention.
And if you're in pain, the E-cise program in chapter 6 combines restoration and recuperation. In that case time is not the key factor. If the supply of motion provided by one's environment is in short supply for whatever reason, an hour a week on the computer or less could be enough to trigger pain.
One final program is offered in chapter 11 to supplement your regular fitness routine and favorite forms of recreation.
## E-cise Preview
I've always believed that readers have the right to read a book any way they want—start at the end, graze spontaneously, or whatever. But as an author, I'd like to suggest that you read through the rest of the book before embarking on an E-cise program. I think you'll come away with a clearer picture of both the problem and the solution.
Whatever you decide, let me quickly run through some important points about doing the E-cises:
• The program will not work if you don't do it. Set aside time each day for the E-cises. Their effect is cumulative.
• Do the entire program from beginning to end in the order presented. The sequence builds on itself.
• Don't pick and choose among the E-cises for those that seem to address your concerns. If you are worried about your wrist or elbow, remember that the site of the pain (or stiffness) is usually not the source.
• Do the E-cises every day. An occasional day off is acceptable, but longer breaks mean that you are losing ground.
• Relax your stomach muscles while doing the E-cises.
• Remember to breathe, and breathe from your diaphragm.
After I present the four main E-cise programs in chapters 6 through , I then discuss eyestrain and nonpain symptoms like dehydration and obesity in chapter 10; show you how to break out of the workplace jail in chapter 11; answer frequently asked questions in chapter 12; and expose the folly of surgery, painkilling drugs, and ergonomic reengineering in chapter 13.
#
**HOME THERAPY**
• **Gravity Drop**
• **Sitting Knee Pillow Squeezes**
• **Static Wall**
• **Sitting Floor**
• **Pelvic Tilts**
• **Hip Crossover**
• **Pelvic Tilts**
• **Three-Position Toe Raises**
• **Sitting Cats and Dogs**
I'd love it if this turned out to be the least-read chapter in the book. But I'm not about to make a bet on it. According to the National Institute of Occupational Safety and Health, 20 percent of those who work with computers have some degree of repetitive stress injury. These figures are bound to go higher as the total pool of computer users grows, and as the general population itself becomes less and less functional due to our motion-starved environment.
Ironically, if PCs were banned from the home and workplace tomorrow, this alarming chronic pain trend would continue to rise anyway. We'd just have to assign another coincidental subset: _30 percent of all VCR remote-control users suffer from some degree of repetitive stress injury_. Name the technological device or tool, and if it requires movement from a dysfunctional user, it can and will be blamed for causing injury.
To me, that's the most alarming pain trend of all.
If you are experiencing pain, drop the E-cise menu that matches your PC user profile and perform the one below. You'll find it helpful to review the instructions in chapter 5, and if you jumped here without reading chapters 1 through , I suggest you go through that material before beginning the E-cises.
I know. It hurts, and the sooner it stops hurting, the better. But plunging directly into the E-cise program will cheat you in two ways. First, you won't have the necessary background to understand what the body is telling you with pain and how the Egoscue Method helps you to deal with it. Second, when the pain goes away, you'll be more inclined to immediately stop doing the E-cises— _no pain, no problem_. But that's wrong. The problem has been building over the long term, and it requires a long-term solution.
How long? It's hard to be precise because of variations in the extent and interrelationships of individual musculoskeletal dysfunctions. In the clinic it's very rare for a client to leave after an hour or two of his or her first E-cise—based therapy program without showing major improvement. The pain may linger, but it steadily decreases as the program continues. You should experience a similar de-escalation of pain over several days.
When the pain abates for two full weeks, you can begin to switch over to the power PC user's home therapy menu. Although you may use a computer only occasionally, the pain indicates that your work and lifestyle are not providing enough motion to maintain proper musculoskeletal function. The power PC user's E-cise program will help counteract this motion deficit. I want you to ease into the transition by using the power PC user menu one day a week on week three (that's one week after two full weeks of being without pain), two days on week four, three days on week five, four days on week six, and five days on week seven. At that point the ratio will be five days of the power PC user menu and two days of the pain menu. This will be your permanent program. If the pain returns, resume a full seven-day program with the pain menu until you again establish a two-week pain-free window.
If there are setbacks, it helps to ask these questions:
• Have I been doing my E-cise program every day?
• Have I been doing the full program?
• Have I been following the instructions carefully?
• Have I changed the amount or type of physical activity that's occurring?
Many people intend to faithfully do their E-cises, but other commitments get in the way. You have to treat your health—particularly when there's pain—as your number one priority.
I strongly urge you not to succumb to the temptation to pick out a few E-cises and customize your own program. It's important to do the entire menu in sequence. Dysfunctions come in layers and in clusters. The sequence is designed to systematically restore functions that serve as gateways to deeper or more inaccessible layers or clusters of dysfunction.
If an E-cise is difficult to do, stay with it. The difficulty is a measure of the magnitude of the dysfunction that it is attacking. It will get easier as you go along. But if the E-cise causes an increase in pain, stop and temporarily drop it from the routine. Try it again in a day or two; you may find that there's no longer a problem. The other E-cises may be sufficient to change the musculoskeletal interactions to allow the other to be brought back into play.
If there is _no_ improvement, consider this important question: If a method that's been so successful treating musculoskeletal disorders is ineffective—and if pain is a symptom—are you actually suffering a musculoskeletal problem, or is it something else? The continuing pain may be the symptom of another condition.
As for my point about making sure you follow the instructions, it probably doesn't need much further explanation. But it is often helpful to have someone else watch you perform the E-cises and compare what you're doing with the instructions that appear in the book.
Finally, pain can return when there is a sudden increase in the amount of physical activity or a change in the type of activity. The E-cises will make you feel better, and when that happens, it is only natural to want to start doing more. "No pain! I can dust off the PC and pull a bunch of all-nighters and weekenders" is the typical reaction. But resist it. Go easy. Gradually, build up the demands you are putting on your body so that your muscles have a chance to strengthen.
Unlike the other E-cise programs, I'm offering one menu for home use only. Why? If you are in pain, the place to be is home. No business as usual, please. I said it earlier—your health is the number one priority. When the pain abates and you've made a transition to the program for power PC users, it is then appropriate to use its office therapy menu.
**E-CISE TIPS**
• **Follow the menu in sequence**.
• **Don't pick and choose among E-cises. Do all of them in order**.
• **Honor the body's bilateral design by repeating the E-cises equally on both sides**.
• **Stop if the E-cise causes pain**.
• **Keep a slow, steady pace**.
• **Do at least one of the menus, home or office, once a day. Doing both would be ideal**.
• **If you miss a day or two, don't worry. Miss three or more—worry!**
• **On any given day, once you've run through the entire office therapy menu, feel free to take spontaneous E-cise breaks by choosing whichever one seems appropriate to the work you've been doing or the way your body is feeling**.
Home Therapy
Total Time: 15 minutes
Frequency: Daily
Special Note: Drop E-cise(s) if pain increases
### • GRAVITY DROP
**Figure 6.1**
**This E-cise (Figure 6.1) promotes hip stability and releases the muscles of the thoracic back**.
**Wearing rubber-soled shoes for traction, stand on a step or stairway as though you were climbing upward. Your feet are parallel on the same step and a shoulder-width apart. Arch your back. With one hand, hold on to the railing or another solid object for support, and edge backward until your heels are off the step and hanging in midair. Keep easing back so that more than half of each foot is off the step. Make sure your feet remain parallel, pointing straight ahead, and that they are a shoulder-width apart. Let the weight of your body press down into your heels to engage the posterior muscles of the leg. Don't bend your knees. Keep your head and shoulders back. Hold for three minutes**.
### • SITTING KNEE PILLOW SQUEEZES
**This E-cise (Figure 6.2) strengthens and stabilizes the pelvis**.
**Sit on the edge of a chair, and arch your back by rolling your hips forward. Pull your head and shoulders back, and make sure your knees and feet are in alignment with your hips. Place a foam block, thick pillow, or folded seat cushion between your knees; you'll need something six to eight inches thick. Using your inner thighs, squeeze thepillow, hold for a half beat, and release it gently. Do a total of forty squeezes, in four sets of ten. Your feet stay parallel and a hip-width apart. Don't let your stomach, upper back, or shoulders participate**.
**Figure 6.2**
**Figure 6.3**
### • STATIC WALL
**This E-cise (Figure 6.3) releases the muscles of the torso, repositions the shoulders, and promotes hip stability**.
**Lie on your back at the foot of a wall. Place your legs straight up against the wall (so that your upper torso and legs are at ninety degrees), with your feet a hip-width apart. Tighten your thighs, and flex your toes and feet back toward the floor. Get your buttocks and hamstrings (the posterior of the thighs) as close to the wall as you can. The smaller the gap, the better. But if your hips come off the floor, back off until they are flat. Concentrate on relaxing your upper body. Keep the toes flexed equally on each foot, and don't let the feet flare out of parallel. Hold this position for three to five minutes**.
### • SITTING FLOOR
**This E-cise (Figure 6.4) establishes proper engagement of the muscles of the trunk, causes shoulder retraction to strengthen the upper body, and stabilizes the hips**.
**Sit on the floor withyour back against a wall and your legs straight out in front of you. Your feet should be a hip-width apart. Squeeze your shoulder blades together, and hold. Do not lift or cock your shoulders. Keep your head back, tighten your thighs, and flex your feet so your toes are pointing back toward you. Your arms can be at your sides or relaxed atop your thighs. Hold this position for four to six minutes**.
**Figure 6.4**
### • PELVIC TILTS
**This E-cise (figures 6.5a and b) strengthens and releases the muscles of the torso**.
**Lie on your back with your knees bent, your feet flat on the floor, and your hands resting at your sides, palms up. Roll your hips toward your head to flatten your lower back into the floor (a). Do not lift your hips off the floor. Then roll your hips away to make the lower back arch off the floor, creating a space between the floor and your back (b). Do these rolls in a smooth continuous motion as youflatten and arch the back. Remember to breathe in sync with the hip movement—inhale up, exhale down. Do ten tilts. Don't move your feet or flap your knees**.
**Figure 6.5a**
**Figure 6.5b**
### • HIP CROSSOVER
**This E-cise (figures 6.6a and b) encourages external rotation of the femur (the thigh bone), thereby strengthening and stabilizing the pelvis**.
**Lie on your back with both knees bent and your feet flat on the floor. Cross your left ankle over your right knee, and press the left knee out toward the feet (a). While maintaining this position, lower your left foot to the right side and place it flat on the floor (b). The right knee stays bent, and both feet are on the floor. Keep the left knee pressing up toward the ceiling to feel a stretch in the area of your left hip. Hold this position for thirty seconds to one minute. Come out of this the same way you went in. Then reverse the directions and repeat on the other side**.
**Figure 6.6a**
**Figure 6.6b**
### • PELVIC TILTS
**Let's do a second set for good measure, now that we've worked on the rotation of the femur. This E-cise demands that the muscles of your torso relax and contract, relax and contract, instead of staying locked in contraction**.
**Use the E-cise instructions and photos onthis page and this page (figures 6.5a and b)**.
### • THREE-POSITION TOE RAISES
**Figure 6.7a**
**This E-cise (figures 6.7a, b, and c) runs both hips through the full flexion-neutral-extension cycle**.
**_Position one_ (a): Near a closed door or wall, stand with your feet a hip-width apart and parallel. Pull your head and shoulders back, and roll the hips forward into extension to arch the lower back. Raise up on your toes, keeping your weight evenly distributed on both feet and your knees straight. Come straight up, don't rock forward. Make sure your weight isn't sloshing to the inside or outside of the feet; keep it even. Raise and lower yourself ten times**.
**_Position two_ (b): Pull your head and shoulders back, and roll your hips forward into extension to arch the lower back. This time your feet should be pigeon-toed, with the big toes touching. Set the heels a hip-width apart, and angle your toes inward until they touch. Check the stance to make sure your weight is balanced between the two feet and distributed evenly over both feet. Keep the arch in your back. Raise and lower yourself ten times**.
**Figure 6.7b**
**Figure 6.7c**
**_Position three_ (c): Stand in extension with your heels together and your feet spread like a duck with the toes pointed out. Raise and lower yourself ten times. Do these slowly to prevent your feet from rolling to the inner or outer edges**.
### • SITTING CATS AND DOGS
**This E-cise (figures 6.8a and b) builds on the last by reuniting the hips to the spine and shoulders during flexion and extension**.
**Sit in a chair with your feet flat on the floor, parallel, and about a hip-width apart. Don't lean back, but sit forward toward the front. Rest your hands palms-down by your thighs. Slowly pull your head, shoulders, and hips back into extension. Feel the arch in your lower back as your head moves back to the rear. Head, hips, and shoulders should be aligned and pointing straight at the ceiling (a). When you get there, pause for half a beat, and slowly relax, letting the back round forward and the shoulders, neck, and head come with it (b). We want the back to leave extension—but don't actually force your upper torso farther than its natural stopping point, where the muscles are fully relaxed. Link each Cat and Dog into a smooth, continuous series. Your hands will track back and forth on top of your thighs. Do ten. Remember to breathe**.
**Figure 6.8a**
**Figure 6.8b**
#
**HOME THERAPY**
• **Arm Circles**
• **Elbow Curls**
• **Foot Circles and Point Flexes**
• **Sitting Floor Twist**
• **Cats and Dogs**
• **Kneeling Groin Stretch**
• **Upper Spinal Floor Twist**
• **Cats and Dogs**
• **Downward Dog**
• **Air Bench**
**OFFICE THERAPY**
• **Standing Chair Stretch**
• **Sitting Overhead Extension**
• **Standing Quad Stretch**
• **Sitting Cats and Dogs**
• **Sitting in Extension**
What I'm offering here is designed as a way for people who use computers for up to roughly three hours a week to avoid problems. Although this usage amounts to only about twenty-five minutes a day, it's time enough to check e-mail, look at the weather report, and do a little on-line shopping. Clearly, the PC is being used not as a major tool, but just enough to make a difference to your musculoskeletal system. Twenty-five minutes of extra demand a day are being put on a system that is already in need of structural stability, muscular strength, and skeletal alignment.
**E-CISE TIPS**
• **Follow the menu in sequence**.
• **Don't pick and choose among E-cises. Do all of them in order**.
• **Honor the body's bilateral design by repeating the E-cises equally on both sides**.
• **Stop if the E-cise causes pain**.
• **Keep a slow, steady pace**.
• **Do at least one of the menus, home or office, once a day. Doing both would be ideal**.
• **If you miss a day or two, don't worry. Miss three or more—worry!**
• **On any given day, once you've run through the entire office therapy menu, feel free to take spontaneous E-cise breaks by choosing whichever one seems appropriate to the work you've been doing or the way your body is feeling**.
**Home Therapy**
**Total Time: 20 minutes**
**Frequency: Daily**
### • ARM CIRCLES
**This E-cise (figures 7.1a and b) is a ball-and-socket booster. Shoulder joints are bifunctional—they hinge forward and back, and they rotate in a ball-and-socket configuration. Using a mouse or keyboard means a lot of hinge demand, which often locks the shoulder in the forward position. This can happen in either the right or left shoulder—or both at the same time. Arm Circles counteract that tendency**.
**Stand with your head up, feet parallel about a hip-width apart, and arms at your sides. Curl the fingers of each hand into a light fist with your thumbs straight. (This is known as a "golfer's grip.") Raise your arms out to your sides, keeping the elbows and arms straight, palms down, and your thumbs pointing forward (a). Lift your arms until they are level with your shoulders. If one shoulderwants to pop up or swing forward, lower both until they stay level. (Pay attention to this, too, when you start doing the circles). Now squeeze your shoulder blades together slightly, and rotate the arms forward in the direction the thumbs are pointing. Make a roughly six-inch-diameter circle. Keep your wrists and elbows straight—the circles must come from the shoulders. Do this twenty-five times at a slow to moderate pace. Reverse the circles by turning the palms up and thumbs back (b). Crank the thumbs around so that your palms are level. Do another twenty-five. Then repeat back the other way for another twenty-five, and repeat again with the same count to the rear, so that you do a total of fifty in each direction. Remember to breathe**.
**Figure 7.1a**
**Figure 7.1b**
### • ELBOW CURLS
**This E-cise (figures 7.2a and b) "oils" the shoulder's hinge function. It also protracts and retracts the shoulder blades across the rib cage, to prevent them from getting too comfortable in the forward position as you lean toward the PC. They are harder than they look. Take your time. The photo shows the model against a wall, but with this E-cise I want you to move away from the wall**.
**Figure 7.2a**
**Figure 7.2b**
**Stand with your feet parallel, a hip-width apart. With your hands in the golfer's grip (see Arm Circles), place the flat area on the back of the index and middle fingers, between the first and second knuckle joints, on the temples in front of your ears; the thumbs extend downward, parallel with the cheeks. Draw your elbows back evenly and in line with the shoulders (a). Don't allow one shoulder to be lazy and not come all the way back. Fromthis starting position, slowly swing your elbows forward until they touch in front (b). Keep your knuckles touching your temples, the thumbs fully extended. Your head should stay erect, not wobble or seesaw. Equalize the work and tension in both sides. Breathe deeply. Do twenty-five Elbow Curls. Each time your elbows touch counts as one curl. If you can't do twenty-five at first, reduce the number and slowly build up to it**.
### • FOOT CIRCLES AND POINT FLEXES
**Now that we've worked on your shoulders, this E-cise (Figure 7.3) prepares your ankles to join the load-bearing team. It promotes blood flow, which is impeded by sitting at your PC. Muscular contraction and relaxation assist the heart with its pumping action, particularly in the lower extremities. This E-cise also strengthens the pelvis to better support the body in a fully upright posture**.
**Lie on your back with one leg extended flat on the floor and the other bent toward your chest with your foot off the floor. Clasp your hands behind your bent knee for support, and circle the foot clockwise thirty times. Meanwhile, keep your other foot on the floorwith the toes pointed straight toward the ceiling. It's not necessary to flex this foot, just keep it straight. When you've done thirty circles, reverse the direction of the circling foot and repeat for another thirty. Change legs, and circle the other foot clockwise thirty times, then counterclockwise thirty times. Make sure the knees stay absolutely still, with the movement coming from the ankle, not the knee. The pace should be slow to moderate. Do the Foot Circles on both legs, in both directions, before starting the Point Flexes**.
**Figure 7.3**
**For Point Flexes, after completing the last set of circles, stay in the same position on your back with one leg extended and the other bent at the knee and held off the ground with your hands clasped behind your knee. On this leg—the one that is bent—bring your toes back toward the shin to flex. Then reverse the direction to point your foot. Do it twenty times. Switch legs, and repeat another twenty times**.
### • SITTING FLOOR TWIST
**Because the PC is directly in front of you, you tend to stay in flexion while work is under way, which puts the spine and hip-extensor muscles under stress. This E-cise (Figure 7.4) counters the propensity for the extensors to lose bilateral strength and function. As you can see, the twisting action wrings out both sides equally**.
**Sit on the floor withyour legs extended in front. Bend your left leg, and cross it over the right knee. Keep the left foot flat on the floor and running parallel to the right leg. The right foot should be pointed at the ceiling. Place your right elbow outside your left knee, twisting the torso to the left. Your head is now facing the rear. Tighten the thigh muscles of the straight leg, and flex the ankle-foot of this leg toward the knee. Place your left hand behind you on the floor for support. Put an arch in your lower back. Hold for one minute (with the ankle-foot flexed), then repeat on the other side. Remember to breathe. Exhaling and inhaling smoothly helps the flexor muscles to relax and allows the extensors to contract**.
**Figure 7.4**
### • CATS AND DOGS
**This E-cise (figures 7.5a and b) provides total range of motion in the pelvis and the back in an anatomically correct and safe manner. It promotes breathing and better circulation. It's very effective, as you may know if you've done yoga**.
**Figure 7.5a**
**Figure 7.5b**
**Get down on the floor on your hands and knees. Make a "table" by aligning your hands under your shoulders and your knees and thighs under your hips. Your arms should be straight and your thighs parallel to them. Keep your legs and feet parallel to each other, as well. The feet are relaxed and resting across the top side of the toes, not flexed or up on the toes. Make sure your weight is distributed evenly. Smoothly round your back upward as your head curls under, to create a curve that runs from the buttocks to the neck—this is a cat with an arched back (a). Smoothly sway the back down while bringing your head up—this is the perky dog (b). Make these two moves continuously back and forth—don't keep them choppy and distinct. Do one set of ten. Exhale as you move into the cat position, inhale during the dog. Make sure, with the dog, that your head comes fully back and up so that you are looking straight ahead and your shoulder blades collapse toward each other. Take your time. The pace should be slow, but not so slow that it breaks the flow between the cat and dog positions**.
### • KNEELING GROIN STRETCH
**You should feel this E-cise (Figure 7.6) in the groin area, thighs, and hips. It releases tension and builds strength**.
**Kneel on the floor. Extend your left leg with the left foot flat on the floor and placed about two to three feet in front of your body. Get your foot out far enough so that your bent knee is behind your left ankle. Keep both knees and feet a hip's-width apart, without twisting your torso to the left or right. With your head up and back straight, put your interlaced hands palm-down on top of your left knee, and lunge forward. The hands are there for balance and to keep your shoulders square. The lunge will carry your left knee forward to a point directly over your left ankle. We don't want the knee to go beyond the ankle. If it does, your left foot needs to be moved farther out in front of your body. Feel the stretch in the hips, groin, and thigh. Hold this position for one minute. Repeat on the other side**.
**Figure 7.6**
### • UPPER SPINAL FLOOR TWIST
**This E-cise (Figure 7.7) puts the neck, arms, and shoulders on the same plane, where they belong in order to interact properly**.
**Lie on your side with your knees together and bent. This will put your knees at a right angle to your trunk. Keeping the elbows straight and the palms together, extend both arms along the floor, level with your shoulders, in the direction of your knees, parallel with the bent legs. Slowly lift the upper arm up and over to rest behind you on the floor palm-up, while you turn your head to face the ceiling. Adjust this arm position, if necessary, by finding a shoulder slot that's comfortable. Relax and breathe deeply. Allow gravity to settle the extended arm to the floor along its entire length, from fingers to shoulder. Meanwhile, make sure the knees don't slide apart. You can hold them in place with the other hand (as the model is doing). When the shoulders have leveled out (it may take several minutes and perhaps several sessions to achieve this fully), lift the extended arm and return it to the starting position while exhaling. Hold for at least three minutes, or longer if you have the time and the shoulder hasn't come down onto the floor. Repeat on the other side**.
**Figure 7.7**
### • CATS AND DOGS
**Yes, we're going to do this one again**.
**See E-cise instructions and photos onthis page–this page (figures 7.5a and b)**.
### • DOWNWARD DOG
**Downward Dog (figures 7.8a and b) uses all the extensor functions on the backside of your body. It's also great for colon and bladder functions, which are compromised by prolonged sitting**.
**Assume the dog position (see Cats and Dogs) (a). Now curl your toes under, and push with your legs to raise your hips and torso, until you are off your knees and your weight is being supported by your hands and feet. Keep pushing until your hips are higher than your shoulders and have formed a tight stable triangle. Your knees should be straight, your calves and thighs tight (b). Don't let your feet flare outward; keep them pointing straight ahead in line with the hands, which need to stay in place—no creeping! Your backshould be flat, not bowed, as the hips push up to create the triangle. Breathe. If you cannot bring your heels flat onto the floor, don't force them. Contract the muscles slowly and steadily to their natural stopping point. You'll know it when you get there. Hold for one minute. It may take several days or weeks to get the heels flat. The muscles will contract a little more each time**.
**Figure 7.8a**
**Figure 7.8b**
### • AIR BENCH
**The Air Bench (Figure 7.9) promotes lower-leg, thigh, and hip strength, and it relaxes the muscles of the torso. These are all functions we need to be pain free at the PC**.
**The best way to get into the starting position is to stand with your back to a wall. Press your hips and the small of your back into the wall. At the same time, walk your feet forward and simultaneously slip down the wall surface into a sitting position. Stop when you've reached approximately a ninety-degree angle. Your knees should be over your ankles, not your toes. (You should be able to see your toes.) If you feel pain in your kneecaps, raiseyour body up the wall to relieve the pressure. Press the low back and midback against the wall, and feel the quadriceps working along the tops of the thighs. Hold for three minutes. Breathe. This can be a struggle. You can start by doing the Air Bench for a few seconds and build to a minute, extend it to two, and then go for three. I've worked with NFL running backs who couldn't get beyond ten seconds at first. When you are finished, scoot back up the wall and walk around for a few minutes**.
**Figure 7.9**
**Office Therapy**
**Total Time: 5 minutes**
**Frequency: At least twice a week**
**Special Note: Remove your shoes**
### • STANDING CHAIR STRETCH
**This E-cise (Figure 7.10) relaxes the muscles of the thoracic back by encouraging hip and lumbar extension, then tops that off with a proper shoulder position. The limited range of motion needed to operate a PC—and most other modern devices—isn't enough to stimulate this interaction**.
**Place one foot on the seat of a chair with your knee bent and the other foot on the floor. (This leg is straight.) Both feet should be pointed straight ahead. Lean your hips and torso toward the chair so that your front knee is over your ankle. Interlace your fingers, place your hands on the back of your head, and push your elbows back. Do not shrug your shoulders. Make sure your back leg remains straight throughout the exercise. Breathe. Hold this position for thirty seconds. Repeat on the other side**.
**Figure 7.10**
### • SITTING OVERHEAD EXTENSION
**By reaching out toward a keyboard or mouse and holding that position, the scapula (part of the shoulder blade) protracts and stays that way. It needs encouragement to retract. A pilot doesn't fly his plane with the wheels down. You shouldn't fly your PC with your shoulder blades hanging out. This E-cise (Figure 7.11) delivers hip extension, relaxes the anterior muscles of the torso, and promotes scapular retraction in the shoulder**.
**Figure 7.11**
**Sit in a chair with your feet flat on the floor, parallel, and about a hip-width apart. Don't lean back—sit forward toward the front edge of the chair. Pull your head and shoulders back, and roll your hips forward and under into extension. You want an arch in your lower back. Your head, hips, and shoulders should be aligned and pointing straight at the ceiling. Interlace your fingers with the palms toward your stomach. Raise your arms, fingers still entwined straight over your head, and roll the palms of your hands toward the ceiling. Tip your head back, and look upward at the back of your hands. Make sure your shoulders are back and the hips are still in extension. Don't shrug your shoulders. Your arms should be on either side of your head, lightly touching your ears. If they're not, and the head and ears are tipped back behind the arms, then your arms and upper body are not fully vertical; push your arms up and back. You'll feel your hips, lower back, and shoulders adjust and come into better alignment. Hold this position for thirty seconds. Remember to breathe, which will be difficult at first**.
### • STANDING QUAD STRETCH
**This E-cise (Figure 7.12) takes the tension off the secondary muscles that flex the pelvis. These muscles end up doing double duty when the primaries are weakened by long periods of being hunkered down in a chair**.
**Figure 7.12**.
**Stand on one foot, and bend the other leg back, placing the top of the foot on a block, a stool, or the back of a chair. You'll want about two and a half feet of elevation, although it depends on how tall you are. The higher the block, the more stretch you'll feel in the quadriceps. Keep your hips and shoulders square and your knees even, and tuck your hips under to feel the stretch. (Roll them back to create an arch in your back.) Hang on to something for balance. Hold this position for one minute, then switch to the other side**.
### • SITTING CATS AND DOGS
**This E-cise (Figure 7.13a and b), like ordinary Cats and Dogs, promotes mobility in the pelvis and back. Doing it while seated provides the additional feature of loading the hip joints, which encourages a vertical posture**.
**Sit in a chair with your feet flat on the floor, parallel, and about a hip-width apart. Don't lean back, but sit forward toward the front. Rest your hands palms-down by your thighs. Slowly pull your head, shoulders, and hips back into extension. Feel the arch in your lower back as your head moves back to the rear. Head, hips, and shoulders should be aligned and pointing straight at the ceiling (a). When you get there, pause for half a beat, and slowly relax, letting the back round forward and the shoulders, neck, and head come with it (b). We want the back to leave extension—but don't actually force your upper torso farther than its natural stopping point, where the muscles are fully relaxed. Link each Cat and Dog into a smooth, continuous series. Your hands will track back and forth on top of your thighs. Do ten. Remember to breathe**.
**Figure 7.13a**
**Figure 7.13b**
### • SITTING IN EXTENSION
**This E-cise (Figure 7.14) strengthens key posture muscles and reminds them what extension and proper alignment feel like. The more the posture muscles are put into this position, the better able they are to hold it on their own. If you can maintain this posture at the PC without deliberately thinking about it, there's little likelihood you'll ever experience computer pain syndrome. That's the alignment and function we're striving for with these E-cises**.
**Sit in a chair with your feet flat on the floor, parallel, and about a hip-width apart. Pull your head, shoulders, and hips back and into extension (arch your lower back). Breathe. Don't just yank your shoulders back or leave the head behind—head, shoulders, and hips must go together. Keep your feet in place. Balance the weight on both cheeks of your buttocks. Hold this position for one minute, and then relax**.
**Figure 7.14**
#
**HOME THERAPY**
• **Arm Circles**
• **Forearm Stretch**
• **Wall Clock**
• **Static Back**
• **Pullovers in Static Back**
• **Pullover Presses in Static Back**
• **Cobra on Elbows**
• **Supine Groin Stretch**
• **Upper Spinal Floor Twist**
• **Cats and Dogs**
• **Air Bench**
**OFFICE THERAPY**
• **Sitting in Extension**
• **Elbow Curls in Extension**
• **Sitting Assisted Hip Lift**
• **Three-Position Toe Raises**
• **Sitting Cats and Dogs**
The therapy in chapter 7 was designed for occasional PC users. I suspect, though, that eventually they will be a rare breed, and that the majority will fall into the category of moderate users. I'm probably being conservative. If PCs take over school classrooms—it's probably more realistic to say _when_ they take over—and come anywhere close to matching TV as a popular medium, the vast majority of us will be power PC users. And that doesn't even take into account business applications.
We're not there yet, so by my definition a moderate PC user is someone who does not depend on a computer solely for his or her livelihood and uses one every day for about an hour in total. A good example would be a sales representative. He or she keeps her contacts on a PC or digital organizer, uses the computer for e-mail, and prepares proposals for customers. Maybe there's time for a video game. Occasionally a couple of back-to-back hours may be spent at the keyboard.
This extended PC use, while it may happen only once or twice a week, is a key reason for having this separate category. An hour or more of concentrated physical effort shouldn't be a big deal. But if I asked you to dig a hole for an hour without stopping, would it be taxing? Probably. And it would be particularly heavy going if you weren't used to doing that kind of work.
Why is that? For a moment forget about skeletal alignment and stability. The simple answer is that your muscles aren't strong enough. The same answer explains why a marathon run on the PC is also taxing. You're making thousands of contractions with muscles that otherwise, in the course of a day, contract only a few hundred times at most. Some hardly contract at all until they come to the PC. If you drive home from work for forty-five minutes, what are the muscles of your hands doing? Right—gripping the steering wheel. If you take the bus or the train, what are they doing? Holding a newspaper or a book, I'll bet.
The muscular effort was minimal in either case, compared with the PC. But as you know by now, simple muscular strength is not the primary issue. Dysfunctions are a wall standing between you and your primary muscles. The E-cises in this chapter restore access to these muscles and work on skeletal alignment and stability.
**E-CISE TIPS**
• **Follow the menu in sequence**.
• **Don't pick and choose among E-cises. Do all of them in order**.
• **Honor the body's bilateral design by repeating the E-cises equally on both sides**.
• **Stop if the E-cise causes pain**.
• **Keep a slow, steady pace**.
• **Do at least one of the menus, home or office, once a day. Doing both would be ideal**.
• **If you miss a day or two, don't worry. Miss three or more—worry!**
• **On any given day, once you've run through the entire office therapy menu, feel free to take spontaneous E-cise breaks by choosing whichever one seems appropriate to the work you've been doing or the way your body is feeling**.
**Home Therapy**
**Total Time: 40 minutes**
**Frequency: Daily**
### • ARM CIRCLES
**This E-cise is a ball-and-socket booster. Shoulder joints are bifunctional—they hinge forward and back, and they rotate in a ball-and-socket configuration. Using a mouse or keyboard means a lot of hinge demand, which often locks the shoulder in the forward position. This can happen in either the right or left shoulder—or both at the same time. Arm Circles counteract that tendency**.
**You may notice that each shoulder responds differently to this E-cise. This indicates that a bilateral structure has become unilateral. Don't favor one side or the other. In time they will strengthen and stabilize equally**.
**Stand with your head up, feet parallel about a hip-width apart, and arms at your sides. Curl the fingers of each hand into a light fistwith your thumbs straight. (This is known as a "golfer's grip.") Raise your arms out to your sides, keeping the elbows and arms straight, palms down, and your thumbs pointing forward (a). Lift your arms until they are level with your shoulders. If one shoulder wants to pop up or swing forward, lower both until they stay level. (Pay attention to this, too, when you start doing the circles.) Now squeeze your shoulder blades together slightly, and rotate the arms forward in the direction the thumbs are pointing. Make a roughly six-inch-diameter circle. Keep your wrists and elbows straight—the circles must come from the shoulders. Do this twenty-five times at a slow to moderate pace. Reverse the circles by turning the palms up and thumbs back (b). Crank the thumbs around so that your palms are level. Do another twenty-five. Then repeat back the other way for another twenty-five, and repeat again with the same count to the rear, so that you do a total of fifty in each direction. Remember to breathe**.
**A**.
**B**.
### • FOREARM STRETCH
**This E-cise (Figure 8.1) releases the tension in your wrists and forearms through the leverage provided by holding the shoulders in the correct position. Gradually you'll be able to position your hands higher on the wall, which should provide you with valuable information about the crucial interaction of the shoulders with the arms, forearms, wrists, and hands. You'll actually feel the interaction becoming less restricted and more complete**.
**Facing a wall, stand with your feet straight and a hip-width apart. Your toes should be four to six inches from the wall. Bend your elbows to a ninety-degree angle, and place your palms against the wall with your fingers pointing down. Where you're able to place your hands will depend on the extent of shoulder function. The less you have, the lower they will be. If you feel wrist pain, lower your handson the wall. If you can't find a hand position without wrist pain, you need to turn to chapter 6 and do the E-cise program there. Otherwise, lean against the wall with the weight on your hands, while squeezing your shoulder blades together. Make sure the heels of your palms are squarely on the wall. Don't shrug your shoulders or roll them toward the wall. They need to be back. Keep your stomach muscles relaxed, and allow the low back to arch. Hold for thirty seconds**.
**Figure 8.1**
**Figure 8.2a**
### • WALL CLOCK
**Your shoulder blades are supposed to move—up and down, back and forth, and in clockwise and counter-clockwise rotation. When they don't, much of the dynamic relationship with the torso is lost, and much of the shoulders' biomechanical capacity is canceled out. This means that arm and hand movement at your PC's keyboard relies mostly on the elbow and wrist. This E-cise (figures 8.2a, b, and c) remedies that and releases the tension in the compensating muscles of your upper back and neck. The Wall Clock is a three-position E-cise**.
**_Position one_ (a): Face the wall, and turn your feet inward in a pigeon-toed stance up against the wall. Raise your arms over your head in the twelve o'clock position. Your hands are gathered in a light fist with your thumbs straight, and the palms are facing each other. With your arms straight and still in contact with the wall, rotate your arms outward from the wall at your shoulders, with the thumbs flaring back at an angle from the wall. Hold this position for one minute**.
**Figure 8.2b**
**_Position two_ (b): Remain in the same pigeon-toed stance. Place your arms over your head in the ten-after-ten position. Your elbows are straight, while your shoulders are rotated away from the wall. The thumbs are pointing away from the wall. Hold for one minute**.
**_Position three_ (c): Remain in the same stance. Place your arms over your head in the quarter-after-nine position. Your elbows are straight, while your shoulders are rotated away from the wall, with the thumbs pointing away from the wall**. **Hold for one minute. If there is pain in your elbow in this position, you need to drop this menu and use the pain menu inchapter 6**.
**Figure 8.2c**
### • STATIC BACK
**This E-cise (Figure 8.3) will settle the hips to the floor and allow the muscles of the upper torso to relax. Imagine what your hips are doing at the PC keyboard. Right—they are tipped back in flexion, instead of offering the spine a flat, neutral platform**.
**Lie on your back, with both legs bent at right angles resting on a chair or block. Rest your hands on your stomach or the floor, below shoulder level, with the palms up. Let the back settle into the floor. Breathe from your diaphragm. The abdominal muscles should rise as you inhale and fall as you exhale. Hold this position for five to ten minutes**.
**Figure 8.3**
**Figure 8.4a**
**Figure 8.4b**
### • PULLOVERS IN STATIC BACK
**This E-cise (figures 8.4a and b) promotes the range of motion in your shoulders and releases the muscles of the neck and upper back. It also helps the diaphragm to work properly.**
**Stay in the basic Static Back position. Clasp your hands together, and extend your arms straight toward the ceiling (a). Continue to hold both arms straight, and bring them back behind your head, either to the floor or as far as they will go without bending (b). Then return to the starting position. Relax your abdominal muscles and don't rush. Do two sets of fifteen each**.
### • PULLOVER PRESSES IN STATIC BACK
**This E-cise (Figure 8.5) works to strengthen the muscles that hold the shoulder blades against the rib cage, instead of leaving them protracted**.
**Continue in the Static Back position. Place an eight-inch blockor a stack of books about an arm-length beyond your head. You'll want to be able to rest your hands squarely on the block during this E-cise. With hands clasped and arms straight, press and release into the block. Do not contract your abdominal muscles. Let your lower back muscles react, and keep your feet parallel. Do three sets of ten**.
**Figure 8.5**
### • COBRA ON ELBOWS
**This E-cise (Figure 8.6) strengthens the lower back muscles, releases tight abdominal muscles, and stabilizes the spine**.
**Lie on the floor on your stomach with your legs straight and your feet pigeon-toed. Use both elbows bent at ninety degrees to prop up the upper body. The elbows should be directly under the shoulder, the forearms straight and parallel. Make lightly clenched fists, with your thumbs pointing straight up. Your head looks straight ahead. Relax your buttocks muscles. Hold for thirty seconds**.
**Figure 8.6**
**Figure 8.7**
### • SUPINE GROIN STRETCH
**This E-cise (Figure 8.7) relaxes and/or engages the primary muscles of hip flexion. It allows the pelvis to move into a neutral position, which isn't happening on its own**.
**Lie on your back, with one leg resting on a two-foot-high block or chair, the knee bent at a ninety-degree angle. The other leg is extended straight out and resting on the floor. Make sure both legs are aligned with the hips and shoulders. The foot of your extended leg should be propped upright to prevent it from rolling to one side. (Use something like a stack of books or a five-gallon paint can.) Relax in this position for at least ten minutes, then switch sides and remain for another ten minutes**.
### • UPPER SPINAL FLOOR TWIST
**This E-cise can be a real eye-opener for people who don't think they have shoulder problems. One side will flatten to the floor readily,but the other may stay elevated. It means that one shoulder is having trouble returning to a neutral position**.
**Lie on your side with your knees together and bent. This will put your knees at a right angle to your trunk. Keeping the elbows straight and the palms together, extend both arms along the floor, level with your shoulders, in the direction of your knees, parallel with the bent legs. Slowly lift the upper arm up and over to rest behind you on the floor palm-up, while you turn your head to face the ceiling. Adjust this arm position, if necessary, by finding a shoulder slot that's comfortable. Relax and breathe deeply. Allow gravity to settle the extended arm to the floor along its entire length, from fingers to shoulder. Meanwhile, make sure the knees don't slide apart. You can hold them in place with the other hand (as the model is doing). When the shoulders have leveled out (it may take several minutes and perhaps several sessions to achieve this fully), lift the extended arm and return it to the starting position while exhaling. Hold for at least three minutes, or longer if you have the time and the shoulder hasn't come down onto the floor. Repeat on the other side**.
### • CATS AND DOGS
**This E-cise works you through cycles of flexion-extension from your hips to your head, providing total range of motion in the pelvis and the back in an anatomically correct and safe manner. It promotes breathing and better circulation. It's very effective, as you may know if you've done yoga.**
**Get down on the floor on your hands and knees. Make a "table" by aligning your hands under your shoulders and your knees and thighs under your hips. Your arms should be straight and your thighs parallel to them. Keep your legs and feet parallel to each other as well. The feet are relaxed and resting across the top side of the toes, not flexed or up on the toes. Make sure your weight is distributed evenly. Smoothly round your back upward as your head curls under, to create a curve that runs from the buttocks to the neck—this is a cat with an arched back (a). Smoothly sway the back down while bringing your head up—this is the perky dog (b). Make these two moves continuously back and forth—don't keep them choppy and distinct. Do one set of ten. Exhale as youmove into the cat position, inhale during the dog. Make sure, with the dog, that your head comes fully back and up so that you are looking straight ahead and your shoulder blades collapse toward each other. Take your time. The pace should be slow, but not so slow that it breaks the flow between the cat and dog positions**.
**A**.
**B**.
### • AIR BENCH
**This E-cise puts the ankles, lower legs, thighs, and hips to work in unison without relying on the back muscles for help. The Air Bench promotes lower-leg, thigh, and hip strength, and it relaxes the muscles of the torso. These are all functions we need to be pain free at the PC**.
**The best way to get into the starting position is to stand with your back to a wall. Press your hips and the small of your back into the wall. At the same time, walk your feet forward and simultaneously slip down the wall surface into a sitting position.**
**Stop when you've reached approximately a ninety-degree angle. Your knees should be over your ankles, not your toes. (You should be able to see your toes.) If you feel pain in your kneecaps, raise your body up the wall to relieve the pressure. Press the low back and midback against the wall, and feel the quadriceps working along the tops of the thighs. Hold for three minutes. Breathe. This can be a struggle. You can start by doing the Air Bench for a few seconds and build to a minute, extend it to two, and then go for three. I've worked with NFL running backs who couldn't get beyond ten seconds at first. When you are finished, scoot back up the wall and walk around for a few minutes**.
**Office Therapy**
**Total Time: 5 minutes**
**Frequency: At least twice a week**
**Special Note: Remove your shoes**
### • SITTING IN EXTENSION
**After the first few times, doing this E-cise will stop feeling strange, and your vertical load-bearing muscles will get stronger and stronger**.
**Sit in a chair with your feet flat on the floor, parallel, and abouta hip-width apart. Pull your head, shoulders, and hips back and into extension (arch your lower back). Breathe. Don't just yank your shoulders back or leave the head behind—head, shoulders, and hips must go together. Keep your feet in place. Balance the weight on both cheeks of your buttocks. Hold the position for one minute, and then relax**.
### • ELBOW CURLS IN EXTENSION
**This E-cise (figures 8.8a and b) releases the tight muscles of the lower back, thereby promoting range of motion in the shoulder and easing the tense muscles of the upper back and neck**.
**Sit in a chair. Move toward the front edge of the seat, away from the back. Set your feet flat on the floor, parallel, and a hip-width apart. Pull your head and shoulders back, while arching your back and rolling your hips forward into extension. Relax your stomach muscles, and breathe. Curl the fingers of both hands into a light fist with your thumbs straight. (This is known as the "golfer's grip.") Place the flat area formed between the first and second knuckle joints of the index and middle fingers on the temples in front of your ears; the thumbs extend downward, parallel with the cheeks**.
**Figure 8.8a**
**Figure 8.8b**
**Draw your elbows back evenly and in line with the shoulders (a). Don't allow one of them to be lazy and not come all the way back. Equalize the work and tension in both sides. From this starting position, slowly swing the elbows forward until they touch in front (b). Keep the knuckles in contact with the temples, the thumbs fully extended, and the head erect. Don't let the hips or head wobble or seesaw. Breathe deeply. Do fifteen Elbow Curls**.
### • SITTING ASSISTED HIP LIFT
**This E-cise (Figure 8.9) activates external rotation of the femur (the thigh bone), thereby promoting hip extension and relaxing the muscles of the lower back and torso. Through no fault of the PC, your hips may rotate right or left and stay that way. We need to give them the capacity to return to a balanced, symmetrical position**.
**Figure 8.9**
**Sit in a chair, toward the front edge of the seat. Your feet should be flat on the floor, parallel, and a hip-width apart. Pull your head and shoulders back, and roll your hips forward into extension. Imagine a vertical line extending through your hips, shoulders, and head to the ceiling. Bend your right leg, and place the ankle on your left knee. You may rest a hand on your bent right knee and use the other to help keep your right foot in place. Without pressing down with the hand, use the muscles of the thigh and hip area to draw your right bent knee toward the floor. Tighten the muscles slowly—you'll feel them pull the leg downward. Hold for thirty seconds. Repeat on the other side. You'll probably find that one side is tighter than the other and will give more resistance when you lower the knee**.
**Once you do both, return to the tighter side for another thirty seconds. You will have more downward play this time**.
### • THREE-POSITION TOE RAISES
**This E-cise (figures 8.10a, b, and c) causes your pelvis to move into a neutral (planar) position while aligning the vertical load-bearing joints of the posture. We want the pelvis to sit flat, as if a shelf. It also runs both hips through the full flexion-neutral-extension cycle**.
**_Position one_ (a): Near a closed door or wall, stand with your feet a hip-width apart and parallel. Pull your head and shoulders back, and roll the hips forward into extension to arch the lower back. Raise up on your toes, keeping your weight evenly distributed on both feet and your knees straight. Come straight up, don't rock forward. Make sure your weight isn't sloshing to the inside or outside of the feet; keep it even. Raise and lower yourself ten times**.
**Figure 8.10a**
**Figure 8.10b**
**Figure 8.10c**
**_Position two_ (b): Pull your head and shoulders back, and roll your hips forward into extension to arch the lower back. This time your feet should be pigeon-toed, with the big toes touching. Set the heels a hip-width apart, and angle your toes inward until they touch. Check the stance to make sure your weight is balanced between the two feet and distributed evenly over both feet. Keep the arch in your back. Raise and lower yourself ten times**.
**_Position three_ (c): Stand in extension with your heels together and your feet spread like a duck with the toes pointed out. Raise and lower yourself ten times. Do these slowly to prevent your feet from rolling to the inner or outer edges**.
### • SITTING CATS AND DOGS
**This E-cise works you through flexion and extension while your hips and torso are under a vertical load. But your hips, lower back, shoulders, and head must all participate**.
**Sit in a chair with your feet flat on the floor, parallel, and about a hip-width apart. Don't lean back, but sit forward toward the front.Rest your hands palms-down by your thighs. Slowly pull your head, shoulders, and hips back into extension**.
**Feel the arch in your lower back as your head moves back to the rear. Head, hips, and shoulders should be aligned and pointing straight at the ceiling (a). When you get there, pause for half a beat, and slowly relax, letting the back round forward and the shoulders, neck, and head come with it (b). We want the back to leave extension—but don't actually force your upper torso farther than its natural stopping point, where the muscles are fully relaxed. Link each Cat and Dog into a smooth, continuous series. Your hands will track back and forth on top of your thighs. Do ten. Remember to breathe**.
**A**.
**B**.
#
**HOME THERAPY**
• **Static Back**
• **Abdominal Contractions in Static Back**
• **Abductor Presses in Static Back**
• **Standing Overhead Extension**
• **Elbow Curls at the Wall**
• **Static Wall with Pullbacks**
• **Static Extension Position**
• **Upper Spinal Floor Twist**
• **Pelvic Tilts**
• **Supine Groin Progressive**
• **Air Bench**
**OFFICE THERAPY**
• **Sitting in Extension**
• **Sitting Arm Circles**
• **Sitting Hip Flexor Lifts**
• **Sitting Chair Twist**
• **Sitting Cats and Dogs**
Give me your hackers, your propeller-heads, your nerds, and all the rest of the _digerati_ who know the difference between an ISP and an IPO (the IPO makes you rich, the ISP keeps you poor). Bring writers, editors, telemarketers, help desk personnel, designers, and all others who point, click, and type.
If you depend on the computer for your livelihood, this chapter is where you want to be for therapy. Timewise, I'm talking about using a PC for a minimum of more than an hour a day, every day. Is that all? Obviously, that's just the start. Six, eight, or ten hours a day may be closer to the norm for many people.
You are a member of the high-risk group. You're first to the future and in danger of being flummoxed by the pain. Not because the PC is dangerous—rather, you are living in a bubble of restricted movement for hour after hour. It's the reason why the total time for home therapy—and don't flip out!—is one hour and twenty minutes a day.
For those of you who haven't thrown this book across the room yet, that amount of time will quickly be whittled down to thirty minutes as you make progress with this E-cise program. The "time hog" that is part of this therapy program is the Supine Groin Progressive, an extremely effective E-cise for reestablishing your hips as a solid musculoskeletal foundation. But as the SGP takes hold, it needs less time. At first you'll have to invest in yourself. It's probably worth it—don't you think? There isn't much of an alternative if you want to remain on the cutting edge of the future.
**E-CISE TIPS**
• **Follow the menu in sequence**.
• **Don't pick and choose among E-cises. Do all of them in order**.
• **Honor the body's bilateral design by repeating the E-cises equally on both sides**.
• **Stop if the E-cise causes pain**.
• **Keep a slow, steady pace**.
• **Do at least one of the menus, home or office, once a day. Doing both would be ideal**.
• **If you miss a day or two, don't worry. Miss three or more—worry!**
• **On any given day, once you've run through the entire office therapy menu, feel free to take spontaneous E-cise breaks by choosing whichever one seems appropriate to the work you've been doing or the way your body is feeling**.
**Home Therapy**
**Total Time: 1 hour and 20 minutes**
**Frequency: Daily**
### • STATIC BACK
**By unloading the spine and hips, this E-cise uses gravity to relax your back muscles, which otherwise would remain in contraction and defeat the purpose of the next two strengthening E-cises. This E-cise will settle the hips to the floor and allow the muscles of the upper torso to relax. Imagine what your hips are doing at the PC keyboard. Right—they are tipped back in flexion, instead of offering the spine a flat, neutral platform**.
**Lie on your back, with both legs bent at right angles resting on a chair or block. Rest your hands on your stomach or the floor, below shoulder level, with the palms up. Let the back settle into the floor. Breathe from your diaphragm. The abdominal muscles should rise as you inhale and fall as you exhale. Hold this position for five to ten minutes**.
**Figure 9.1**
### • ABDOMINAL CONTRACTIONS IN STATIC BACK
**This E-cise (Figure 9.1) promotes the use of the diaphragm and helps release the tight muscles in your trunk. We're teaching the body that you can have a flat stomach _and_ breathe with your diaphragm, too. Most PC users roll forward at the keyboard, isolate their abs, and end up taking quick shallow breaths with their torso muscles, which operate only a small portion of the lungs**.
**In the Static Back position, inhale deeply and allow your stomach to rise. As you exhale, allow your stomach to fall. At the end of the exhalation, contract your abdominal muscles for a count of two and release. Repeat ten times**.
### • ABDUCTOR PRESSES IN STATIC BACK
**This E-cise (Figure 9.2) strengthens and releases the muscles of the pelvis that abduct the leg (that move it away from the center line), which promotes hip stability. You may notice as you do this menu that you'll start to address the PC squarely, rather than scrunching to one side or the other. Abductor Presses to the rescue!**
**Figure 9.2**
**In the Static Back position, place a strap around your knees (just above the kneecaps on the thighs). Secure the strap so that your knees are together (touching), with the feet remaining a hip-width apart. Press outward against the strap, hold for one beat, and release. You should feel your hips doing the work. Keep your upper body relaxed. Do three sets of ten each**.
### • STANDING OVERHEAD EXTENSION
**This E-cise (Figure 9.3) opens up the thoracic back and the abdominal cavity, increases oxygen flow, and strengthens the muscles of extension in the back**.
**Stand with your feet parallel, a hip-width apart. Draw your head and shoulders back, and roll your hips forward into extension. You want an arch in your lower back. Interlace the fingers of your handswith the palms toward your stomach. Raise your arms, fingers still entwined, straight over your head, and roll the palms of your hands toward the ceiling. Make sure your shoulders are back and your hips still in extension. The arms should be on either side of the head, lightly touching the ears. Tip your head back and look upward at the back of your hands. Hold for thirty seconds. Remember to breathe, which will be difficult at first**.
### • ELBOW CURLS AT THE WALL
**This E-cise eases the tension in the muscles of the upper back and neck, while promoting range of motion in the shoulder. Doing them against the wall prevents the head movement that will occur in people whose neck and shoulders are forward. I included it in the menu for light users inchapter 7, without the wall, because I've observed that most power PC users have so totally isolated their shoulder function that they cannot do Elbow Curls at first without a whole lot of head-shaking going on. Elvis wanted the hips to shake, not the head**.
**Figure 9.3**
**Stand with your back and head against a wall, with feet parallel and placed a hip-width apart. Put your hands in the golfer's grip, with fingers curled, knuckles flexed, and thumbs extended. Raise them palm-out so that the flat area on the backs of the index and middle fingers, between the first and second knuckle joints, rest onthe temples in front of the ears; your thumbs extend downward, parallel with your cheeks. Draw the elbows back evenly and in line with the shoulders until both touch the wall (a). Don't allow one of them to be lazy and not come all the way back. From this starting position, slowly swing the elbows forward until they touch in front (b). Keep the knuckles in contact with the temples, the thumbs fully extended, and the head erect. Don't allow your head to wobble or seesaw off the wall. Breathe deeply. Do twenty-five Elbow Curls**.
**A**.
**B**.
### • STATIC WALL WITH PULLBACKS
**This E-cise (Figure 9.4) engages, strengthens, and stabilizes the hip**.
**Lie on your back at the foot of a wall. Place your legs straight up against the wall (so that your upper torso and legs are at ninety degrees), with your feet a hip-width apart. Tighten your thighs, and flex your toes and feet back toward the floor. Get your buttocks and hamstrings (the posterior of the thighs) as close to the wall as you can. The smaller the gap, the better. It may take several rounds of this E-cise to be able to get close to the wall. If your hips lift off the floor, back off until they are flat. Concentrate on relaxing your upper body. This is the Static Wall position**.
**For Pullbacks, with your thighs contracted, make sure your toes are flexed toward you and your legs are straight. Pull your right heel off the wall toward you by two or three inches, then return it to the wall. Do one set of fifteen. Repeat on the other side. You'll feel this in your thighs and hips**.
**Figure 9.4**
### • STATIC EXTENSION POSITION
**This E-cise (Figure 9.5) releases the contracted muscles in your trunk and builds strength in your hips. Try reading your e-mail from a notebook computer while doing this. I'm kidding, but it's not a bad idea**.
**Get down on the floor on your hands and knees. Your hands should be about six inches forward of yourshoulders to start, rather than directly under them. Let your back and head relax toward the floor as the shoulder blades come together. Relax. There should be a pronounced arch in your back. Keep your arms straight, and shift your hips forward six to eight inches so that they are not aligned with the knees. This will also bring your shoulders into line over your wrists. Hold for one to two minutes**.
**Figure 9.5**
### • UPPER SPINAL FLOOR TWIST
**Having released your contracted shoulder and upper torso muscles with the last E-cise, this one restores full range of motion to the shoulders**.
**Lie on your side with your knees together and bent. This will put your knees at a right angle to your trunk. Keeping the elbows straight and the palms together, extend both arms along the floor, level with your shoulders, in the direction of your knees, parallel with the bent legs. Slowly lift the upper arm up and over to restbehind you on the floor palm-up, while you turn your head to face the ceiling. Adjust this arm position, if necessary, by finding a shoulder slot that's comfortable. Relax and breathe deeply. Allow gravity to settle the extended arm to the floor along its entire length, from fingers to shoulder. Meanwhile, make sure the knees don't slide apart. You can hold them in place with the other hand (as the model is doing). When the shoulders have leveled out (it may take several minutes and perhaps several sessions to achieve this fully), lift the extended arm and return it to the starting position while exhaling. Hold for at least three minutes, or longer if you have the time and the shoulder hasn't come down onto the floor. Repeat on the other side**.
### • PELVIC TILTS
**This E-cise strengthens and releases the muscles of the torso**.
**Lie on your back with your knees bent, your feet flat on the floor, and your hands resting at your sides, palms up. Roll your hips** **toward your head to flatten your lower back into the floor (a). Do not lift your hips off the floor. Then roll your hips away to make the lower back arch off the floor, creating a space between the floor and your back (b). Do these rolls in a smooth continuous motion as you flatten and arch the back. Remember to breathe in sync with the hip movement—inhale up, exhale down. Do ten tilts. Don't move your feet or flap your knees**.
**A**.
**B**.
### • SUPINE GROIN PROGRESSIVE
**This E-cise (Figure 9.6) unlocks tight hip flexor muscles, which keep the pelvis tipped down to the rear in the flexion position. It is one of the most effective dysfunction-busters for a power PC user who spends hours sitting with his or her hips cranked into flexion**.
**You need a two-foot block, bench, or chair without arms. Also obtain a stepladder, shelving, or a cabinet with drawers that can bepulled open to function like the apparatus we use in the clinic. What's required is something that steps down from fifteen inches to ten, to five, and to the floor. Lie on your back with one leg resting on the chair or block; bend the knee at a ninety-degree angle, and let the foot hang over the edge unsupported. Extend the other leg straight, and place the heel of the foot on the fifteen-inch rung of the ladder. (You can also start at ten.) Use a book or another heavy object to brace the foot in an upright position; otherwise it will want to roll outward. Hold this position for at least ten minutes. Lower the foot to the next level down, and hold for another ten minutes. Lower the foot to the next level (or to the floor, if you started at ten inches), and hold for ten minutes. Switch legs and repeat on the other side. Breathe from your diaphragm. Relax**.
**Figure 9.6**
**This E-cise is time-consuming but worth it. The ideal way to determine when you are ready to drop to the next level is to contract your thigh muscles. If there is a solid contraction in the middle of the thigh, about halfway between the hip and the knee, you are ready to lower the leg. You are not ready if the knee or hip jerks or twitches when the thigh muscles contract. Overall, what you are looking for is a relaxation and release of tension from the ankle to the groin. The more you do this E-cise, the less time it takes. Eventually, a couple of minutes at each level will be enough. Getting to that point may take anywhere from one month to over a year, depending on how entrenched your dysfunctions are. In the process, though, it's a great way to watch TV or listen to music**.
### • AIR BENCH
**This is a team-building E-cise. Your hips, knees, and ankles need to practice working together while the major muscle groups are under contraction. The Air Bench promotes lower-leg, thigh, and hip strength, and it relaxes the muscles of the torso. These are all functions we need to be pain free at the PC**.
**The best way to get into the starting position is to stand with your back to a wall. Press your hips and the small of your back intothe wall. At the same time, walk your feet forward and simultaneously slip down the wall surface into a sitting position. Stop when you've reached approximately a ninety-degree angle. Your knees should be over your ankles, not your toes. (You should be able to see your toes.) If you feel pain in your kneecaps, raise your body up the wall to relieve the pressure. Press the low back and midback against the wall, and feel the quadriceps working along the tops of the thighs. Hold for three minutes. Breathe. This can be a struggle. You can start by doing the Air Bench for a few seconds and build to a minute, extend it to two, and then go for three. I've worked with NFL running backs who couldn't get beyond ten seconds at first. When you are finished, scoot back up the wall and walk around for a few minutes**.
**Office Therapy**
**Total Time: 5 minutes**
**Frequency: Daily**
**Special Note: Remove your shoes**
### • SITTING IN EXTENSION
**Do this E-cise enough, and you won't need or want a fancy desk chair**.
**Sit in a chair with your feet flat on the floor, parallel, and about a hip-width apart. Pull your head, shoulders, and hips backand into extension (arch your lower back). Breathe. Don't just yank your shoulders back or leave the head behind—head, shoulders, and hips must go together. Keep your feet in place. Balance the weight on both cheeks of your buttocks. Hold this position for one minute, and then relax**.
### • SITTING ARM CIRCLES
**This E-cise (figures 9.7a and b) promotes hip extension and strengthens the muscles of the upper body**.
**Sit toward the front edge of a chair, with your head and shoulders back and your hips rolled forward in extension; your feet are squared about a hip-width apart, and your arms are at your sides. Put your hands in the golfer's grip, with fingers curled, knuckles flexed, and thumbs extended. Raise your arms out to your sides, keeping the elbows straight, palms down, and thumbs pointing forward (a). Lift your arms until they are level with your shoulders. If one shoulder wants to pop up or swing forward, lower both until they stay level. (Pay attention to this, too, when you start doing the circles.) Now squeeze the shoulder blades together slightly, and rotate the arms forward in the direction the thumbs are pointing. Make a roughly six-inch-diameter circle**.
**Figure 9.7a**
**Keep the elbows straight—the rotation must be in the shoulders. Do it twenty-five times. Reverse the circles by turning the palms up and thumbs back (b). Do another twenty-five. Then repeat back the other way for another twenty-five, and repeat again with the same count to the rear, so that you do a total of fifty in each direction**.
**Figure 9.7b**
### • SITTING HIP FLEXOR LIFTS
**This E-cise (Figure 9.8) is red meat for your hip flexor muscles. It is a deceptively simple strengthening routine**.
**Sit toward the front edge of a chair, with your head and shoulders back, your arms at your sides, and your hips rolled forward into extension; your feet are parallel and a hip-width apart. Keep your weight evenly balanced on both cheeks of the buttocks. Lift your right foot about an inch off the floor, using your thigh muscles. Hold it a half beat, and lower it. Do this ten times. Switchto the other leg for another count of ten. Make sure you don't lean to the side or lift with the hips. Keep the lift to an inch or less, otherwise the thigh muscles will be bypassed**.
**Figure 9.8**
### • SITTING CHAIR TWIST
**This E-cise (Figure 9.9) promotes trunk stability by strengthening those muscles and releasing tension. Your PC is never going to demand bilateral hip and trunk rotation. It's happy if you just sit there with little or no rotation at all. Problems occur when you get up and need the rotation for other purposes—like backing the car out its parking space**.
**This works best in a chair with arms. Sit with your feet on the floor, parallel, and a hip-width apart. Pull your head and shoulders back, and roll your hips forward into extension. Rotate your upper body to the right by grasping the right arm of the chair with your left hand. Bend your right arm over the chair back to grasp its left edge or the other arm. Keep your head level, and don't let your knees spread farther apart. Don't shrug your shoulders. Hold this position for twenty to thirty seconds. Breathe. Repeat on the left side**.
**Figure 9.9**
**A**.
### • SITTING CATS AND DOGS
**This E-cise is about as close as you can come to a do-it-yourself back massage. But not only does it feel good, it strengthens muscles and functions**.
**Sit in a chair with your feet flat on the floor, parallel, and about a hip-width apart. Don't lean back, but sit forward toward the front. Rest your hands palms-down by your thighs. Slowly pull your head, shoulders, and hips back into extension. Feel the arch in your lower back as your head moves back to the rear. Head, hips, and shoulders should be aligned and pointing straight at the ceiling (a). When you get there, pause for half a beat, and slowly relax, letting the back round forward and the shoulders, neck, and head come with it (b)**.
**B**.
**We want the back to leave extension—but don't actually force your upper torso farther than its natural stopping point, where the muscles are fully relaxed. Link each Cat and Dog into a smooth, continuous series. Do ten. Remember to breathe**.
#
**"When you're working at the PC, your eyes are as busy as your hands, wrists, and arms."**
Pain is a powerful motivator. It's probably the main reason you bought this book. But what if you had been in no pain or there was only a remote possibility that a painful condition might arise?
I can probably answer the question myself: _Spotted your tome in the bookstore, Pete, but bought a copy of_ Using Visual C+++ Basic6 _instead_.
Okay, I understand. Human nature is human nature. _You_ should understand, though, that symptoms of underlying musculoskeletal dysfunction can be present even when pain is absent. The E-cises in chapters 6, , , and address them effectively, but not— _not_ —if you decide that since the pain's gone, it's pointless to continue with the E-cises.
When pain abates, many people play what I call _pain-pong:_ It hurts—they do something—it stops hurting. They go back to business as usual, until it starts to hurt again. They do something, it stops hurting, and... on and on. With each cycle there is more damage and a steeper recovery curve to climb. Eventually, the pain settles in and becomes chronic.
I don't want you to play pain-pong. In this chapter and those that follow, I'm going to try and provide you with some continuing motivation, starting with good old-fashioned fear.
What is pain? Pain is a _next_ -to-last-resort symptom. Paralysis comes next.
The final stop is death.
Whoa!
I am absolutely serious. Pain is the highest form of communication that the body possesses. When it occurs, a priority message is being sent. One of the reasons that the body resorts to this rude attention-grabbing device is that we've ignored other messages that came in more genteel forms. Skeletal misalignment, for instance, is a way to notify us that something is wrong. Long before a muscle pulls or a joint swells, there is an outward visible sign—a symptom—of illness. Catch it at that stage, and there's no problem. Wait until there's damage, however, and the slide to paralysis begins.
Not long ago, I was running behind a twentysomething woman beside the railroad track that stretches along the bluff above the Pacific Ocean near my home in California. It's a spectacular place for a workout, but I was looking at her rather than at the view. She seemed very fit, yet as she ran, her knees were tracking inward instead of pushing through flexion and extension directly over her feet. It was as if she were running knock-kneed. This is a common condition, known as valgus stress. The body's weight is being projected to the inside of the knees and ankle joints. As a result the design of all these structures is seriously impaired. The shock of the foot's impact is not being absorbed squarely by either the knees or by the ankles; as they open and close, a violent torquing or lateral twisting is occurring in the joint capsules.
**KNEE KNOWLEDGE**
**A functional knee "looks" in the direction that the feet are pointing. To see how functional yours are, stand facing a full-length mirror with your feet pointed straight ahead. (Wear a pair of shorts so you can see your knees.) If the kneecap(s) squints or scrunches off to the left or right, it means your femur, the thigh bone, is being twisted and repositioned in the hip socket. This symptom of joint misalignment explains why many people with wrist and shoulder pain also have problems with their knees and ankles. It confirms how interrelated the body is from head to toe**.
Valgus stress is a symptom. In the runner's case, it's a symptom of a broken ankle. She doesn't know it, but in a week, a month, a year, five years, she will step out of the shower or off the curb and break an ankle. Maybe her knee will blow first. Either way, she is a casualty-in-waiting. The symptom is there. Once the accident happens, her days of serious running are over. There may be other recreational activities—biking or in-line skating—yet over time there will be a pattern of less and less motion.
This gradual dwindling of motion can be deceptive. The body is so strong and so innately apprehensive of immobility that it's able to adjust downward by making small sacrifices of functional movement on the assumption that the motion deficit will eventually be corrected. The decline happens gradually; it fools us into thinking we are "aging" or making lifestyle choices or that we are "too busy." Worse, we don't even notice this slide. With the loss of vertical load-bearing, little by little we forfeit our unhindered capacity to move. Incrementally, it drains away. Pain comes and goes, as do other symptoms. Discomfort sets in, accidents happen. One day there is a major event like a stroke or heart attack.
This death spiral is sobering, but its logic should give us great hope. Instead of quickly flipping a switch and shutting down, the body buys time to allow corrective action. Until very late in the game, intervention can have dramatically positive results. My objective here is to call these nonpain symptoms to your attention. Then you can take action. Better yet, the action is already an ongoing process.
## The Eyes Have It
There are estimates that 80 percent of regular PC users complain of eyestrain, eye fatigue, burning, blurring, and what have you. A good reason to continue the E-cises is that they are all working to counteract these conditions by restoring ocular muscular functions and the musculoskeletal structures that support them. Let me show you what I mean.
Take a deep breath.
Deeper.
And another.
**AIR RAID**
**The diaphragm is a large, flat, shelflike muscle that sits under the lungs. By contracting and relaxing, it pumps air in and out of the lungs. As we lose vertical load-bearing, with the head, shoulders, and rib cage moving forward and down, the diaphragm is being constricted by the structures of the thoracic and abdominal cavities. This is a major impediment to oxygen intake, which makes it more difficult for our muscles to function properly. Given the intense muscular activity in the eye, which is burning up energy at a high rate, the eyes are quick to feel this oxygen deprivation**.
You just fed your muscles and the rest of the body's tissue. All muscles, large and small, are acutely dependent on blood flow and the oxygen it delivers. Furthermore, when they are healthy and fully functional, these muscles are all instrumental in facilitating the delivery of oxygen throughout the body; some, like the diaphragm, are direct participants, while others work indirectly. Funny thing about that—somehow the lungs just don't inhale and exhale on their own.
Another funny thing: A muscle that makes few contractions is using commensurably less energy than one that makes many contractions. It seems obvious, but our big, showy muscles are not necessarily the major consumers of the body's store of energy. Although relatively small, the ocular muscles, as they focus and scan, are among the body's most active muscles. When you're working at the PC, your eyes are as busy as your hands, wrists, and arms. In addition, the optic nerve uses more oxygen than any other nerve in the body. This means eyes have a huge appetite for oxygen. Nonetheless, eye muscles experience the same ill effects of skeletal misalignment and resulting muscular dysfunction as our major posture muscles and prime movers.
The poets say the eye is the window of the soul. If you know what to look for when you peer into those windows, you can see a hell of a fight going on. Muscles that are located in the skull—jaw, eyes, nose, and ears—are caught in the middle of a war zone. Two other "armies" are fighting for a limited supply of oxygen. These more powerful forces are the brain and the muscles of the cervical spine—the section between the shoulders and the base of the skull. The power comes from desperation.
The brain always dominates. It lays immediate claim to the largest share of the oxygen flow, and it will use the central nervous system to ruthlessly curtail other functions to get what it needs. Meanwhile, the cervical spine is struggling frantically with a major concern of its own. With the loss of vertical load-bearing, the head moves forward and down, and the cervical spine must fend off gravity to keep the head upright.
By design, as the spinal column ascends, it gets slimmer and more flexible. This is a sensible arrangement, since there's no longer an involvement in major upper-torso functions, such as hefting the more massive thoracic back and shoulder girdle. There's less surface area, however, for flexion and extension. DROM, design range of motion, did not foresee the need to counterbalance eight to ten pounds of skull that wants to roll south. Nor did DROM figure on hip flexion reshaping the spine's S-curve into a C. Hence, to keep the head upright, the overwhelmed neck muscles start locking into flexion. A contracted muscle is like an open spigot: energy spews through it wildly to maintain contraction.
See the problem? Between the greedy brain and the desperate neck muscles, the muscles of the eye are being run dry. With the E-cises that have been presented, we're helping to reposition the hips and allow the cervical spine to release from flexion. We're turning off the spigot.
Not only does that decrease the demand for energy from the neck area, but the muscles can resume participating in their role of aiding the uphill flow of blood to the skull as they mechanically contract-relax-contract in flexion and extension adjacent to the arteries carrying the blood.
At the same time, as the S-curve of the spine is restored, lung capacity increases because the upper body is no longer collapsing down on the diaphragm. There's generally more oxygen in circulation. Our underlying metabolic rate picks up, which reinvigorates all the body's tissues and functions.
As the neck recovers its proper function, you may notice that another nonpain symptom abates. Your head will begin to be able to turn more easily to the left and right. To look over our shoulders, we need to be able to access shoulder muscles and functions. A neck frozen in contraction can't do that. Have you had a few fender benders lately, or near misses when changing lanes?
## Hindsight About Far Sight
We already discussed how the body suspends muscles and functions it doesn't use. Just for the sake of consistency, doesn't it make sense for underutilized eye functions to also be put on hold? There's strong evidence that native peoples, American Indians, Australian Aborigines, and others who predate so-called civilization rarely developed routine vision problems. The probable reason for this helps explain what's happening with your eyes in front of the PC.
Whether they were indigenous fishers and hunters of the arctic circle or nomadic desert foragers and herders, a common phrase in their separate languages roughly translates to "He who looks far." To survive day by day, those people used their eyes to "look far." Today we look close. Most of our work is done at less than arm's length. Functions that provide us with extended vision are rarely accessed.
What we no longer use, we lose. Try to remember the last time you really focused on a distant point on the horizon. Compare that one event to the number of close-ups that occur. The ratio is enormously unbalanced. Extended vision for many people amounts to looking down the highway by one or two car lengths (or less!). But you may wonder, "If extended vision is being lost, why am I having fatigue when I use my eyes for close work on the PC?"
**EYES: GOING THE DISTANCE**
• **Choose an object in the far distance, another in the middle, and one up close. You should be able to focus on them by shifting your eyes without changing the head position. Now, look at the far object, and bring it into focus as sharply as you can. Once focus is achieved, switch to the middle object without moving your head. Focus again. Finally, shift to the nearest object, and _take as long as you need_ to bring it into focus. Again, don't shift your head position. Repeat the cycle by shifting back to the distant object**.
• **Do this twenty times, twice a day. At first you will notice that your eyes are really working hard to achieve focus. There will be a different feel in each zone. Gradually it will become easier and more uniform. Also, if you pay attention to the time it takes to focus on the close object, you'll discover that this will become much quicker to lock in**.
• **Burning, blurring, and eye fatigue should start to improve in about two weeks. Check with your eye doctor to make sure there aren't other underlying conditions like diabetes or high blood pressure**.
The answer is that the two functions work together and mutually support each other. Compromise one, and the other is affected. Likewise, you can strengthen the whole unit. The exercise on this page is one we use in the clinic to help people with headaches and vision problems.
Headaches are also incorrectly blamed on PCs. Here again, oxygen deprivation is at work. As with eyestrain, restoring vertical alignment and musculoskeletal function is the key to getting relief. The most common forms of headaches are the result of nerve fibers at the base of the skull, in the scalp, and on the face being impinged by dilated blood vessels that are under stress from oxygen loss and are reacting to intense muscular contractions in the neck. All the E-cise programs serve as quick oxygen boosters.
When I was a teenager, my mother was a migraine sufferer. She used to lie down in a dark room with wet towels over her eyes. It was one of the only things that would relieve the pain. As the moisture in the towels condensed and cooled, it induced the capillaries, which had increased their normal surface areas in order to soak up as much scarce oxygen as possible, to shrink again. It worked—temporarily. Before long, though, once my mother got back on her feet, the continued lack of oxygen would start to bedevil the blood vessels again. The terrible cycle would repeat itself. Today I'd urge her to use the E-cises to release the contracted muscles in her cervical and thoracic spinal curves.
## Water Works
Those who experience frequent migraines and other less intense forms of headaches share a common nonpain symptom with many PC users—dehydration. Lack of motion and the musculoskeletal dysfunctions that result disrupt the body's metabolic processes. When we don't fuel the body properly, it literally starts running dry. Perversely, our survival instinct and mechanisms make matters worse. Sensing that there is a drought, the body switches off the desire for water to help get us through the crisis. The less water we drink, the less we think we need to drink.
**ON THE BLINK**
**I could tell when my friend Adrien was getting really successful with his Internet startup company: He stopped moving and blinking. He sits in meetings or on the telephone all day instead of hustling to round up business. The last time we met, I asked him, "Are your eyes bothering you?"**
**"How did you know? They burn something awful."**
**I told him that he had hardly blinked at all in forty-five minutes. Adrien was dehydrated**.
**The eye lubricates itself by blinking. When there is no natural moisture, the blink rate falls off. A dry eyelid is irritating and might abrade the eyeball. If your eyes are dry or burning, like Adrien's, it may be a symptom of success**.
The drought keeps getting worse. The less we drink, the less we move. The less we move, the more we undermine the metabolic process. Your E-cise program will counter that if you focus on what your body is telling you, as opposed to what your habits are saying. Metabolism aside, you are probably out of the habit of drinking enough water to hydrate your system. The E-cises will make you thirsty again, but habit will try to distract you.
"I don't drink water."
"I don't like water."
"I prefer cola."
"Water goes through me too fast, and I have to pee every ten minutes."
Name the excuse, and I've heard it. I can stroll through any Silicon Valley firm, and what I will see are the accoutrements of pain: cola cans and coffee cups, sugary fruit potions, and the megacaffeine drinks that Gen-Xers love to binge on; plus candy, potato chips, and other salty snacks. What we are trying to do with these sweet beverages and sodium-laden starches is to jolt the system and get it back up to speed.
The temporary blast from the salt, sugar, or caffeine wears off quickly. Furthermore, by messing with your blood sugar levels, it tricks your system into assuming that the body has been properly and nutritionally refueled— _Where else would the extra sugar be coming from, if_ _not from carbohydrates?_ Thus, the sugar is stored as fat, while the more accessible muscle tissue is burned off for energy.
**A LIQUID E-CISE**
**With your right or left hand, grasp a large drinking cup (10–12 ounces). Fill this container with water from a filtered system or a bottle of still spring water. (Carbonation is gas and it's competing with oxygen.) Start with the elbow held at ninety degrees, and slowly raise the forearm, hand, and cup to the lips. Drink. Do this throughout the day to consume at least ten full cups. There will be an additional motion dividend in the trips you take back and forth to the bathroom. Enjoy the walk!**
Now, in this horror scenario, do you see three more nonpain symptoms? I do: obesity, high blood pressure, and fatigue. The last two are natural by-products of a system that is struggling to make do with fewer and fewer resources. It's hard not to be fatigued when the metabolic process can't deliver the energy we need. And being "overweight" is usually the definition of obesity, but a more accurate standard is a disproportionate ratio of fat to muscle. This manifests itself in a body type that seems prevalent among serious male PC users—sorry, guys—a small and growing paunch on an otherwise lean frame. You might call this "slimbesity" as opposed to obesity: With the upper and lower extremities disengaged, muscle mass and definition are receding toward the abdomen and hips.
That physique is a nonpain symptom, too. It has very little to do with genetics. And it certainly has nothing to do with computers. PCs will surely change our lives, but we are the ones who are transforming our bodies from _motion-full_ to _motion-less_.
#
**"Modern life is increasingly conducted inside of an invisible box floating directly in front of you that covers an area from about midthigh to the shoulders."**
During the Vietnam war, American POWs were often punished by their North Vietnamese jailers by being confined to tiny "tiger cages" that were about four feet wide, four feet deep, and five feet high. The prisoners sat there for days and weeks at a time. When they were released, these brave men could hardly crawl.
Today you may spend days and weeks confined to a similar-size cage called a "computer workstation." Imagine the space that you usually work in delineated by bars or cold cement walls. I'm not talking about a cubicle or tiny office—those are bad in their own right. I'm interested in that bit of real estate that holds your keyboard, screen, mouse, and chair. If you were, in fact, sealed off from the rest of the world, it would be psychologically intolerable. But when the walls are invisible, there is an illusion of space that is comforting. I want you to start thinking like a prisoner and begin planning how to escape.
It's not necessary to quit your job or junk the PC. Just open the door and let yourself out of jail from time to time.
The object is to break the patterns of restricted motion that have become habitual or those that seem to be dictated by technology and work requirements. This is no easy task. We're conditioned to take motion for granted. And why wouldn't we? It happened naturally for millions of years. Without our having to give it a thought, our more than six hundred skeletal muscles were regularly accessed, engaged, and put to work. Now modern men and women can do a day's labor using roughly two hundred muscles, or about 30 percent of the total. A few more are called on sporadically for walking and other activities. But the same "suspects" are rounded up day after day and made to toil away.
**ESCAPISM**
• **Move the wastebasket to a different spot every day (never within easy reach)**.
• **Place the phone console on the far side of your desk**.
• **If you are right-handed, answer the phone with your left hand**.
• **Never use a telephone headset (if you can help it)**.
• **When possible, take calls standing up**.
• **When put on hold, inhale and exhale deeply using your diaphragm for the duration of the wait**.
• **Make it a point to stand when a colleague enters your work area to conduct a conversation**.
• **Stand up at the end of each discrete task**.
• **Change the height of your desk chair every day**.
• **Switch your style of desk chair each week (and the less chair the better)**.
• **Change your monitor position each morning and afternoon**.
• **Raise or lower your keyboard daily**.
• **Place working materials and references on the floor so that you must bend over to get them**.
• **Rearrange the furniture in your work area once a month**.
• **Place frequently used material on the top shelf of a tall bookcase**.
• **Place frequently used material on the bottom shelf of a bookcase**.
• **Use a rest room that is upstairs, downstairs, or in an inconvenient spot**.
• **Take a walk for half your lunch hour, or go to the gym to work out**.
• **When the boss isn't looking, lean back and put your feet on your desk**.
**TELE-MUSCLES**
**I wince whenever I see someone using a telephone headset. It's another example of being drawn into the "box." Reaching for the phone uses important shoulder, arm, and hand functions. Grasping the receiver is also useful work, as is holding it to your ear. For those whose work requires a headset, you should be doing the nonpain E-cise programs inchapter 6 as a way to replace the lost muscular demand**.
**I'm often asked if it is harmful to raise your shoulder to pin the receiver against your ear. There's no problem if your head and shoulders are in functional positions to start with. When you hang up the phone, they'll simply move back into proper alignment. The difficulty arises when the head (neck) and shoulder are misaligned by being rounded forward. If that's the case, you are reinforcing and strengthening the misalignment**.
This is where the patterns come from and how they are reinforced. It's a variation on Parkinson's law: "Work expands to fit the time available." What's happening is that muscles and functions shrink to fit the work available. Obligingly, the work shrinks further, as technology evolves to replace muscles. There is a simultaneous and circular downsizing of muscles, work, and patterns of motion under way.
The noose is tightening. The PC "tiger cage" is actually spacious compared with the next step down. Modern life is increasingly conducted inside an invisible box floating directly in front of you that covers an area from about midthigh to the shoulders; and it's about the depth of a forearm, with the elbow bent at a ninety-degree angle.
Bingo! Our portable work zone. It makes the "tiger cage" look like a penthouse.
We bring work to this box, or it is carried to us by technology and tools. Move to the left or right, and the box travels along. All of us have heavy-duty, sophisticated musculoskeletal functions to handle chores within a much larger radius, but most people hardly ever use them. When they do—and immediately start feeling pain, discomfort, or restriction—they'll pull back inside the comfort zone of the box. Before long these vital functions are inaccessible.
Notice how rarely you reach outside of this box. When it happens, what do you feel? Is there stiffness? Do you have to work harder? More ominously, do you notice the creation of another even smaller box? A PC, particularly one with a keyboard that has a built-in pointing device, is creating a box within a box. Hand, wrist, arm, elbow, and shoulder movement all seem to be pulled down and into a seven-by-fifteen-inch area. The head is coming along for the ride, too. This wouldn't be a problem, however, if a fully functional musculoskeletal system were involved. In that case we'd be able to spend the day in almost any size box and climb right out again without strain.
Is it too late for that?
No. If you've been conscientiously doing your E-cise program, the body is raring to start breaking patterns.
Will it be easy?
Yes, surprisingly so. Start small with a few suggestions from the "Escapism" list earlier in this chapter, and build from there.
## Picture Show
Patterns of motion carry over from work to play. It figures, really. The muscles and functions we rely on day after day are the ones that are readily accessible to support leisure and recreational activities. The problem is, we end up strengthening those "usual suspects" again.
Later in this chapter I'll provide you with an additional program of six E-cises to help break out of this pattern, but first I would like you to see how self-defeating it can be to "buff" your dysfunctions at a health club or on home gym equipment or just by going for a healthful walk around the block.
In Figure 11.1, the model is working out on a treadmill, a favorite piece of equipment because it allows the gym rat to sweat without using any of the right muscles. Like most people who sit down to work, her back is in flexion. Notice the lack of curve in the lower back, and the way her head and shoulders are rolled forward. By imagining a vertical line arising from her hip, you can see how out of position the head really is. This is helping to keep her hips rolled back, with the result that the muscles in the front and rear of the thighs are not engaged. There's stress in the hip's ball-and-socket joint and in the knees. She's waddling with her peripheral hip muscles rather than walking in a DROM gait pattern.
**Figure 11.1 A treadmill workout that is not working out**.
This woman likes the treadmill because she doesn't want to put a lot of impact on her right ankle, which is "weak," and the machine gives her a good aerobic blast. Actually, as she bypasses the prime movers in her thighs and hips, most of the aerobic benefits are lost. She's aerobically tuning her body to lesser, secondary muscles, which I believe destabilizes the cardiovascular system rather than strengthening it. The "weak" ankle feels that way because it is not operating in synchronization with the knee. And as a result it is weak.
Take another moment to look at the drawing. You may get it, and I certainly hope you do, but eight out of ten people who see this drawing tell me that it looks like any other normal woman (or man) on a treadmill.
And that's the problem! She does look "normal." Serious musculoskeletal dysfunctions have become so commonplace, we look right past them. It's as if one day we all woke up in the morning, and our left arms were an inch shorter. Then every year on the same date, it happens again: another inch disappears. Would we notice eventually, or would we come to assume that it's normal to have a shorter left arm? Or finally, that it's normal to have only one arm?
**Figure 11.2 Functional skeletal alignment on the treadmill is important**.
It's an extreme example, admittedly. Wouldn't we notice by comparing pictures of people from an earlier period? You'd think so, but there are plenty of pictures of people from fifty or a hundred years ago who did not walk or stand like our "normal" model. They also didn't have epidemics of RSI and chronic musculoskeletal pain that the Bureau of Labor Statistics reported cost $20 billion a year in workers' compensation claims.
In Figure 11.2 the model is hitting the treadmill with her musculoskeletal system fully functional. Look at the head, shoulders, spine, and hips. The work is going to the right posture muscles. The joints are opening and closing smoothly.
When you are on a treadmill, which model do you resemble? The answer is an important one because it helps explain why your workout programs may not be working—or working _against_ your fitness and health. Bypassing prime movers to build strength in secondary muscles is the way to strengthen dysfunctions. Take a look in the gym's mirrors. Check your back and shoulders.
The model in Figure 11.3 is using a popular overhead weight machine. She should stop what she's doing. As she pulls down on the bar, the curve in her spine is being flexed as though Robin Hood were drawing back the string on his trusty longbow. The vertebral disks of the spine are being squeezed under enormous pressure. To make matters worse, her right hip is actually engaging properly—the right foot indicates that by being pointed straight ahead—so the pressure on the spine isn't balanced left to right. Now it's like pinching the disk with a pair of pliers, using the force of whatever weight the machine is set on. Look at the head and shoulders—she is actually using her neck muscles to help bear the weight. It's going to do wonders for her headaches.
**Figure 11.3 Weight machines and musculoskeletal dysfunctions are a bad combination**.
Personally, I love to lift weights. But this kind of stuff—and I'm showing you another "normal" view of what goes on in the weight room—drives me crazy. The equipment makers and health club owners avoid being bankrupted by liability suits only because their customers don't hurt themselves while they are using the gear. A month or two later, they're in agony from picking up a heavy suitcase. Oh, well. Accidents happen.
The model in Figure 11.4 is in a functional position and has the apparatus under control. Her hips and shoulders are participating in the lifts. Any pressure on the spine is flowing smoothly downward to the hips, using the entire surface area of each vertebra and the full disk between them. The rotator cuffs of the shoulder (in the area of the shoulder blades) are not being yanked forward this time, which means that the scapula (the blade of the shoulder blade) is no longer frozen in place. Her neck muscles are back to doing their primary assignment—supporting the head.
**Figure 11.4 Weight machines will not unduly stress properly aligned joints**.
**Figure 11.5 Hip and back flexion are detriments on stationary bikes**.
Like treadmills, exercise bikes are popular in gyms. "Spinning" is very trendy these days. But you don't want to be spinning like the model in Figure 11.5. He is giving his inner-thigh muscles a great workout. These muscles are strong anyway, since he uses them for walking and holding himself in chairs. But the more powerful they become, the more difficult it is to release the hips from flexion. That's why his back is shaped like a C. He is leaning slightly to the left to get his thoracic back muscle—about midway up—to kick in and help the inner thigh muscles. This creates a situation where the bike rider is conditioning his back muscles to help him walk. In time he will wonder why his midback is so stiff and sore. Must be his PC.
In Figure 11.6 the model's thoracic back muscles are minding their own business—supporting the thoracic back. The muscles in the front of his thighs—the quadriceps—are engaged, as are the glutes and hamstrings, located on the backs of the thighs and buttocks. This stabilizes the knees and ankles.
The same thing is happening outside the gym. Bikers, runners, inline skaters, and weekend athletes of all sorts aren't getting the full benefits of the time and money they are investing in physical fitness. Tragically, many of them are actually undermining their health. Poised on the edge of injury by their lifestyles and occupations, they topple over into injury and illness by pursuing activities that should be fun and rewarding.
**Figure 11.6 A stationary bike delivers full benefits to a functional rider**.
Our priorities must be to take care of the foundation first—the musculoskeletal system—and then rebuild strength, health, and well-being.
## Restoring the Foundation
Occasional, moderate, and power PC users may just add the E-cise menu in this section as a prelude or warm-up to their regular exercise and recreational routines. If you are still feeling pain or stiffness after a couple of weeks of doing your daily E-cise program for pain, double-check to make sure you are following the instructions. Also, slow down. Sometimes we're in a rush to get through them, and it impairs the performance. By all means put your other conditioning and training activities on hold—no running, weights, and the like. Playing through the pain is a loser's game.
When you are pain free, use these next six E-cises as a prelude to your favorite workout or as a stand alone program once or twice a week, if you're in the mood for extra activity.
**A**.
### • ARM CIRCLES
**This E-cise gives the shoulders a chance to use their ball-and-socket joints. Shoulder joints hinge forward and back and rotate in a ball-and-socket configuration. When we pitch a softball it's the shoulder's ball-and-socket doing the work. Likewise, serving a tennis ball relies on the ball-and-socket. But rowing a boat with a pair of oars takes the shoulder's hinge function (paddling a canoe uses both). Operating a mouse or keyboard means a lot of forward hinge demand, which often locks the shoulders in that forward position. It can happen in either the right or left shoulders—or both at the same time. Arm Circles counteract that tendency**.
**Stand with your head up, feet parallel about a hip-width apart, and arms at your sides. Curl the fingers of each hand into a light fist with your thumbs straight. (This is known as a "golfer's grip.") Raise your arms out to your sides, until they are level with your shoulders. If one shoulder wants to pop up or swing forward, lower both until they stay level. (Pay attention to this, too, when you start doing the circles.) Keep the elbows and arms straight, palms down, and your thumbs pointing forward (a). Lift your arms. Now squeeze your shoulder blades together slightly, and rotate the arms forward in the direction the thumbs are pointing. Make a roughly six-inch-diameter circle. Keep your wrists and elbows straight—the circles must come from the shoulders. Do this twenty-five times at a slow to moderate pace. Reverse the circles by turning the palms up and thumbs back (b). Crank the thumbs around so that your palms are level. Do another twenty-five. Then repeat back the other way for another twenty-five, and repeat again with the same count to the rear, so that you do a total of fifty in each direction. Remember to breathe**.
**B**.
### • ELBOW CURLS
**Now it's the hinges' turn. This E-cise activates the shoulders' hinge function. It also protracts and retracts the shoulder blades across the rib cage to prevent them from getting stuck in the forward position. If you like to swim, this will give you more power with overhand strokes and help the backstroke. It also aids balance when you're back on dry land walking, running, biking, or in-line skating**.
**Stand with your feet parallel, a hip-width apart. With your hands in the golfer's grip (see Arm Circles), place the flat area on the back of the index and middle fingers, between the first andsecond knuckle joints, on the temples in front of your ears; the thumbs extend downward, parallel with the cheeks. Draw your elbows back evenly and in line with the shoulders (a). Don't allow one shoulder to be lazy and not come all the way back. From this starting position, slowly swing your elbows forward until they touch in front (b). Keep your knuckles touching your temples, the thumbs fully extended. Your head should stay erect, not wobble or seesaw. Equalize the work and tension in both sides. Breathe deeply. Do twenty-five Elbow Curls. Each time your elbows touch counts as one curl. If you can't do twenty-five at first, reduce the number and slowly build up to it**.
**A**.
**B**.
### • STANDING OVERHEAD EXTENSION
**This E-cise provides three important services: It opens up the thoracic back and the abdominal cavity, it increases oxygen flow, and it strengthens the muscles of extension in the back. It's a big help to weight lifters, ballet dancers, and even chess players**.
**Stand with your feet parallel, a hip-width apart. Draw your head and shoulders back, and roll your hips forward into extension. You want an arch in your lower back. Interlace the fingers of your hands with the palms toward your stomach. Raise your arms, fingers still entwined, straight over your head, and roll the palms of your hands toward the ceiling. Make sure your shoulders are back and your hips still in extension. The arms should be on either side of the head, lightly touching the ears. Tip your head back and look upward at the back of your hands. Hold for thirty seconds. Remember to breathe, which will be difficult at first**.
### • STANDING SPREAD FOOT FORWARD BEND
**This E-cise (figures 11.7a, b, and c) is one of my bulldozers. It puts your hips into a neutral position and allows your prime movers to do their jobs without the secondary muscles getting in the way. If you're a golfer, you'll add power to your tee shots just because of the improved weight transfer in your hips**.
**Stand with your legs spread about three to three and a half feet apart. Keep your feet pointed straight ahead and flat on the floor**.
**Figure 11.7a**
**Figure 11.7b**
**Figure 11.7c**
**(Don't let them roll.) Bend over at your hips and touch the floor directly in front of you. If that's too difficult, you may use a block, book, or other prop for support to rest your hands on. Tighten your thighs, and relax your torso toward the floor (a). Hold this position for one minute. Next, without straightening up again, slide your hands to your right foot (moving the prop, if you're using one). Keep both thighs tight and your torso relaxed (b). Hold that position for one minute. Then, slide left to the center briefly before moving your hands to your left foot (c). Again, keep your thighs tight and torso loose. Hold for one minute. Finally, move to the center, bend your knees, and roll your torso upright from the hips**.
### • STATIC EXTENSION POSITION
**This E-cise is a powerful muscle relaxant. It releases the contracted muscles in your trunk and builds strength in your hips. You'll find this a big help if you play "explosive" sports like basketball** , **volleyball, and tennis. In general, though, there isn't a sport or activity that doesn't benefit from relaxed trunk muscles and stronger hips**.
**Get down on the floor on your hands and knees. Your hands should be about six inches forward of your shoulders to start, rather than directly under them. Let your back and head relax toward the floor as the shoulder blades come together. Relax. There should be a pronounced arch in your back. Keep your arms straight, and shift your hips forward six to eight inches so that they are not aligned with the knees. This will also bring your shoulders into line over your wrists. Hold for one to two minutes**.
### • CATS AND DOGS
**If you have trouble understanding the principle of flexion and extension, this E-cise will at least let you feel it. As the cat flexes and the dog extends, this E-cise strengthens muscles and functions in a coordinated sequence. You need to break out of flexion to maximize the benefits of any sport, gym routine, or physical activity. ThisE-cise provides total range of motion in the pelvis and the back in an anatomically correct and safe manner. It promotes breathing and better circulation. It's very effective, as you may know if you've done yoga**.
**Get down on the floor on your hands and knees. Make a "table" by aligning your hands under your shoulders and your knees and thighs under your hips. Your arms should be straight and your thighs parallel to them. Keep your legs and feet parallel to each other, as well. The feet are relaxed and resting across the top side of the toes, not flexed or up on the toes. Make sure your weight is distributed evenly. Smoothly round your back upward as your head curls under, to create a curve that runs from the buttocks to the neck—this is a cat with an arched back (a). Smoothly sway the back down while bringing your head up—this is the perky dog (b). Make these two moves continuously back and forth—don't keep them choppy and distinct. Do one set of ten. Exhale as you move into the cat position, inhale during the dog. Make sure, with the dog, thatyour head comes fully back and up so that you are looking straight ahead and your shoulder blades collapse toward each other. Take your time. The pace should be slow, but not so slow that it breaks the flow between the cat and dog positions**.
**A**.
**B**.
Does all this seem like more than you bargained for? If it does, try the programs for a week. Then evaluate where you stand. Ask yourself, "Is there still pain?" "Has it diminished?" "Has it moved?" "How do I feel overall?" Don't be too quick to decide. Many of us expect to be disappointed and jump to the conclusion that therapy isn't working when, in fact, we've made great progress. For instance, if the pain was constant before the E-cise program started and becomes intermittent after a week, you're gaining ground. Don't stop now!
Remember, even if you are in your twenties or thirties (or a teenager, unfortunately), these dysfunctions have been digging in for years. They won't disappear instantly. And they will never let go until you take responsibility for your own health.
#
**"The worst downside of carpal tunnel surgery is that it is unnecessary and will ultimately fail."**
I spend most of my workday answering questions, even though I've found that the best answer, quite often, is another question. This Socratic dialogue is a way to learn about our health and our responsibilities for maintaining it. The human body is my favorite teacher.
I've assembled here some questions that we frequently field at the clinic:
**Q: If the PC at work isn't causing wrist pain, why does my wrist stop hurting over the weekend when I'm at home and resume first thing Monday morning as I boot up? It seems like cause and effect to me**.
**A:** The reason the pain goes away over the weekend is that you've changed the demand on your body. In other words, the motion requirements at home are different from those at work. If you spend all day Saturday in the car doing errands or Sunday afternoon in front of the TV watching football, your muscles and joints aren't being stimulated in the same way. Even if a more strenuous routine is involved—gardening, home improvement, a pickup basketball game—there may be enough function or dysfunctional compensation to avoid overt pain symptoms over the short run. These functions that are being put to use relatively briefly on the weekend are not the same ones being utilized for forty hours a week on the job. Give them time, and they too will start to hurt.
Take a fairly basic example. A serious runner—and carpal tunnel syndrome sufferer—will clock several miles of road work on her day off and feel great. She's not using her wrists and hands—therefore, she feels no pain. It seems like a great weekend, but she doesn't notice that her knees are gradually getting tender and unstable. It may take months of weekend running before she is aware that there is a problem—a problem that is coming from the same source as her sore wrists and hands: weak posture muscles and skeletal misalignment.
Meantime, she goes back to work Monday morning and doesn't put much demand on her knees and ankles. It's her arms, wrists, and hands that are taking a beating. In both cases the stress is coming from the musculoskeletal dysfunction. Now she's feeling one and not the other. Eventually, both will be heard from.
**Q: Can I take painkillers and still do the E-cises?**
**A:** You certainly can, but keep in mind that the drugs will mask the pain and interfere with _you_ making an accurate assessment of the effectiveness of the E-cises. Pain is a message. If you pay attention to that message—where it's coming from, its intensity, and its other qualities—you'll know how your body is responding to treatment. One of my cardinal rules is: If it hurts, stop doing it. But if you're taking a painkiller, you won't know if it hurts. In that case who's in charge? Who makes the decision to go on or to stop?
This question really addresses the need to take a more direct and active role in managing one's health. If your PC suddenly started making strange sounds or the screen display changed colors, you'd be wide awake. But many of us are oblivious to the same kind of messages sent by the body. If we do a better job of tuning in, we can develop a very accurate assessment of what the body needs. Then we can make the decision rather than being passive.
One of the strengths of the Egoscue Method is that it is self-reinforcing. The E-cises go right to work: Positive changes occur, you know you're gaining on the problem, and so you keep at it. The validation is almost immediate. When you take painkillers, that payoff isn't as pronounced. There could be a tendency to slack off the therapy. In that way the drug is acting as a disincentive.
One other factor is that the E-cises will change your metabolic rate, since they engage the major posture muscles. As a result, a smaller dosage may be needed and that's on top of the pain alleviation that is already occurring from the E-cise. You could end up overmedicating yourself.
Notice that I'm not providing a yes or no answer. I'm giving you information so that _you_ can reach a yes or no decision.
**Q: Did I aggravate my carpal tunnel problem by playing the guitar? Would it be better to choose hobbies that don't require so much finger and wrist involvement?**
**A:** No, and no. The PC's keyboard didn't cause the pain, nor did the guitar's strings. By going after the underlying musculoskeletal problems, you can do both without pain. Plucking or strumming the strings and playing the chords on a guitar are quite different from operating a PC keyboard. To play the instrument, the musician brings a different demand to the body, which is very desirable. The more stimulus and the more varieties of stimulus, the better! You'd lose that by giving up the guitar, and you'd lose access to the functions involved.
Furthermore, I believe that our choice of hobbies is an accurate gauge of what gives us pleasure. Work may not be enjoyable, but we do it anyway for the paycheck. The urge to play the guitar confirms that you know instinctively that the instrument is not causing the pain. You wouldn't give the guitar a second thought if it were really hurting you. We need to relearn the ability to listen to what the body is telling us.
**Q: If alignment is so important, why does the body allow the skeleton to fall into misalignment?**
**A:** The body doesn't discriminate between good and bad stimuli. It's all the same. What the environment hands out, the muscles, joints, and other components absorb. This anything-and-everything-goes approach assumes that the environment in due course will ask us to walk, run, stretch, leap, bend at the waist, make throwing motions, pull, push, carry heavy burdens, twist, turn, crawl, squat, and so on. Every function was engineered by environmental demand that came at us from every direction. It's the secret of our survival skills as a species. The ultimate opportunists, we respond to our surroundings.
As the ultimate inventors and problem-solvers, we changed our surroundings as well. What's happening with skeletal misalignment is that the environment has stopped offering the rich, wide range of motion demand that it did in the past. But as always, the body is taking the available stimuli and using them. Only now the stimuli are no longer balanced. They come at us in limited, specific forms. Meanwhile, the parts that aren't being stimulated weaken and are soon overpowered by those that are getting more use. Unfortunately, it's mostly the peripheral and secondary muscles that are prospering at the expense of the prime movers and big posture muscles. Without these "heavy hitters," skeletal alignment is compromised. Once that happens, the body has no built-in mechanism to restore equilibrium—other than motion. It's a real catch-22.
Unlike our ancestors, we have the power and technology to shape our own environment in large and small ways. Until we deliberately replace this lost motion, the musculoskeletal system is in trouble and our health is in jeopardy.
**Q: Fifteen years ago I used to spend several hours a day using a typewriter without any problem. I had to change jobs this year because the PC was killing me. Isn't there a difference in the keyboards that accounts for this?**
**A:** It would be a cinch to rig up an old Remington manual typewriter to function as a PC keyboard. To input data, you'd be required to insert a sheet of paper, roll it through, and align the margins. Then you'd hammer away at the keys, banging on the "shift," and stopping at the end of each line to flick the lever to get the carriage to return to start another line. When you made a mistake, you'd have to pump the "backspace" key several times, erase, and retype. What a great workout!
The problem is, the "information highway" would run right off a cliff. A keyboard requiring that kind of demand would make Ralph Nader's old Corvair seem as safe and benign as a Volvo. There'd be lawsuits, congressional hearings, and federal regulations to curb the epidemic of pain caused by...? That's right, the Remington manual typewriter.
Most of us no longer have the posture muscles required to sit in front of a typewriter for several hours, the way Great-Aunt Gladys did. If you went back to a typewriter and tried to do a PC's work with it, you would be in worse pain than you are right now. In the intervening fifteen years, the level of the "motion ocean" that kept you afloat has receded dramatically. Those musculoskeletal functions are high, dry, and largely inaccessible. The increasing incidental rate of chronic pain associated with the PC indicates that the level is still dropping.
**Q: You don't seem to stress monitor or keyboard placement. Why is that?**
**A:** Fiddling with the monitor and keyboard is a form of symptom management. It does not address the source of the problem or prevent it from happening in the first place.
I've watched many PC users at work in front of video monitors that have been adjusted to account for the chair, the workstation, and the individual's height. "Set the monitor at eye level," the mantra goes. Within a matter of minutes, this careful arrangement is made irrelevant by the head moving forward and down toward the screen. I half expect to hear a giant sucking sound and see them disappear into the monitor. As for the keyboard, moving it higher or lower will change the body's response to the task in superficial ways, but the basic misalignment problem is still there, still creating friction and stress. No matter what you do with the keyboard, rounded shoulders and a slumping back will always prevail.
To see what I mean, put both your hands on a PC keyboard in the typing position. Pull your head and shoulders all the way back while watching your hands. Notice that the wrist end of the hand is being raised via the action of the elbow. Now let the shoulders and back relax; the wrist and hand are being pushed down by the elbow. Move the keyboard lower, and this will still happen. Plus, the back rounds more. Raise it, change the angle, and the elbows gain even more of a mechanical advantage against the wrist.
If you're experiencing chronic pain, you may have discovered that its intensity varies according to the way you address the keyboard. You get "comfortable" by sitting on your right side and hunching the left shoulder, or fall into some other contortion. All that means is that the friction is being transferred to another less sensitive location. After a while, it will start to hurt there, too.
**Q: I wasn't having any problem with my PC until I lost about twenty-five pounds. Can you explain that?**
**A:** The chances are good that your weight-loss routine burned off muscle along with fat, leaving the body with even less capacity to maintain an upright posture. Don't forget that the reason fat is so hard to get rid of is that the body is programmed to store excess calories in case there's a famine. This surplus is a valuable commodity in an environment of scarcity. We actually protect it by first burning muscle tissue for energy once the intake of calories drops below a subsistence level. The body only reluctantly draws down its store of fat.
We really are superb managers of resources. From a musculoskeletal standpoint, the body has a way of making fine adjustments to avoid a crisis. We can live for months or years on the edge of chronic pain without being aware that anything is wrong. Suddenly, an event comes along to tip the balance—like muscle loss from a crash diet—and there's pain.
By the way, don't even think about fixing the problem by regaining the twenty-five pounds! You need to work on building muscle and activating functions with the E-cises in chapters 6 through 9.
**Q: Is there an ideal sport or recreational activity that will help me avoid chronic pain?**
**A:** All of them. With the possible exception of bungee jumping, popular mainstream sports and recreational activities are ideal chronic pain antidotes because they provide motion that would otherwise be unavailable. Bear in mind, though, that since most of us work more than we play, the dysfunctions we feed on the job are brought home on the weekend.
The guy who rarely so much as turns a doorknob on Monday to Friday goes to a tennis court on Saturday, where he performs the exact same functional motion to deliver a wicked forehand across the net. He hits the ball dozens of times—hard! When his elbow starts hurting, he concludes that tennis is to blame and gives it up. And that's too bad. He loses out on the benefits of the motion without curing the tennis elbow, which will become PC elbow or calculator elbow or cash register elbow.
The chronic pain is not caused by the sport or the demands of a job. The back, shoulder, and upper arm are designed to work with the elbow to pronate and supinate the hand (move the palm to face up or down). But our friend has rounded shoulders, which can't rotate. It means the elbows do most of the work. Eventually, there's a breakdown. Whereupon we hear the five words I dread the most: "I got hurt playing —–." Followed by the next five: "So I gave it up."
I recommend that you make an effort to vary your sports and recreational activities. We often end up playing with the muscles we work with because they are strong in the first place. One of the reasons for the biking boom is that it is an ideal sport for someone who sits in a chair all day and whose hips and back are locked in flexion.
**Q: Is there a sport to avoid, like running?**
**A:** No, no, no. We were designed to run. People get hurt running, or while performing any sport, primarily because they are attempting to run or play with weakened and unstable musculoskeletal systems. Most sports accidents—football included—could be avoided if the players came to the game with fully functional bodies.
**Q: I'm considering carpal tunnel surgery. It sounds fairly straightforward. What's the downside?**
**A:** I don't know, and neither does your doctor. There isn't enough reliable research on what really happens over the long run to a wrist whose transverse carpal ligament has been surgically severed. I'll give you my opinion, though. The ligament is in there for two reasons: strength and stability. For me, those are convincing reasons for leaving it alone. Ask your physician questions like "Will I recover full hand and wrist function?" and "How do you define full hand and wrist function?"
The answer to this second question can be very revealing. Often you'll be told that the hand will probably be _close_ to normal, but you won't be able to "do handstands" or work as many hours as you once did on the PC. To me, that's _not_ normal.
The worst downside of carpal tunnel surgery is that it is unnecessary and will ultimately fail. The problem is lack of function and misalignment. That's not going to be cured by surgery.
**Q: I've seen exercises for carpal tunnel syndrome that work directly on the hand and wrist, such as balling your hand into a fist and releasing, or straightening the wrist and relaxing the fingers. Why is your E-cise approach so different?**
**A:** Sorry about answering a question with another question. But what happened the last time you got a kick in the shins or caught your fingers in the door? You rubbed the injury, and it felt better because more blood and oxygen were being sent to the area. Therapy that works directly on a painful wrist, elbow, neck, or shoulder is doing the same thing. Most of the chronic pain we are discussing in this book comes from either nerve impingement or inflammation. Both types involve restricted oxygen flow. Direct therapy addresses that but doesn't affect the underlying problem.
**Q: Won't wrist and back braces solve the problem of skeletal misalignment?**
**A:** They merely shift the problem elsewhere. Worse, braces usurp functions that need to be strengthened, not isolated and immobilized. A third reason to avoid braces is that they interfere with the close interactions of the body's various structural components. If you change how the elbow or wrist operates, it affects the shoulder and the neck. Once that happens, every part of the body is in play.
But I'm glad the question arose, because there will be more on this subject in the next chapter.
**Q: Can I do the E-cises after surgery?**
**A:** If you mean "Is it too late after surgery to do the E-cises?" the answer is no, it's never too late to restore lost musculoskeletal functions. Alignment is not going to happen by itself—at least not for most modern men and women. The E-cises are the best vehicle for achieving that objective before or after surgery.
**Q: From what you say about alignment, it seems like good posture is the key to avoiding pain. Wouldn't it be enough to pay attention to sitting up straight and keeping your head and shoulders back?**
**A:** It can't be done. As soon as we shift our focus off the command—"Sit up straight"—and start doing something else, our posture goes back to autopilot and our dysfunctions take over. By strengthening muscles and accessing the proper functions, we are reprogramming the autopilot to keep us in alignment without having to think about it.
**Q: I don't have pain, and I don't want pain. But how will I know when I can safely stop doing the E-cises?**
**A:** Read my lips—N-E-V-E-R. I'm afraid that our "motion ocean" is going to keep on receding. Just as we have to feed ourselves, we must dish up a daily minimum requirement of motion. It's a life sentence, but the good news is that the more you move, the more you want to move. Movement is a chore only when we're dysfunctional. In that case the pleasure is gone.
Watch young children. They move for the sheer joy of it. Adults think we outgrow this exuberance. What's happening, though, is that we grow into a culture that expects proper adults to be "still." It is stillness, not aging, that deprives us of our instinctive love of motion.
**Q: I still don't get flexion and extension, particularly when it comes to the hips**.
**A:** Join the crowd. Think of the pelvis as forming a big hinge where it joins with the spine. Bend over and touch your toes—the hinge closes (full flexion). Stand straight—the hinge opens (full extension). The problem is that when most people stand up, they are not straight—they are still in partial flexion; the hinge never opens completely. I can demonstrate this if you'll sit on the floor, squarely on your bottom, with your feet straight out in front. Without using your hands on the floor for support, square your shoulders and straighten your back. Okay, now put an arch in your lower back. No hands! No seesawing back and forth. It's tough. Most people can't do this because I'm asking them to fully open the hip-hinge. Key muscles of the pelvis aren't strong enough to obey. One of the reasons is that the contracting muscles that hold the hinge closed in partial flexion get so much use, they are stronger than those that open the hinge. By asking you to sit on the floor to arch your back, I'm making you rely almost exclusively on these weak pelvis muscles to achieve extension, rather than helping out with knee, thigh, and thoracic back contortions. If you repeat the demo standing up, and pay close attention to your knees, you find that they are tightening appreciably when you try to arch your back. The knee-hinge is opening fully and attempting to go past full extension (by twisting or popping) to compensate for the partial opening of the hip-hinge. The knee is attempting to flip the hip back into the proper extended position. It's another example of how one dysfunctional component puts stress on another. In this case, the lazy hips are getting a free ride at the expense of the hard-working knees. Eventually, the knees will start breaking down. We need to get all the body's hinges to open and close without restriction or extra stress by eliminating muscular imbalances.
In Figure 12.1 the model is doing two things. He is thinking, and he has put himself into flexion. The pose is reminiscent of the famous sculpture _The Thinker_ by Rodin. It's interesting that we associate this posture with introspection and intellectual activity. In contrast there is the monumental _David_ , hewn out of marble by Michelangelo. The biblical giant-killer stands tall in full extension, ready to take action. We have to work to preserve both of these inherent musculoskeletal capabilities. Go ahead, think; lean forward and study the situation closely. Then get up and go do something about it. Flexion and extension; thought and action.
**Q: Women have more flexibility in their hips. Does that make them more vulnerable to chronic pain?**
**A:** No, the body is very democratic. Men and women are equally vulnerable to chronic pain if there is insufficient proper motion to maintain their musculoskeletal systems. Women need to watch out for socially mandated roles and expectations that assign them to a more motionless status than men. It makes my day to see women in hard hats and getting paid to slam-dunk a basketball.
**Figure 12.1 _The Thinker_ goes digital**.
I know, however, that many women bristle at the idea that they are "motionless." Modern women are busy; they work hard. But distinctly unequal patterns of motion are commonplace. Women, for example, are not expected to have more than minimal upper body strength. Watch otherwise-fit and hugely competent female road warriors struggle to get luggage into the overhead storage compartment on an airplane. Often a male passenger will help out. It's assumed that he has the required upper-body strength (even though he may not).
I'm not knocking good manners. My point is that gender stereotyping leads us to accept the idea that lack of upper-body strength is okay in women. It's not. There are health consequences. Among them are headaches, stiff necks, lack of balance, and osteoporosis. The major posture muscles in the upper body are necessary to maintain skeletal integrity.
**Q: Could my TMJ be computer related?**
**A:** TMJ, or temporomandibular joint dysfunction, is a disorder that affects the joint that attaches the lower jaw to the skull. People with TMJ have trouble opening and closing their mouths. Chewing can become agony. The pain is telling you that you are in danger of becoming headless. I'm serious. Your head has moved so far forward that the neck muscles have largely frozen into flexion, and they've recruited the muscles of the jaw and skull to help prevent your head from falling to the floor.
You can stop working on a PC tomorrow, but the position of your neck and head will remain the same when you drive, watch TV, or sit at the dinner table. Rather than blaming the computer, it is more accurate to say that TMJ is lifestyle-related. You need to restore vertical skeletal alignment to allow the jaw's muscles to resume their proper functions.
**Q: Are school-age children spending too much time using computers?**
**A:** Far too much. The early years of childhood are extremely important for developing stable musculoskeletal structure and function. The only way that can happen is for kids to spend hours on the move. It's not necessary for them to be athletes or fitness freaks; if they get out into the world, they'll find trees to climb and puddles to jump.
Once the foundation is in place, young people can spend as much time as they want studying or playing games on a computer. But like adults, they'll have to feed themselves motion in large enough helpings to keep their functions from crumbling. It is particularly true if we continue to insist that children need to work more and play less. Recess and athletic programs are vanishing from many of our schools, replaced by academic activities that are designed to prepare students for top colleges and careers. Let's hear it for the fast track! But I doubt that people in chronic pain can be among the very best, brightest, and fastest for long.
**Q: How much motion is enough?**
**A:** I hate that question. It begs for a pat answer—"Twenty minutes a day is enough for every man, woman, and child." And that's nonsense. For some people twenty minutes is enough. Their environment is richer in motion, and it supplies the rest of what's needed. Others aren't so lucky. They may need an hour or more.
On the other hand, there's no such thing as too much motion when the body is functional. That doesn't mean you're Superman. At some point fatigue will set in, and the body will tell you in no uncertain terms to stop and rest. But I don't have much sympathy for the less-is-more school of fitness that is being advocated these days. I believe there is a direct positive correlation between the time we spend in active motion and the time we spend pain free.
#
**"Ergonomics practices serial sacrifice—serial carnage—as we destroy joint after joint, function after function, in the crusade for ergonomic solutions."**
Gil is my poster boy. I've written about him before, and I'll probably keep telling his story because it perfectly captures the paradigm of pain.
Gil was on the move a lot and traveled light. He didn't lug around a notebook computer or personal digital organizer. The most important item in his carry-on luggage was a single fingerless glove, rumpled and well worn. It covered his right hand like a second skin, reminiscent of what gunslingers once wore.
I'm not sure, but I'd guess Gil was computer illiterate. He never bothered to turn on a PC or surf the web (although he'd probably like playing Doom). What he enjoyed was a sport that historians seem to think was invented in an eighteenth-century Irish jail.
He could play a mean game of handball.
Gil was a national champion. Was. When he came to my clinic a few years ago, he was a wreck of a thirtysomething athlete, who wanted only to play and win just one more major tournament. This is how I recall our consultation:
"What's the problem?" I asked.
"My elbow hurts."
"I know. I can tell by the way you're holding it," I said. Surprised by the comment, he tried to move his right shoulder back, but it was rounded so far forward that it was nearly impossible to budge.
Gil was very candid. He explained that over the years the elbow pain had gotten increasingly severe. To play, he had resorted to frequent cortisone shots administered directly to the elbow joint.
I nodded, taking note of his use of the word _frequent_. Cortisone and frequent don't mix.
"Now I'm here because I can't have any more shots," Gil said.
"Why not?"
He stood up. "Feel my elbow."
I used my thumb and index finger like calipers to gently assess the swelling. With hardly any pressure at all, my thumb slid up and into the elbow capsule, pushing the skin before it like slipping on a glove. The thumb went in as far as the first joint. This didn't seem to give Gil any more pain than he was already enduring, but it was a total shock to me.
If you've ever been walloped by an elbow in the ribs or head, you know what a blunt instrument it is: a tough, three-way joint chock full of bone condyles, cartilage, tendons, and ligaments. I knew at once that numbed by cortisone, Gil had played and played until his elbow turned to mush.
There's not much that exercise therapy can do for a joint that has ceased to exist. So Gil had doctor-shopped. He moved from physician to physician conning them into cortisone treatments by not revealing his full medical history. Finally, the consequences were impossible to hide; no ethical doctor would provide another injection. Cortisone is just too destructive in large doses.
Gil killed the pain—temporarily—by permanently killing his elbow.
I tell this story because painkilling has become a huge industry. But we need to think carefully before buying its products and services. It's time to question whether seemingly more benign versions of cortisone are being administered in the form of surgery, drugs, and ergonomically correct devices to millions of people, with equally destructive effects.
Will we wake up in twenty or thirty years to find another author telling much the same story? Instead of Gil and his horribly mangled elbow, will it be a tale of young people with sore wrists or stiff necks, who wanted only to work without pain to build good lives? Will it be a tragedy of artificial joints, pills and their side effects, braces, and lives of lost mobility?
My prevailing optimistic side hesitates to answer—it's skittish about being disappointed. But the trends are not good. An estimated 120 million Americans suffer from some type of chronic pain. Pain is the leading cause of worker absenteeism, with 50 million lost days a year and $3 billion in lost wages. One out of six American households has someone with severe chronic pain. As for treatment costs, I've seen figures ranging from $100 million a year for carpal tunnel surgery to $100 billion to cover RSI-related conditions affecting computer users. Migraines, back pain, and arthritis ring up an estimated $40 billion; on top of that, ergonomic reengineering, the business of designing "worker-friendly" tools, furniture, and work space, takes in approximately $3 billion a year.
The statistics are frightening from at least two standpoints. One, the sheer number of people in pain; and two, the profit potential that is driving the search for pain cures into areas that may lead to quick short-term solutions that bring on long-term damage.
Let's start with the human toll. If roughly 40 percent of the U.S. population is in pain, it's time to ask a basic question: What is going on?
The answer is also quantifiable. A 1996 study by the U.S. Surgeon General found that 60 percent of the adult population are not physically active on a regular basis, 25 percent are not active at all, and half the young people between the ages of 12 and 21 are also not vigorously active.
Like the nesting Russian dolls that split open to reveal other smaller dolls inside, these figures on physical inactivity are the outer shell that holds the core reason for such enormously high rates of chronic pain. An executive summary that accompanied the study identified the source of chronic pain by being both bureaucratically oblique and precise at the same time:
Regular activity that is performed on most days of the week reduces the risk of developing or dying from some of the leading causes of illness and death in the United States. Regular physical activity improves health in the following ways:
Reduces the risk of dying prematurely.
Reduces the risk of dying from heart disease.
Reduces the risk of dying from diabetes.
Reduces the risk of developing high blood pressure.
Helps reduce high blood pressure in people who already have high blood pressure.
Reduces the risk of developing colon cancer.
Reduces the feeling of depression and anxiety.
Helps control weight.
Helps build and maintain healthy bones, muscles, and joints.
Helps older adults become stronger and better able to move without falling.
Promotes psychological well-being.
Given the numerous health benefits of physical activity, the hazards of inactivity are clear. Physical inactivity is a serious nationwide problem. Its scope poses a health challenge to reducing the national burden of unnecessary illness and death.1
I agree that "The hazards of inactivity are clear," and my professional experience corroborates the study's findings. But unfortunately the government's message is likely to be ignored by its target audience. People do what gives them pleasure, and they avoid what doesn't. It's the reason that 60 percent of the U.S. population are not regularly active: Physical activity is unpleasant.
We are not by nature or culture sedentary, but in the last fifty years a sit-down, drive-by, tune-in, and kick-back lifestyle has eclipsed an older, established norm that provided a richer variety of motion and physical activity that, without conscious effort, kept our grandparents fit enough to derive pleasure from the effort. As a rule, they did not fall below a certain level of functionality until late in life.
My grandfather was an example. When I was ten or eleven, he reluctantly gave up his big house in the country and moved into town. One day I asked him if he missed his house. He replied, "Yes, I'd like to have those stairs back." I was amazed and wondered why in the world he missed that set of steep stairs to the second floor. He lived now in a nice one-level place with my aunt. I suggested he go to the park where there was a staircase he could climb. "It's not the same," Grandpa said.
It wasn't the same. I know that now. Those stairs were part of his life. The daily routine of trudging up and down the stairs had been broken. He looked back on them with pleasure and fondness, yet he wasn't about to climb the park's stairs just for the exercise. It wasn't long before his health began to fail.
Actually, Grandpa was lucky because at least he had a memory that linked pleasure with physical activity. If he had been allowed to go back home, it might have provided enough incentive for him to recover the functions he had so quickly lost by living on one level. But most of the inactive young people cited in the surgeon general's report don't have that advantage. Their functions haven't been lost—they were never developed in the first place. It's awfully hard to convince a teenager that physical activity is worthwhile when it is not only extremely unpleasant but, in many cases, painful.
We've spent a lot of time in this book discussing chronic pain symptoms—both pain and nonpain. Our inactivity as a nation is symptomatic of dysfunction: We don't move because physical activity is unrewarding, uncomfortable, or unpleasant. It explains the extraordinary levels of inactivity _and_ chronic pain. We no longer move enough to cross the threshold where the value to be gained compensates for the effort being made. The consequence is chronic pain and the long list of illnesses that the surgeon general enumerated.
## The Usual Business of Business as Usual
Any market that encompasses 120 million people is an irresistible target for profit-making businesses. For years I've been questioning the wisdom of 85 to 90 percent of the elective orthopedic surgery that is performed in the United States. We've been too quick to cut and be cut, mainly because there is an abundant supply of surgical talent and technology on hand. American doctors conduct surgery for lower back conditions five times more frequently than their British counterparts. Is that due to our genetically weaker backs? I doubt it. The more likely explanation is that the perennially cash-strapped British National Health Service opts for more economical and conservative treatment. The overwhelming majority of British physicians are GPs, not surgeons or other specialists. This is fortunate for the average Briton, since recent studies have shown that of the four possible courses of action—doing nothing, drug treatment, physical therapy, and surgery—surgery tends to be the least successful. (Doing nothing is the most successful, which I'll address below.)
Fortunately, the medical community has begun to recognize the problem. Increasingly, it is offering surgery as a last-resort option for many musculoskeletal problems, and patients are being strongly advised to consider less invasive procedures. Managed health care, in addition, has moved the United States somewhat closer to the British model, with the difference that private insurance companies, rather than the central government, are guarding the purse strings.
The downside is that drugs and gadgetry are assuming a larger role. They are cheaper than surgery, but both share the same defect: They treat a symptom, not the problem. Statistically, "doing nothing" is the most effective treatment for back pain because the patient actually does _something_. Motivated by the pain, he modifies his behavior (as does she). It doesn't take all that much. The body is so resilient and adaptable that simply resting for a few days or getting a new chair can be enough to alleviate musculoskeletal pain and keep it at bay for weeks or months. Of course, the underlying problem remains, even though the symptom abates temporarily.
A painkilling drug takes this a step farther into dangerous territory. It allows us to continue our behavior—no rest, no new chair—but it eliminates the pain symptom. Remember Gil? That's what cortisone did for him. He continued to play and continued to obliterate his elbow. The cortisone was destructive in its own way, but the mechanical abuse of the joint was equally to blame. Masking pain with antiinflammatory drugs removes the incentive to take action that can give the body a fighting chance to respond to the problem in the short term. Business as usual means the usual business of traumatizing muscles and joints. As the damage accumulates, the drug's dosage must increase proportionally until pain finally breaks through or pops up in another place.
Many people who come to my clinic have been advised by their physicians that they have nerve damage. It's the equivalent of being told "there's nothing more we can do." But the diagnosis often turns out to be incorrect. The nerves have not been permanently damaged; they have merely been affected by skeletal misalignment and muscular dysfunction. Once those circumstances are corrected, the nerves return to health. I'm convinced that what we are seeing is the drug _mask_ at work. The nerves are being rubbed, irritated, and impinged on beyond their level of tolerance, but the painkiller has pulled the plug on that circuit to prevent it from shutting down the system. In due course the nerves start showing signs of severe wear and tear.
_Breathalyzers_ are now attached to automobile ignitions to prevent alcohol abusers from driving while intoxicated. I'd like to see something similar hooked up to a PC to stop those who are using painkillers from booting up. And that doesn't mean the PC is dangerous—the dysfunctional operator is dangerous to him or herself.
Something tells me Microsoft isn't about to add an _Egoscue-lyzer_ to its Windows operating system, so I'll supply a warning right here on this screen:
**GPF #1: If You've Taken a Painkiller for Musculoskeletal Pain**
**Save Your Work**
**Press Cancel**
**Go Home**
I'm adamant about this, because relying on painkillers to go about business as usual is a huge mistake. The drug does nothing to eliminate the musculoskeletal problem that is causing the pain. That problem—let's assume for our purposes that it's a restricted elbow joint—is aggravated by arm movement. But you won't know that. The painkiller has numbed your elbow.
I can hear the excuse—and it's a good one: _I just need to finish this project_. Yet every time you reach for the mouse or tap the keys, you are damaging the elbow joint. We've got to stop making excuses—they're hurting us.
It is so easy and so misleading to fool ourselves into believing that when the pain goes away, the problem leaves with it. No. It happens only when we take action to strengthen muscles, restore skeletal alignment, and stabilize the entire musculoskeletal system.
Some prescription drugs and alcoholic beverages carry warnings about the hazards of operating automobiles and other potentially dangerous pieces of equipment while consuming those products. The warning label deserves to be plastered on your PC—not because the computer equipment is dangerous—it's being operated by a dysfunctional body that is a danger to your health.
## The Workerless Workplace
Like drugs and surgery, ergonomic gadgets are also market-driven products and the product of good intentions. The whole idea is to help people. Even so, the massive reengineering of the workplace is actually a hindrance. For one thing, it persuades people that the problem has been solved and that no further effort on their part is required. This external solution to a set of internal circumstances breeds dependence on a never-ending series of technological "fixes." Gradually, we cede direct control of the world around us. But the subservience offers no payoff. Since it is only a temporary and symptomatic solution, the pain increases along with a sense of helplessness.
Second, it leads to a proliferation of symptoms and an escalating crisis. In almost every RSI case we see in the clinic, the individual presents multiple symptoms. Often they are the direct result of an ergonomic solution, like a new keyboard or a wrist brace, that shifted the problem from the wrist to the elbow, the shoulder, or the neck. The rationale is that the shift allows the injured or inflamed joint to heal. But that never happens because the source of the problem isn't addressed. The transfer becomes permanent, and as such it undermines another musculoskeletal component. Before long the pain spreads.
And the third strike against ergonomics is basic economics. The ultimate outcome of a worker-friendly, ergonomically correct workplace is a workerless place full of robots and automated systems. If we accept the idea that less motion is the desired end, the musculoskeletal system will grow weaker and less stable until any motion—no matter how limited—is excruciating. Perforce, business will replace humans with machines to lower costs and uncertainty, and to increase productivity. Even the simplest tasks, like pushing a button or turning a dial, require muscle power. If the ability to keep the body erect is compromised, even such trivial physical demands will overtax our resources. Jobs aren't going to just "go south," they are just going to go away.
Ironically, the logical fallacy to ergonomics is the belief that repetitive motion can be cured by repetitive motion. This fallacy rests on the assumption that there is good motion and bad motion. For instance, by raising the height of a work surface to eliminate the need to bend at the waist or crane the neck (bad), we are restricting the individual to mostly forearm and hand movement (good) for several hours a day. Meanwhile, key functions—bending forward, straightening up, stretching, and lateral movement—that support the spine and the ability to remain upright are not being utilized. They will weaken. In due course there will be back pain, but perhaps before that happens, the worker will enjoy a pleasant weekend at home in the garden with time for a little weeding. Suddenly, his or her back will go out. Is the ergonomic solution to blame? No, of course not. Weeding caused the problem!
The body's musculoskeletal functions are so balanced, unified, and interdependent that attempts to manage movement lead to innumerable unintended consequences. In the last example, no one set out to cause a back problem by changing the height of the work surface. Yet inevitably, such ergonomic tinkering attempts to improve upon the body's natural processes by choosing the right way to move (painless) as opposed to the wrong way (painful). Once the choice is made, the next step is to compartmentalize or isolate right from wrong. One compartment moves, the other doesn't.
That's where things turn ugly. As motion is restricted, supporting functions shared by the "good" and the "bad" are undermined or lost entirely. The quest to eliminate bad movement by administering concentrated doses of good movement actually leads to worse movement. This drags the ergonomic expert deeper into the role of redesigning the workers as well as the workplace. There are alternating episodes of _pain/pain abatement through motion management/and more pain_ as ergonomics selects which functions are deemed necessary and discards those that are not. There's no stopping the merry-go-round. It wouldn't be a big deal if we were just talking about substituting one piece of furniture for another. This amounts to practicing surgery without a knife. The pile of discarded functions gets larger and larger.
Here's another example of motion management run amok, one that specifically applies to the PC. A wrist brace discards unrestricted flexion and extension in the wrist. The elbow is expected to replace the lost functions. But the normal rollover or crossover function of the two bones in the forearm is limited by the brace, which means that the elbow cannot perform this task very well and is under increased stress. The shoulder then gets involved, pulling the neck and upper back forward and down. Hence, the original dysfunction—loss of vertical alignment—is aggravated.
An ergonomically correct keyboard, mouse, workstation, or chair does basically the same thing. It shifts work to other musculoskeletal components. The dysfunctional muscular compensation that is already present responds with even more compensation. In the short run, there may be pain relief that convinces us that we are on the right track. But that's an illusion. All that is happening is that we are sacrificing another virgin to appease the gods of unintended consequences. A formerly functional elbow or other joint is now being thrown into a dysfunctional state. Misaligned and overtaxed, it too is headed for breakdown. Ergonomics practices serial sacrifice—serial carnage—as we destroy joint after joint, function after function, in the crusade to reengineer the human body.
## Natural Acts
Earlier in the book, when we discussed design range of motion, I pointed out that the human body is capable of "doing what it can do." By that I mean that the ability to perform a given function—muscular contraction, joint articulation, or what have you—confirms that nothing unnatural is happening. A ballerina's ability to dance on her toes is natural; she has the supporting muscles and other mechanisms. But the ballerina cannot expect to use her body only for that one purpose. The body is a total unit. Its functions interact in a balanced way from head to foot. What the dancer does with her head is as important as what happens with her feet and toes.
A PC user is the functional antithesis of the ballerina: Work is done by ten fingers instead of ten toes. In both cases, though, being pain free depends on the total functional integrity of the body. If the ballerina wears a knee brace, she affects the interaction between the hip and the knee, and the hip, knee, and ankle. It will change the way she dances. Likewise, the PC user who wears a wrist brace is altering the interaction between the fingers and the wrist, and the fingers, wrist, elbow, and shoulder. Moreover, the kinetic chain doesn't stop there. For both of them, it extends down the back (and up) to the hips, knees, ankles, and feet.
At any point patching or reengineering a link in the chain will have a direct effect on all the others. The next major articulating joint down the line from the brace will get hit the hardest. Before long it too is a candidate for a brace, which makes vulnerable the next major articulating joint, and so on until the body is bundled and bandaged like an Egyptian mummy.
Preventive bracing or preventive ergonomic reengineering is just as bad. These musculoskeletal interrelationships are being changed no matter whether the worker is functional or dysfunctional. Insurance company rules that encourage companies to force workers to wear back braces are actually making pain and back problems more likely. The brace is designed to provide the back with a stronger foundation to allow for heavy lifting. But it prevents the hips—which are the strong foundation—from doing their job; they weaken as a result.
Many grocery store chains and trucking firms require that vestlike back braces be worn by their employees. Whenever I see a clerk or a driver wearing his or her brace undone, I ask about it. Every time they say, "Damned brace gets in my way!" And it does. Those are the functional workers speaking. They don't need the help. The dysfunctional workers do, but they end up losing what minimal hip strength and stability remains. When they go home without the brace, they are in maximum danger of injury because their hips have been reengineered right out of business.
I'll make a prediction: Before long some genius in an insurance company or the government is going to get the idea of requiring all PC users to wear wrist braces. They'll pass it off as being the same thing as forcing drivers and their passengers to wear seat belts. If and when that happens, we'll look back on 120 million people in chronic pain as the golden age of health and fitness.
My favorite illustration in this book, Figure 13.1, is artist Wendy Wray's version of a Digital Age knight in a suit of armor. The original idea behind it was to show you the ridiculous position we're going to be in if we continue subscribing to the false promise of ergonomic solutions: _You've got mail!—But first put on your chain mail_.
What Wendy discovered, when she did her research, was that old suits of armor that are on display in museums all over the world are actually fossil records of the oldest and best brace of them all—the human body. The makers of suits of armor molded the product to fit the fully functional design of their customers: head high, shoulders back, spine curved, chest expanded, hips square. These "tin men" didn't come off a drawing board. What's visible on the outside is a product of what was once on the inside: muscles to bear lances and lanterns, bones to stand and deliver. The knight in shining armor was sculpted by days of fluid motion.
**Figure 13.1 A Knight on-line and in-line**.
PCs don't need to be redesigned, nor do we. The design we were born with is right and ready for all seasons. It can take us from Camelot to cyberspace and beyond. Time's arrow stops only if we do. As always, the art of being—from being human to being digital—starts with being in motion. Look into the glittering surface of the armor, look into the past, and see the future—a future that doesn't have to hurt.
1. _The Surgeon General's Report on Physical Activity and Health_ , July 11, 1996; Department of Health and Human Services, Washington, DC.
# Acknowledgments
I feel like I'm rounding up the usual suspects. The first is Roger Gittines, my coauthor. A beautiful friendship continues, as well as a solid partnership that has now yielded three books—with more to follow. Thanks again to Brian Bradley, the Egoscue Method Clinic director, and Erica Lusk, video therapy director, for being such good functional models and good sports. Therapists Liba, Paul, and Jamie provided valuable assistance.
Artist Wendy Wray's drawings give new meaning to the old line "Seeing is believing." Photographer Scott Crain came through for us with high-quality work under tight deadline pressure. Robin Michaelson, our editor, made life pain free, and her boss Irwyn Applebaum gave us a second chance. He runs a first-class operation.
_Also by Pete Egoscue with Roger Gittines_
_PAIN FREE_
A Revolutionary Method for Stopping Chronic Pain
#
ABOUT
THE
AUTHORS
**Pete Egoscue** , an anatomical physiologist since 1978, operates the Egoscue Method Clinic in San Diego. His exercise therapy program is acclaimed worldwide for treating chronic musculoskeletal pain attributed to workplace and sports injuries, accidents, aging, and other conditions. He is also author with Roger Gittines of _Pain Free: A Revolutionary Method for Stopping Chronic Pain_ and _The Egoscue Method of Health Through Motion_.
**Roger Gittines** is a writer living in Washington, D.C.
**_Free yourself of chronic pain—right now_**
**PAIN
FREE**
**A Revolutionary Method for Stopping Chronic Pain**
**— Pete Egoscue —**
**with Roger Gittines**
**_Pain Free_ offers detailed photographs and step-by-step instructions for dozens of E-cises that will have you feeling positive results within twenty to thirty minutes. And the best part is that you won't have to give up or limit your favorite activities, purchase an expensive mattress, or pop a daily dose of prescription pills**.
___ **10630-9 $23.95/$32.95**
**Ask for this book at your local bookstore or use this page to order**.
Please send me the book I have checked above. I am enclosing $_____(add $2.50 to cover postage and handling). Send check or money order, no cash or C.O.D.'s, please.
Name_______________________________________________________
Address_____________________________________________________
City/State/Zip______________________________________________
Send order to: Bantam Books, Dept. NF 5, 2451 S. Wolf Rd., Des Plaines, IL 60018 Allow four to six weeks for delivery.
Prices and availability subject to change without notice.
| {
"redpajama_set_name": "RedPajamaBook"
} | 33 |
I had my first hockey bus trip and it was very fun. We drove 10 hours to Fargo, ND and then played in the tournament and came home. On the way there, I slept most of the time because we had to be on the bus at 7am and I am not a morning person at all. I sat with my best friend/the other goalie on my team and we listened to music and watched Netflix and we all just had so much fun.
Once we got to Fargo we went to Walmart and on the way to Walmart a couple of the girls on my team and I saw a restaurant called "Space Aliens" and we thought it looked so fun so we decided to go there that night to eat because it was walking distance from our hotel. The food at the restaurant was really good and they had a little arcade there so after dinner we played a bunch of games and ran around.
On Friday, we had our first game, we all loaded into the bus with our gear and we went to the rink. The rink was really nice. It had two ice surfaces and really smooth ice on both. We won our first game 5-2 which was really nice. On Saturday we had our second game and we won 5-1 and I played. In our third game we lost 2-1.
We didn't place in the tournament because there were 16 teams and you had to win all the games to place but we still got to play a game on Sunday and we lost 1-0 and I played. It's was just a "friendly" game.
On the way back from Fargo everyone was so tired. We all slept for most of the ride again, except the last one or two hours we all got a lot of energy and we were playing music and singing.
When we were on the trip, if the bus was going to the mall or going somewhere to eat we all had to go on the bus or we had to stay at the hotel because no parents had their cars. The coaches and manager for my team did a really amazing job of getting us to the arenas and everywhere on time all weekend.
I had so much fun in Fargo. It was an amazing experience. It was a lot of fun on the bus playing music and hanging out with my team. That's how my first bus trip went and it was super fun. | {
"redpajama_set_name": "RedPajamaC4"
} | 291 |
The Corporate Challenge presented by Chick-fil-A Birmingham gives local businesspeople a fun and unique outlet to celebrate their own company's culture of healthy behaviors, and also the chance to compete against their neighbors! The Corporate Challenge will be full of fiercely fought battles between companies of similar size including games of tug of war, corn hole and kickball, as well as t-shirt contests and charity fundraising. In addition to the fun aspect of the event, the Corporate Challenge will also allow you to make contacts and develop professional relationships with at least 50 other influential companies in the Birmingham area. Get excited for warmer weather and a day of tailgating with your family and friends while cheering on your co-workers!
Participants and family members in the Corporate Challenge can park free of charge in the Innovation Depot parking lot and throughout downtown.
For any general questions related to the Corporate Challenge or interest in getting involved in some capacity, please contact Caleb Schmidt (caleb@knighteady.com).
You are encouraged to use the Corporate Challenge presented by Chick-fil-A Birmingham logo. Show it off and promote your company's participation in the Corporate Challenge. Below are logo files that may be used in both internal and external promotions, including your company t-shirts!
All equipment required for each event, such as basketballs, jump ropes, soccer balls, corn hole sets, ropes, and footballs, will be provided. Participants are not required to bring any sports equipment apart from shoes. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,090 |
{"url":"https:\/\/en.wikipedia.org\/wiki\/Supersingular_elliptic_curve","text":"# Supersingular elliptic curve\n\nIn algebraic geometry, supersingular elliptic curves form a certain class of elliptic curves over a field of characteristic p\u00a0>\u00a00 with unusually large endomorphism rings. Elliptic curves over such fields which are not supersingular are called ordinary and these two classes of elliptic curves behave fundamentally differently in many aspects. Hasse (1936) discovered supersingular elliptic curves during his work on the Riemann hypothesis for elliptic curves by observing that in positive characteristic elliptic curves could have endomorphism rings of unusually large rank 4, and Deuring (1941) developed their basic theory.\n\nThe term \"supersingular\" has nothing to do with singular points of curves, and all supersingular elliptic curves are non-singular. It comes from the phrase \"singular values of the j-invariant\" used for values of the j-invariant for which a complex elliptic curve has complex multiplication. The complex elliptic curves with complex multiplication are those for which the endomorphism ring has the maximal possible rank 2. In positive characteristic it is possible for the endomorphism ring to be even larger: it can be an order in a quaternion algebra of dimension 4, in which case the elliptic curve is supersingular. The primes p such that every supersingular elliptic curve in characteristic p can be defined over the prime subfield ${\\displaystyle F_{p}}$ rather than ${\\displaystyle F_{p^{m}}}$ are called supersingular primes.\n\n## Definition\n\nThere are many different but equivalent ways of defining supersingular elliptic curves that have been used. Some of the ways of defining them are given below. Let ${\\displaystyle K}$ be a field with algebraic closure ${\\displaystyle {\\overline {K}}}$ and E an elliptic curve over K.\n\n\u2022 The ${\\displaystyle {\\overline {K}}}$-valued points ${\\displaystyle E({\\overline {K}})}$ have the structure of an abelian group. For every n, we have a multiplication map ${\\displaystyle [n]:E\\to E}$. Its kernel is denoted by ${\\displaystyle E[n]}$. Now assume that the characteristic of K is p\u00a0>\u00a00. Then one can show that either\n${\\displaystyle E[p^{r}]({\\overline {K}})\\cong {\\begin{cases}0&{\\mbox{or}}\\\\\\mathbb {Z} \/p^{r}\\mathbb {Z} \\end{cases}}}$\nfor r = 1, 2, 3, ... In the first case, E is called supersingular. Otherwise it is called ordinary. In other words, an elliptic curve is supersingular if and only if the group of geometric points of order p is trivial.\n\u2022 Supersingular elliptic curves have many endomorphisms over the algebraic closure ${\\displaystyle {\\overline {K}}}$ in the sense that an elliptic curve is supersingular if and only if its endomorphism algebra (over ${\\displaystyle {\\overline {K}}}$) is an order in a quaternion algebra. Thus, their endomorphism algebra (over ${\\displaystyle {\\overline {K}}}$) has rank 4, while the endomorphism group of every other elliptic curve has only rank 1 or\u00a02. The endomorphism ring of a supersingular elliptic curve can have rank less than 4, and it may be necessary to take a finite extension of the base field K to make the rank of the endomorphism ring 4. In particular the endomorphism ring of an elliptic curve over a field of prime order is never of rank 4, even if the elliptic curve is supersingular.\n\u2022 Let G be the formal group associated to\u00a0E. Since K is of positive characteristic, we can define its height ht(G), which is 2 if and only if E is supersingular and else is\u00a01.\n\u2022 We have a Frobenius morphism ${\\displaystyle F:E\\to E}$, which induces a map in cohomology\n${\\displaystyle F^{*}:H^{1}(E,{\\mathcal {O}}_{E})\\to H^{1}(E,{\\mathcal {O}}_{E})}$.\nThe elliptic curve E is supersingular if and only if ${\\displaystyle F^{*}}$ equals 0.\n\u2022 We have a Frobenius morphism ${\\displaystyle F:E\\to E}$, which induces a map on the global 1-forms\n${\\displaystyle F^{*}:H^{0}(E,\\Omega _{E}^{1})\\to H^{0}(E,\\Omega _{E}^{1})}$.\nThe elliptic curve E is supersingular if and only if ${\\displaystyle F^{*}}$ equals 0.\n\u2022 An elliptic curve is supersingular if and only if its Hasse invariant is 0.\n\u2022 An elliptic curve is supersingular if and only if the group scheme of points of order p is connected.\n\u2022 An elliptic curve is supersingular if and only if the dual of the Frobenius map is purely inseparable.\n\u2022 An elliptic curve is supersingular if and only if the \"multiplication by p\" map is purely inseparable and the j-invariant of the curve lies in a quadratic extension of the prime field of K, a finite field of order p2.\n\u2022 Suppose E is in Legendre form, defined by the equation ${\\displaystyle y^{2}=x(x-1)(x-\\lambda )}$, and p is odd. Then E is supersingular if and only if the sum\n${\\displaystyle \\sum _{i=0}^{n}{n \\choose {i}}^{2}\\lambda ^{i}}$\nvanishes, where ${\\displaystyle n=(p-1)\/2}$. Using this formula, one can show that there are only finitely many supersingular elliptic curves over K (up to isomorphism).\n\u2022 Suppose E is given as a cubic curve in the projective plane given by a homogeneous cubic polynomial f(x,y,z). Then E is supersingular if and only if the coefficient of (xyz)p\u20131 in fp\u20131 is zero.\n\u2022 If the field K is a finite field of order q, then an elliptic curve over K is supersingular if and only if the trace of the q-power Frobenius endomorphism is congruent to zero modulo p.\nWhen q=p is a prime greater than 3 this is equivalent to having the trace of Frobenius equal to zero (by the Hasse bound); this does not hold for p=2 or 3.\n\n## Examples\n\n\u2022 If K is a field of characteristic 2, every curve defined by an equation of the form\n${\\displaystyle y^{2}+a_{3}y=x^{3}+a_{4}x+a_{6}}$\nwith a3 nonzero is a supersingular elliptic curve, and conversely every supersingular curve is isomorphic to one of this form (see Washington2003, p.\u00a0122).\n\u2022 Over the field with 2 elements any supersingular elliptic curve is isomorphic to exactly one of the supersingular elliptic curves\n${\\displaystyle y^{2}+y=x^{3}+x+1}$\n${\\displaystyle y^{2}+y=x^{3}+1}$\n${\\displaystyle y^{2}+y=x^{3}+x}$\nwith 1, 3, and 5 points. This gives examples of supersingular elliptic curves over a prime field with different numbers of points.\n\u2022 Over an algebraically closed field of characteristic 2 there is (up to isomorphism) exactly one supersingular elliptic curve, given by\n${\\displaystyle y^{2}+y=x^{3}}$,\nwith j-invariant 0. Its ring of endomorphisms is the ring of Hurwitz quaternions, generated by the two automorphisms ${\\displaystyle x\\rightarrow x+\\omega }$ and ${\\displaystyle y\\rightarrow y+x+\\omega ,x\\rightarrow x+1}$ where ${\\displaystyle \\omega ^{2}+\\omega +1=0}$ is a primitive cube root of unity. Its group of automorphisms is the group of units of the Hurwitz quaternions, which has order 24 and contains a normal subgroup of order 8 isomorphic to the quaternion group.\n\u2022 If K is a field of characteristic 3, every curve defined by an equation of the form\n${\\displaystyle y^{2}=x^{3}+a_{4}x+a_{6}}$\nwith a4 nonzero is a supersingular elliptic curve, and conversely every supersingular curve is isomorphic to one of this form (see Washington2003, p.\u00a0122).\n\u2022 Over the field with 3 elements any supersingular elliptic curve is isomorphic to exactly one of the supersingular elliptic curves\n${\\displaystyle y^{2}=x^{3}-x}$\n${\\displaystyle y^{2}=x^{3}-x+1}$\n${\\displaystyle y^{2}=x^{3}-x+2}$\n${\\displaystyle y^{2}=x^{3}+x}$\n\u2022 Over an algebraically closed field of characteristic 3 there is (up to isomorphism) exactly one supersingular elliptic curve, given by\n${\\displaystyle y^{2}=x^{3}-x}$,\nwith j-invariant 0. Its ring of endomorphisms is the ring of quaternions of the form a+bj with a and b Eisenstein integers. , generated by the two automorphisms ${\\displaystyle x\\rightarrow x+1}$ and ${\\displaystyle y\\rightarrow iy,x\\rightarrow -x}$ where i is a primitive fourth root of unity. Its group of automorphisms is the group of units of these quaternions, which has order 12 and contains a normal subgroup of order 3 with quotient a cyclic group of order 4.\n\u2022 For ${\\displaystyle \\mathbb {F} _{p}}$ with p>3 the elliptic curve defined by ${\\displaystyle y^{2}=x^{3}+1}$ with j-invariant 0 is supersingular if and only if ${\\displaystyle p\\equiv 2{\\text{(mod 3)}}}$ and the elliptic curve defined by ${\\displaystyle y^{2}=x^{3}+x}$ with j-invariant 1728 is supersingular if and only if ${\\displaystyle p\\equiv 3{\\text{(mod 4)}}}$ (see Washington2003, 4.35).\n\u2022 The elliptic curve given by ${\\displaystyle y^{2}=x(x-1)(x+2)}$ is nonsingular over ${\\displaystyle \\mathbb {F} _{p}}$ for ${\\displaystyle p\\neq 2,3}$. It is supersingular for p = 23 and ordinary for every other ${\\displaystyle p\\leq 73}$ (see Hartshorne1977, 4.23.6).\n\u2022 The modular curve X0(11) has j-invariant \u221221211\u22125313, and is isomorphic to the curve y2 + y = x3x2 \u2212 10x \u2212 20. The primes p for which it is supersingular are those for which the coefficient of qp in \u03b7(\u03c4)2\u03b7(11\u03c4)2 vanishes mod p, and are given by the list\n2, 19, 29, 199, 569, 809, 1289, 1439, 2539, 3319, 3559, 3919, 5519, 9419, 9539, 9929,...\n\u2022 If an elliptic curve over the rationals has complex multiplication then the set of primes for which it is supersingular has density 1\/2. If it does not have complex multiplication then Serre showed that the set of primes for which it is supersingular has density zero. Elkies (1987) showed that any elliptic curve defined over the rationals is supersingular for an infinite number of primes.\n\n## Classification\n\nFor each positive characteristic there are only a finite number of possible j-invariants of supersingular elliptic curves. Over an algebraically closed field K an elliptic curve is determined by its j-invariant, so there are only a finite number of supersingular elliptic curves. If each such curve is weighted by 1\/|Aut(E)| then the total weight of the supersingular curves is (p\u20131)\/24. Elliptic curves have automorphism groups of order 2 unless their j-invariant is 0 or 1728, so the supersingular elliptic curves are classified as follows. There are exactly \u230ap\/12\u230b supersingular elliptic curves with automorphism groups of order 2. In addition if p\u22613 mod 4 there is a supersingular elliptic curve (with j-invariant 1728) whose automorphism group is cyclic or order 4 unless p=3 in which case it has order 12, and if p\u22612 mod 3 there is a supersingular elliptic curve (with j-invariant 0) whose automorphism group is cyclic of order 6 unless p=2 in which case it has order 24.\n\nBirch & Kuyk (1975) give a table of all j-invariants of supersingular curves for primes up to 307. For the first few primes the supersingular elliptic curves are given as follows. The number of supersingular values of j other than 0 or 1728 is the integer part of (p\u22121)\/12.\n\nprime supersingular j invariants\n2 0\n3 1728\n5 0\n7 1728\n11 0, 1728\n13 5\n17 0,8\n19 7, 1728\n23 0,19, 1728\n29 0,2, 25\n31 2, 4, 1728\n37 8, 3\u00b1\u221a15","date":"2017-06-26 11:09:30","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 46, \"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\": 0.9382873773574829, \"perplexity\": 166.63130996455249}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-26\/segments\/1498128320707.69\/warc\/CC-MAIN-20170626101322-20170626121322-00183.warc.gz\"}"} | null | null |
Quick Hit Movie Reviews #10: 'What If' & 'A Man Called Ove'
In the #10 edition of quick hit movie reviews, Eclectic Pop takes a slightly more expanded look at two marvelous movies. The first is an indie from 2013 and the second is an Oscar nominated Swedish-language dramedy. Both are quality films that tackle separately familiar premises with a unique voice.
"What If" and "A Man Called Ove" intricately combine comedy with drama and romance with reality, which is no easy feat. This is how they did it…
"What If" (2013)
What if this is one of the cutest romantic comedies of the 2000s? Well, it is. "What If" follows the palatable hipster duo, Chantry (Zoe Kazan) and Wallace (Daniel Radcliffe), as the 20-somethings embark on a quirky and "strictly platonic" relationship.
Immediately cast into the "friend zone" by Chantry, who is involved in a long-term relationship with her stuffy boyfriend, Wallace quickly realizes his feelings for Chantry fall into the more romantic side of the equation. Does Chantry feel the same way and is it worth risking their friendship to find out?
Other movies have delved into this subject with varying success, while "What If" knocks it out of the park. Chantry and Wallace make sense together from the moment they first meet and the anxiety as to whether they will figure this out is genuinely suspenseful.
The ending of most romantic comedies feels inevitable, and "What If's" never does. Radcliffe and Kazan's easygoing chemistry falls right into place as they usher one of the millennium's best rom-coms to the finish line. Rating: 8/10
"What If" is available to stream on Amazon Prime throughout August 2017.
[Image by Nordisk Films]
"A Man Called Ove" (2016)
Not too long ago, I privately pondered why there are so few movies currently being made that focus on telling a fictional character's life story. Movies like "Forrest Gump" that shepherd viewers through life's all-encompassing chapters. "A Man Called Ove" does just that.
The Swedish film tells the story of Ove (an outstanding Rolf Lassgård), a recent widower who keeps a vigilant eye on his neighbors, much to their chagrin and quiet appreciation. Having recently been let go from his job, the curmudgeonly Ove is faced with a crossroads, as his life systematically flashes before his eyes.
"A Man Called Ove" is tenderly crafted, phenomenally acted, and divinely directed. It consistently plays its poignancy to a perfection rarely captured, such as in one particular scene of heart-rending romance, which is guaranteed to leave an indelible impression upon all who see it. As a whole, it is moving without getting mushy and entirely inspiring thanks to the thoughtful spotlight it shines on all of its characters. Rating: 9.5/10
"A Man Called Ove" is streaming on Amazon Prime throughout August 2017. It is also available on Netflix via their mail service.
[Featured Image by Entertainment One]
Labels: Amazon Prime, movies, Quick Hit Movie Reviews | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,673 |
A git tool with an easy terminal interface.
# Features
- [x] git status
- [x] git add [files]
- [x] git reset -- [files]
- [x] git commit [files]
- [x] git log
- [x] git reset <commit>
- [x] git diff file
- [x] git branch
- [ ] git merge (handling conflict)
- [ ] git pull/push
# Install & Usage
```bash
$ npm install -g git-commander
$ git-commander
```
# Requirements
- **git** >= 2.4
- **nodejs** >= 0.12
- **blessed** >= 0.1.7
- **lodash** >= 3.0
# Key Configuration
We have two key sets _vi_ and _mc_ preconfigured. The default one is _vi_.
##### Using the mc key set
You will need to place a file at `~/.config/git-commander/config.json` with the following content:
```
{
"keySet": "mc"
}
```
##### Redefining keys one by one
You also can redefine keys one by one if you would like. You'll need to extend your `~/.config/git-commander/config.json` file with a key called `keys` and put all your key definitions there. For example if you would like to use the _mc_ key set and make key _x_ quit the application, you'll need to add the following:
```
{
"keySet": "mc",
"keys": {
"common": {
"quit": [
"x"
]
}
}
}
```
You can find [default settings here](https://github.com/golbin/git-commander/tree/master/config/key).
# Troubleshootings
## ANSI color codes are displayed
ANSI color codes are being displayed if you set "always" for color settings in your **.gitconfig**. For fixing this, set "auto" for color settings like below.
```
[color]
# diff = always
diff = auto
status = auto
ui = auto
branch = auto
```
## Non-ascii character problem
If you use non-ascii character for source files, You need to disable
the **core.quotepath** option using following command:
```bash
$ git config --global core.quotepath false
```
# License
MIT
| {
"redpajama_set_name": "RedPajamaGithub"
} | 416 |
Elevate guest experiences with Staging Concept's decks, rails, and platforms that create the ultimate VIP Spaces for your venue.
From custom drink rails to premium portable seating, Staging Concepts can design a VIP deck or space that is perfect for your venue. Give your guests an unrivaled view and make their time in your facility memorable! In addition to superior design, product strength and durability, the flexibility of Staging Concepts' products make its equipment a great choice for any venue. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,199 |
Starbucks, citing ocean threat, is ditching plastic straws
Many Maine restaurants have also stopped offering plastic straws.
NEW YORK — Starbucks will eliminate plastic straws from all of its locations within two years, citing the environmental threat to oceans.
The company becomes the largest food and beverage company to do so as calls to cut waste globally grow louder . Plastic straws have become a flashpoint.
More Maine restaurants opting for alternatives to plastic straws
A week after its hometown banned plastic drinking straws and utensils, the Seattle company said Monday that by 2020, it will be using straws made from biodegradable materials like paper and specially designed lids. The company already offers alternative straws in Seattle.
Other cities, like Fort Meyers, have banned plastic straws. Similar proposals are being considered in places like New York and San Francisco.
The waste issue is coming up in company boardrooms, though Starbucks is taking the lead among global companies on straws.
In February, Dunkin' Donuts said that it would eliminate polystyrene foam cups from its stores by 2020.
McDonald's shareholders voted down a proposal requesting a report on plastic straws in May.
McDonald's recently said it would switch to paper straws in the United Kingdom and Ireland by next year, and test alternatives to plastic straws in some U.S. locations. The burger chain said this year that it would use only recycled or other environmentally friendly materials for its soda cups, Happy Meal boxes and other packaging by 2025.
While plastic drinking straws have become one of the more high-profile issues environmentally, they make up only about 4 percent of the plastic trash by number of pieces, and far less by weight. Straws add up to about 2,000 tons of the nearly 9 million tons of plastic waste that ends up in waters around the globe each year.
The strawless lids will begin to appear in Seattle and Vancouver Starbucks this fall, with phased rollouts within the U.S. and Canada to follow next year. A global rollout of the strawless lids will follow, beginning in Europe where the will be used in select stores in France and the Netherlands, as well as in the United Kingdom.
'We're still around': Young activists continue to push for racial equity | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,378 |
package org.jitsi.impl.neomedia.rtp.remotebitrateestimator;
/**
* webrtc/webrtc/modules/remote_bitrate_estimator/include/bwe_defines.h
*
* @author Lyubomir Marinov
*/
public enum BandwidthUsage
{
kBwNormal,
kBwUnderusing,
kBwOverusing,
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,496 |
Malaysia's Johor Darul Ta'zim to miss Asian CL
71dReuters
Johor Darul Ta'zim forced out of Asian Champions League after Malaysia refuses to lift travel restrictions
HONG KONG -- Malaysian champions Johor Darul Ta'zim (JDT) will not travel to Qatar for the resumption of the Asian Champions League after the team was refused permission to leave the country by government officials.
Border closures implemented by Malaysia in March to limit the spread of the coronavirus will not be lifted to permit the club to complete their commitments in the continental championship, which restarts next week in Doha.
"Our policy remains the same. The borders are still closed," Malaysia's defence minister Ismail Sabri Yaakob was quoted as saying by local media when asked about JDT's hopes of travelling to Qatar.
Teams from across the east of the continent are due to travel to the Gulf state to play in a centralised tournament after the competition was paused in March when international travel came to a halt.
JDT, who were set to feature alongside Japan's Vissel Kobe as well as two-times champions Guangzhou Evergrande and Suwon Bluewings in the group phase of the competition, confirmed they would not challenge the government's stance, which will also affect the domestic Malaysia Cup tournament.
"While JDT are extremely disappointed in not being able to participate in Asia's highest club competition and the Malaysia Cup, we respect the decision by the Malaysian Government and understand that such safety measures need to be enforced due to the rising cases of the Covid-19 pandemic," Alistair Edwards, the club's technical director, said in a statement issued on social media. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 673 |
{"url":"http:\/\/www.emathzone.com\/tutorials\/geometry\/general-form-of-equation-of-circle.html","text":"# General Form of Equation of Circle\n\nConsider the equation of circle in general form is\n\nWhere $g,f,c$ are any constant values.\nRearrange the terms of the above equation (i) of circle, we have\n\nIn this equation we use the method of completing squares, so for this we need to add ${g^2}$ and ${f^2}$ on both sides of the equation (ii). i.e.\n\nCompare this equation of circle with standard equation of circle ${\\left( {x - h} \\right)^2} + {\\left( {y - k} \\right)^2} = {r^2}$ we get the radius $\\sqrt {{g^2} + {f^2} - c}$ and centre $\\left( { - g, - f} \\right)$.\nThis shows that the equation ${x^2} + {y^2} + 2gx + 2fy + c = 0$ represents a circle with centre $\\left( { - g, - f} \\right)$ and radius $\\sqrt {{g^2} + {f^2} - c}$. This is called the general equation of circle.\n\nExample: Find the centre and radius of the circle with the given equation of circle\n\nSolution: We have given equation of circle is\n\nWe observe that in this equation of circle the coefficients of ${x^2}$ and ${y^2}$ is 7, but in the general form of equation of circle coefficients must be equal to 1.\nTo convert the given equation in form of general equation, dividing given equation both sides by 7, we get\n\nThe above equation cam be written as\n\nCompare this equation with the general equation of circle as\n\nWe have the values $g = \\frac{9}{7}$, $f = - \\frac{5}{7}$ and $c = 2$.\n\nHence the centre of the circle is $\\left( { - g, - f} \\right) = \\left( { - \\frac{9}{7}, - \\left( { - \\frac{5}{7}} \\right)} \\right) = \\left( { - \\frac{9}{7},\\frac{5}{7}} \\right)$\n\nRadius of the circle is $r = \\sqrt {{g^2} + {f^2} - c} = \\sqrt {{{\\left( { - \\frac{9}{7}} \\right)}^2} + {{\\left( {\\frac{5}{7}} \\right)}^2} - 2} = \\frac{{2\\sqrt 2 }}{7}$","date":"2016-10-28 06:25:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 16, \"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\": 24, \"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\": 0.9149675369262695, \"perplexity\": 137.28570536926708}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-44\/segments\/1476988721558.87\/warc\/CC-MAIN-20161020183841-00371-ip-10-171-6-4.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction}
In recent years, concepts which has been restricted to foundation of quantum
mechanics have been considerably enlarged by spreading out to different
domains of physics. With the introduction of measurements such as separability
\cite{Peres,Horodecki,Simon} and concurrence \cite{Wootters,Werner}, and
the\ wider understanding that entanglement, and so nonlocality, is at the core
of many-body phenomena as quantum-phase transition \cite{Latorre},
superconductivity \cite{BCS} and Bose-Einstein condensation \cite{Pan05}, we
are considerably far from the time when entanglement and nonlocality were
confined to fundamental aspects of quantum mechanics. On the other hand, the
experimental techniques developed over the last decades for manipulating
atom-field interaction have enabled the building of macroscopic atomic
ensembles and the experimental verification of fundamental concepts in
macroscopic scales \cite{Korbicz}.\ It is worth mentioning the rapid growth of
quantum information theory which has conferred to its basic ingredients ---
the phenomena of superposition of states and decoherence, entanglements and
nonlocality --- a great deal of advances towards the accomplishments of
quantum logical devices.
Among the standard tools to generate and detect multipartite entanglements,
experiments in Bose-Einstein condensates (BECs) in dilute gases have deepened
our incursion towards the quantum nature of macroscopic systems. In
particular, experiments with a trapped gas of $^{87}$Rb atoms with two
different hyperfine sublevels prompt the engineering of a Josephson-like
coupling between two condensates by a laser-induced Raman
transition~\cite{Myatt97,Matthews98}. Such \textquotedblleft
internal\textquotedblright\ Josephson effect \cite{LeggettRMP} mediates
intraspecies collisions apart from interspecies one. These atom-atom
interactions empowered the investigation of the dynamics of the relative phase
of coupled condensates \cite{Hall98b} and Rabi oscillations \cite{Matthews99}
on macroscopic systems. Moreover, precise measurements of scattering lengths
has also been accomplished \cite{Hall98a}, aiming to quantify properly the
non-linear dynamics associated with collisions. In the two-mode approximation,
the coupled condensates has been employed to investigate entanglement
dynamics~\cite{Hines03,Sanz03,Pan05} and the possibility to prepare, control
and detect macroscopic superposition
states~\cite{CiracGBEC98,Gordon99,Dunningham01}. Beyond this achievements, the
analysis of the Josephson effect in this two-mode exactly soluble model may
provide a clue for the examination of macroscopic coupling arising in less
tractable form of the general theory of BECs \cite{LeggettRMP}.
Whereas in real experiments the trap potential may be considered to be a
time-independent function, excepting for small fluctuations, time-varying
scattering lengths are usually produced through Feshbach resonances while, as
pointed out in Ref. \cite{LeggettRMP}, the amplitude and phase of the laser
field may vary in time. In this connection, the present paper is devoted to
the TD version of the two-mode Hamiltonian (TMH), where the effective
frequency of the trap potential for both atomic species are TD functions, as
well as the Rabi frequency and the scattering lengths. A similar approach was
employed in Refs.~\cite{Vedral,Chen04} where, however, only the phase of the
external field inducing the Raman transition~was assumed to be a TD slowly
varying function. Instead, our treatment considers time dependence of all
Hamiltonian parameters, focusing on two particular subjects: the analyzes of
geometric phase acquired by wave function of the whole system and the
control\textbf{\ }of the dynamics of pseudo-spin states governed by the TD
TMH. Starting from Bloch states, whose preparation is achieved by applying a
laser pulse~to atoms condensed in a single hyperfine level \cite{Hall98a}, we
demonstrate that its evolution, visualized as a vector on the Bloch sphere,
can be used to control the geometric phase and the population imbalance
following from the whole wave function of the condensates. Our treatment also
permits a detailed analyzes of the relative phase between the condensed states.
In Ref.\cite{Milburn}, the authors studied the dynamics of a strongly driven
two-coupled BECs in two spatially localized modes of a double-well potential,
where the tunneling coupling between the two modes is periodically modulated.
In our work we also study the TD TMH associated to the \textquotedblleft
external\textquotedblright\ Josephson effect, analyzing its differences with
relation of the \textquotedblleft internal\textquotedblright\ Josephson effect.
Similarly to the above mentioned fundamental phenomena, the geometric phase
has overtaken its striking rule on fundamental physics to widening our
understanding of phenomena as quantum Hall effect \cite{Baily,Bruno,Kats} and
for the implementation of fault-tolerant quantum gates \cite{Zanardi}. After
its discovery by Berry on adiabatic processes \cite{Berry98}, it has been
generalized to nonadiabatic~\cite{Aharonovl87}, noncyclic~\cite{Samuel88} and
nonunitary~\cite{Tong04,Piza} quantum evolutions. Recently, it has been
investigated in different areas of physics, ranging from BECs \cite{Vedral}
and cavity quantum electrodynamics \cite{Carollo,Duzzioni} to condensed matter
\cite{Bliokh} and quantum information theory \cite{Zanardi}. In particular,
the Berry phase of mesoscopic spin in Bose-Einstein condensates, induced by a
TD slowly varying driven field, has been investigated under the TMH
\cite{Vedral,Chen04}. In our treatment, the evolution of the geometric phase
of this mesoscopic system is evaluated in a more general scenario, where all
the Hamiltonian parameters are assumed to be TD.
The paper is organized as follows. In Sec.~II we introduce and solve the
Schr\"{o}dinger equation associated to the TD TMH, presenting the evolution
operator. The dynamics of BECs for initial Bloch states is analyzed in Sec.
III, where we show that they remain as Bloch states apart from a global phase
factor accounting for the elastic collision terms. The geometric phase
acquired by the state vector of the system is presented in Sec. IV and a
detailed analyzes of its time evolution is found in Sec. V for different
regimes of the parameters. In Sec. VI we take the problem of a TMH from a
different perspective, considering the external Josephson effect instead of
the internal one. Finally, Sec. VII is devoted to our concluding remarks.
\section{The time-dependent TMH}
Under the two-mode approximation, where the quantum field operators $\Psi
_{a}=\varphi_{a}\left( \mathbf{r},t\right) a$ and $\Psi_{b}=\varphi
_{b}(\mathbf{r},t)b$ are restricted to the fundamental states $\varphi_{\ell
}\left( \mathbf{r},t\right) $ ($\ell=a,b$) \cite{CiracGBEC98,Milburn1997},
the coupled Bose-Einstein condensates are described by the TD Hamiltonian
($\hbar=1$)
\begin{align}
H\left( t\right) & =\sum_{\ell=a,b}\left[ \omega_{\ell}\left( t\right)
\ell^{\dagger}\ell+\gamma_{\ell}\left( t\right) \ell^{\dagger}\ell^{\dagger
}\ell\ell\right] +\gamma_{ab}\left( t\right) a^{\dagger}ab^{\dagger
}b\nonumber\\
& -g\left( t\right) \left( e^{-i\delta\left( t\right) }a^{\dag
}b+e^{i\delta\left( t\right) }ab^{\dag}\right) \text{,} \label{1}%
\end{align}
where $a$ and $b$ are standard bosonic annihilation operators, associated with
condensation in hyperfine levels $\left\vert 2,1\right\rangle $ and
$\left\vert 1,-1\right\rangle $, respectively
\cite{CiracGBEC98,Gordon99,Villain99}. The phase $\delta\left( t\right) $ is
associated to the detuning $\Delta(t)$ from the Raman resonance between the
atomic transition $\left\vert 2,1\right\rangle $ $\leftrightarrow\left\vert
1,-1\right\rangle $, which may be a TD function (by varying the laser
frequency), through the expression $\delta\left( t\right) =\int_{t_{0}}%
^{t}\Delta(\tau)$ $d\tau+$ $\delta_{0}$. The TD trap frequencies $\omega
_{\ell}$, the interspecies and intraspecies collision parameters $\gamma_{ab}$
and $\gamma_{\ell}$, and the Rabi frequency $g$, follow from
\begin{subequations}
\label{2}%
\begin{align}
\omega_{\ell}\left( t\right) & =\int d^{3}{\mathbf{r}}\varphi_{\ell}%
^{\ast}\left( \mathbf{r},t\right) \left[ -\frac{1}{2m}\nabla^{2}+V_{\ell
}\left( \mathbf{r},t\right) \right] \varphi_{\ell}\left( \mathbf{r}%
,t\right) \text{,}\label{2a}\\
\gamma_{\ell}\left( t\right) & =\frac{4\pi A_{\ell}\left( t\right) }%
{2m}\int d^{3}{\mathbf{r}}\left\vert \varphi_{\ell}\left( \mathbf{r}%
,t\right) \right\vert ^{4}\text{,}\label{2f}\\
\gamma_{ab}\left( t\right) & =\frac{4\pi A_{ab}\left( t\right) }{m}\int
d^{3}{\mathbf{r}}\left\vert \varphi_{a}\left( \mathbf{r},t\right)
\varphi_{b}\left( \mathbf{r},t\right) \right\vert ^{2}\text{,}\label{2g}\\
g\left( t\right) & =\frac{\Omega\left( t\right) }{2}\int d^{3}%
{\mathbf{r}}\varphi_{a}^{\ast}\left( \mathbf{r},t\right) \varphi_{b}\left(
\mathbf{r},t\right) , \label{2d}%
\end{align}
where $m$ is the atomic mass. We assume that the time dependence of the trap
potential $V_{\ell}\left( \mathbf{r},t\right) $ is generated by
adiabatically varying the trapping magnetic field.\textbf{\ }Such adiabatic
variation of the trapping field has been assumed to ensure the validity of the
two-mode approximation. The time-varying scattering lengths $A_{ab}(t)$ and
$A_{\ell}(t)$, are accomplished via Feshbach resonances, by tuning a bias
magnetic field \cite{Vogels}. Finally, as mentioned above, in real experiments
with atomic BECs the Rabi frequency may be a time-varying function since the
amplitude and phase of the pumping fields may vary in time \cite{LeggettRMP}.
Except for the Josephson-like coupling, the Fock states are eigenstates of all
the terms in Hamiltonian (\ref{1}). Thus, in order to get rid of this TD
coupling in (\ref{1}), we consider a transformation with the unitary operator%
\end{subequations}
\begin{equation}
V(t)=\exp\left[ \frac{r(t)}{2}\left( \operatorname*{e}\nolimits^{i\phi
(t)}ab^{\dagger}-\operatorname*{e}\nolimits^{-i\phi(t)}a^{\dagger}b\right)
\right] \text{,} \label{3}%
\end{equation}
(analogous to that defined in Ref.~\cite{Chen04}) to obtain the transformed Hamiltonian%
\begin{equation}
\mathcal{H}(t)=V^{\dagger}HV-iV^{\dagger}\partial_{t}V=\sum_{\ell
=a,b}\widetilde{\omega}_{\ell}(t)n_{\ell}+\mathcal{H}_{el}(t)+\mathcal{H}%
_{inel}(t)\text{,} \label{4}%
\end{equation}
where $n_{\ell}=\ell^{\dagger}\ell$ is the number operator associated to each
condensate having effective frequency
\begin{equation}
\widetilde{\omega}_{\ell}\left( t\right) =\omega_{\ell}\left( t\right)
+\left( 2\delta_{\ell b}-1\right) g\left( t\right) \cos\left[ \phi\left(
t\right) -\delta\left( t\right) \right] \tan\left[ r\left( t\right)
/2\right] \text{.} \label{5}%
\end{equation}
In the framework associated to the transformation (\ref{3}), the system ends
up with an inelastic collision term apart from the elastic one already present
in (\ref{1}). The Hamiltonians accounting for such interactions, also weighted
by the TD function $\Lambda(t)=\gamma_{a}(t)+\gamma_{b}(t)-\gamma_{ab}(t)$,
are given by%
\begin{subequations}
\label{6}%
\begin{align}
\mathcal{H}_{el}(t) & =\left\{ \gamma_{a}(t)\cos^{2}\left[ r(t)/2\right]
+\gamma_{b}(t)\sin^{2}\left[ r(t)/2\right] -\frac{\Lambda(t)}{4}\sin
^{2}\left[ r(t)\right] \right\} \left( a^{\dagger}\right) ^{2}%
a^{2}\nonumber\\
& +\left\{ \gamma_{a}(t)\sin^{2}\left[ r(t)/2\right] +\gamma_{b}%
(t)\cos^{2}\left[ r(t)/2\right] -\frac{\Lambda(t)}{4}\sin^{2}\left[
r(t)\right] \right\} \left( b^{\dagger}\right) ^{2}b^{2}\nonumber\\
& +\left\{ \gamma_{ab}(t)+\Lambda(t)\sin^{2}\left[ r(t)\right] \right\}
a^{\dagger}ab^{\dagger}b\text{,}\label{6a}\\
\mathcal{H}_{inel}(t) & =\left\{ \frac{\left[ \gamma_{b}(t)-\gamma
_{a}(t)\right] }{2}\sin\left[ r(t)\right] -\frac{\Lambda(t)}{4}\sin\left[
2r(t)\right] \right\} \operatorname*{e}\nolimits^{-i\phi(t)}\left(
a^{\dagger}\right) ^{2}ab\nonumber\\
& +\left\{ \frac{\left[ \gamma_{b}(t)-\gamma_{a}(t)\right] }{2}\sin\left[
r(t)\right] +\frac{\Lambda(t)}{4}\sin\left[ 2r(t)\right] \right\}
\operatorname*{e}\nolimits^{-i\phi(t)}a^{\dagger}b^{\dag}b^{2}\nonumber\\
& +\frac{\Lambda(t)}{4}\sin^{2}\left[ r(t)\right] \left( \operatorname*{e}%
\nolimits^{-i\phi(t)}a^{\dagger}b\right) ^{2}+\mathrm{h{.c.}}\text{.}
\label{6b}%
\end{align}
The form of Hamiltonian (\ref{4}) is established provided that the TD
parameters $r(t)$ and $\phi(t)$ satisfy the coupled differential equations
\end{subequations}
\begin{subequations}
\label{7}%
\begin{align}
\overset{.}{r}(t) & =2g(t)\sin\left[ \phi\left( t\right) -\delta\left(
t\right) \right] \mathrm{,}\label{7a}\\
\overset{.}{\phi}(t) & =\omega(t)+2g(t)\cot\left[ r(t)\right] \cos\left[
\phi\left( t\right) -\delta\left( t\right) \right] \text{{,}} \label{7b}%
\end{align}
where
\end{subequations}
\begin{equation}
\omega\left( t\right) =\omega_{a}\left( t\right) -\omega_{b}\left(
t\right) \text{.} \label{8}%
\end{equation}
The expression (\ref{8}) represents an effective frequency for the system
composed by the two-mode condensate, which plays an important role in the
solutions of the characteristic equations (\ref{7}). In the Appendix we
present a comprehensive analyzes of the analytical solutions of the Eqs.
(\ref{7}) for the on- and off-resonant regimes which are defined by comparing
the effective frequency $\omega(t)$ with the detuning between the laser field
and Raman transition $\Delta(t)$. The on-resonant regime, where $\Delta
(t)=\omega\left( t\right) $, implies that the detuning from Raman transition
must equals the effective frequency of the two-mode condensate. Otherwise, we
have the off-resonant regime, where $\Delta(t)=\omega(t)-\varpi$, $\varpi$
being some constant.
Similar coupled differential equations were obtained by Smerzi \textit{et al}.
\cite{Smerzi 1997} in a semi-classical treatment of the double-well problem,
and by Chen \textit{et al}. \cite{Chen04} in a full quantum approach of the
BECs in the two-mode approximation. In both references all the parameters in
their Hamiltonians are constants, except for $\delta\left( t\right) $ which,
in Ref. \cite{Chen04}, is an adiabatically time-varying parameter.
After the experiments by Hall and co-workers with $^{87}$Rb \cite{Hall98a},
where the scattering lengths satisfy the relation $A_{a}:A_{ab}:A_{b}%
=1.03:1:0.97$, and consequently $\gamma_{a}\simeq\gamma_{b}\simeq\gamma
_{ab}/2$ (assuming spatial Gaussian function), a number of papers have driven
attention to this particular case \cite{Liliana,Chen04} whose Schr\"{o}dinger
equation is exactly soluble. However, if the proportion $1.03:1:0.97$ is
broken, the system is not exactly integrable, but admits approximated
solutions as shown in Refs. \cite{Chen04,Vedral}. In our paper we are
concerned with specific solutions of the characteristic equations (\ref{7}),
under the rotating-wave approximation, which turn negligible the contribution
of the inelastic interactions compared to the elastic one. This is done by
substituting the solutions for $r(t)$ and $\phi(t)$, obtained in the Appendix,
into Eqs. (\ref{5}) and (\ref{6}), and rewriting Hamiltonian (\ref{4}) in the
interaction picture. Thus, after a time average of the TD parameters appearing
in this Hamiltonian, we analyze the conditions leading to the effective
interaction
\begin{equation}
\mathcal{H}_{eff}(t)\simeq\sum\nolimits_{\ell=a,b}\widetilde{\omega}_{\ell
}(\tau)n_{\ell}+\mathcal{H}_{el}(\tau)\text{.} \label{9}%
\end{equation}
By adopting this procedure, where the inelastic interactions becomes
despicable, we get he evolution operator $\mathcal{U}\left( t,t_{0}\right)
=\exp\left( -i\int_{t_{0}}^{t}\mathcal{H}_{eff}(\tau)d\tau\right) $ and,
consequently, a prepared state $\left\vert \psi\left( t_{0}\right)
\right\rangle $ evolves according to Hamiltonian (\ref{1}) as
\begin{equation}
\left\vert \psi\left( t\right) \right\rangle =V\left( t\right)
\mathcal{U}\left( t,t_{0}\right) V^{\dagger}\left( t_{0}\right) \left\vert
\psi\left( t_{0}\right) \right\rangle \text{.} \label{10}%
\end{equation}
\section{Dynamics of BECs for initial Bloch states}
Following Arecchi \textit{et al.}~\cite{Arecchi72} and Dowling \textit{et
al.}~\cite{Dowling94}, we recall that the Bloch states (BS), also called
atomic coherent states, spanned in the Dicke basis $\left\vert
j,m\right\rangle $, where $j=N/2$ and $\left\vert m\right\vert \leq j$, are
obtained through a specific rotation on the reference state $\left\vert
j,j\right\rangle $,
\begin{equation}
\left\vert \alpha,\beta\right\rangle =e^{\frac{\alpha}{2}\left( e^{i\beta
}\hat{J}_{-}-e^{-i\beta}\hat{J}_{+}\right) }\left\vert j,j\right\rangle
\text{,} \label{15}%
\end{equation}
where $N$ is the number of condensed particles, $J_{+}$, $J_{-}$ (together
with $J_{z}$), are the generators of the $su(2)$ algebra, and $\left(
\alpha,\beta\right) $ are the polar and the azimuthal angles, respectively,
defined on the Bloch sphere. The Heisenberg angular-momentum uncertainty
relation for the BS reduces to
\begin{equation}
\langle\left( \Delta J_{x^{\prime}}\right) ^{2}\rangle\langle\left( \Delta
J_{y^{\prime}}\right) ^{2}\rangle=\frac{1}{4}\left\vert \langle J_{z^{\prime
}}\rangle\right\vert ^{2}\text{,} \label{16}%
\end{equation}
with the mean values being calculated in a rotated coordinate system
$x^{\prime},y^{\prime},z^{\prime}$,where $z^{\prime}$ is an axis in the
($\alpha$,$\beta$) direction through the center of the Bloch sphere.
Therefore, the Bloch vector is defined as the unit vector
\begin{equation}
\mathbf{n}=\left( \sin{\alpha}\cos{\beta}\text{,}\sin{\alpha}\sin{\beta
}\text{,}\cos{\alpha}\right) \text{,} \label{17}%
\end{equation}
in $z^{\prime}$-axis. Using the Schwinger relations
\begin{subequations}
\label{17l}%
\begin{align}
J_{x} & =\frac{1}{2}\left( a^{\dagger}b+ab^{\dagger}\right) \text{,}%
\label{17la}\\
J_{y} & =\frac{1}{2i}\left( a^{\dagger}b-ab^{\dagger}\right)
\text{,}\label{l7lb}\\
J_{z} & =\frac{1}{2}\left( a^{\dagger}a-b^{\dagger}b\right) \text{.}
\label{17lc}%
\end{align}
with $J_{\pm}=J_{x}\pm iJ_{y}$ and the basis states $\left\{ \left\vert
j,m\right\rangle =\left\vert N/2,\left( N_{a}-N_{b}\right) /2\right\rangle
\right\} \equiv\left\{ \left\vert N_{a}\right\rangle \left\vert
N_{b}\right\rangle \equiv\left\vert N_{a},N_{b}\right\rangle \right\} $,
where $N_{a}$ and $N_{b}$ ($N=N_{a}+N_{b}$) stand for the number of atoms in
the condensates, such that $\left\vert j,j\right\rangle \Longleftrightarrow
\left\vert N,0\right\rangle $, it is straightforward to check that the BS can
be defined through bosonic operators as
\end{subequations}
\begin{equation}
\left\vert \alpha,\beta\right\rangle =\frac{1}{\sqrt{N!}}\left[ \cos\left(
\frac{\alpha}{2}\right) a^{\dagger}+\sin\left( \frac{\alpha}{2}\right)
\operatorname*{e}\nolimits^{i\beta}b^{\dagger}\right] ^{N}\left\vert
0,0\right\rangle \text{.} \label{18}%
\end{equation}
This state has a well-defined relative phase $\beta$ between the two bosonic modes.
Now, it is evident from relations (\ref{17l}) that the unitary transformation
$V\left( t\right) $ turns to be exactly the rotation operator $e^{\frac
{\alpha}{2}\left( e^{i\beta}\hat{J}_{-}-e^{-i\beta}\hat{J}_{+}\right) }$, if
one considers $r\left( t\right) =\alpha$ and $\phi\left( t\right) =\beta$.
Therefore, it is easy to demonstrate through Eq. (\ref{10}) that an initial BS
$\left\vert \psi\left( t_{0}\right) \right\rangle =$ $\left\vert \alpha
_{0},\beta_{0}\right\rangle $ $=$ $\left\vert r_{0},\phi_{0}\right\rangle $
evolves to another BS%
\begin{align}
\left\vert {\psi}(t)\right\rangle & =\frac{e^{-iN\varphi_{N}(t)}}{\sqrt{N!}%
}\left[ \cos\left( \frac{r(t)}{2}\right) a^{\dagger}+\sin\left(
\frac{r(t)}{2}\right) e^{i\phi\left( t\right) }b^{\dagger}\right]
^{N}\left\vert 0,0\right\rangle \text{,}\nonumber\\
& =e^{-iN\varphi_{N}(t)}\left\vert r(t),\phi\left( t\right) \right\rangle
\label{19}%
\end{align}
apart from the global phase factor $e^{-iN\varphi_{N}(t)}$, where%
\begin{align}
\varphi_{N}(t) & =\int_{t_{0}}^{t}\left\{ \widetilde{\omega}_{a}%
(\tau)+(N-1)\left[ \gamma_{a}(\tau)\cos^{2}\left[ r(\tau)/2\right] \right.
\right. \nonumber\\
& +\left. \left. \gamma_{b}(\tau)\sin^{2}\left[ r(\tau)/2\right]
-\frac{\Lambda(\tau)}{4}\sin^{2}\left[ r(\tau)\right] \right] \right\}
d\tau\text{.} \label{19a}%
\end{align}
The relative phase between the condensates $\phi(t)$ is associated to the mean
values $\left\langle J_{x}(t)\right\rangle =N\sin\left[ r(t)\right]
\cos\left[ \phi(t)\right] /2$ and $\left\langle J_{y}(t)\right\rangle
=N\sin\left[ r(t)\right] \sin\left[ \phi(t)\right] /2$, whereas $r(t)$ is
related to the population imbalance, $\Delta N(t)=\left\langle N_{a}%
-N_{b}\right\rangle =2\left\langle J_{z}(t)\right\rangle $, through the
relation
\begin{equation}
\Delta N(t)=N\cos\left[ r(t)\right] \text{.} \label{20}%
\end{equation}
We stress that according to the evolution operator, Eq. (\ref{10}), the
evolved state (\ref{19}) remains a BS (apart from a global phase factor),
since $\alpha_{0}=r_{0}$ and $\beta_{0}=\phi_{0}$. Note that the collision
parameters are restricted to the global phase $\operatorname{e}^{-iN\varphi
_{N}(t)}$, being irrelevant to the analyzes developed below of the
nonadiabatic geometric phases acquired by the state vector. On the other hand,
collisions become relevant when considering other initial states as the
product of Glauber's coherent states $\left\vert \alpha_{0}\right\rangle
\left\vert \beta_{0}\right\rangle $ instead of the BS \cite{Liliana}.
\section{Geometric phases of the BS}
To study the evolution of the geometric phase in the two-mode BECs we use the
kinematic approach developed by Mukunda and Simon \cite{Mukunda1993}, where
the geometric phase $\phi_{G}$ is obtained as the difference between the total
phase $\phi_{T}(t)=\arg(\left\langle \psi(t_{0})\right\vert \left.
\psi(t)\right\rangle )$ and the dynamical phase $\phi_{D}(t)=-i\int_{t_{0}%
}^{t}\left\langle \psi(\tau)\right\vert \frac{\partial}{\partial\tau
}\left\vert \psi(\tau)\right\rangle d\tau$, resulting in
\begin{equation}
\phi_{G}(t)=\arg(\left\langle \psi(t_{0})\right\vert \left. \psi
(t)\right\rangle )+i\int_{t_{0}}^{t}\left\langle \psi(\tau)\right\vert
\frac{\partial}{\partial\tau}\left\vert \psi(\tau)\right\rangle d\tau.
\label{23}%
\end{equation}
The expressions for $\phi_{G}(t)$ and $\phi_{D}(t)$ as function of the system
parameters are, respectively,%
\begin{align}
\phi_{G}(t) & =N\arg\{\cos\left( r_{0}/2\right) \cos\left[ r(t)/2\right]
+\operatorname{e}^{i\left[ \phi(t)-\phi_{0}\right] }\sin\left(
r_{0}/2\right) \sin\left[ r(t)/2\right] \}\nonumber\\
& -\frac{N}{2}\int_{t_{0}}^{t}\overset{.}{\phi}(\tau)\left\{ 1-\cos\left[
r(\tau)\right] \right\} d\tau, \label{24}%
\end{align}
and%
\begin{equation}
\phi_{D}(t)=-N\left[ \varphi_{N}(t)-\varphi_{N}(t_{0})\right] +\frac{N}%
{2}\int_{t_{0}}^{t}\overset{.}{\phi}(\tau)\left\{ 1-\cos\left[
r(\tau)\right] \right\} d\tau, \label{25}%
\end{equation}
where $\varphi_{N}(t)$ was given in Eq. (\ref{19a}). In
Ref.\cite{Balakrishnan}, the authors also obtain Eq.(\ref{24}), through the
Gross-Pitaevskii equation, for the geometric phase acquired by the wave
function of a BEC in the double-well problem, under the two-mode approximation.
The time evolution of the BS can be followed\textbf{\ }on the Bloch sphere
through the vector $\mathbf{n}\left( t\right) =(\sin[r(t)]\cos[\phi(t)]$,
$\sin[r(t)]\sin[\phi(t)]$, $\cos[r(t)])$, for the different solutions $r(t)$
and $\phi(t)$ presented in the Appendix. To follow such evolution and,
consequently, to analyze its geometric phase $\phi_{G}(t)$, we must estimate
the integrals in Eq.(\ref{2}), i.e., the typical values for trap frequencies,
Josephson-like coupling, intraspecies, and interspecies collision rates. For
the sake of simplicity we model the effective frequency for both atomic
species as harmonic trap potentials where the TD distribution for each
condensate $\varphi_{\ell}\left( \mathbf{r},t\right) $ can be approximated
by a stationary Gaussian function such that
\begin{equation}
\varphi_{\ell}\left( \mathbf{r}\right) =\left( \frac{1}{2\pi x_{\ell}^{2}%
}\right) ^{3/4}e^{-\mathbf{r}^{2}/4x_{\ell}^{2}}\text{,} \label{26}%
\end{equation}
where $x_{\ell}=\sqrt{\hbar/2m\omega_{\ell}}$ stands for the position
uncertainty in each harmonic oscillator ground state \cite{Milburn}. With this
assumption the integrals in Eq.(\ref{2}) are immediately estimated using
typical physical parameters of the experiments with $^{87}$Rb atoms
\cite{Hall98a,Albiez2005,Gordon1998}: $m=1.4\times10^{-25}$ Kg, $\omega_{\ell
}\sim10^{1-2}$ Hz, $A_{\ell}\sim5$ nm, and $\Omega\sim10^{3}$ Hz\textbf{.} To
obtain some insights of \ the pseudo-spin dynamics under the TD Hamiltonian
parameters, we consider the trap and Rabi frequencies as harmonic functions,
oscillating around the typical constant values, as follow
\begin{subequations}
\label{27}%
\begin{align}
\omega_{\ell}\left( t\right) & =\omega_{\ell0}+\widetilde{\omega}_{\ell
}\sin{\left( \chi_{\ell}t+\xi_{\ell}\right) ,}\label{27a}\\
g(t) & =g_{0}+\widetilde{g}\sin(\mu t)\text{,} \label{27b}%
\end{align}
with the parameters $\omega_{\ell0}$, $\widetilde{\omega}_{\ell}$, $\chi
_{\ell}$, $\xi_{\ell}$, $g_{0}$, $\widetilde{g}$, and $\mu$ being constant.
Since the elastic collisions contribute only to a global phase factor, they
will be assumed as the standard constant parameters in the literature
\end{subequations}
\begin{subequations}
\label{28}%
\begin{align}
\gamma_{\ell} & =\frac{4\pi A_{\ell}}{2m}\text{,}\label{28a}\\
\gamma_{ab} & =\frac{4\pi A_{ab}}{m}\text{.} \label{28b}%
\end{align}
\section{Nonadiabatic Geometric Phases and Pseudo-Spin Dynamics in BECs}
In this section we present a detailed study of the geometric phase acquired by
the whole wave function of the two-mode condensates. To this end, we plot the
time evolution of the geometric phase (\ref{24})\textbf{, }and analyze its
behavior through the evolution of Bloch vector (a map of the wave function of
the BECs on Bloch sphere). This procedure allows for a better understanding
and visualization of the concept of geometric phase for open trajectories
introduced by Samuel and Bhandari \cite{Samuel88}. In particular, we are
interested in the dependence of the geometric phase on the constant of motions
coming from the solutions of the characteristic equations (\ref{7}) and also
on the time dependence of the Hamiltonian parameters. In spite of the general
solutions presented in the Appendix for these equations, we have assumed, for
the analysis developed below, $N=1$, $\delta_{0}=0$, and $g_{0}=625\pi$ Hz.
\subsection{Solutions for $r$ constant}
Before analyzing the geometric phases for the on- and off-resonant solutions,
it is instructive to present their evolutions for the simple case where the
parameter $r$ is kept constant while $\phi\left( t\right) $ obeys
Eq.(\ref{A9}) (since $g=0$). In this case, the expression for the geometric
phase coming from Eq. (\ref{24}), becomes%
\end{subequations}
\begin{equation}
\phi_{G}(t)=N\left\{ \arg\left\{ \cos^{2}\left( r/2\right) +e^{-i\left[
\phi(t)-\phi_{0}\right] }\sin^{2}\left( r/2\right) \right\} -\frac{\left(
1-\cos r\right) }{2}\left[ \phi(t)-\phi_{0}\right] \right\} \text{.}
\label{fg1}%
\end{equation}
In Fig.1 the absolute value for $\phi_{G}(t)$ is plotted against the
dimensionless $\tau=\omega_{a0}t$, assuming typical values $\omega
_{a0}=2\omega_{b0}=62.5\pi$ Hz. For $r=\pi/2$, with the Bloch vector standing
on the equatorial plane, and $\widetilde{\omega}_{a}=\widetilde{\omega}_{b}%
=0$, the geometric phase evolves by jumps, as indicated by the thick solid
line. These jumps occur every time the relative phase $\phi$ connecting the
final to the initial Bloch vectors equals $\left( 2n+1\right) \pi$, $n$
being an integer. The jump discontinuities occur because there are an infinite
number of small geodesic-lengths connecting the vectors extremities, rendering
the geometric phase undefined \cite{Polavieja}. On the other hand, we observe
that before jumping to $\phi_{G}(\tau)=\pi$, i.e., for $\tau<2\pi$, the
geometric phase remain null since the small geodesic-length connecting the
extremities equals the Bloch-vector trajectory itself. As soon as the Bloch
vector acquires a relative phase larger than $\pi$, the small geodesic-length
connecting the extremities completes a loop over the equator, making the
acquired geometric phase proportional to $nN\pi$, where $n$, as defined above,
turns out to be the winding number, i.e., the number of loops around the
$z$-axis of the sphere.
The same interpretation given above for the geometric phase holds for the two
other curves obtained for $r=\pi/2.1$, except that the jump discontinuities
are substituted by high-slope curves around the points where $\phi=(2n+1)\pi$.
Moreover, the net effect coming from the TD parameters of the Hamiltonian is
to delay or advance the sequential increments of the relative phase $\phi$
and, consequently, of the geometric phase, as observed from Fig.1. The solid
line, obtained for $r=\pi/2.1$ and $\widetilde{\omega}_{a}=\widetilde{\omega
}_{b}=0$, shows that the increments of the geometric phase, besides being
smaller, present the same rate of variation when compared to the case
$r=\pi/2$. When the trap frequencies are oscillating functions, with
$\widetilde{\omega}_{a}=\widetilde{\omega}_{b}=\omega_{a0}/4$, $\chi_{a}%
=\chi_{b}=\omega_{a0}/2$, $\xi_{a}=0$, and $\xi_{b}=\pi/2$, the
time-dependence shown by the dashed line, results in the oscillations of the
time intervals between the increments of the geometric phase.
To better visualize the above discussion about geometric phases acquired in
open trajectories, in Fig.2 we plot the evolution of the Bloch vectors for the
cases $r=\pi/2$ and $r=\pi/2.1$, with $\widetilde{\omega}_{a}=\widetilde
{\omega}_{b}=0$, considering the same time interval $\tau=4\pi$. The black and
grey vectors indicate the coincident positions of the initial and final Bloch
vectors, for the cases $r=\pi/2.1$ and $r=\pi/2$, respectively, after a
complete rotation around the sphere whose directions are indicated by the
arrows. The trajectories described by the black and grey vectors are indicated
by solid and dashed curves, respectively. Evidently, the geometric phase
acquired during the evolution of the Bloch vector in the case $r=\pi/2.1$ (the
solid angle comprehended by the semi-hemisphere above the solid
circumference), is smaller than that for the case $r=\pi/2$ (the solid angle
corresponding to the north hemisphere, equal to $2\pi$).
The solution with $r$ constant means steady population imbalance $\Delta N$,
whereas the relative phase $\phi(t)$, another parameter examined by
experimentalists and necessary to completely define the BS, is a linear
function of time when $\widetilde{\omega}_{a}=\widetilde{\omega}_{b}=0$ or an
oscillating function when $\widetilde{\omega}_{a}=\widetilde{\omega}%
_{b}=\omega_{a0}/4$. Note that the dynamics of the population imbalance and
the relative phase may be followed through the projection of the Bloch vector
trajectory on $z$-axis and $x$-$y$ plane, respectively.
\subsection{On-resonant solution}
As indicated in the Appendix, through the constant of motion $\mathcal{C}%
=\sin\left[ r(t)\right] \cos\left[ \phi(t)-\delta(t)\right] $ we obtain
the solution of the characteristic equations (\ref{7}) in the on-resonant
regime where $\Delta(t)=\omega(t)$. All the possible trajectories in the
portrait space $r(t)$ $\times$ $\left( \phi(t)-\delta(t)\right) $, are
restrained to the level curves obtained as projection of the surface plotted
in Fig.3, which follows from $\mathcal{C}$.
To better understand the geometric phase acquired by the state vector
$\left\vert \Psi(t)\right\rangle $ in the on-resonant solutions, we consider
two different cases, $\Delta=0$ and $\Delta\neq0$, and analyze its dependence
on the constant $\mathcal{C}$, through the relation%
\begin{align}
\phi_{G}(t) & =N\arg\left\{ \cos\left( r_{0}/2\right) \cos\left[
r\left( t\right) /2\right] +e^{-i\left[ \phi(t)-\phi_{0}\right] }%
\sin\left( r_{0}/2\right) \sin\left[ r\left( t\right) /2\right] \right\}
\nonumber\\
& -\frac{N}{2}%
{\displaystyle\int\limits_{t_{0}}^{t}}
dt^{\prime}\left\{ \omega(t^{\prime})\left\{ 1-\cos\left[ r\left(
t^{\prime}\right) \right] \right\} +\frac{2\mathcal{C}g(t^{\prime}%
)\cos\left[ r\left( t^{\prime}\right) \right] }{1+\cos\left[ r\left(
t^{\prime}\right) \right] }\right\} \text{.} \label{fg2}%
\end{align}
\subsubsection{The case $\Delta=0$}
In Fig.4 we plot the evolution of the geometric phase against $\tau=g_{0}t$,
considering $\widetilde{\omega}_{a}=\widetilde{\omega}_{b}=\widetilde{g}=0$.
The thick solid line on the abscissa axis corresponds to the choice $r_{0}%
=\pi$ and $\phi_{0}=\pi/2$, leading to $\mathcal{C}=0$, under which the
geometric phase is null or undefined as indicated by the open dots over the
abscissa axis. Note that for $r_{0}=\pi$ we get, at $t=0$, an undetermined
equation (\ref{A4b}) for $\phi(t)$. To circumvent such indetermination we
impose on Eq.(\ref{A3}) the constraint $\phi(t)-\delta(t)=(2n+1)\pi/2$ over
any time interval, to determine $\phi(t)$ independently of Eq.(\ref{A4b}).
Since for $\Delta=0$ it follows that $\delta(t)=\delta_{0}$, implying that
$\phi(t)=\delta_{0}+(2n+1)\pi/2$, the geometric phase for the case
$\mathcal{C}=\Delta=0$ simplifies to $\phi_{G}(t)=N\arg\left\{ \cos\left[
\left( r\left( t\right) -r_{0}\right) /2\right] \right\} $ and,
consequently, $\phi_{G}(t)$ is null for $\left\vert r\left( t\right)
-r_{0}\right\vert \leq\pi$ and undefined for $\left\vert r\left( t\right)
-r_{0}\right\vert =\pi$. Still in Fig. 4, the solid and dashed lines,
associated to the pairs $(r_{0}$, $\phi_{0})=(\pi/5$, $\pi/4)$ and $\left(
\pi/4\text{, }3\pi/10\right) $, respectively, correspond to the same constant
$\mathcal{C}\simeq0.41$. These curves exhibits similar behaviors due to the
fact that, with the same constant $\mathcal{C}$, they present the same
trajectory on the portrait space of Fig.3, despite starting from different
initial conditions. The dotted and dashed-dotted lines, associated to the
pairs $\left( \pi/3\text{, }0\right) $ and $\left( \pi/3\text{, }%
\pi\right) $, and corresponding to the constants $\mathcal{C}\simeq0.87$ and
$\mathcal{C}\simeq-0.87$, respectively, are symmetric around the abscissa axis
$\tau$. Such property of symmetry reflection of the geometric phase $\phi
_{G}\rightarrow-\phi_{G}$, is consequence of the change $\phi_{0}%
\rightarrow\phi_{0}\pm\pi$, implying that $\mathcal{C}\rightarrow-$
$\mathcal{C}$. It is worth noting that the larger the absolute value of
$\mathcal{C}$ the smaller the acquired geometric phase and \textit{vice-versa}%
. \
In Fig.5 we plot the evolution of the Bloch vectors coming from the
on-resonant solution with the initial conditions $\left( \pi\text{, }%
\pi/2\right) $ and $\left( \pi/3\text{, }0\right) $ corresponding to
$\mathcal{C}=0$ and $\mathcal{C}\simeq0.87$, whose initial and final positions
are represented by the black and grey vectors, respectively. As in Fig.2, we
consider the evolution of both vectors during the same time interval $\tau
=\pi$. Through the solid line trajectory described by the black vector, which
oscillates between the north and south poles, it is straightforward to
conclude that the geometric phase is null during the whole time evolution,
except when the vector reaches the north pole, where the geometric phase
becomes undetermined. As the dashed trajectory of the grey vector is not
restricted to a meridian, as in the case $\mathcal{C}=0$, the geometric phase
acquired is evidently non-null.
\subsubsection{The case $\Delta\neq0$}
As we are interested in the dependence of the geometric phase on constant
$\mathcal{C}$ and, now, on the effective frequency of the two-mode condensate
$\Delta(t)=\omega\left( t\right) $, we consider all the parameters of the
Hamiltonian being time-independent, $\widetilde{\omega}_{a}=\widetilde{\omega
}_{b}=\widetilde{g}=0$, except for $\delta(t)=\delta_{0}+%
{\displaystyle\int\nolimits_{t_{0}}^{t}}
\omega(t^{\prime})dt^{\prime}$. In Fig.6 we plot the geometric phase against
$\tau=g_{0}t$ for different initial conditions ($r_{0}$, $\phi_{0}$) and
effective frequencies $\Delta$. As indicated by the thick solid line
associated to the initial conditions $\left( \pi\text{, }\pi/2\right) $,
corresponding to $\mathcal{C}=0$, with $\omega_{a}=2\omega_{b}=g_{0}/10$, the
geometric phase is not null, differently from the case $\Delta=0$. The
discontinuity exhibited by this curve follows from the $\arg$ function, whose
characteristic jumps occurs whenever $\tau_{n}=\left[ \left( 2n-1\right)
\pi g_{0}\right] /2\omega$, $n$ being a positive integer. As indicated by the
solid and dashed lines, the property of symmetry reflection of the geometric
phase in the abscissa axis still follows when changing, simultaneously,
$\phi_{0}\rightarrow\phi_{0}\pm\pi$, and $\omega$ to $-\omega$. In fact, the
solid line corresponds to the initial condition $\left( \pi/3\text{,
}0\right) $ with $\mathcal{C}\simeq0.87$ and $\omega_{a}=2\omega_{b}%
=g_{0}/10$, while the dashed line corresponds to $\left( \pi/3\text{, }%
\pi\right) $, with $\mathcal{C}\simeq-0.87$ and $\omega_{b}=2\omega_{a}%
=g_{0}/10$. When the change $\phi_{0}\rightarrow\phi_{0}\pm\pi$, are not
followed by that $\omega$ $\rightarrow$ $-\omega$, such a symmetry is not
accomplished as indicated by the dotted line corresponding to the initial
conditions $\left( \pi/3\text{, }\pi\right) $ with $\mathcal{C}\simeq-0.87$
and, now, $\omega_{a}=2\omega_{b}=g_{0}/10$.
To visualize the acquisition of the geometric phase we again return to the
evolution of the Bloch vector. As observed from Fig.7, the solid trajectory
described by the vector associated to $\mathcal{C}=0$, whose coincident
initial and final positions are indicated by the black vector, leads to a
finite solid angle and, consequently, a finite geometric phase (during the
time evolution $\tau=\pi$\ considered for both cases presented). The control
of this solid angle may be accomplished through the parameter $\Delta$ --- the
larger $\Delta$ the larger the solid angle and \textit{vice-versa} --- as
demonstrated experimentally through the polarization vector of a photon
undergoing a Mach-Zehder interferometer \cite{Kwiat}. The evolution of the
grey vector, associated to $\mathcal{C}\simeq0.87$, exhibits a dashed
trajectory where the initial and final positions are slightly different. As
the time evolution proceeds, such trajectory leads to a geometric phase which
easily exceed that of the case $\mathcal{C}=0$, as indicated in Fig.6.
The population imbalance $\Delta N$ for the cases $\Delta=0$ and $\Delta\neq0$
is a time-oscillating function strictly dependent on the shape of Rabi
frequency $g(t)$, thus exhibiting a strong connection between the\ dynamics of
population inversion in two-level systems and population imbalance of BECs. In
fact, when written the Hamiltonian (\ref{1}) through the quase-spin operators
in Eqs.(\ref{17}), we obtain, apart from the collision terms, a driven
interaction. On the other hand, the relative phase $\phi(t)$ depends also on
the detuning $\delta(t)$ besides $g(t)$, as shown by Eqs.(\ref{A4}).
\subsection{Off-resonant solution}
To analyze the off-resonant solution, where the detuning $\Delta
(t)=\omega(t)-\varpi$ is controlled by adjusting the parameter $\varpi$, we
impose a constant Rabi frequency $g(t)=g_{0}$ which implies a constant of
motion $\mathcal{C}=\eta\sin\left[ r(t)\right] \cos\left[ \phi
(t)-\delta(t)\right] -\cos\left[ r(t)\right] $. Similarly to the
on-resonant case, all the possible trajectories for the off-resonant $r(t)$
and $\phi(t)$ are restrained to the level curves of the surface following from
$\mathcal{C}$, presented in Fig.8. When $\eta=$ $2g_{0}/\varpi\gg1$ it is
verified that the constant $\mathcal{C}$ reduces to that of the on-resonant
solutions, unless for the multiplicative factor $\eta$, and the surface
presented in Fig.8 also reduces to that of Fig.3. However, for $\eta\ll1$ we
obtain an approximated constant value of $r$. Finally, when $\eta\sim1$, we
obtain the surface whose level curves encapsulate all the possible
trajectories in the portrait space $r(t)$ $\times$ $\phi(t)-\delta(t)$, as
shown in Fig.8.
To study the effect of $\eta$ on the off-resonant geometric phase, given
by\textbf{ }%
\begin{align}
\phi_{G}(t) & =N\arg\left\{ \cos\left( r_{0}/2\right) \cos\left[
r\left( t\right) /2\right] +e^{-i\left[ \phi(t)-\phi_{0}\right] }%
\sin\left( r_{0}/2\right) \sin\left[ r\left( t\right) /2\right] \right\}
\nonumber\\
& -\frac{N}{2}%
{\displaystyle\int\limits_{t_{0}}^{t}}
dt^{\prime}\left\{ \omega(t^{\prime})\left\{ 1-\cos\left[ r\left(
t^{\prime}\right) \right] \right\} +\varpi\cos\left[ r\left( t^{\prime
}\right) \right] \frac{C+\cos\left[ r\left( t^{\prime}\right) \right]
}{1+\cos\left[ r\left( t^{\prime}\right) \right] }\right\} \text{.}
\label{fg3}%
\end{align}
we plot in Fig.9 the evolution of $\phi_{G}(t)$ for different values of $\eta
$, all starting from the point ($\pi/3$, $0)$, with $\omega_{a0}=2\omega
_{b0}=g_{0}/10$ and $\widetilde{\omega}_{a}=\widetilde{\omega}_{b}=0$. The
dotted line, following from the case where $\eta=40$, indicates a similar
behavior to the corresponding case of the on-resonant solution (represented by
the solid line in Fig. 6). For $\eta=0.1$, the solid line shows that the
geometric phase is a strongly oscillating function, a behavior that is better
visualized through the evolution of the corresponding vector in Bloch sphere,
Fig.10. Finally, when $\varpi\sim g_{0}$, as for $\eta=2$, the geometric phase
shows discontinuities, as indicated by the thick solid line, which turns out
to be a signature of the off-resonant solution. We note that the property of
reflection exhibited by the geometric phase coming from the on-resonant
solution is also present here when substituting, simultaneously, $\phi
_{0}\rightarrow\phi_{0}\pm\pi$, $\omega\rightarrow-\omega$, and $\eta
\rightarrow-\eta$.
In Fig.10 we present the evolution of the Bloch vectors in the time interval
$\tau\simeq9\pi/10$, for the cases $\eta=0.1$ and $\eta=2$, both starting from
the common point $\left( \pi/3\text{, }0\right) $. The black vector for
$\eta=0.1$, presents a behavior limited to the north hemisphere, described by
the solid trajectory, which exhibits periodic up and down motions on the
parallels, responsible for the oscillations of the geometric phase showed in
Fig.9. The grey vector for $\eta=2$, by its turn, indicates a rather
complicated dashed trajectory which descends to the south hemisphere and goes
back to the north.
Besides depending on the Rabi frequency, as in the on-resonant case, the
population imbalance for the off-resonant solution also depends on the
detuning $\varpi$ which makes its mean value not null. The relative phase
depends on $\delta(t)$, $g(t)$, and the detuning $\varpi$.
\subsection{Time-Dependent Effects on the Geometric Phases}
The behavior of the geometric phase when both, the trap and Rabi frequencies
are TD harmonic functions, as described by Eq.(\ref{27}), is analyzed in
Fig.11, where we plot $\phi_{G}(\tau)$ against $\tau=g_{0}t$, considering the
same initial conditions $(\pi/3$, $0)$ for all the curves. Starting with the
resonant solution with $\Delta=0$, we obtain the dotted curve for the
parameters $\widetilde{\omega}_{a}=\widetilde{\omega}_{b}=0$ and
$\widetilde{g}=\mu=g_{0}$, to be compared with the dotted curve of Fig.4. We
observe that both dotted curves are very close to each other, with the the
increasing rate of the geometric phase being modulated by the TD Rabi
frequency in Fig.11. The solid line corresponds to the on-resonant solution
with $\Delta\neq0$, for the parameters $\omega_{a0}=2\omega_{b0}=g_{0}/10$,
$\widetilde{\omega}_{a}=\widetilde{\omega}_{b}=0$, and $\widetilde{g}%
=\mu=g_{0}$. This curve is to be compared with the solid line in Fig.6,
showing again that the increasing rate of $\phi_{G}$ can be controlled through
the TD Rabi frequency. The dashed line, also corresponding to $\Delta\neq0$,
with $\omega_{a0}=2\omega_{b0}=g_{0}$, $\widetilde{\omega}_{a}=\widetilde
{\omega}_{b}=0$, and $\widetilde{g}=\mu=g_{0}$, shows that the increasing rate
of the geometric phase may also be controlled through the trap frequencies.
Finally, the thick solid line, corresponding to the off-resonant solution,
with $\omega_{a0}=2\omega_{b0}=g_{0}$, $\widetilde{\omega}_{a}=\widetilde
{\omega}_{b}=\chi_{a}=\chi_{b}=g_{0}/2$, $\xi_{a}=0$, $\xi_{b}=-\pi/2$, and
$\widetilde{g}=0$, to be compared with the thick solid line of Fig.9, also
indicates the important role played by the time dependence of the trap
frequency in the geometric phase. We finally observe that, evidently, these TD
effects have direct implications on the population imbalance and relative
phase between the condensates.
\section{Geometric Phases and the External Josephson Effect}
In this section we analyze the two-mode condensates from a different
perspective: as a single atomic specie trapped in a symmetric or asymmetric
double-well potential. As the internal Josephson effect is here substituted by
the tunneling interaction, the laser pumping becomes unnecessary and we impose
that $\Delta=0$, such that $\delta=0$. Moreover, in the external Josephson
effect the interspecies collision rate correspond to a second order correction
compared to the intraspecies collision rates, justifying the assumption that
$\gamma_{ab}\simeq0$ \cite{Milburn1997,Ketterle}.
The Hamiltonian (\ref{1}) applied to this different physical situation leads,
under the above restrictions, to a similar transformed interaction (\ref{4})
and characteristic equations (\ref{7}). Therefore, the different solutions of
the coupled differential equations apply directly to the external Josephson
effect, with the on- and off-resonant processes describing the symmetric
($\omega=0$) and asymmetric ($\omega\neq0$) wells solutions, respectively.
\subsection{Symmetric wells}
>From the above discussion we readily verify that the solutions for $r(t)$ and
$\phi(t)$, coming from the symmetric wells, are give by Eqs.(\ref{A4}) and
(\ref{A4c}) with the constant of motion $\mathcal{C}=\sin\left[ r(t)\right]
\cos\left[ \phi(t)\right] $. We observe that the TD tunneling rate $g(t)$ is
accomplished by modulating the amplitude of the counter propagating classical
fields that generate the barrier. Similarly to the internal Josephson effect,
all the possible trajectories for $r(t)$ and $\phi(t)$ follow from the level
curves of the surface plotted in Fig.8, assuming $\delta=0$. The same level
curves were obtained, by numerical methods, in Ref.\cite{Balakrishnan}. The
geometric phases acquired by the evolution of the state vector of the BECs are
given by Fig.4 and the Bloch-vector trajectories by Fig.5, both obtained from
the on-resonant solution of the internal Josephson effect with $\delta=0$.
\subsection{Asymmetric wells}
The solutions of the characteristic equations for the asymmetric wells follow
by imposing constant values for the effective frequency $\omega=\varpi$ (since
$\Delta=0$) and the tunneling rate $g=g_{0}$. We thus obtain the solutions
(\ref{A6}) with $\eta$ replaced by $\widetilde{\eta}=2g_{0}/\omega$ and
$\delta=0$. The constant of motion becomes $\mathcal{C}=\widetilde{\eta}%
\cos\left[ \phi(t)\right] \sin\left[ r(t)\right] -\cos\left[ r(t)\right]
$. The phase-space portrait $r(t)\times\phi(t)$ is given by Fig.8 (with
$\delta=0$), whose level curves indicate all the possible trajectories for
$r(t)$ and $\phi(t)$. The same level curves were obtained by numerical methods
in Ref.\cite{Balakrishnan}. As an example of the geometric phase acquired by
the evolution of the state vector in the asymmetric wells, we take the dotted
line curve of Fig.9, corresponding to the case $\omega=\varpi=g_{0}/20$. (The
other two curves in Fig.9 do not satisfy the condition $\omega=\varpi$.) The
trajectory of the Bloch vector associated to $\omega=g_{0}/20$ is
approximately give by the dashed curve in Fig.7.
\section{Concluding Remarks}
In the present work we analyze the dynamics of two interacting condensates,
with a full TD Hamiltonian. Starting from the Hamiltonian (\ref{1}) under the
two-mode approximation, an effective interaction (\ref{9}) is established
under the RWA, provided that the polar $r(t)$ and azimuthal $\phi(t)$ angles,
which define a Bloch state, satisfy coupled differential equations. This
procedure enable us to define a detuning $\Delta(t)$ from the Raman resonance
between the atomic transition, together with an effective frequency for the
condensates $\omega\left( t\right) $, as in Eq. (\ref{8}). Thus, two
different solutions arise for the differential equations coupling the
parameters\ $r(t)$ and $\phi(t)$, the on-resonant solution, where
$\Delta(t)=\omega\left( t\right) $, and the off-resonant solution where
$\Delta(t)=\omega\left( t\right) +\varpi$, $\varpi$ being a constant. After
solving analytically the coupled equations for both regimes, we present a
detailed analyzes of the geometric phases acquired by the Bloch state of the
system, also discussing the relative phase and population imbalance.
A main result of our work is the connection between geometric phases and
constant of motions of the interacting condensates which are identified
through the analytical solutions of the coupled differential equations for
$r(t)$ and $\phi(t)$. For each on- or off-resonant solution we assign a
constant of motion which determine the dynamical behavior of the state of the
system and, consequently, its geometric phase. We also note that these
constants of motions follow from level curves in the portrait space which are
also obtained analytically.
To better visualize the time-evolution of the geometric and relative phases
acquired by the state vector, together with population imbalance, we also
analyze the trajectory of the state vector mapped on Bloch sphere. Finally, we
present a brief discussion of the TD effects of the trap and Rabi frequencies
in the geometric phases together with the connection between its evolution in
both cases of internal and external Josephson coupling.
As in this work we studied only the evolution of an initial Bloch state, the
collision parameters were restricted to the global phase of the evolved state,
which remains a Bloch state under the two-mode approximation. Therefore,
collisions terms, which are also assumed as TD parameters, do not play a
decisive role in our present analyzes. It is worth to consider distinct
initial state to analyze the effects of the collisions parameters in the
dynamics of the geometric phase and population imbalance.
\textbf{Acknowledgments}
We wish to express thanks for the support from CNPq and FAPESP, Brazilian agencies.
\section{Appendix}
\subsection{Analytical solutions of the characteristic equations (\ref{7})}
In this Appendix we present some specific solutions of the characteristic
equations (\ref{7}), following a more detailed treatment in \cite{Salomon}. We
investigate two different regimes of the laser field amplification, the
on-resonant and off-resonant regimes, which are defined comparing the
effective frequency of the two-mode condensate, $\omega(t)$, with the detuning
between the laser field and the Raman transition $\Delta(t)$. As mentioned
above, in the on-resonant regime, where $\Delta(t)=\omega\left( t\right) $,
the rate of time variation of the laser field equals the effective frequency
of the two-mode condensate. Otherwise, we have the off-resonant regime.
\subsection{On-resonant process}
Defining $\chi(t)\equiv\phi(t)-\delta(t)$, the characteristic equations
(\ref{7}) becomes%
\begin{subequations}
\label{A1}%
\begin{align}
\overset{.}{r}(t) & =2g(t)\sin\left[ \chi(t)\right] \text{,}\label{A1a}\\
\overset{.}{\chi}(t) & =\omega(t)-\Delta(t)+2g(t)\cos\left[ \chi(t)\right]
\cot\left[ r(t)\right] \text{{,}} \label{A1b}%
\end{align}
such that, in the on-resonant regime we are left with the first-order
differential equation
\end{subequations}
\begin{equation}
\frac{dr}{d\chi}=\tan\chi\tan r\mathrm{.} \label{A2}%
\end{equation}
After integrating Eq.(\ref{A2}) we obtain the constant of motion
\begin{equation}
\sin\left[ r(t)\right] \cos\left[ \phi(t)-\delta(t)\right] =\mathcal{C},
\label{A3}%
\end{equation}
with $\mathcal{C}$ depending on the initial values $r_{0}$, $\phi_{0}$, and
$\delta_{0}$. Thus, the resonant solutions of Eqs.(\ref{A1}), are given by
\begin{subequations}
\label{A4}%
\begin{align}
\cos\left[ r(t)\right] & =\sqrt{1-\mathcal{C}^{2}}\sin\left[
u(t,t_{0})+\arcsin\left( \frac{\cos r_{0}}{\sqrt{1-\mathcal{C}^{2}}}\right)
\right] ,\label{A4a}\\
\phi(t) & =\delta(t)+\arccos\left\{ \frac{\mathcal{C}}{\sin\left[
r(t)\right] }\right\} , \label{A4b}%
\end{align}
where
\end{subequations}
\begin{equation}
u(t,t_{0})=-2\int_{t_{0}}^{t}g(\tau)d\tau\mathrm{.} \label{A4c}%
\end{equation}
\subsection{Off-resonant process}
Considering the off-resonant regime, where $\Delta(t)=\omega(t)-\varpi$,
$\varpi$ being a constant, Eqs. (\ref{A1}) can again be solved by quadrature
as far as we assume the Rabi frequency $g$ to be also a constant $g_{0}$. In
this regime, defining $\eta=$ $2g_{0}/\varpi$, Eq.(\ref{A3}) is replaced by
\begin{equation}
\eta\cos\left[ \phi(t)-\delta(t)\right] \sin\left[ r(t)\right]
-\cos\left[ r(t)\right] =\mathcal{C}\mathrm{,} \label{A5}%
\end{equation}
which again depends on the initial values $r_{0}$, $\phi_{0}$, $\delta_{0}$.
The solutions for this case are given by
\begin{subequations}
\label{A6}%
\begin{align}
\cos\left[ r(t)\right] & =\frac{\eta\sqrt{1+\eta^{2}-\mathcal{C}^{2}}%
}{1+\eta^{2}}\sin\left\{ -\varpi\sqrt{1+\eta^{2}}\left( t-t_{0}\right)
\right. \nonumber\\
& \left. +\arcsin\left[ \frac{\left( 1+\eta^{2}\right) \cos
r_{0}+\mathcal{C}}{\eta\sqrt{1+\eta^{2}-\mathcal{C}^{2}}}\right] \right\}
-\frac{\mathcal{C}}{1+\eta^{2}}\mathrm{,}\label{A6a}\\
\phi(t) & =\delta(t)+\arccos\left\{ \frac{\mathcal{C}+\cos\left[
r(t)\right] }{\eta\sin\left[ r(t)\right] }\right\} \mathrm{.} \label{A6b}%
\end{align}
\bigskip
\subsection{A constant solution for $r$}
Another solution for $r(t)$ and $\phi(t)$ arises when we impose that $r$
remains constant in time. Through this solution, given by
\end{subequations}
\begin{align}
r(t) & =r_{0},\label{A8a}\\
\phi(t) & =\delta(t)+n\pi=\phi_{0}+\int_{t_{0}}^{t}\left[ \omega
(\tau)+2(-)^{n}g\left( \tau\right) \cot\left( r_{0}\right) \right]
d\tau\text{, } \label{A8b}%
\end{align}
with $r_{0}\neq n\pi$ and $n$ being an integer, the state vector of the system
acquire only relative phase $\phi(t)$. This formal solution for $\phi(t)$ can
be even simplified noting that the physical implementation of this regime
requires, necessarily, that $g\simeq0$. In fact, for the population imbalance
to be null, due to the constant value for $r$, the Rabi frequency must also be
null. therefore, Eq.(\ref{A8b}) simplifies to%
\begin{equation}
\phi(t)=\phi_{0}+\int_{t_{0}}^{t}\omega(\tau)d\tau\text{.} \label{A9}%
\end{equation}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,630 |
Burna Boy Unveils Tickets for Madison Square Garden Concert Next Year | WATCH
Nigerian singer, Burna Boy has shared the link to buy tickets for his concert next year at the prestigious Madison Square Garden in New York.
Shortly after revealing that he will headline his own concert at the Madison Square Garden, Burna Boy has now announced that the tickets for the show have gone live. This was shared via Instagram on Friday, the 17th of December 2021.
Earlier this year, Burna Boy staged his very first headline concert at the O2 Arena in London and it was a blast. The singer was joined on stage at the O2 concert by singers like Rema, Omah Lay, Ruger, and King Promise of Ghana. Burna Boy himself gave fans a special experience when he arrived at the concert floating in on a spaceship.
The singer also had his very first Hollywood Bowl concert this year and it was packed to the brim as well as a Paris concert with 20k capacity crowd. Burna Boy has also recently announced his plans to stage a stadium concert in the UK next year.
READ ALSO: Burna Boy Reveals His New Mantra Towards Life | SEE
Announcing the release of the Madison Square Garden, the promoter for Burna Boy's concert wrote via Instagram;
🗽New York City will never be the same again. Tickets now on sale!!! Run it up Quickly.
@burnaboygram live at @thegarden
A post shared by Duke (@dedukeosy)
18 Unforgettable Ghana and Nigeria Music Collaborations from the 2000s till date
Global Citizen CEO Responds to Burna Boy's UK Stadium Concert Idea | READ
WATCH: Omah Lay Links up With Burna Boy in the Studio | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 563 |
Data Bags
---------
Chef data bags
| {
"redpajama_set_name": "RedPajamaGithub"
} | 582 |
Harvard Magazine is a 501(c)3 affiliate of Harvard University with excellent access to University news and news sources—but as an editorially independent publication, the magazine is written, edited, and produced with readers' interests foremost in mind. This differs in purpose from many alumni publications across the United States that primarily serve the needs of their University news and development departments.
As a hybrid business—producing two-thirds of its revenue and receiving a subsidy from Harvard University for the remainder—the magazine can maintain its editorial independence and use this freedom to enlarge the scope of its reporting and pursue the best possible journalism about this exceptional University.
The chart below shows our progress toward acquiring the necessary funding to produce Harvard Magazine in print and online for fiscal year 2019 (July 2018 through June 2019).
View our fiscal year 2018 audited financial statements.
Contact Felecia Carter, director of circulation and fundraising, at [email protected] or 617-496-6694. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,048 |
First-Generation College Students
Chester Gillis Awardees Embody Liberal Arts Education in the Jesuit Tradition
Heather Yu Huang (C'23) studies and works to address cultural and educational inequities, and Jennifer Martínez Sánchez (C'22) applies her studies in sociology and public health to advance immigrants' rights.
Georgetown Reach Program Guides Rising Eighth-Graders Through College Application Process
The new Georgetown Reach program focuses on preparing rising eighth-grade students and their families for the college application process and the college experience.
First-Generation College Student Aspires to Pursue Immigration Policy and Law
Alicia Barry (SFS'20) conducts research with Georgetown associate professor of government Diana Kapiszewski (G'94) for a Georgetown database project called States and Institutions of Governance in Latin America…
Georgetown Urges Supreme Court to Allow DACA to Continue in Amicus Brief
Georgetown today joined 18 other colleges and universities in filing an amicus brief with the U.S. Supreme Court in support of the Deferred Action for Childhood Arrivals (DACA) program, in a case that eventually…
News, Student Experience
Georgetown Community Greets First-Years, Helps Them Settle at Georgetown
Each year, Georgetown alumni, faculty and staff volunteers meet unaccompanied first-year students at airports, train or bus stations through the Georgetown Scholars Program's (GSP) Project Move-in.
Discovery & Impact
Pre-College Programs Strive to Make Higher Education Accessible to All
Georgetown's college preparatory programs reinforce the university's commitment to improved access to higher education for students from diverse socioeconomic backgrounds.
RISE Program Helps First-Year Law Students From Underrepresented Backgrounds Thrive
Georgetown Law's RISE Program supports incoming law students from geographic, first-generation college and other backgrounds that have been historically underrepresented in law school.
Georgetown Welcomes New and Returning Students
Georgetown welcomes new and returning undergraduate, graduate, medical and law students for the 2019-2020 academic year with programs, orientation, traditional ceremonies and activities leading up to the first day of…
Social Justice Advocate, Prize Winner to Address Incoming Class of First-Years
Omoyele Okunola (C'20), the 2019 McTighe Prize winner, will advise the incoming Class of 2023 on the importance of advocating for others and self care during New Student Convocation.
Georgetown Hosts Summer Institute on Equity in the Academic Experience
Teams from 18 colleges and universities from across the country convened on campus for the first annual Summer Institute on Equity in the Academic Experience, hosted by Georgetown and The… | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,576 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.