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\section{Benchmark Constraints}
We present the initial constraints and safety constraints for all benchmarks in this section.
\subsection{Classical Control}
The classical control benchmarks and pretrained models come from \cite{zhu_inductive_2019}. Initial and safety constraints are in table \ref{tab: cc_details}.
\begin{table}[!htp]\centering
\caption{Classical Control Benchmarks}\label{tab: cc_details}
\scriptsize
\begin{tabular}{lccc}\toprule
Benchmarks &Initial Constraints &Safety Constraints \\\midrule
Pendulum &\thead{$-0.3 < x_i < 0.3$, for $0 \leq i \leq 1$} &\thead{$-0.5 < x_i < 0.5$, for $0 \leq i \leq 1$} \\\midrule
4CarPloon &\thead{$-0.1 < x_i < 0.1$, for $0 \leq i \leq 6$} &\thead{$-2 < x_0 < 2$, $-0.5 < x_{1, 3, 5} < 0.5,$ \\ $-0.35 < x_2 < 0.35$, $-1 < x_{4, 6} < 1$} \\\midrule
8CarPloon &\thead{$-0.1 < x_i < 0.1$, for $0 \leq i \leq 14$} &\thead{$-2 < x_0 < 2, -0.5 < x_{1, 3, 5, 7, 9, 11, 13} < 0.5$, \\ $-1 < x_{2, 4, 6, 8, 10, 12, 14} < 1$} \\\midrule
Helicoptor &\thead{$-0.002 < x_i < 0.002$, for $0 \leq i \leq 7$ \\ $-0.0023 < x_i < 0.0023$, for $8 \leq i \leq 27$} &\thead{$-10 < x_{13} < 10$, $-9 < x_{14} < 9$ \\ $-8 < x_i < 8$, for $0 \leq i \leq 27 \land i \neq 13, 14$} \\
\bottomrule
\end{tabular}
\end{table}
\subsection{F16GCAS}
\label{appendix:f16}
The F16GCAS benchmark is modelled with 16 variables. The meaning of
each, along with initial space and constraints are shown in
Table \ref{tab: F16_details}. When the initial space is 0, this
variable is always initialized with 0.
\begin{table}[!htp]\centering
\caption{F16 Ground Collision Avoidance System}\label{tab: F16_details}
\scriptsize
\begin{tabular}{llllll}\toprule
Variables &Meanings &Initial Space &Safety Constraints &Units \\\midrule
$V$ &Airspeed &[491, 545] &[300, 2500] &ft/s \\
$\alpha$ &Angle of attach &[0.00337, 0.00374] &[-0.1745, 0.7854] &rad \\
$\beta$ &Angle of side-slip &0 &[-0.5236, 0.5236] &rad \\
$\phi$ &Roll angle &[0.714, 0.793] &(-inf, inf) &rad \\
$\theta$ &Pitch angle &[-1.269, -1.142] &(-inf, inf) &rad \\
$\psi$ &Yaw angle &[-0.793, -0.714] &(-inf, inf) &rad \\
$P$ &Roll rate &0 &(-inf, inf) &rad/s \\
$Q$ &Pitch rate &0 &(-inf, inf) &rad/s \\
$R$ &Yaw rate &0 &(-inf, inf) &rad/s \\
$p_n$ &Northward displacement &0 &(-inf, inf) &ft \\
$p_e$ &Eastward displacement &0 &(-inf, inf) &ft \\
$h$ &Altitude &[3272, 3636] &[0, 45000] &ft \\
$pow$ &Engine thrust &[8.18, 9.09] &(-inf, inf) &lbf \\
$\int N_{z_e}$ &Integral of down force error &0 &[-3, 15] &g's \\
$\int P_{s_e}$ &Integral of stability roll rate error &0 &[-2500, 2500] &rad \\
$\int (N_y+r)_e$ &Integral of side force \& yaw rate error &0 &(-inf, inf) &mixed \\
\bottomrule
\end{tabular}
\end{table}
\subsection{Pybullet}
\label{appendix:pybullet}
For initial constraints, one may refer to
$\mathtt{robot\_locomotors.py}$ in the pybullet
repo\footnote{\href{https://github.com/bulletphysics/bullet3/blob/ac3dc0eea5298109c3755c45bc497f06f86111f7/examples/pybullet/gym/pybullet_envs/robot_locomotors.py}{pybullet
robot\_locomotors.py}}. The initial spaces of different joints are
defined in the $\mathtt{robot\_specific\_reset()}$ function.
Safety constraints are defined in the $\mathtt{alive\_bonus()}$
function in the same file. These constraints focus on 2 variables,
the height $\mathtt{z}$ and the pitch $\mathtt{p}$ of the robot, as well
as the joint contacts with the ground. When the $\mathtt{alive\_bonus()}$
returns a value that is smaller than 0, the agent violates these constraints and the simulation terminates immediately. We present
the safety constraints in Table \ref{tab: pybullet_constraints}.
\begin{table}[H]\centering
\caption{PyBullet Benchmarks safety constraints}\label{tab: pybullet_constraints}
\scriptsize
\begin{tabular}{lrr}\toprule
Benchmarks &Safety Constraints \\\midrule
Hopper &$\mathtt{z} > 0.8 $ $\land$ $\mathtt{|p|} < 1$ \\
HalfCheetah & \thead{$\neg contact(joint 1, 2, 4, 5) \land |\mathtt{p}| < 1$} \\
Ant &$\mathtt{z} > 0.26$ \\
Humanoid &$\mathtt{z} > 0.78$ \\
\bottomrule
\end{tabular}
\noindent $\neg contact$ means that the joints do not contact with the ground.
\end{table}
\section{Attack Transferability}
Transferability is a general property of many adversarial attacks.
Recall that given a policy $\pi_0$ in a system $M$ with initial states
$S_0$, an adversarial set $\texttt{Adv}_\epsilon (\pi_0, M, S_0)$ is discovered with
a Bayesian Optimization (BO) attack. Now, considering another policy
$\pi_1$ on the same system $M$, we wish to know what percentage of
$\texttt{Adv}_\epsilon (\pi_0, M, S_0)$ is also an adversarial state for policy
$\pi_1$. We call this the \emph{transferable ratios} for the benchmark. Several policies trained with different RL algorithms are
available on the Ant, HalfCheetah, and Hopper environments. We measured the adversarial
transferability between these different policies trained for the same
robot system. Figure~\ref{fig:attck_transferability} shows these
results.
\begin{figure}[!h]
\centering
\begin{minipage}[!H]{\linewidth}
\includegraphics[width=0.33\linewidth]{image/Hopper_trans.png}
\includegraphics[width=0.33\linewidth]{image/HalfCheetah_trans.png}
\includegraphics[width=0.33\linewidth]{image/Ant_trans.png}
\end{minipage}
\caption{Attack transferability between a given robot's policies. Each row is the adversarial state ratio of one adversarial state set on different policies. i.e, for Hopper, the row a2c, column ppo means $13 \%$ of the adversarial state set of a2c are also adversary states for ppo. The diagonal is always $100 \%$ because states of one policy's adversary dataset are always unsafe for that algorithm. The numbers in the tables are the transferable ratios.}
\label{fig:attck_transferability}
\end{figure}
Because adversarial states can be transferred between different
policies, the transferable ratio varies on different systems and
policies. For HalfCheetah, adversarial states are less likely to be
transferred into other policies when compared with Hopper and Ant. It
is also true that an adversary state set can have a relatively high
transferable ratio overall policies. For example, the adversarial
state of Ant-ddpg(row) has greater than a $78\%$ transferable ratio
on all policies. On the contrary, an adversary state set can also have
a low transferable ratio for all policies excepted for its own as
evidenced by HalfCheetah-sac(row). A policy can be vulnerable or
resistant to the adversarial state of other policies. For example,
Hopper-a2c(column) has $98\%$ and $97\%$ transferable ratio on
adversarial states for ppo and trpo respectively, while the
Hopper-ppo(column) has only $13\%$ and $23\%$ transferable ratio on
adversarial states for a2c and trpo, respectively.
\section{Feature Importance}
Not all features in an application are equally related to safety
specifications. Taking the Humanoid robot as an example - its safety
specification $\varphi$ is to stay upright ($z > 0.78$). This goal is
directly dependent on the height of the robot, thus the height feature
is highly related to safety. By applying feature selection on the
attack results, we can rank feature importance automatically. In our
experiments, we selected the top-$20\%$ most important features to
reduce the attack dimension (the dimension of filter $\phi$ defined in
Section \ref{sec:approach}) of Humanoid-ppo. Their importance is
marked as orange in Figure~\ref{fig:feature_importance}. We also analyzed the
feature importance of the F16 Ground Collision Avoidance System in
Figure~\ref{fig:feature_importance}. The top-$3$ important features
related to the ground collision are airspeed, pitch angle, and
attitude in order.
\begin{figure}[!tp]
\centering \setlength{\leftskip}{-110pt}
\begin{minipage}[!H]{1.4\linewidth}
\includegraphics[scale=0.68]{image/feature_importance/Humanoid-ppo_feature_importance.png}
\includegraphics[scale=0.68]{image/feature_importance/F16GCAS-ppo_feature_importance.png}
\end{minipage}
\caption{Humanoid-ppo \& F16GCAS-ppo Feature Importance}
\label{fig:feature_importance}
\end{figure}
\section{Shield Intervention Analysis}
If the shield does not adequately intervene with the original policy,
the original policy is vulnerable to states found in $\texttt{Adv}_\epsilon$. On
the contrary, since our auxiliary policies are only trained to assist
the original policy to be safe, too many shield interventions
initiated by auxiliary policies can reduce the performance of the
system. To measure the impact of shield interventions, we crafted
experiments to control the number of interventions. Given an input
state $s$, our detector gives scores to safe and unsafe labels, and
outputs the label with the higher score. For state $s$, suppose the
scores which the detector gives to the safe and unsafe labels are
$S_{safe}(s)$ and $S_{unsafe}(s)$ respectively. In the general
setting, if $S_{safe}(s) > S_{unsafe}(s)$, the detector marks $s$ as
safe. Now, we change this setting as the detector can mark $s$ safe
iff $S_{safe}(s) > S_{unsafe}(s) + C$. Otherwise, mark $s$ as
unsafe. $C$ is an \emph{approximating constant} - as it increases,
more states will be marked as unsafe, thus there will be more shield
interventions triggered by the auxiliary policy. For small values of
C, more states will be marked as safe, and thus fewer shield
interventions will be triggered.
Thus, by changing the value of the approximating constant, we can measure
the relationship between defense success rates and shield interventions,
as well as the relationship between performance and shield
interventions. For the first case, we initialized our simulation with
all the states in the adversarial state set $\texttt{Adv}_\epsilon(\pi_0, M, S_0)$
for original policy $\pi_0$. In this case, if there is no shield
intervention, the system will violate the safety specification. For
the second one, we measured the performance reward by initializing the
system around one trajectory, which is the same setting as described
in Section \ref{sec:perf of shield}. We decide the range of the
approximating constant with the detector training set derived from the
attack phase. For each state $s$ in the training set, we calculated
the difference $S_{safe}(s) - S_{unsafe}(s)$ and selected the smallest
and largest difference as the lower bound $l$ and upper bound $h$ of
the approximating constant. Given a sample range $[l, h]$, when $C >
h$, all states in this set will be marked as unsafe; when $C < h$,
all states in this set will be marked as safe. For each benchmark, we
sample 10 approximating constant values in this interval equally
separated.
We analyzed shielded policies on Ant in
Fig \ref{fig:ant_shield_intv_analysis}. As the approximating constant
$C$ increases, more interventions are involved and the defense success
rate increases. However, the performance reward decreases dramatically
due to these increasing interventions. The results on HalfCheetah are
shown in Figure~\ref{fig:halfcheetah_shield_intv_analysis}. Similar to
Ant, as $C$ increases, the defense success rate also increases. For
most policies, the performance reward decreases as $C$ increased, but
when policies are not well-trained, such as PPO, the performance
reward actually increases since the system becomes safer and thus the
robot learns a more accurate reward. The results of Hopper and
Humanoid are shown in Figure~\ref{fig:hopper_shield_intv_analysis} and
Figure~\ref{fig:humanoid_shield_intv_analysis}, respectively. Unlike
the results shown for Ant and Halfcheetah, we find that too many
interventions can lead to unsafety. This is because the auxiliary
policies are only trained to assist the original policy. As long as it
can pull the system to safe states for the original policies, it can
gain a decent reward. However, the auxiliary policy itself may not be
a safe policy independently. On the other hand, if the number of
interventions is small, the system is vulnerable to the following
states in $\texttt{Adv}_\epsilon$. Our shielded policies perform best when $C$ is
around 0 since the auxiliary policy is trained under the instruction
of detector when $C$ is $0$. Similar to Ant and HalfCheetah, when $C
> 0$, the performance reward decreases as the number of interventions
increases on Hopper and Humanoid. Results of classical control and F16GCAS benchmarks are in
Figure \ref{fig:cc_f16_shield_intv_analysis}. Excessive interventions on the (inverted) pendulum, $4$-carploon, and $8$-carploon can make the system unsafe and decrease performance reward. When interventions are infrequent, these applications become vulnerable to adversarial perturbations. Shielded policies worked best when $C$ is close to 0. For Helicopter and F16GCAS, more interventions lead to safer behavior without comprising performance.
\begin{figure}[!htp]
\centering \setlength{\leftskip}{-70pt}
\begin{minipage}[!H]{\linewidth}
\includegraphics[scale=0.7]{image/detector_strictness/AntBulletEnv-v0_defense.png}
\includegraphics[scale=0.7]{image/detector_strictness/AntBulletEnv-v0_perf.png}
\end{minipage}
\caption{Ant Shield Intervention Analysis}
\label{fig:ant_shield_intv_analysis}
\end{figure}
\begin{figure}[!htp]
\centering \setlength{\leftskip}{-70pt}
\begin{minipage}[!H]{\linewidth}
\includegraphics[scale=0.7]{image/detector_strictness/HalfCheetahBulletEnv-v0_defense.png}
\includegraphics[scale=0.7]{image/detector_strictness/HalfCheetahBulletEnv-v0_perf.png}
\end{minipage}
\caption{HalfCheetah Shield Intervention Analysis}
\label{fig:halfcheetah_shield_intv_analysis}
\end{figure}
\begin{figure}[!htp]
\centering \setlength{\leftskip}{-70pt}
\begin{minipage}[!H]{\linewidth}
\includegraphics[scale=0.7]{image/detector_strictness/HopperBulletEnv-v0_defense.png}
\includegraphics[scale=0.7]{image/detector_strictness/HopperBulletEnv-v0_perf.png}
\end{minipage}
\caption{Hopper Shield Intervention Analysis}
\label{fig:hopper_shield_intv_analysis}
\end{figure}
\begin{figure}[!htp]
\centering \setlength{\leftskip}{-70pt}
\begin{minipage}[!H]{\linewidth}
\includegraphics[scale=0.7]{image/detector_strictness/HumanoidBulletEnv-v0_defense.png}
\includegraphics[scale=0.7]{image/detector_strictness/HumanoidBulletEnv-v0_perf.png}
\end{minipage}
\caption{Humanoid Shield Intervention Analysis}
\label{fig:humanoid_shield_intv_analysis}
\end{figure}
\begin{figure}[!htp]
\centering \setlength{\leftskip}{-70pt}
\begin{minipage}[!H]{\linewidth}
\includegraphics[scale=0.7]{image/detector_strictness/cc_f16_defense.png}
\includegraphics[scale=0.7]{image/detector_strictness/cc_f16_perf.png}
\end{minipage}
\caption{Classical Control \& F16GCAS Shield Intervention Analysis}
\label{fig:cc_f16_shield_intv_analysis}
\end{figure}
\section{Hyper-parameters}
\subsection{Attack Hyper-parameters}
When running the Bayesian optimization attack, we used the same
hyper-parameters for all benchmarks. The acquisition function is
Expected Improvement (EI). The $\xi$ of EI is 0.01. We use Gaussian
Process (GP) with Matern kernel as a surrogate model. The
hyper-parameters of the Matern kernel use the default tuned values in the
{\tt skopt} \footnote{\href{https://scikit-optimize.github.io/stable/modules/generated/skopt.gp_minimize.html}{skopt.gp\_minimize}}
library. Before approximating the initial state-reward function with
GP, we randomly sample 10 points. We then evaluate the initial state-reward
function with points gotten by optimizing on acquisition function 30
times.
\subsection{Defense Hyper-parameters}
The Hopper's detectors are random forests. Each of them has 100 trees
with 50 max depth. The other detectors are neural networks. The search
categories of neural network detectors' hyper-parameters are given in
Table \ref{tab:nn_hyper}.
\begin{table}[H]\centering
\caption{Hyper-parameters of Neural Network Detector}\label{tab:nn_hyper}
\scriptsize
\begin{tabular}{lrr}\toprule
Hyper-parameter &Search Categories \\\midrule
Network Structure &obs\_dim x 128 x 128 x 128 x 2 \\
Learning Rate &[1e-4, 1e-3] \\
Mini-batch Size &[64, 128, 256, 512, 1024] \\
Training Epoch &[5, 10, 20, 50] \\
Optimizer &Adam \\
\bottomrule
\end{tabular}
\end{table}
The auxiliary policies of Hopper, HalfCheetah and Ant are trained with DDPG, while the Humanoid, classical control and F16GCAS benchmarks are equipped with PPO auxiliary policy. The search categories of the auxiliary policy are listed in table \ref{tab:ddpg_hyper} and \ref{tab:ppo_hyper}.
\begin{table}[!htp]\centering
\caption{Hyper-parameters of DDPG}\label{tab:ddpg_hyper}
\scriptsize
\begin{tabular}{lrr}\toprule
Parameters & Search Categories \\\midrule
Actor Network Structure &obs\_dim x 64 x 64 x action\_dim \\
Critic Network Structure &obs\_dim x 64 x 64 x 1 \\
Discount Factor $\gamma$ & [0.99, 0.999] \\
Update Rate $\tau$ & [1e-3, 1e-4] \\
others & Default values \footnotemark \\
\bottomrule
\end{tabular}
\end{table}
\footnotetext[5]{\href{https://stable-baselines.readthedocs.io/en/master/modules/ddpg.html}{Stable-Baselines DDPG}}
\begin{table}[!htp]\centering
\caption{Hyper-parameters of PPO}\label{tab:ppo_hyper}
\scriptsize
\begin{tabular}{lrr}\toprule
Parameters & Search Categories \\\midrule
Policy Network Structure &obs\_dim x 128 x 128 x action\_dim \\
Training Step &[1e5, 5e5, 1e6, 2e6, 4e6] \\
Clipping Range &[0.01, 0.05, 0.1, 0.2] \\
Discount Factor \((\gamma)\) &[0.99, 0.999, 1] \\
Entropy Cocfficicnt &0.01 \\
GAE \((\lambda)\) &0.95 \\
Gradient Norm Clipping &0.5 \\
Learning Rate &[2.5e-3, 2.5e-4, 2.5e-5] \\
Number of Actors &[4, 8, 16] \\
Optimizer &Adam \\
Training Epochs per Update &[4, 10] \\
Training Mini-batches per Update & [4, 16, 64, 128]\\
Unroll Length/n-step & [64, 128, 256, 512, 1024]\\
Value Function Coefficient &0.5 \\
\bottomrule
\end{tabular}
\end{table}
\section{Introduction}
Deep reinforcement learning (RL) approaches have shown promise in
synthesizing high-quality controllers for sophisticated cyber-physical
domains such as autonomous vehicles and robotics~\citep{BP+18,DR+17}.
However, because these domains are characterized by complex
environments with large feature spaces, they have proven vulnerable to
various kinds of adversarial attacks~\citep{GD+20} that trigger
violations of safety conditions the controller must respect. For
example, a safe controller for an unmanned aerial navigation system
must account for a myriad of factors with respect to
weather, topography, obstacles, etc., that may maliciously
affect safe operation, only a fraction of which are likely to have been
considered during training. Ensuring that controllers are robust in the face
of adversarial attacks is therefore an important ongoing challenge.
Although the state space over which the controller's actions take
place is intractably large, the need to conform to physical realism
greatly reduces the attack surface available to an adversary, in
practice. For example, an adversarial attack on a UAV cannot generate
an obstacle from thin air, suspend gravity, or instantaneously
eliminate prevailing wind conditions. A meaningful attack is thus
expected to generate states that are \emph{natural}~\citep{GD+20},
i.e., states that can be derived from perturbations of
realizable states as defined by the physics of the application domain
under consideration. We are interested in identifying such states
along a trajectory representing a rollout of the controller's learnt
policy.
Successful attacks manifest as a safety failure in this policy. While
these kinds of falsification methods are certainly
important~\citep{ghosh_verifying_2018} to assess the overall safety of
a controller, devising a defensive strategy that prevents unsafe
operation resulting from such attacks is equally valuable. In
black-box, model-free RL settings where a policy's internal structure
is unknown, shield-based defenses are typically
required~\citep{alshiekh_safe_2017}.
This paper considers the generation of such defenses that comprise
three distinct components: (1) a mechanism to efficiently explore
adversarial attacks within a realistic bounded area of the states
found in simulated and seemingly safe trajectories; (2) a detector
policy that predicts safe and unsafe states based on previously
observed successful attacks; and, (3) an auxiliary policy that is
triggered whenever the detector identifies an unsafe state; the role
of the policy is to propose a new action that re-establishes a safe
trajectory. To be practical, each of these components requires new
insights on adversarial attack and defense in RL. Effective attack
and detection strategies in realistic cyber-physical environments must
necessarily reduce a high-dimensional state space to a lower
dimensional one focused on features most relevant to an adversarial
attack. While an effective defense must be tuned with respect to the
detector to protect against identified attacks, any useful methodology
must also be able to generalize the shield to successfully prevent
unseen attacks, i.e., attacks for which the detector has not been
trained against.
\begin{figure}
\centering
\includegraphics[width=\textwidth,scale=.5]{image/adv_ant.png}
\caption{\small Simulation of a shielding defense against an
adversarial attack on an Ant robotics controller. The top row
shows the effect of a successful attack. The bottom row
illustrates an execution starting from the same initial (unsafe)
state augmented with a shielded defense.}
\end{figure}
Our contributions are three-fold:
\begin{enumerate}
\item We present an adversarial testing framework that identifies
natural unsafe states found near safe ones in a simulated trajectory
of learning-enabled controllers. The RL controller is guaranteed to
produce trajectories that lead to a safety violation from these
states.
\item We learn detector classifier from these unsafe trajectories that
precisely classify safe and unsafe states, and auxiliary
policies triggered when the detector identifies an unsafe state;
applying a shield on a presumed unsafe state yields a new safe
trajectory, i.e., a trajectory that satisfies desired safety
properties.
\item We provide a detailed experimental evaluation over a range of
well-studied RL benchmarks, including the PyBullet
suite of robotic environments and the F16 ground collision avoidance
system. Our results justify our claim that the robustness of
black-box RL-enabled controllers can be significantly enhanced using
learning-based detection and shielding approaches, without noticeable
loss in performance.
\end{enumerate}
Our overarching goal in this paper is to overcome inherent
deficiencies in RL policies that do not account for environment
conditions which can be maliciously or unintentionally perturbed.
These conditions potentially comprise a large attack surface, but in
the black-box setting we consider here, fine-tuning the model is not
possible. Our approach thus provides a meaningful pathway to identify
and mitigate attacks that exploit unrecognized weaknesses of the
deployed model, resulting in learning-enabled RL controllers that
provide much higher degrees of assurance than the state-of-the-art,
\emph{without} requiring re-training or white-box analysis.
The remainder of the paper is organized as follows. In the next
section, we present some relevant background material.
Section~\ref{sec:statement} formalizes the problem we consider and our
goals. Section~\ref{sec:approach} presents details about our
approach. Experimental results are given in~\ref{sec:expt}. Related
work and conclusions are presented in Sections~\ref{sec:related}
and~\ref{sec:conc}.
\section{Background}
\label{sec:background}
\paragraph{Optimum Policies for Discrete-time Continuous Systems}
We consider discrete-time systems $M=\langle S,A,f,R \rangle$ with non-linear dynamics $f$, continuous state space $S\subseteq \mathbb{R}^n$ and action space $A\subseteq \mathbb{R}^k$.
Here $s_{t+1} = f(s_t,u_t)$ where $s_t\in S$ is the state at time step $t$ and $f$ is a complex unknown non-linear function. The objective, given a reward function $R:S\times A \rightarrow \mathbb{R}$, is to find a policy $\pi: S\rightarrow \Delta(A)$ where $\Delta(A)$ is a probability distribution over $A$ that maximizes the discounted return $\mathbb{E}_{\pi,S_o}[\underset{t=0..T}{\sum} \gamma^t R(s_t,a_t)]$ where $\gamma\in(0,1)$ is the discount factor and $S_o$ is the initial state space. Given a policy $\pi$ a trajectory $\tau=(s_0,...,s_T)$ is the sequence of states obtained when $s_{t+1} = f(s_t,\pi(s_t))$ up to a horizon $T$.
\paragraph{Bayesian Optimization}
Bayesian optimization (BO) is a black-box optimization approach which aims at finding the global minimum for a black-box function $F(x)$ by querying a constrained number of times. This constraint is motivated by the expectation that evaluating the objective function often requires significant computational resources.
BO models $F(x)$ with a prior (frequently Gaussian Process-based) and uses an acquisition function to query values of $F(x)$ while trading off exploration and exploitation.
\section{Problem Statement}
\label{sec:statement}
\newcommand{\texttt{Att}_\epsilon}{\texttt{Att}_\epsilon}
\newcommand{\texttt{Adv}_\epsilon}{\texttt{Adv}_\epsilon}
Consider a continuous-state system $M$ where user-defined \emph{safe} ($S_s$) and \emph{unsafe} states ($S_u$) form a partition over the entire state space $S$ of $M$.
A rollout of a trained agent policy $\pi_o$ on $M$ yields a state trajectory $\tau_o = (s_0,...,s_T)$.
Let $\mathcal{T}(\pi_o,M,S_o)$ be the set of \emph{safe} trajectories formed by rollouts of policy $\pi_o$ in the system $M$ with initial state space $S_o$
(\textit{i.e.} trajectories in this set do not contain any states in $S_u$).
We consider the state dimensions which are used for computing the input of the agent policy $\pi_o$. These are often related to spatial characteristics such as joint position, angle, velocity, and robot center of mass. Define a filter $\phi(s)$ that yields a subset of modifiable state dimensions. Applying $\phi(s)$ to a trajectory $\tau$ yields $\phi(\tau) = (\phi(s_0),...,\phi(s_T))$.
Define a $\epsilon$-state perturbation of a state $s$ on the filtered dimensions in $\phi(s)$ to be another state $s'\in S$ that is within $\epsilon$ distance away from $s$ by varying the set of dimensions in $\phi(s)$. We choose the $L_\infty$ norm to measure state distances. Given a state $s$, denote $P_\epsilon(s)$ to be the set of all possible perturbations on $s$.
\begin{wrapfigure}{H!}{0.39\textwidth}
\begin{minipage}{0.45\textwidth}
\begin{algorithm}[H]
\DontPrintSemicolon
\SetKwFunction{Shield}{Shield}
\SetKwProg{Fn}{Function}{:}{}
\Fn{\Shield{$state$}}{
Given $\texttt{detector}$, $\pi_o$, $\pi_{\mathit{aux}}$
\eIf {\texttt{detector} ($state$)}{
\KwRet $\pi_{\mathit{aux}}$\;
}{
\KwRet $\pi_o$\;
}
}
\label{algo:def}
\caption{Shield Defense Outline}
\end{algorithm}
\end{minipage}
\end{wrapfigure}
We define an \emph{Adversarial State Attack} $\texttt{Att}_\epsilon(\tau_o)$ to be a set of states in which each state $s \in \texttt{Att}_\epsilon(\tau_o)$ is an $\epsilon$-state perturbation on a state in the trajectory $\tau_o$ that causes the new trajectory to be unsafe.
In other words, $s \in \texttt{Att}_\epsilon(\tau_o)$ if, for some $k$ and $s'$, $0\leq k \leq T$, $s'\in P_\epsilon(s_k)$, and executing the policy $\pi_o$ from $s'$ leads to a state in $S_u$. This can be thought of as a state perturbation at an arbitrary time index along the trajectory that results in safety failure.
These perturbations can be minute, a small shift of a robot due to a bump on the ground, or mild turbulence affecting the positioning of a jet in midair.
If $\epsilon$ is unconstrained, perturbations can be unrealistic, unlikely to occur in practice, or impossible to defend against given existing environment transition dynamics.
We thus concern ourselves with values of $\epsilon$ that lead to perturbed states in Section \ref{sec:epsilon_selection}.
We aim to find a way to defend against adversarial state attacks leading to a more robust control strategy that is still performant.
In real-world black-box scenarios, we have no access to both controller internals (underlying control policy) and environment conditions.
Thus, an effective defense must treat the original policy $\pi_o$ as a black box and make no assumptions about the (hidden) environment dynamics.
With these constraints in mind, we divide this problem into two stages. The first step is to detect adversarial state attacks, knowledge of which can be used to act differently, by
shielding $\pi_o$ from malicious state perturbations (the second step)
One defense outline is in the style of \citep{alshiekh_safe_2017} where a shield modulates actions taken by $\pi_o$ based on the observation provided by the environment. We structure a simple two-level function to represent the shield shown in Algorithm~\ref{algo:def}.
The upper level would be able to detect that an $\texttt{Att}_\epsilon$ attack has occurred while the lower level would be a policy to bring the system back to a safe state.
We call the upper level function the \textit{detector}
and the lower level policy the \textit{auxiliary policy} ($\pi_{\mathit{aux}}$).
With this setup, the constructed defense then uses the detector to decide whether to follow the original policy $\pi_o$ or switch to $\pi_{\mathit{aux}}$.
If these two functions are accurate, this approach is robust to adversarial state attacks for a given $\epsilon$.
Our goal is thus to learn these two functions keeping in mind the restrictions placed on the defense scheme.
\section{Approach}
\label{sec:approach}
Based on the definition of Adversarial State Attack $\texttt{Att}_\epsilon$ (Section~\ref{sec:statement}), given a trained policy $\pi_o$, a system $M$ with some initial states $S_o$, we aim to find a set of state-based adversarial attacks $\texttt{Adv}_\epsilon(\pi_o, M, S_o)$ defined as:
$$\texttt{Adv}_\epsilon(\pi_o, M, S_o) = \{s\ \vert\ {s \in \texttt{Att}_\epsilon(\tau)} \wedge \tau \in \mathcal{T}(\pi_o,M,S_o)\}$$
Our defense strategy follows the outline described in Algorithm~\ref{algo:def}.
\subsection{Safety Specifications}
Similar to~\cite{ghosh_verifying_2018}, we consider a safety specification $\varphi$ consisting of multiple predicates denoted as $\rho$ connected using Boolean operators including conjunction and disjunction:
$$
\varphi := \rho\ \vert\ \varphi \wedge \varphi\ \vert\ \varphi \vee \varphi\ \ \ \ \rho := t = t'\ \vert\ t \neq t'\ \vert\ t \le t'\ \vert\ t<t'\ \vert\ t \ge t'\ \vert\ t>t'
$$
A term $t$ is any real-valued function defined over system variables. For example, consider a robot with the height of the center of mass being $z$. One safe height specification $\varphi_{\mathit{safe}}$ is $z_{\mathit{safe}} < z$ where $z_{\mathit{safe}}$ is a height threshold.
\subsection{Attack}
\label{sec:att_approach}
The search problem for $\texttt{Adv}_\epsilon(\pi_o, M, S_o)$ as defined above is in general intractable. We thus require a more precise objective that is easy for optimization.
To tractably find $\texttt{Adv}_\epsilon(\pi_o, M, S_o)$, we define a \textit{safety reward} function $L(\varphi):S \rightarrow \mathbb{R}$ for $M$. A key feature of $L(\varphi)$ is that, given a state $s \in S$, $\varphi$ holds on $s$ iff $L(\varphi)(s) > 0$. We define $L(\rho)$ recursively. First, $L(t<t') := t'- t$. For the above robot example, $L(\varphi_{safe}) := z-z_{safe}$. We have $L(t = t') := \delta[t = t']$ where $[\cdot]$ is an indicator function and $\delta$ is a user-configurable constant, $L(t \neq t') := L(t < t' \vee t > t')$, and $L(t \le t') := L(t < t' \vee t = t')$. $L(\varphi)$ is also recursively defined: $L(\varphi \wedge \varphi') := \min (L(\varphi), L(\varphi'))$ and $L(\varphi \vee \varphi') := \max(L(\varphi), L(\varphi'))$.
Given a trajectory $\tau$, its \textit{safety reward} is
\begin{align*}
L(\varphi)(\tau)=\underset{s\in \tau}{\min}\ L(\varphi)(s)
\end{align*}
\paragraph{Attack setup}
With $L(\varphi)$ defined above as an effective proxy for safety measurement, given a (set of) trajectory $\tau$ of a system $M$ from $S_o$ i.e. $\tau \in \mathcal{T}(\pi_o,M,S_o)$, we search in $\underset{s \in \tau}{\bigcup}{P_\epsilon(s)}$ a set of state $S'$ with the objective of minimizing the safety reward $L(\varphi)(\tau')$ where $\tau'\in\mathcal{T}(\pi_o,M,S')$.
Observe that $L(\varphi)(\tau')$ is essentially a function over states (parameterized by the first state of $\tau'$ and the policy $\pi_o$).
The ability of Bayesian Optimization (BO) in optimizing black-box functions (e.g. $L(\varphi)(\tau')$) makes it qualified as an optimization scheme for our purpose.
We thus use BO to find states in $\texttt{Adv}_\epsilon(\pi_o, M, S_o)$ that lead to trajectories with a negative $L(\varphi)$ reward and hence unsafe.
In our experiments, we use EI (Expected Improvement) \citep{jones1998efficient} as the acquisition function and GP (Gaussian Processes) \citep{rasmussen2003gaussian} as the surrogate model.
\paragraph{Feature Selection}
Na\"ive BO does not scale with the dimensionality of a controller's feature space. One way to improve scalability is to optimize over a reduced set of features. For example, \citet{ghosh_verifying_2018} used REMBO \citep{wang2013bayesian} to create a reduced input space. We apply feature selection using a 2-stage approach. First, we run BO attacks
without feature selection and collect unsafe and safe trajectories. We then train a random forest with the collected data, selecting the top-$k$ features based
on a mean decrease in impurity i.e. refining the filter operator $\phi$ in Sec.~\ref{sec:statement}. We rerun the attack on these features again, searching for more unsafe trajectories.
\subsection{Defense}
\paragraph{Training the Detector} Our defense approach must be aware of potential unsafe states that occur when using the original policy $\pi_o$.
To this end, we train a classifier (the detector) with data derived during the attack phase. When we attack policy $\pi_o$ with BO, we obtain batches of trajectories via simulation in the environment, some of which starting from states in $\texttt{Adv}_\epsilon(\pi_o, M, S_o)$ are unsafe, and others are safe.
For a safe trajectory, we label all included states as safe, while
for an unsafe trajectory $\tau$, all states that follow a state found in $\texttt{Att}_\epsilon(\tau)$ are labelled as unsafe. Training a classifier with this data yields a detector that differentiates between states that are safe from those that produce unsafe trajectories affected by states in $\texttt{Adv}_\epsilon(\pi_o, M, S_o)$.
\paragraph{Auxiliary Policy}
When running a system, we use the detector to monitor current system states.
If the detector identifies a potentially vulnerable state, the defense strategy must yield an alternative action (sequence) to prevent the agent from entering an unsafe region. The auxiliary policy should be able to defend against attacks in $\texttt{Att}_\epsilon$.
To obtain the final building block of our defense, we use the trained detector to provide a reward signal for training an auxiliary policy ($\pi_{\mathit{aux}}$)
with PPO \cite{DBLP:journals/corr/SchulmanWDRK17} and DDPG \citep{pmlr-v32-silver14}.
Specifically, we train $\pi_{\mathit{aux}}$ on a slightly modified version of $M$, $M'=\langle S,A,f,R_{M'}\rangle$. The reward function $R_{M'}$ has two components:
\begin{enumerate}[leftmargin=*]
\item
We integrate the detector as a part of the reward function to train the auxiliary policy. We choose a simple reward signal based on the detector output. For an input state of the reward function, if the detector finds the state
safe, the action is given a reward 1 and otherwise a reward 0 is given. We call it \textit{detector reward}.
This reward component aims to bring the agent into a safe state identified by the detector.
\item The safety reward defined in Sec. \ref{sec:att_approach} is also an indicator of safety. A straightforward way to use this information is to add it as well to the reward signal for training the auxiliary policy. Optimizing the safety reward of each rollout maximizes policy safety. This reward component encourages $\pi_{\mathit{aux}}$ to behave safely.
\end{enumerate}
\paragraph{Deployment of the defense}
Intuitively, $\pi_{\mathit{aux}}$ only focuses on safety and does not care about performance.
Running the original policy $\pi_o$ in tandem with $\pi_{\mathit{aux}}$ (Algorithm~\ref{algo:def})
can retain performance provided by $\pi_o$ while ensuring safety provided by $\pi_{\mathit{aux}}$.
\section{Experiments}
\label{sec:expt}
\paragraph{PyBullet} A number of our experiments are conducted in PyBullet \citep{coumans2019}, a well-studied open-source suite of robotic environments.
The specific environments tested on were the Ant, HalfCheetah, Hopper and Humanoid robots. The objective of each of these environments is to stay upright and sustain forward motion.
The robots are modeled using the velocity, orientation, and position of their joints.
For example, Ant's 8-D action space is used to control each individual motor while navigating its 29-D state space. Its observation has 28 dimensions consisting of 4 dimensions of feet contact information, and 24 dimensions of joint information with body location and velocity. Its primary safety constraint is to remain upright; additional details are provided in Appendix A.3.
For more details of the environments, one may refer to the models' XML definition in the PyBullet repo \footnote{\href{https://github.com/bulletphysics/bullet3/tree/master/examples/pybullet/gym/pybullet_data/mjcf}{PyBullet Mujoco XML definitions}}.
For the attacked policy, we used an open-source implementation of popular RL algorithms \citep{stable-baselines} with the saved models provided\footnote{\href{https://github.com/araffin/rl-baselines-zoo/tree/625646308d98d92400470e2ff3b5bf8e8913c433}{RL pretrained policy}} which are trained on stochastic versions of the environment (to simulate sensor noise).
\paragraph{F16 Ground Collision Avoid System} The F16 environment is a model of the jet's navigation control system\citep{heidlauf2018verification}.
The F16 is modeled with 16 variables
and with non-linear differential equations as dynamics. The safety constraints are provided based on the aircraft flight limits and boundaries of the model.
Our objective is to keep the jet level and flying within the specified constraints.
Further details on the state dimensions, initialization and safety bounds are given in Appendix A.2.
The attacked policy of this model is trained with PPO.
\paragraph{Classic Control Environments} In addition to the above environments, we include several classical control benchmarks including (Inverted) Pendulum, $n$-Car platoon and large helicopter.
The (Inverted) Pendulum's goal is to swing a pendulum to vertical.
$n$-Car platoon models multiple ($n$) vehicles forming a platoon maintaining a safe distance relative to one another \citep{schurmann2017optimal}.
Large helicopter \citep{gopalakrishnan_spaceex_2011} models a helicopter with 28 variables and has constraints on each variables. These benchmarks' constraints are provided in Appendix A.1.
We trained the Helicopter with DDPG while the other models use the pretrained DDPG \citep{pmlr-v32-silver14} policies given in \citep{zhu_inductive_2019}.
\subsection{Evaluation}
\begin{table}[!htp]\centering
\setlength{\leftskip}{-5pt}
\scriptsize
\begin{tabular}{lcccccccc}\toprule
{\sf Benchmarks} &{\sf \thead{dims \\(obs/state)}}& {\sf \thead{simu. traj. \\ length}} &{\sf \thead{Attack \\ $\varepsilon$}} & {\sf \thead{rand. \\ attack}} &{\sf \thead{BO \\ attack}} &{\sf \thead{defense \\succ. rate}} &{\sf \thead{\tiny attack improvement \\ \tiny using shielded policy}} \\\midrule
Hopper-a2c &\multirow{3}{*}{15/12} &\multirow{3}{*}{1000} &\multirow{3}{*}{0.001} &1.29\% &2.18\% &91.40\% &43.51\% \\
Hopper-ppo & & & &0.41\% &5.27\% &97.80\% &27.97\% \\
Hopper-trpo & & & &1.71\% &1.97\% &97.90\% &48.16\% \\\midrule
HalfCheetah-a2c &\multirow{7}{*}{26/17} &\multirow{7}{*}{1000} &\multirow{7}{*}{0.02} &0.36\% &9.43\% &91.40\% &34.46\% \\
HalfCheetah-acktr & & & &0.90\% &14.54\% &92.80\% &65.23\% \\
HalfCheetah-ddpg & & & &1.63\% &11.84\% &88.20\% &67.27\% \\
HalfCheetah-ppo2 & & & &0.38\% &4.68\% &97.80\% &50.53\% \\
HalfCheetah-sac & & & &4.40\% &5.88\% &97.90\% &62.12\% \\
HalfCheetah-trpo & & & &0.77\% &4.83\% &97.90\% &49.02\% \\\midrule
Ant-a2c &\multirow{6}{*}{28/29} &\multirow{6}{*}{1000} &\multirow{6}{*}{0.0075} &0.17\% &1.26\% &82.60\% & 66.20\% \\
Ant-ddpg & & & &0.42\% &4.43\% &94.30\% &93.57\% \\
Ant-ppo & & & &1.47\% &11.78\% &88.70\% &91.39\% \\
Ant-sac & & & &2.82\% &14.83\% &96.00\% &94.02\% \\
Ant-td3 & & & &5.79\% &12.79\% &93.60\% &72.52\% \\ \midrule
Humanoid-ppo &44/47 &1000 &0.001 &0.38\% &2.00\% &91.90\% &22.93\% \\\midrule
Pendulum-ddpg &2/2 &200 &* &0.03\% &8.72\% &100.00\% &100.00\% \\
4carploon-ddpg &7/7 &1000 &* &0.01\% &3.82\% &100.00\% &94.71\% \\
8carploon-ddpg &15/15 &2000 &* &0.72\% &4.13\% &100.00\% &100.00\% \\
Helicopter-ddpg &28/28 &2000 &* &0.00\% &0.26\% &100.00\% &100.00\% \\\midrule
F16-ppo &8/16 &2000 &* &0.01\% &2.60\% &96.40\% &96.69\% \\
\bottomrule
\end{tabular}
* Use allowed variance of initial state which is given by the benchmark itself
\caption{Experimental Results. Benchmarks are of the form, E-A where E is the Environment and A is the type of controller attacked.}
\label{tab: eval_table}
\end{table}
\paragraph{Selecting Attack Range}
\label{sec:epsilon_selection}
As mentioned in Sec.~\ref{sec:statement}, an Adversarial State Attack $\texttt{Att}_\epsilon$
requires a meaningful $\varepsilon$-state perturbation.
We choose $\varepsilon$ with following strategy.
For a specific robot in the PyBullet benchmarks, we initialized our $\varepsilon$ to be 0.001. We randomly perturbed initial states and run simulations 1000 times for every available policy. If there is a policy that does not find any unsafe states, we increase $\varepsilon$ by 0.0005, and repeat this process until unsafe states are found in all policies.
We believe this is a sensible strategy because none of these benchmarks
are equipped with constraint specifications that indicate the range of
acceptable states that can be generated by the environment. For all the other benchmarks,
constraints on these ranges were available and used directly.
\paragraph{Attack Results}
\begin{wrapfigure}{!H}{0.5\linewidth}
\includegraphics[width=\linewidth]{image/Humanoid_bo.png}
\caption{Attack success rate for Humanoid-ppo under different feature dimension reduction percentages.}
\label{fig: BO_humanoid}
\end{wrapfigure}
Table~\ref{tab: eval_table} shows two attack strategies. The first,
{\sf rand. attack} indicates the percentage of safety violations
detected when initializing the state randomly around a sampled
trajectory with respect to the chosen $\varepsilon$. For each
benchmark, we randomly sampled 40K states within the bounds determined
by $\varepsilon$ and initialized the simulations accordingly. Column
{\sf BO attack} shows the attack success rate when using BO to
discover attacks. The GPs of the method are initialized with 10
randomly sampled states and the BO algorithm samples the safety reward
30 times. For each state in one trajectory, we generate 40 sampled
trajectories. If the length of an attacked trajectory was $L$, $40
\times L$ trajectories would be collected in one attack. We then count
the unsafe trajectories in these simulations.
For high-dimensional
benchmarks like Humanoid, our attack focused on the top 20\% most
important features (9 features); these features were selected using
the approach described in \ref{sec:att_approach}. With this feature
reduction in place, our technique achieves an average 2\% attack
success rate, compared to just a 0.38\% success rate using a randomized
attack strategy. Results for other dimension reduction choices are
given in Figure~\ref{fig: BO_humanoid}.
\paragraph{Defense Results}
We trained detectors with the states generated by our attack and
learned auxiliary policies with the detector and corresponding safety
reward. We measured the quality of our defense in two ways. First,
we want to know how successful our detector and auxiliary policies are
in preventing attacks on the original policy that would otherwise lead
to a safety violation. Second, given a shielded policy, i.e., a
policy that integrates the original, defense, and auxiliary policy, we
measure how effective this combined policy is in reducing the number
of unsafe states available to an attack, compared to the original
policy.
To answer the first question, we run BO attacks on the original
policy, employing our detector and shield policy to detect and avoid unsafe
trajectories. Note that we may still find unsafe trajectories because
not all attacks are necessarily preventable for reasons discussed
below. The defense success rate on the PyBullet benchmarks ranges
from 82.6\% to 100\%. On the simpler classical control benchmarks, the
defense success rate can achieve 100\% while the F16GCAS benchmark has
a 96.4\% defense success rate. These results support our claim that
$\varepsilon$-state perturbations used in adversarial attacks in
these environments can be effectively mitigated. We note that our
defense method does not provide verifiable guarantees of safety.
There are two primary reasons for this: \textbf{a)} the possible
existence of states in our attack which are not recoverable by any
policy (eg: a robot whose forward momentum will cause it to fall
regardless of any possible shield action that may be taken); and,
\textbf{b)} covariate shift due to our black-box setting that does not
provide insight into environment dynamics, making it impossible to
provide guarantees on detector accuracy during testing since the
detector and auxiliary policy are trained only with the adversarial
states discovered by previously seen BO attacks. In other words, even
if the detector is accurate, it is also untenable to assert that the
auxiliary policy ($\pi_{\mathit{aux}}$) trained by RL is always
reliable due to variations while training.
The {\sf attack improvement using shielded policy} column shows the
percentage reduction in unsafe states discovered by a BO attack when
applied to the shielded policy as compared to the original. The
trajectories admitted by the shielded policy are more constrained than
the original since the policy is derived as a mixture of both the
original and the auxiliary (safety) policy. Consequently, we would
expect a fewer number of unsafe states to be discoverable under this new
policy when compared against a policy in which safety was not taken
into account. Indeed, the results shown in the column justify this
intuition. For all benchmarks, the use of a shielded policy reduces
the number of unsafe states found by a BO attack by at least 22.93\%.
The use of this blended policy on the three Classical Control tasks
demonstrates 100\% empirical robustness, while the F16 benchmark is
very close behind at 96.69\%. Several of the PyBullet benchmarks such
as Ant-ddpg and Ant-sac show similar improvement.
\begin{figure}
\centering \setlength{\leftskip}{-120pt}
\includegraphics[width=1.5\textwidth,
height=0.28\textwidth]{image/perf.png}
\caption{Average Reward for Original Policy and Shielded Policy}
\label{fig:eval_perf}
\end{figure}
\paragraph{Performance of the Shielded Policy}
\label{sec:perf of shield}
The experiments in Figure \ref{fig:eval_perf} investigate the impact
of considering safety (and thus shield interventions) on performance.
We randomly initialized the simulation around the attacked trajectory
within a range bounded by $\varepsilon$. For each benchmark, we run a
simulation 1000 times and count the (normalized) average return
yielded with the original policy and shielded policy. The y-axis is
the trajectory return scaled by a constant shared among each
environment's benchmarks. It represents the performance of the
corresponding policy(i.e., moving fast with low electricity cost). The result in Figure \ref{fig:eval_perf}
supports our claim that the cost of shield interventions is typically
modest, on average only 5.78\% variance compared to the performance
exhibited by the original.
\section{Related Work}
\label{sec:related}
As discovered in \cite{huang_adversarial_2017}, by adding tiny or even invisible perturbations to inputs at each time-step, neural network RL policies are vulnerable to adversarial attacks, which can lead to abnormal system behavior and significant performance drop. Simple generation algorithms such as fast gradient sign method (FSGM)~\cite{goodfellow_explaining_2015} can craft adversarial examples for some RL algorithms that are less resistant to adversarial attack. However, our approach can effectively attack a wide range of modern RL algorithms. In the black-box setting where gradient information is not available, \cite{behzadan_vulnerability_2017} proposed a policy induction attack that exploits the transferability of adversarial examples~\cite{szegedy_intriguing_2014}. To attack, it obtains adversarial state perturbations from a replica of the victim's network, e.g. using FSGM, and trains the replica to simulate the victim's network. In contrast, our approach does not attempt to replicate the victim's network but uses Bayesian optimization and dimension reduction to approximate only part of the search space that is relevant to insecure model behavior. \cite{lin_tactics_2017} also proposed to find adversarial attacks in the black-box setting. It pushes the RL agent to achieve the expected state under the current state by generating adversarial perturbations from action sequence planning enabled by model-based learning. As opposed to this approach, our work is model-free as we do not need to learn an environment model to guide the search of adversarial examples. While using Bayesian optimization for crafting adversarial examples was previously explored in~\cite{ghosh_verifying_2018}, that work focuses on environment parameters such as initial and goal states. Our work exploits Bayesian optimization to attack at various time-steps in a rollout. In~\cite{GD+20}, the attacker solves an RL problem to generate an adversarial policy creating natural observations and acting in a multi-agent environment to defeat the victim policy. The setting of our problem is substantially different as we assume the input distribution to the victim policy is not significantly changed at test time to better mirror realistic behaviors. Importantly, our technique differs from these previous approaches by training an auxiliary policy to shield and defend the victim network.
To defend an RL policy, prior work has applied adversarial training to improve the robustness of deep RL policies. Adversarial RL training fine-tunes the victim policy against adversary policies by exerting a force vector or randomizing many of the physical properties of the system like friction coefficients~\cite{dexterous,rarl,Mandlekar_2017,Pattanaik_2018}. The trained policy can robustly operate in the presence of adversarial polices that apply disturbance forces to the system. Defenses based on this idea also generalize to multi-agent RL environments~\cite{GD+20} which shows that repeated fine-tuning can provide protection to a victim policy against a range of adversarial opponents. Our approach differs from these techniques because we consider black-box settings, and do not attempt to fine-tune the internals of a victim policy. Instead, a shield-based auxiliary policy is trained to improve the victim policy's resistance to adversarial perturbations. There exists recent work that synthesizes verified shields to protect RL policies leveraging formal methods ~\cite{zhu_inductive_2019,mps,cpsshield}. However, unlike our approach, these techniques do not scale to high-dimensional environment and adversarial disturbances.
\section{Conclusions}
\label{sec:conc}
Learning-enabled controllers for CPS systems are subject to
adversarial attacks in which small perturbations to the states
generated by an environment in response to a controller's actions can
lead to violations of important safety conditions. In this paper, we
present a new framework that uses directed attack generation to learn
defense policies that accurately differentiate between safe and unsafe
states and an auxiliary shielding policy that aims to recover from an
unsafe state. Notably, our methodology operates in a completely
black-box setting in which environment dynamics are unknown.
Experimental results demonstrate our approach is highly effective over
a range of realistic sophisticated controllers, with only modest
impact on overall performance.
\section{Broader Impact}
Machine learning has demonstrated impressive success in a variety of
applications relevant to the core thrust of this paper. In
particular, autonomous systems such as self-driving cars, UUVs, UAVs,
etc. are examples of the kind of learning-enabled CPS systems whose
design and structure are consistent with the applications considered
here. These systems are characterized by intractably large state
spaces, only a small fraction of which are explored during training.
Because the space of possible environment actions is so large, it is
unrealistic to expect that the environment models learnt used to train
these controllers represent all possible behaviors likely to be
observed in deployment. These covariate shifts can affect controller
behavior resulting in violations of important safety constraints.
These violations can have significant negative repercussions in light
of the common use case for these applications which often involves
operating in environments with high levels of human activity. Our
shielding policy shows significant benefit in improving controller
safety without requiring expensive retraining post-deployment.
| {
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Liverpool is by far one of the best party cities in England, and as it's historically a port town there are plenty of bars and clubs to hit up. You'll find a variety of quirky places some with booking only secret codes like Ex Directory others are just plain quirky Aloha, and Smugglers Cove to name a few. The Merchant and Jenever, are two of the best Gin bars in the city with plenty on offer. The best happy hour deals are found at Be At One, but we also can't help but mention the best themed and trendy bar in Liverpool Revolucion De Cuba. There are way too many to choose from which is why Liverpool is perfect as a Stag night out.
Stags will love the endless quirky bars and restaurants, the great list of activities and the excellent choice of hotels. Sports fans will also find exclusive dedicated bars and venues to enjoy. It's a city that truly welcomes stag parties and wild nights of fun, so there's no limits on what you can do for your Stag weekend. | {
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Biopharma giant Merck inaugurates $20 million lab in Singapore
Ojaswita Kutepatil September 20, 2018 Health
Merck, the Germany-based multinational biopharmaceutical, chemical and life sciences company, has reportedly announced to have opened a $20 million lab in Singapore. Reports cite, the laboratory would be constructed near Pasir Panjang.
Spanning over an area of 3,800 square feet, the facility would be housing the company's first BioReliance lab in the area. It would also be offering services like cell culture media development, biologics drug safety testing, and purification process optimization, cite sources.
Reportedly, the laboratory would provide faster, more accessible testing services for biological drug products to pharmaceutical companies in Asia who previously could only avail these services by working with two BioReliance labs of Merck in Britain and USA.
Singapore's Senior Minister of State for Trade and Industry, Dr. Koh Poh Koon reportedly stated that Merck's investment is a well-timed venture as regional and global healthcare demands are growing at a rapid pace. Dr. Koh further stated that the pharmaceutical firms looking for new opportunities can now leverage Singapore's strengths to expand their businesses in the nation.
A spokesperson from Merck reportedly stated that the new lab offers consumers with assurance of quick availability of validated next-gen drugs for treatment as the time taken to validate critical tests, process, and launch the drug into the market would be reduced.
For the record, the Government of Singapore has been investing in technology, infrastructure, and talent to help boost the industry's growth. Some of the examples of these investments are the Tuas Biomedical Park that houses over 31 manufacturing plants and professional conversion program for the biologics and pharmaceutical domains. The program has benefited approximately 350 individuals since its inception in 2014.
Reportedly, the laboratory would allow a quicker turnaround to its Asian customers and would significantly contribute to Singapore's biomedical sciences industry which is a crucial part of the nation's economy. The industry contributes around 4% to the nation's GDP and employs over 22,000 individuals with many well-paying, high-skilled jobs, cite sources.
Roche announces global availability of FoundationOne®Liquid
Novartis announces FDA, EMA approval of SPMS drug, Siponimod
Sunil Hebbalkar October 8, 2018 | {
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Volkswagen I.D. Familiy is growing
Forth car, I.D. Vizzion is mixing electric propulsion with luxury and autonomous drive
After the Dieselgate scandal, Volkswagen took very different direction. Soon after 'dirty stuff' started emerging on surface, company switched attention into developing then emerging technology of electric cars. Few years later first results came in the form of new family of electric cars and its first three examples: I.D. Buzz, I.D. and I.D. Crozz. They made their public debut in Frankfurt last year and are apparently going to get into production by the end of 2019.
Today, Volkswagen has announced a new step on their path to realize the plan of presenting 20 new electric cars by the year 2025 as the fourth member of I.D. family has been presented. Well, the new car, that bears a name I.D. Vizzon has not really been presented yet, since the first prototype is going to be revealed on this year's car show in Geneva. Volkswagen did however revealed many details about the car that made us even more curious.
Button-less cabin, car will be complitly gesture/voice operated
For instance, one of the key features, built into the car is going to be so-called digital chauffeur. The car is not only going to drive autonomously, there will also going to be no buttons inside the luxurious cabin. Instead, systems like air conditioning, satnav or infotainment are going to be operated either via hand gestures or by voice commands.
Even though I.D. Vizzion is still 'only' a prototype, Volkswagen has already revealed key technical data about the car and its power plant. 5.11 meters long vehicle is going to be powered by a pair of electric motors with a total output of 225 kilowatts. This will enable the car to reach a top speed of 180 kilometers. Adding a battery pack with a capacity of 111 kWh car will be able to travel for up to 665 kilometers on a single charge. This number might vary a lot, since the car is going to be equipped with braking regeneration technology.
Feb. 20, 2018 Driving photo: Newspress
I.D. Vizzion Volkswagen
Is Volkswagen planning a game changer?
A small crossover with a price under 20.000 euros is unofficially being planned to hit production within a couple of years.
VW I.D. R Pikes Peak to participate on this year's famous race
With its newest electric car, Volkswagen is about to return in Colorado for the first time in more than 30 years.
I.D. Buggy actually comming to life?
Rumors might just lead into a production vehicle. | {
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El cigarrillo electrónico (también, cigarro electrónico, en inglés «e-Cigarette», «vaporizador», «vapeador», «vape») es un sistema electrónico inhalador diseñado en su origen para simular el consumo de tabaco sin quemarlo directamente, diferenciándose del cigarrillo tradicional.
Estos dispositivos utilizan una resistencia, batería para calentar y vaporizar una solución líquida. La solución líquida, llamada líquido de vapeo, e-Liquid, e-Juice o esencia, puede o no contener aromas. Estas soluciones líquidas suelen tener propilenglicol, glicerina, nicotina, saborizantes, aunque varía según la solución, pues también las hay sin ninguno de estos componentes.
Desde su introducción al mercado a principios de este siglo, fue popularizándose en la década del 2010, como una alternativa para dejar el cigarrillo tradicional; así también para su uso recreativo, esto último especialmente en personas no fumadores. En sus inicios, su diseño imitaba los cigarrillos, puros o pipas. En la actualidad hay variados diseños de más de 400 marcas de cigarrillos electrónicos; algunos de los modelos más populares se encienden automáticamente al inhalar, y otros, por medio de un botón.
Si bien se cree que el principal beneficio sobre el uso de los cigarrillos electrónicos es que son una alternativa al cigarro tradicional como terapia de reemplazo de nicotina para dejar de fumar; se desconocen los efectos a largo plazo del uso de cigarrillos electrónicos. Según estudios recientes, en algunos casos pueden ser igual o peor de dañinas que los cigarrillos convencionales, por lo tanto su venta y uso es regulado por ley en varios países del mundo.
Tipos
La composición de un cigarrillo electrónico consiste en dos elementos diferenciados:
El atomizador. En él se coloca la resistencia y se produce el calentamiento del líquido.
El "mod". El que suministra la corriente necesaria para calentar la resistencia.
Estos dos elementos no siempre están diferenciados, puesto que existen cigarrillos electrónicos que entran en la llamada categoría de "AIO" ("All In One", "Todo en uno" en inglés) que aún tanto atomizador como suministrador de corriente en un mismo dispositivo.
Los atomizadores y mods se pueden categorizar en distintos tipos.
Atomizadores
Llamamos atomizador a una pieza construida generalmente con partes metálicas donde podemos colocar la resistencia, así como en los atomizadores con tanque colocar el líquido. Las resistencias pueden ser de dos tipos: las resistencias artesanales en las que insertar manualmente el algodón y las resistencias comerciales, que se compone de un hilo resistivo rodeado de algodón, compactado dentro de un cilindro con orificios laterales.
Para el suministro de corriente, los atomizadores emplean un pin metálico situado en la parte inferior de la rosca. Las roscas, son la parte que conectan el suministrador de corriente con el atomizador; existen dos roscas mayormente estandarizadas en el mercado: 510 y eGo. Aun así existen fabricantes que emplean roscas propietarias.
Podemos catalogar los atomizadores según su funcionamiento y la clase de resistencia que emplean:
Claromizador: Es un atomizador generalmente con tanque, que emplea resistencias construidas específicamente para ese atomizador o una serie de atomizadores. El fabricante crea modelos distintos de resistencias ya construidas que sólo es necesario enroscar en el interior. En este caso, las resistencias vienen con un valor establecido. Si nuestro kit cuenta con variación de potencia, es muy importante que sepamos localizar en la misma resistencia los rangos de potencia recomendados por cada fabricante. Si no fuese posible ver esta información, a partir de la pantalla de nuestro dispositivo comprobaremos que el valor V (voltaje) nunca supera los 4.2V. Con esto nos aseguraremos de no dar una potencia excesiva a nuestra resistencia. Si nuestro dispositivo, en cambio, no tiene opciones de cambio de potencia, entonces aplicaremos una norma básica por la cual cuanto menor sea el valor de nuestra resistencia, más potencia sacaremos. En cambio, cuanto más valor tiene se dice que la calada es más floja, pero también puede traducirse en una calada más cerrada, con similitud a un cigarrillo convencional.
Rebuildable Atomizer o Atomizador Reparable (RBA): Son atomizadores que poseen en su interior una base con conexiones en paralelo para emplazar resistencias, permiten libertad a la hora de colocar resistencias ya que se emplean bobinas que se colocan en los postes de la base. Según los principios de diseño del atomizador, existen varias categorías para este tipo de atomizadores.
Rebuildable Dripping Atomizer o Atomizador Reparable de Vapeo en Seco (RDA): Atomizadores que no poseen tanque, contienen la base reparable justo debajo de la boquilla sin hacer uso de una chimenea. Para recargar el líquido se ha de gotear sobre el algodón colocado en la resistencia. Son populares por dar un buen sabor. Dentro de este tipo, existen una variante con el pin de conexión perforado para ser usado en conjunto con un mod "Bottom Feeder" o de alimentación inferior, sirviendo de entrada de líquido.
Rebuildable Tank Atomizer o Atomizador Reparable con Tanque (RTA): Atomizadores con tanque, contienen la base reparable conectada a una chimenea que conduce el vapor hacia la boquilla. Emplean Capilaridad para conducir el líquido hacia la resistencia. Dentro del tanque se observan aberturas que sirven como entradas de líquido a la piscina que contiene al algodón que es calentado por la resistencia.
Rebuildable Dripping Tank Atomizer o Atomizador Reparable con Tanque de Vapeo en Seco (RDTA): Aunque parezca contradictorio, este tipo de atomizador mezcla los conceptos de Tanque y de Vapeo en Seco. Contienen la base reparable en la parte superior, cercana a la boquilla, y el tanque en la parte inferior. Se ha de girar para poder impregnar el algodón.
Mods
Son los suministradores de corriente y poseen un cabezal que hace la conexión al atomizador con un pin metálico. Generalmente contienen una o más baterías en su interior que se encarga de suministrar el potencial para calentar la resistencia del atomizador. Suelen tener un botón que activa el suministro de corriente.
Pueden dividirse según el tipo de batería que empleen:
Mod de batería interna: Aquellos que poseen una batería no reemplazable por el usuario, generalmente usan una batería.
Mod de batería intercambiable: Aquellos que poseen un compartimento para baterías que pueden ser reemplazadas por el usuario. No existe un estándar para el tamaño de batería, pero sí hay varias extremadamente popularizadas como la 18650. Pueden usar una o más baterías dependiendo de la decisión de diseño del fabricante. También existen modelos que en lugar de usar baterías convencionales emplean baterías de polímero de litio, aunque su cuota de mercado es residual.
Independientemente del tipo de batería, podemos catalogarlos por su funcionamiento o diseño:
Mod electrónico: Aquellos que poseen electrónica en su interior para regular sus funciones: Ajuste de voltaje, encendido y apagado o recarga USB entre otras; son el tipo más popularizado y más seguro, ya que su placa electrónica suele poseer mecanismos de protección frente a cortocircuitos o descargas inesperadas de potencial. Los más avanzados poseen pantallas para visualizar datos, ajustar el voltaje o usar perfiles predefinidos de uso.
Mod mecánico: Aquellos que no poseen ningún tipo de electrónica en su interior, de un funcionamiento y construcción muy simple que no posee más que cables y un botón para suministrar la corriente. No usan baterías internas en ningún caso (y sería absurdo ya que sin electrónica, no se podría recargar). Se consideran peligrosos si se utilizan sin conocimiento básico de circuitos dado que no existe una protección electrónica para cortocircuitos y problemas similares, sin embargo son populares por sus elaborados diseños, su salida de potencia y por no requerir una resistencia mínima. Algunos usuarios le colocan un fusible como protección.
Mod Bottom Feeder o de Alimentación Inferior: Aquellos que poseen un pin de conexión perforado y un compartimento para una botella de plástico. Dicha botella puede apretarse para suministrar de líquido al atomizador a través del pin. Pueden ser electrónicos o mecánicos.
AIO
"All In One" o "Todo En Uno". Dispositivos que aúnan atomizador y mod en su construcción, no poseen una rosca para la conexión dado que están construidos de manera que ambos elementos están integrados en uno sólo. Suelen emplear resistencias diseñadas específicamente para dichos dispositivos. Recientemente han aparecido nuevos modelos más compactos llamados "Pod" (del Inglés, cápsula) diseñados específicamente para usar con líquidos que contengan sales de nicotina. Una gran diferencia es que no suelen tener un botón para suministrar corriente sino que algunos incorporan un sensor para detectar cuando el usuario aspira y entonces dar la corriente.
Beneficios y riesgos
Argumentos a favor
King's College de Londres
El 27 de febrero de 2019, en un comunicado de prensa, el Public Health England (PHE o Salud Pública de Inglaterra) da a conocer un informe independiente del King's College de Londres, realizado por encargo del PHE. En este informe recomienda a los Servicios de Salud británicos "hacer más para alentar a los fumadores que desean dejar de fumar con la ayuda de un cigarrillo electrónico".
El texto menciona que un ensayo clínico del Reino Unido encontró que los cigarrillos electrónicos, combinados con el apoyo de personal médico, "son hasta dos veces más efectivos para dejar de fumar que otros productos de reemplazo de nicotina, como los parches o goma de mascar".
Las autoridades sanitarias de Reino Unido iniciaron una campaña con el objetivo de contrarrestar la creencia entre los fumadores de posibles efectos negativos del cigarro electrónico y hacerles ver que este recurso es "un 95% menos dañino" que los cigarros tradicionales.
Royal College of Physicians
El 28 de abril de 2016, el Royal College of Physicians publicó su informe «Nicotine without smoke: Tobacco harm reduction» con la intención de proporcionar una actualización sobre el uso de la reducción del daño en el tabaquismo, en relación con todos los productos de nicotina sin tabaco, pero particularmente los cigarrillos electrónicos. Muestra que, a pesar de todos los riesgos potenciales, la reducción de daños tiene un enorme potencial para prevenir la muerte y la discapacidad del consumo de tabaco y para acelerar nuestro progreso hacia una sociedad libre de tabaco.
Recomendaciones clave:
Fumar es la mayor causa evitable de muerte y discapacidad en el Reino Unido.
El suministro de la nicotina a la que los fumadores son adictos sin los componentes nocivos del humo de tabaco puede prevenir la mayor parte del daño causado por el tabaquismo.
La terapia de reemplazo de nicotina (TRN) es más efectiva para ayudar a las personas a dejar de fumar cuando se usan junto con el apoyo de profesionales de la salud, pero mucho menos efectiva cuando se usan solas.
Los cigarrillos electrónicos se comercializan como productos de consumo y están demostrando ser mucho más populares que las TRN como sustituto y competidor de los cigarrillos de tabaco.
Los cigarrillos electrónicos parecen ser efectivos cuando los fumadores los utilizan como una ayuda para dejar de fumar.
Los cigarrillos electrónicos no se fabrican actualmente con los procedimientos estandarizados y esos puede hacerlos más peligrosos que las TRN. Sin embargo, es poco probable que el riesgo para la salud implicado en inhalar el vapor que producen estos cigarros electrónicos exceda el 1.2% del daño causado por el tabaco tradicional.
Los desarrollos tecnológicos y los estándares de producción mejorados de estos productos podrían reducir el riesgo a largo plazo de los cigarrillos electrónicos.
Existe la preocupación de que los cigarrillos electrónicos aumenten el tabaquismo al normalizar el acto de fumar, actuando como una puerta de entrada al tabaquismo en los jóvenes. Sin embargo, la evidencia disponible hasta la fecha indica que los cigarrillos electrónicos se usan casi exclusivamente como alternativas más seguras al tabaco por fumadores confirmados que intentan reducir el daño a sí mismos o a otros al fumar, o para dejar de fumar por completo.
Existe una necesidad de regulación para reducir los efectos adversos directos e indirectos del uso de cigarrillos electrónicos, pero esta regulación no debe inhibir el desarrollo y uso de productos de reducción de daños por parte de los fumadores.
Es del interés de la salud pública promover el uso de cigarrillos electrónicos, TRN y otros productos de nicotina distintos del tabaco lo más ampliamente posible como sustituto del tabaquismo.
FDA
El 28 de julio de 2017 el entonces comisionado de la FDA, Scott Gottlieb, dio un discurso titulado «Protegiendo a las familias estadounidenses. Enfoque integral sobre nicotina y tabaco» en el que declara:
El tabaco continúa siendo la principal causa de muertes por enfermedades prevenibles en los Estados Unidos. Pero mucho ha cambiado en el marco de la regulación en la producción de tabaco y en la capacidad de la FDA de abordar esta crisis de salud pública.
Abordar la crisis de adicción que está tomando las vidas de jóvenes y haciendo daño a las familias estadounidenses es la tarea más apremiante de la FDA. En particular, examinar la presencia de nicotina en cigarrillos de combustión como parte de una estrategia mucho más generalizada. Me he comprometido con tomar pasos agresivos para abordar la epidemia de adicción a opioides. Veo nuestra oportunidad de confrontar la adicción a la nicotina con la misma obligación. Buscaré reducir la adicción a la nicotina con el mismo vigor.
Además del costo humano devastador del uso de tabaco, el tabaquismo también es culpable de costos directos en asistencia médica y pérdida de productividad por un valor anual aproximado de 300 mil millones de dólares. Por lo que también hay costos económicos importantes para la sociedad.
Debemos hacer más para ayudar a estos estadounidenses y sus familias a llevar vidas más saludables, y evitar o liberarse de la adicción nociva a los cigarrillos. La clave yace en tomar un enfoque nuevo y generalizado para regular la nicotina.
La nicotina es increíblemente adictiva. Y cuando la nicotina se combina con partículas de humo del cigarrillo, no solo se vuelve altamente adictiva, sino también una mezcla química adictiva de enfermedades y muerte. [...] Pero la nicotina en cigarrillos no es la responsable directa del cáncer, las enfermedades pulmonares y las enfermedades cardiovasculares que matan a cientos de miles de estadounidenses cada año. Sí, los volvió adictos y los mantiene adictos por mucho tiempo [...] Pero son los otros componentes químicos en el tabaco, y en el humo creado al prenderle fuego al tabaco, la causa directa y principal de las enfermedades y las muertes, no la nicotina. Por lo tanto debemos volver a revisar la nicotina como tal, y como la adicción que esta ocasiona está relacionada con el daño potencial de su mecanismo de administración.
¿Cómo podemos abordar la nicotina de forma innovadora y generalizada?
Debemos reconocer el potencial de la innovación para llevarnos a productos menos nocivos, que, con la vigilancia de la FDA, puede ser parte de la solución. Aunque falta mucha investigación por hacer sobre estos productos y los riesgos que pueden tener, también pueden ofrecer beneficios que debemos considerar.
Debemos imaginar un mundo donde los cigarrillos pierden su potencial adictivo mediante niveles reducidos de nicotina. Y un mundo donde formas alternativas, menos nocivas y eficientes de administrar niveles deseados de nicotina estén disponibles para aquellos adultos que los necesiten o los deseen.
Para iniciar este proceso, desarrollaremos una Notificación Previa de Normas Propuestas para identificar los problemas que la FDA deberá abordar para usar nuestra autoridad bajo la disposición de estándar de producto en la Ley de Control del Tabaco para regular la nicotina en cigarrillos combustibles y volverlos mínimamente adictivos o nada adictivos.
Nuestro enfoque en volver la nicotina el centro de nuestros esfuerzos regulatorios y acompañarlos con reglas y estándares base para productos nuevos. Entre otras cosas, trabajaremos en reglas que establecerán las bases para las solicitudes de Equivalencia Sustancial, Productos de Tabaco de Riesgo Modificado, y solicitudes Previas a la Comercialización de Productos Tabaco; en caso que y cómo, eximiríamos a cigarros prémium de la regulación; cómo podemos regular sabores atractivos para niños en productos como Sistemas Electrónicos de Administración de Nicotina (o ENDS por su siglas en inglés); y si debemos prohibir el mentol en cigarrillos y sabores en cigarrillos - factores que son determinantes en el tabaquismo en jóvenes.
A medida que avanzamos en nuestro enfoque, también debemos volver a revisar con nuevos ojos el lado no combustible del enfoque. Y es por eso que la tarea de la Oficina de Control de tabaco es volver a considerar aspectos de la implementación de la regla final desde un punto de vista que promueva la innovación, donde la innovación pueda marcar una diferencia real en la salud pública, y asegurándonos que las bases de las normas que necesitamos implementar sean transparentes, predecibles y sostenibles a largo plazo.
A medida que avanzamos, espero que todos podamos ver los beneficios potenciales para los fumadores de cigarrillos tradicionales, en un mercado adecuadamente regulado, de productos con la capacidad de administrar nicotina sin tener que quemar el tabaco. El beneficio potencial puede ser mayor para el grupo de fumadores de cigarrillos actuales que no pueden o no quieren dejar de fumar. Como reguladores debemos explorar tanto los beneficios potenciales a la salud pública como los riesgos de esta nueva tecnología con una mente abierta.
The New England Journal Of Medicine
El 30 de enero de 2019 la revista médica The New England Journal of Medicine publicó un artículo sobre un experimento que involucró a 886 participantes a quienes se les suministraron combinaciones de distintos dispositivos para dejar de fumar durante tres meses, entre ellos parches de nicotina y vaporizadores, además de terapia por al menos cuatro semanas. En un año el grado de efectividad de abstinencia en quienes usaron cigarrillos electrónicos fue del 18%, frente al 9.9% de quienes utilizaron parches.
Otros
Recientemente se realizaron estudios por las Universidades de Massachusetts y Lovaina que indican que los cigarrillos electrónicos son un medio viable para ayudar a dejar el tabaquismo.
Recientemente (2021), la Cochrane Library ha publicado una revisión sobre el uso del cigarrillo electrónico (CE) con nicotina como terapia en el abandono del tabaco, en la que señala que existe una evidencia moderada de que los CE con nicotina aumentan las tasas de abandono del tabaquismo en comparación con las terapias de reemplazo de nicotina.
Argumentos en contra
Organización Mundial de la Salud
La Organización Mundial de la Salud (OMS) ha advertido a los consumidores que no considera que el cigarrillo electrónico sea un tratamiento legítimo para quienes estén tratando de dejar de fumar y que los distribuidores de cigarrillos electrónicos deben dejar de reivindicar efectos terapéuticos no demostrados o se digan reconocidas por este organismo, debido a la carencia de estudios rigurosos que demuestren la efectividad del cigarro electrónico como terapia de reemplazo o sus niveles de toxicidad. Sin embargo, la OMS no descarta su utilidad si se realizan estudios clínicos y toxicológicos en el marco reglamentario adecuado. En noviembre de 2016, en la séptima Conferencia de las Partes en el Convenio Marco de la OMS para el Control del Tabaco llevada a cabo en Delhi (India) se presentó un informe sobre Sistemas electrónicos de administración de nicotina (SEAN) y sistemas similares sin nicotina (SSSN) en el que se señala que "si la gran mayoría de fumadores de tabaco que son incapaces o no desean abandonar el tabaco pasaran sin demora a utilizar una fuente alternativa de nicotina que conlleve menos riesgos sanitarios y, con el tiempo, dejaran de utilizarla, supondría un logro contemporáneo considerable en materia de salud pública. Esta circunstancia solo sucedería si la incorporación de menores y no fumadores a la población dependiente de la nicotina no es superior a la correspondiente al tabaquismo y, algún día, se reduce a cero. Que los SEAN/SSSN puedan cumplir esta función sigue siendo objeto de debate entre quienes desean que se promueva y apruebe rápidamente su uso partiendo de las pruebas disponibles, y quienes piden precaución dadas las incertidumbres de carácter científico y la variabilidad en el desempeño de los productos y la diversidad de comportamiento de los usuarios" y se presenta una lista no exhaustiva de las opciones que las Partes podrían estudiar de conformidad con su legislación nacional con el propósito de cumplir los objetivos relativos a los SEAN/SSSN.
Sociedad Española de Neumología y Cirugía Torácica (España)
La Sociedad Española de Neumología y Cirugía Torácica (SEPAR) afirma que pueden causar cambios en los pulmones a corto plazo muy parecidos a los que se producen al fumar los cigarros normales, pero solo al tener nicotina dentro.
En marzo de 2014, el Complejo Hospitalario Universitario de La Coruña (CHUAC) diagnosticó el primer caso en España de neumonía lipoidea que fue asociada al cigarrillo electrónico y relacionada con la presencia de glicerina vegetal entre los componentes de las cargas. El grupo Ecigarrete Research en su página web publica una carta del Dr. Farsalinos que rebate dicha afirmación, afirmando que una sustancia soluble no lipídica como la glicerina no puede ser acumulada en un ambiente hidrófugo como el observado en las formaciones lipoideas características de esta patología.
Prohibición en Míchigan (Estados Unidos)
En septiembre de 2019 en Míchigan se decretó la prohibición de venta de cigarrillos electrónicos tras confirmarse la muerte de 5 personas por su uso, convirtiendo a este estado en el primero que prohíbe estos productos.
Administración de Alimentos y Medicamentos (Estados Unidos)
La estadounidense Administración de Alimentos y Medicamentos (FDA) en 2009 alertó de la presencia de nitrosaminas (agentes cancerígenos) y otras sustancias tóxicas (como dietilenglicol) en un estudio preliminar de varias marcas analizadas.
Asociación Estadounidense de Médicos de Salud Pública
La Asociación Estadounidense de Médicos de Salud Pública (AAPHP) ha recomendado, respecto de la revisión del Reglamento Estatal de Cigarrillos Electrónicos, añadir dos principios al mismo: 1) mantener y fortalecer la prohibición de vender productos derivados del tabaco y de la nicotina sin receta médica, y 2) aconsejar las terapias de reemplazo de nicotina (que incluyen el uso de cigarrillos electrónicos, entre otros) para aquellos casos en que se ha fracasado en el intento de dejar de fumar o no se quiere dejar de fumar.
Su uso para consumo de marihuana
Recientemente, con la legalización de la marihuana en algunos estados de EUA, los consumidores de la droga han comenzado a usar un extracto en forma de aceite de la planta, utilizando cigarrillos electrónicos para vaporizar el producto. Esta forma de consumo no libera el olor característico ya que no existe combustión en el proceso, permitiendo a los consumidores el pasar completamente indetectados en áreas públicas o en presencia de otras personas. Las autoridades están preocupadas pues el mismo método de consumo está siendo utilizado en estados donde aún no es legal el consumo de la droga.
Otros
El uso del cigarrillo electrónico ha sido cuestionado por dañar los pulmones, ser cancerígeno y sus efectos se homologan a los del tabaco.
Sociedad Española de Salud Pública y Administración Sanitaria
En 2014, la Gaceta Sanitaria publicó el estudio Prevalencia y perfil de uso del cigarrillo electrónico en España, que muestra un rápido aumento del uso del cigarrillo electrónico entre los jóvenes, además de un alto porcentaje de uso dual del cigarrillo electrónico con otros productos de tabaco, particularmente con el cigarrillo convencional.
En agosto de 2013 fue publicado un estudio financiado por la asociación CASAA(The Consumer Advocates for Smoke-free Alternatives Association, traducido: Asociación de defensa de los consumidores para alternativas a la prohibición de fumar) y realizado por el profesor Igor Burstyn, de la Escuela de Salud Pública de la Universidad de Drexel en el cual se hicieron pruebas a los componentes químicos en el vapor de los cigarrillos electrónicos. Según el estudio los resultados prueban que los niveles de contaminantes son extremadamente bajos comparados con el cigarrillo tradicional de tabaco y completamente inofensivos para los llamados "vapeadores de segunda mano", refiriéndose a aquellos que sin ser necesariamente usuarios activos de los cigarrillos electrónicos, aspiran de manera indirecta el vapor producido por estos.
En un estudio del Departamento de Sanidad neozelandés por parte del Dr. Murray Laugesen se examinaron los niveles de nitrosaminas del cigarro electrónico encontrando que estos niveles son muy bajos en comparación al cigarro normal. Este estudio reporta un máximo total de nitrosaminas de 8,16 nanogramos por cartucho mientras que en las principales marcas cigarrillos convencionales se reportan de 1300 a 6300 nanogramos por gramo (1,3 - 6,3 microgramos/gramo). También indicaron que el nivel de nicotina en los cartuchos del cigarrillo electrónico no es diferente de la concentración de nicotina en los parches de nicotina. Este estudio concluyó que sobre la base de la información del fabricante, la composición del líquido del cartucho no es peligroso para la salud, si se usa debidamente. El departamento de sanidad neozelandés aprobó los cigarrillos electrónicos.
El 22 de abril de 2014, el grupo del Dr. Konstantinos Farsalinos, investigador jefe del Centro Onassis de Cirugía Cardíaca, publicó el estudio sobre el uso de estos dispositivos con mayor tamaño muestral hasta la fecha, más de 19 441 usuarios. En este trabajo se demostró que el 81 % de los usuarios de estos dispositivos habían abandonado por completo el tabaco mientras que el resto redujo el consumo de tabaco de 20 a 4 cigarrillos por día. Por otro lado, sólo el 0,4 % declararon no ser fumadores en el momento de inicio del consumo, utilizando mayoritariamente los líquidos con baja o nula concentración de nicotina y ninguno de ellos pasó de consumir cigarrillos electrónicos a consumir tabaco.
Sus defensores lo presentan como una alternativa que permitiría sustituir el tabaco por un método de administración de nicotina, sin el resto de los componentes tóxicos, y ninguno de los cancerígenos presentes en la combustión del tabaco. El humo del tabaco porta más de 4000 sustancias químicas, muchas de ellas irritantes y más de 40 cancerígenas; además más de 60 sustancias son añadidas en el proceso de manufactura. Los cigarrillos electrónicos además permiten simular el acto de fumar, cuando en realidad solo es vapor. En este sentido alegan que complementan la administración del componente químico más adictivo del tabaco, la nicotina, con la simulación del comportamiento del fumador, tanto en su manipulación como en el acto de emitir vapor a semejanza del humo del tabaco. En este sentido se propugna su uso como una terapia de reemplazo que, además, permite disminuir los niveles de nicotina contenidos en el líquido hasta hacerlos desaparecer.
También hay un estudio (realizado entre septiembre de 2011 y mayo de 2012) a favor de los cigarros electrónicos, publicado por PlosOne, pero que no se diseñó como prueba para dejar de fumar.
Los expertos insisten en que cualquier producto relacionado con el tabaco sigue siendo potencialmente perjudicial y recomiendan cesar su consumo, ya sean cigarrillos convencionales como electrónicos con nicotina. "El tabaquismo se mantiene como la primera causa de muerte evitable en España. El consumo de tabaco también supone el mayor factor de riesgo de contraer cáncer de pulmón", asegura el neumólogo Carlos Jiménez, director del Programa de Investigación Integrada en Tabaquismo Sociedad Española de Neumología y Cirugía Torácica (Separ). "Hay que tener claro que todos los productos relacionados con el tabaco son dañinos para la salud, pero no significa que vapear y fumar sean lo mismo."
Legislación
Está prohibido: Argentina (prohibido desde el 9 de mayo de 2011), Australia, Grecia, Brasil, Lituania,Panamá (prohibido solo en áreas públicas), Singapur, Uruguay, Venezuela
Similar al tabaco (se vende en los mismos establecimientos que el tabaco o su consumo tiene las mismas limitaciones): España, Francia, Malta, Estados Unidos (en julio de 2009 la Food and Drug Administration intentó prohibir su importación y regularlos como dispositivos farmacéuticos, pero en enero de 2010 el juez Richard León dictó sentencia a favor de los importadores por entender que la FDA no tiene competencia para dictar tal prohibición y que deben regularse como derivados del tabaco. Debido a la ausencia de regulación federal, muchos estados y ciudades han optado por sus propias regulaciones, asimilándolo al tabaco, limitando su uso en lugares públicos o prohibiendo su venta a los menores de edad)
Similar a un medicamento (regulación similar a los parches de nicotina): Austria, Alemania, Dinamarca, Eslovaquia, Estonia, Finlandia, Hungría, Países Bajos, Reino Unido, Rumanía, Suecia
Según su composición (si tiene extracto de tabaco como el tabaco, si tiene nicotina como medicamento): Canadá, Bélgica, Luxemburgo
Según su composición (si tiene nicotina como tabaco, si no la tiene sin restricciones): Costa Rica
Prohibido a menores: Italia (menores de 16 años)
Nueva regulación del Tabaco para los cigarrillos electrónicos
La Nueva Directiva del Tabaco, sobre productos relacionados con el tabaco, entró en vigor el día 19 de mayo de 2017.Y apela de lleno al Cigarrillo Electrónico en todas sus formas (Hardware, Líquidos y accesorios) Fija las normas en lo referente a la fabricación, presentación y venta de los productos relacionados con el tabaco: cigarrillos, tabaco de liar, tabaco de pipa, puros, puritos, tabaco de uso oral, cigarrillos electrónicos y productos a base de hierbas para fumar.
En el Boletín regula esta nueva Directiva que sustituye a la 2001/37/CE y entre los que podemos destacar los siguientes puntos:
Prohíbe los cigarrillos y el tabaco de liar con aromas característicos.
Obliga a la industria tabacalera a informar de los ingredientes que utiliza en sus productos (en particular, los cigarrillos electrónicos).
Exige que se incluyan advertencias sanitarias en los envases de los productos del tabaco.
La Directiva 2001/37/CE queda derogada con efecto a partir del 20 de mayo de 2016 sin que se vean afectadas las obligaciones de los Estados miembros relativas a los plazos de transposición al Derecho nacional de dicha Directiva.
Historia
En 1968, Herbert A. Gilbert patentó "un cigarrillo sin tabaco y sin humo". En su patente, Gilbert describió cómo su dispositivo funcionaba, por "sustitución de tabaco en combustión y papel con aire aromatizado caliente y húmedo." El Dispositivo de Gilbert no involucra nicotina, y los fumadores del dispositivo de Gilbert disfrutaron un vapor saborizado. Los intentos de comercializar el invento de Gilbert fallaron y su producto cayó en el olvido. Sin embargo, merece una mención como la primera patente para un cigarrillo electrónico.
Más conocido es la invención del farmacéutico chino Hon Lik, quien patentó el primer cigarrillo electrónico basado en nicotina en 2003. Al año siguiente, Hon Lik fue la primera persona en fabricar y vender ese producto, por primera vez en el mercado chino y luego a nivel internacional. Desarrollado en China por Hon Lik de Ruyan, el producto ya patentado se vende en Europa, Japón y Estados Unidos.
Presentación y formato
El aparato adopta la forma de una pajita, ligeramente más larga que un cigarrillo normal (los que imitan exactamente a un cigarrillo normal no suelen ser una opción adecuada por lo general) aunque los hay en formatos más voluminosos que cuentan con más autonomía y mayor capacidad de generar vapor.
El aparato contiene un cartucho o atomizador recambiable o recargable lleno de líquido. Las principales sustancias que contiene el líquido son: propilenglicol (generalmente alrededor del 70%) y/o glicerina vegetal (generalmente alrededor del 30%), nicotina en diferentes dosis como opcional (por lo general entre 0 mg y 24 miligramos por mililitro) y aromas opcionales.
Cuando el usuario inhala a través del aparato, en algunos modelos, el flujo de aire es detectado por un sensor. Un microprocesador activa entonces un nebulizador (popularizado por la industria como atomizador), que inyecta minúsculas gotitas del líquido en el aire que fluye y lo activa también un led de color naranja (que en los últimos modelos puede ser de otros colores: verde, azul, rosa, etc.) en la punta del aparato para simular mejor el acto auténtico de fumar. El cigarrillo calienta el líquido hasta 60 grados. Un hecho a subrayar es que, dado que al contrario del cigarrillo tradicional, no hay combustión, hace que los efectos negativos en la salud sean mucho menos importantes, siendo éste afirmado por muchos profesionales de la salud, tabacólogos y neumonólogos)
Generalmente, los cigarrillos electrónicos utilizan una batería recargable como fuente de energía. La duración de la batería varía entre distintos aparatos. Esto depende de su capacidad en mAh y el uso que se haga del aparato. La experiencia de los usuarios es que la duración de las baterías cargadas va de 2 a 5 horas en los modelos más convencionales, a 12 a 24 horas en los modelos avanzados.
Las baterías son de dos tipos: automáticas, en las que la inhalación es detectada lo cual son su gran ventaja ganando en mucha comodidad de uso, pero resultando más fáciles de ser dañadas si pasa e-liquid o agua hacia la misma lo que es probable que ocurra y la arruine irreparablemente o a veces el mecanismo detector de inhalación se bloquea y también la hace inservible (actualmente están cayendo en desuso limitándose a un par de modelos); y manuales, en las que se debe oprimir un pequeño botón al inhalar, lo cual no es tan práctico pero el vapeador genera rápidamente el hábito, y su gran ventaja es que son blindadas lo que las hace absolutamente seguras contra entrada de fluidos a diferencia de las anteriores.
Otros dispositivos: PCC simula un paquete de cigarrillos, pero tiene una batería incorporada que se carga previamente y sirve para ir cargando las baterías de los e-cigs en forma portátil, cargadores USB para computadoras; Passtrough que permite vapear solo conectando un dispositivo que simula una batería de e-cig al puerto USB prescindiendo de la batería; como pasa con los cartuchos la innovación es permanente en este campo. Existe también el que ya viene "preensamblado" y listo para el uso. Estos desechables no son recargables y como su nombre lo indica, al terminar su uso se desechan. Generalmente son equivalentes a dos cajetillas o packs, aproximadamente 40 cigarrillos regulares de tabaco.
Solución de nicotina, líquidos y aromas
Los líquidos utilizados en los cigarrillos electrónicos se encuentran habitualmente con una gran variedad de formulaciones, con distintos sabores (p.ej. a frutas, a mentas, a cremas, tabaquiles) y diferentes concentraciones de nicotina. En los niveles más altos de concentración de nicotina, fumar cigarrillos electrónicos se pretenden aportar dosis de nicotina que se aproximan a las consumidas con los cigarrillos de tabaco, para ser utilizadas como terapia de deshabituación y con la pretensión de aportar únicamente una de las sustancia responsables de la adicción tabáquica. Es de destacar que la nicotina es solo una de las aproximadamente 4000 sustancias presentes en el cigarrillo tradicional, la que se considera responsable en mayor medida de la adicción al tabaco y se utiliza del mismo modo que se proporciona en otras terapias de deshabituación, aunque mediante un sistema que imita de una manera más natural la administración de la droga que los chicles, parches o comprimidos de uso farmacéutico. Al poder escoger la concentración de nicotina en los líquidos el cigarrillo electrónico permite disminuir paulatinamente el consumo de la droga reduciendo el síndrome de abstinencia.
Al no producirse combustión de la mezcla, las sustancias consideradas más tóxicas del tabaco no se encuentran presentes en los vapores generados por los cigarrillos electrónicos, aunque si lo está la nicotina. Es de destacar que los líquidos también se encuentran en formulaciones que carecen de nicotina, por lo que en este caso su orientación es más lúdica y tiene menor relación con la pretensión de establecer estos dispositivos como sistemas de dosificación de nicotina.
Dependiendo del aparato, los cartuchos o atomizadores son válidos para entre 40 y 400 caladas. Los cartuchos (que son de muchos tipos y principios de funcionamiento: cartuchos con perlón que absorbe el E-liquid a vaporizar que son de diferentes formas como redondos, semiplanos y planos, cartomizadores -que suman cartucho + atomizador en una sola pieza, son descartables o rinden de tres a cinco recargas- claromizadores -ídem pero transparentes- E-Tank -ídem cartucho pero sin perlón- y más que se van inventando e incorporando, cada uno tiene sus pro y contras) vacíos pueden reemplazarse por otro nuevo o bien rellenarse con más solución. Esta solución, también llamada "E-líquid", se vende a menudo en frascos de 6 a 30 ml. La solicitud de patente de Ruyan menciona cuatro fórmulas diferentes para la solución de nicotina:
Una gran mayoría de e-líquidos tiene sólo tres componentes: Propilenglicol USP (alrededor del 30 %), Glicerina Vegetal USP (65%) y aromas (>5%). La presencia del Propilenglicol se critica, sin embargo esta sustancia (si bien puede tener ligeros efectos irritantes de las mucosas) ha sido declarada por todos los organismos públicos de salud como de baja toxicidad, por lo que se usa en multitud de medicamentos (incluyendo inhaladores, medicamentos de uso pediátrico y dispensadores de nicotina), alimentos y productos de cosmética. En distintos ambientes laborales e industriales se usa normalmente el Propilenglicol en forma vaporizada a altas concentraciones como por ejemplo los cañones de niebla en discotecas y teatros.
Se puede subrayar que el e-líquid se puede también obtener usando sólo Glicerina Vegetal (y aromas si uno desea). Así se obtiene un e-líquido "bio" pero su alta viscosidad dificulta el drenaje a la resistencia/s debiendo disponer de atomizadores de gran caudal de drenaje o reducir la viscosidad del líquido con vodka o agua destilada.
Mantenimiento y requisitos del cigarrillo electrónico
Uno de los problemas que presenta el cigarrillo electrónico es su mantenimiento y requisitos. Los defensores del cigarrillo electrónico muchas veces se quejan de que no todas las empresas que lo venden asesoran correctamente a sus clientes acerca del mantenimiento y de sus requisitos para que sea una opción válida y efectiva para dejar de fumar, y eso repercute negativamente en el "boca a boca" y la imagen de este medio para dejar de fumar, al no acometer sus funciones de forma correcta. Generalmente una buena transición se logra participando y preguntando en grupos de vapeo donde hay mucha gente dispuesta a ayudar a las nuevas generaciones de vapers.
Los especialistas en cigarrillo electrónico recomiendan que los usuarios tengan muy presente que los atomizadores se constituyen de componentes consumibles (resistencias, mechas) y han de ser reemplazados periódicamente. Además hay que prestar atención al elegir estos componentes, al igual que se ha de estar suplido de E-líquids de forma constante, es necesario también que los componentes de los atomizadores no lleguen a un desgaste excesivo y el flujo de "vapor" llegue a ser insuficiente, propiciando la recaída en el tabaco tradicional.
Véase también
Lesión pulmonar asociada al uso de cigarrillos electrónicos o al vapeo (EVALI)
Referencias
Enlaces externos
OMS, agosto de 2016. «Sistemas electrónicos de administración de nicotina y sistemas similares sin nicotina»
Portal informativo sobre los cigarros electrónicos (DSLN) en España. «Dispositivos Susceptibles de Liberación de Nicotina en España»
Artículos de fumador | {
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Список лауреатов кинонаграды MTV в категории Лучший новый режиссёр. Последний раз премия вручалась в 2002 году.
Ссылки
Победители MTV Movie Awards | {
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Carotid artery dissection is a separation of the layers of the artery wall supplying oxygen-bearing blood to the head and brain and is the most common cause of stroke in young adults. (Dissection is a blister-like de-lamination between the outer and inner walls of a blood vessel, generally originating with a partial leak in the inner lining.)
Dissection may occur after physical trauma to the neck, such as a blunt injury (e.g. traffic collision), strangulation, but can also happen spontaneously.
Signs and symptoms
The signs and symptoms of carotid artery dissection may be divided into ischemic and non-ischemic categories:
Non-ischemic signs and symptoms:
Localised headache, particularly around one of the eyes
Neck pain
Swollen tongue
Decreased pupil size with drooping of the upper eyelid (Horner syndrome)
Pulsatile tinnitus
Ischemic signs and symptoms:
Temporary vision loss
Ischemic stroke
Causes
The causes of internal carotid artery dissection can be broadly categorized into two classes: spontaneous or traumatic.
Spontaneous
Once considered uncommon, spontaneous carotid artery dissection is an increasingly recognized cause of stroke that preferentially affects the middle-aged.
The incidence of spontaneous carotid artery dissection is low, and incidence rates for internal carotid artery dissection have been reported to be 2.6 to 2.9 per 100,000.
Observational studies and case reports published since the early 1980s show that patients with spontaneous internal carotid artery dissection may also have a history of stroke in their family and/or hereditary connective tissue disorders, such as Marfan syndrome, Ehlers-Danlos syndrome, autosomal dominant polycystic kidney disease, pseudoxanthoma elasticum, fibromuscular dysplasia, and osteogenesis imperfecta type I. IgG4-related disease involving the carotid artery has also been observed as a cause.
However, although an association with connective tissue disorders does exist, most people with spontaneous arterial dissections do not have associated connective tissue disorders. Also, the reports on the prevalence of hereditary connective tissue diseases in people with spontaneous dissections are highly variable, ranging from 0% to 0.6% in one study to 5% to 18% in another study.
Internal carotid artery dissection can also be associated with an elongated styloid process (known as Eagle syndrome when the elongated styloid process causes symptoms).
Traumatic
Carotid artery dissection is thought to be more commonly caused by severe violent trauma to the head and/or neck. An estimated 0.67% of patients admitted to the hospital after major motor vehicle accidents were found to have blunt carotid injury, including intimal dissections, pseudoaneurysms, thromboses, or fistulas. Of these, 76% had intimal dissections, pseudoaneurysms, or a combination of the two. Sports-related activities such as surfing and Jiu-Jitsu have been reported as causes of carotid artery dissection.
The probable mechanism of injury for most internal carotid injuries is rapid deceleration, with resultant hyperextension and rotation of the neck, which stretches the internal carotid artery over the upper cervical vertebrae, producing an intimal tear. After such an injury, the patient may remain asymptomatic, have a hemispheric transient ischemic event, or have a stroke.
Artery dissection has also been reported in association with some forms of neck manipulation. There is significant controversy about the level of risk of stroke from neck manipulation. It may be that manipulation can cause dissection, or it may be that the dissection is already present in some people who seek manipulative treatment. At this time, conclusive evidence does not exist to support either a strong association between neck manipulation and stroke, or no association.
Pathophysiology
Arterial dissection of the carotid arteries occurs when a small tear forms in the innermost lining of the arterial wall (known as the tunica intima). Blood is then able to enter the space between the inner and outer layers of the vessel, causing narrowing (stenosis) or complete occlusion. The stenosis that occurs in the early stages of arterial dissection is a dynamic process and some occlusions can return to stenosis very quickly. When complete occlusion occurs, it may lead to ischaemia. Often, even a complete occlusion is totally asymptomatic because bilateral circulation keeps the brain well perfused. However, when blood clots form and break off from the site of the tear, they form emboli, which can travel through the arteries to the brain and block the blood supply to the brain, resulting in an ischaemic stroke, otherwise known as a cerebral infarction. Blood clots, or emboli, originating from the dissection are thought to be the cause of infarction in the majority of cases of stroke in the presence of carotid artery dissection. Cerebral infarction causes irreversible damage to the brain. In one study of patients with carotid artery dissection, 60% had infarcts documented on neuroimaging.
Treatment
The goal of treatment is to prevent the development or continuation of neurologic deficits. Treatments include observation, anti-platelet agents, anticoagulation, stent implantation, carotid endarterectomy, and carotid artery ligation.
Epidemiology
70% of patients with carotid arterial dissection are between the ages of 35 and 50, with a mean age of 47 years.
See also
Aortic dissection
Vertebral artery dissection
References
External links
Diseases of the aorta
Vascular diseases
Medical emergencies | {
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Q: Error adding a foreign key in Laravel 5.2 through migrations I have two migrations as shown below:
2016_02_03_071404_create_company_users_table.php
use Illuminate\Database\Schema\Blueprint;
use Illuminate\Database\Migrations\Migration;
class CreateCompanyUsersTable extends Migration
{
/**
* Run the migrations.
*
* @return void
*/
public function up()
{
Schema::create('company_users', function (Blueprint $table) {
$table->bigIncrements('id');
$table->bigInteger('company_id')->unsigned();
$table->foreign('company_id')->references('id')->on('companies');
$table->char('role', 20);
$table->text('first_name');
$table->text('last_name');
$table->integer('age');
$table->string('email')->unique();
$table->text('password');
$table->text('login_type');
$table->string('phone_number')->unique();
$table->integer('verified')->default(0);
$table->text('profile_picture');
$table->text('facebook_id');
$table->text('twitter_id');
$table->text('linkedIn_id');
$table->text('google_plus_id');
$table->text('current_location');
$table->text('established_year');
$table->text('device_type');
$table->text('device_token');
$table->text('device_model');
$table->text('device_os_version');
$table->text('last_login');
$table->timestamps();
});
}
/**
* Reverse the migrations.
*
* @return void
*/
public function down()
{
Schema::dropifExists('company_users');
}
}
2016_01_28_144808_create_jobs_table.php
<?php
use Carbon\Carbon;
use Illuminate\Database\Schema\Blueprint;
use Illuminate\Database\Migrations\Migration;
class CreateJobsTable extends Migration
{
/**
* Run the migrations.
*
* @return void
*/
public function up()
{
Schema::create('jobs', function (Blueprint $table) {
$table->bigIncrements('id');
$table->text('job_title');
$table->text('job_description');
$table->text('job_industry');
$table->text('job_location');
$table->integer('job_experience');
$table->text('employment_type');
$table->bigInteger('recruiter_id')->unsigned();
$table->foreign('recruiter_id')->references('id')->on('company_users');
$table->tinyInteger('status')->default(1);
$table->timestamp('posted_date')->default(Carbon::now()->toDateTimeString());
});
}
/**
* Reverse the migrations.
*
* @return void
*/
public function down()
{
Schema::dropifExists('jobs');
}
}
When I run php artisan migrate I get the following error:
[Illuminate\Database\QueryException]
SQLSTATE[HY000]: General error: 1215 Cannot add foreign key constraint (SQL: alter table jobs add constraint jobs_recruiter_id_foreign foreign
key (recruiter_id) references company_users (id))
[PDOException]
SQLSTATE[HY000]: General error: 1215 Cannot add foreign key constraint
Please help.
A: I figured it out... it was basically the order of execution of the migration files. So i changed the timestamps of the migration files to reorder the execution.... Works like charm.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,373 |
UK Markets open in 2 hrs 4 mins
Sweden's MTG core profit rises, CEO to leave
STOCKHOLM (Reuters) - E-sports and gaming firm MTG <MTGb.ST> reported a bigger than expected jump in quarterly core earnings on Thursday despite a hit to its e-sports business from the coronavirus pandemic, but its shares fell on news its long-time CEO was stepping down.
The Swedish company also said chairman David Chance had announced his intention to stand down at the annual shareholders' meeting in 2021.
MTG shares, which were up ahead of the news, were down 1% by 1250 GMT.
The company said in a statement the board had "reluctantly accepted" CEO Jorgen Madsen Lindemann's resignation.
"After 26 years of service, he has decided to step down to free up time to pursue other challenges and for the company to facilitate its long-term CEO succession planning," it said.
MTG said in its second-quarter report that its e-sports business had performed better than anticipated, while the gaming business had its best quarterly result ever.
The firm expects an adjusted operating profit of 250-300 million Swedish crowns (22-26 million pounds) in the second half of the year, supported by a strong performance in gaming and savings in its e-sports firms ESL and DreamHack.
Its second-quarter adjusted operating profit (EBITDA) rose to 167 million crowns from 88 million a year earlier, while revenues were unchanged at 1.1 billion crowns.
MTG said earlier on Thursday that ESL and DreamHack had entered a partnership agreement with live streaming platform Huya <HUYA.N>, as it seeks to expand in the booming Chinese e-sports market.
(Reporting by Helena Soderpalm; editing by Johannes Hellstrom and Mark Potter) | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,822 |
\section{Introduction}
CP violation has been observed in the decay and mixing
of neutral mesons containing strange, charm and bottom quarks. Currently all measurements of CP violation,
either in decay, mixing or in the interference between the two, have been consistent with the presence of a single phase in the CKM matrix.
An observation of anomalously large CP violation in \Bs\ oscillations can indicate the existence of physics beyond the
standard model (SM)~\cite{smprediction}.
Measurements of the like-sign dimuon asymmetry by the D0 Collaboration~\cite{dimuon1, dimuon2} show evidence
of anomalously large CP-violating
effects using data corresponding to 9~fb$^{-1}$ of integrated luminosity.
Assuming that this asymmetry originates from mixed neutral $B$ mesons,
the measured value is $\aslb = C_d \asld + C_s \asls = \left[-0.787 \pm 0.172 \, (\rm{stat.}) \pm 0.021 \, (\rm{syst.}) \right]\%$,
where $a^{s(d)}_{sl}$ is the time-integrated
flavor-specific semileptonic charge asymmetry in \Bs (\Bd) decays that have undergone flavor mixing
and $C_{d(s)}$ is the fraction of \Bd (\Bs ) events. The value of \asls\ and \asld\ are extracted from this
\noindent measurement and found to be
$\asls = (-1.81 \pm 1.06)\%$ and $\asld = (-0.12 \pm 0.52)\%$~\cite{dimuon2}.
This Note presents a short summary of the measurements of \asls\ \cite{d0asls} and \asld\ \cite{d0adsl} using the full Tevatron data sample with
an integrated luminosity of 10.4~fb$^{-1}$.
The asymmetry \aslq\ is defined as
\begin{equation}
\aslq =
\frac
{\Gamma \left(\barBq \rightarrow \Bq \rightarrow \ell^+ \nu X \right) - \Gamma \left(\Bq \rightarrow \barBq \rightarrow \ell^- \bar{\nu} \bar{X} \right)}
{\Gamma \left(\barBq \rightarrow \Bq \rightarrow \ell^+ \nu X \right) + \Gamma \left(\Bq \rightarrow \barBq \rightarrow \ell^- \bar{\nu} \bar{X} \right)},
\end{equation}
where in these analyses $\ell=\mu$. The flavor of the \Bq\ meson at the time of decay is identified using the charge of the associated muon, and these analyses do not make use of
initial-state tagging. We assume there is no production asymmetry between \Bq\ and \barBq\ mesons,
that there is no direct CP violation in the decay of charm mesons to the indicated states or in the
semileptonic decay of $B^0_q$ mesons, and that any CP violation in
\Bq\ mesons only occurs in mixing. We also assume that any direct CP violation in the decay of $b$ baryons and charged $B$ mesons is negligible.
\section{The semi-leptonic charge asymmetry in \Bs\ mesons}
The measurement of the semi-leptonic charge asymmetry in \Bs\ mesons is measured using the decay $\Bs (\barBs) \rightarrow D_{s}^\mp \mu^\pm X$ decays, with $D_s^{\mp} \rightarrow \phi \pi^\mp$ and $\phi \rightarrow K^+ K^-$. The measurement is performed using the raw asymmetry
\begin{equation}
\label{raw}
A = \frac{ N_{\mu^+D_s^{-}} - N_{\mu^-D_s^{+}}}{ N_{\mu^+D_s^{-}} + N_{\mu^-D_s^{+}}},
\end{equation}
where $N_{\mu^+D_s^{-}}$ ($N_{\mu^-D_s^{+}}$) is the number of reconstructed $\Bs \rightarrow \mu^+ D_s^{-} X$
($\barBs \rightarrow \mu^- D_s^{+} X$) decays. The time-integrated
flavor-specific semileptonic charge asymmetry in \Bs\ decays which have undergone flavor mixing, \asls , is then given by
\begin{equation}
\asls \cdot {F_{\Bs}^{\rm{osc}}} = A - A_{\mu} -A_{\rm{track}} - A_{KK} ,
\label{Eq:asls}
\end{equation}
where $A_{\mu}$ is the reconstruction asymmetry between positive and negatively charged
muons in the detector~\cite{d0det}, $A_{\rm{track}}$
is the asymmetry between positive and negative tracks,
$A_{KK}$ is the residual kaon asymmetry from the decay of the $\phi$ meson, and $F_{\Bs}^{\rm{osc}}$ is the fraction of $D_s^- \rightarrow \phi \pi^-$
decays that originate from the decay of a \Bs\ meson after a $\barBs \rightarrow \Bs$ oscillation.
The $F_{\Bs}^{\rm{osc}}$ factor corrects the measured asymmetry for the fraction of events in which the \Bs\ meson is mixed under the assumptions outlined earlier that no other physics asymmetries are present in the other $b$-hadron backgrounds. The fraction of mixed events integrated over time is extracted using Monte Carlo (MC) simulations.
The raw asymmetry (Eq.~\ref{raw}) is extracted by fitting the $M(\phi\pi^\mp)$ distribution of
the $D_s^\mp$ candidates using a $\chi^2$ minimization.
The fit is performed simultaneously, using the same models, on the sum (Fig.~\ref{Fig:WeightedDSCandidates}) and
the difference (Fig.~\ref{Fig:DifferencePlot}) of the $M(\phi\pi^-)$ distribution associated with a positively charged muon and $M(\phi\pi^+)$ distribution associated with a negatively charged muon.
\begin{figure}[!h]
\centering
\begin{minipage}[t]{.48\textwidth}
\includegraphics[width=0.95\textwidth]{fig01}
\caption{\label{Fig:WeightedDSCandidates}
The weighted $K^+K^-\pi^\mp$ invariant mass distribution for
the $\mu^{\pm}\phi\pi^\mp$ sample with the solid line representing the signal fit and the dashed line showing the background fit.
The lower mass peak is due to the decay $D^{\mp} \rightarrow \phi \pi^\mp$ and the second peak is due to the $D_s^{\mp}$ meson decay. Note the zero-suppression on the vertical axis.
}
\end{minipage}
\hspace{0.02\textwidth}
\vspace{0pt}
\begin{minipage}[t]{.48\textwidth}
\includegraphics[width=0.95\textwidth]{fig02}
\caption{\label{Fig:DifferencePlot}
The fit to the difference distribution for the data with the solid line representing the fit (for clarity the data has been rebinned).
}
\end{minipage}
\end{figure}
The raw asymmetry is corrected by
$ A_{\mu} + A_{\text{track}} +A_{KK} = \left[ 0.13 \pm 0.06 \thinspace (\mbox{syst})\right]\%$,
including the statistical uncertainties combined in quadrature. The fraction of \Bs\
decays in the sample and the time-integrated oscillation
probability, we find $F_{\Bs}^{\text{osc}} = 0.465$. The resulting time-integrated
flavor-specific semileptonic charge asymmetry is found to be
\begin{align}
\asls = \left[ \rm{-1.12} \pm 0.74 \thinspace (\text{stat}) \pm 0.17 \thinspace (\text{syst}) \right]\%.
\end{align}
\section{The semi-leptonic charge asymmetry in \Bd\ mesons}
The measurement of the semi-leptonic charge asymmetry in \Bd\ mesons is measured using two separate orthogonal decay channels:
\begin{enumerate}
\item $\Bd \rightarrow \mu^+ \nu D^{-} X$, with $D^{-} \rightarrow K^+ \pi^- \pi^-$ (plus charge conjugate process);
\item $\Bd \rightarrow \mu^+ \nu D^{*-} X$,
with $D^{*-} \rightarrow \bar{D}^0 \pi^-, \bar{D}^0 \rightarrow K^+ \pi^-$
(plus charge conjugate process);
\end{enumerate}
The two channels are treated separately, with each being used to extract $a^d_{\text{sl}}$,
before the final measurements are combined.
The time-integrated
flavor-specific semileptonic charge asymmetry in \Bd\ decays which have undergone flavor mixing, \asld , is then given by
\begin{equation}
\asld \cdot {F_{\Bd}^{\rm{osc}}} = A - A_{\mu} - A_{K} + 2 A_{\pi},
\label{Eq:asld}
\end{equation}
where $A_\pi = A_{\rm{track}}$ and $A_{K}$ is the residual kaon asymmetry.
The \Bd\ meson has a mixing frequency $\Delta M_d = 0.507 \pm 0.004$~ps$^{-1}$,
of comparable scale to the lifetime $\tau(\Bd) = 1.518 \pm 0.007$~ps~\cite{pdg}.
Hence the fraction of oscillated \Bd\ mesons is a strong function of the measured decay time.
The best precision is obtained by binning the data as a function of the transverse decay length.
Small values of the transverse decay length should have negligible contributions from oscillated \Bd\ mesons, and are
not included in the final $a^d_{\rm{sl}}$ measurement. They represent a control region in which the
measured raw asymmetry should be dominated by the background contribution.
The raw asymmetries for each decay channel and each decay length bin are extracted using $\chi^2$
minimization.
The fits are performed simultaneously on the sum and
the difference (Fig.~\ref{fig:rawresults}) of the $\mu D$ and $\mu D^\ast$ distributions.
\begin{figure*}[ht]
\centering
\subfigure[$\mu D$ channel]
{\includegraphics[width=0.45\columnwidth]{Fig3b.eps}}
%
\subfigure[$\mu D^*$ channel]
{\includegraphics[width=0.45\columnwidth]{Fig3d.eps}}
\caption[]{Examples of the raw asymmetry fit for the two decays channels,
for the fifth visible proper decay length (\Bd ) bin corresponding to ($0.10 < \text{VPDL}(\Bd ) < 0.20$)~cm.
The plots show the difference distributions.
In both cases, the solid line represents the total fit function, with the background part
shown separately by the dashed line.}
\label{fig:rawresults}
\end{figure*}
The extracted raw asymmetries are corrected for background asymmetries on a bin-by-bin basis along with the systematic uncertainties. Once the uncertainties on the individual $a^d_{\text{sl}}$ measurements are established,
the combination between VPDL bins, and then between channels, is performed.
For each channel, the combined $a^d_{\text{sl}}$ value is obtained by a weighted average
of the four individual measurements where the weights are the inverse of the sum in quadrature of statistical
and systematic uncertainties for that measurement.
The central values and uncertainties for the combinations are again determined by performing
ensemble tests, with all inputs varied, and examining the effect on the
final values of $a^d_{\rm{sl}}$ from each channel. This procedure yields the following results:
\begin{eqnarray}
a^d_{\text{sl}}(\mu D) & = & [0.43 \pm 0.63 \text{ (stat.)} \pm 0.16 \text{ (syst.)}]\%,\text{ ~ ~} \\
a^d_{\text{sl}}(\mu D^*) & = & [0.92 \pm 0.62 \text{ (stat.)} \pm 0.16 \text{ (syst.)}]\%.\text{ ~ ~}
\end{eqnarray}
Finally, the combination is extended to give the full weighted average of the two channel-specific
measurements, with full propagation of uncertainties, to yield the final measurement:
\begin{eqnarray}
a^d_{\text{sl}} & = & [0.68 \pm 0.45 \text{ (stat.)} \pm 0.14 \text{ (syst.)}]\%.
\end{eqnarray}
\section{Combination of D0 results}
The D0 measurements of $a^d_{\text{sl}}$, $a^s_{\text{sl}}$, can be combined with the two-dimensional
constraints on ($a^d_{\text{sl}}$, $a^s_{\text{sl}}$) from the D0
measurement of the dimuon charge asymmetry $A^b_{\text{sl}}$~\cite{dimuon2}.
The full two-dimensional fit yields the following values:
\begin{eqnarray}
a^d_{\text{sl}}(\text{D0 comb}) & = & (0.10 \pm 0.30)\%, \\
a^s_{\text{sl}}(\text{D0 comb}) & = & (-1.70 \pm 0.56)\%,
\end{eqnarray}
with a correlation coefficient of $-0.50$. The $\chi^2$ of this fit is 2.9, and the standard model $p$-value is $0.0036$,
corresponding to a 2.9 standard deviation effect. Figure~\ref{fig:combo} shows the two-dimensional contours from this combination.
\begin{figure}[ht]
\centering
\includegraphics[width=0.8\columnwidth]{B12EF09b}
\caption[]{Combination of measurements of the D0 measurements of $a^d_{\text{sl}}$, $a^s_{\text{sl}}$, and the two impact-parameter-binned constraints from the same-charge dimuon asymmetry $A^b_{\text{sl}}$ (D0~\cite{dimuon2}). The bands represent the $\pm 1$ standard deviation uncertainties on each measurement. The ellipses represent the 1, 2, 3, and 4 standard deviation two-dimensional confidence level regions of the combination.}
\label{fig:combo}
\end{figure}
\section{Updated World Averages}
The D0 measurements of \asls\ and \asld\ can be combined with all other measurements to form updated world averages. I use a simple weighted average, assuming that the measurements are fully independent. The D0~\cite{d0asls} and the preliminary LHCb~\cite{LHCb} measurements of \asls\ are combined:
\begin{equation}
\asls (\rm{WA}) = \left( -0.60 \pm 0.49 \right) \%.
\end{equation}
The B-factories average~\cite{hfag}, the D0~\cite{d0adsl} and the new preliminary BaBar~\cite{BaBar} measurement of \asld\ are also combined,
\begin{equation}
\asld (\rm{WA}) = \left( 0.23 \pm 0.26 \right) \%.
\end{equation}
These numbers can be combined with
$A^b_{\text{sl}}$, we obtain the
following values:
\begin{eqnarray}
a^d_{\rm{sl}}(\text{comb}) & = & (-0.03 \pm 0.21)\%, \\
a^s_{\rm{sl}}(\text{comb}) & = & (-1.10 \pm 0.41)\%,
\end{eqnarray}
where the two parameters have a correlation coefficient of $-0.31$. The results are shown in Fig.~\ref{fig:comboAll}, with the
two dimensional contours overlaid on the four constraints from the input measurements.
The fit returns a $\chi^2$ of 3.8 for 2 degrees-of-freedom.
The $p$-value of the combination with respect to the SM point is $0.0148$,
corresponding to an inconsistency at the 2.4 standard deviation level.
\begin{figure}[ht]
\centering
\includegraphics[width=1.0\columnwidth]{Combination_April2013-WA_20130418}
\caption[]{Combination of measurements of the new world averages of $a^s_{\text{sl}}$ (D0~\cite{d0asls} and LHCb~\cite{LHCb}), $a^d_{\text{sl}}$
($B$ factories average~\cite{pdg}, D0~\cite{d0adsl} and the new BaBar result~\cite{BaBar}), and the two impact-parameter-binned constraints from the same-charge dimuon asymmetry $A^b_{\text{sl}}$ (D0~\cite{dimuon2}). The bands represent the $\pm 1$ standard deviation uncertainties on each measurement. The ellipses represent the 1, 2, and 3 standard deviation two-dimensional confidence level regions of the combination.}
\label{fig:comboAll}
\end{figure}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,128 |
\section{Introduction}
\label{Introduction}
Regions containing extremely dense matter are a common feature of all the big-bang inflationary cosmological space-times. The consistent description of such high energy states in the evolution of the Universe requires certain ``higher curvature'' extensions of Einstein-Hilbert (EH) gravity, involving powers (of the traces) of the Riemann tensor, believed to take into account the short distance quantum effects. Such corrections to the EH action are known to arise as counter-terms in the \emph{perturbative} quantization both of matter in curved spaces \cite{BirrelDavies} and of pure EH gravity as well \cite{'tHooft:1974bx, Stelle:1976gc}. The main problem with ``higher curvature'' gravity theories concerns the presence of higher derivatives of the metric in the equations of motion, which in general lead to causal and unitarity inconsistencies \cite{'tHooft:1974bx, Stelle:1976gc} when considered out of the framework of superstring theory. Nevertheless, the extensive studies of such models, in particular the so called modified $f(R)$-gravities, have found interesting applications in different areas of modern cosmology (see, e.g., \cite{Nojiri:2010wj, Capozziello:2011et, Clifton:2011jh} and references therein).
The present paper is devoted to the investigation of the effects caused by the higher curvature terms in a particular cosmological model in four dimensions, based on the simplest ``most physical'' extended gravity, given by the following cubic action for Quasi-Topological Gravity \cite{Oliva-Ray1}:
\begin{eqnarray}
&\hspace{-1cm} S_{\mathrm{GBL}} = \int\! \frac{\sqrt{-g} \, {\mathrm{d}}^4x}{\varkappa^2} \Big\{ R - \lambda L^2 \left[ 2 R^2 - 8 R_{\alpha\beta} R^{\alpha\beta} + 2 R_{\alpha\beta\mu\nu}R^{\alpha\beta\mu\nu} \right]\nonumber \\
&\hspace{-1cm} + \frac{\mu L^4}{4} \Big[R^3 + 18 R^{\alpha\beta\gamma\delta}R_{\gamma\delta\mu\nu}R^{\mu\nu}{}{}_{\alpha\beta} - 40 R^{\alpha\beta}_{}{}_{\gamma\delta}R^{\gamma\mu}{}{}_{\beta\nu}R^{\delta\nu}_{}{}_{\alpha\mu} \nonumber \\
&\hspace{-1cm}-36 R^{\alpha\beta\gamma\delta}R_{\alpha\gamma}R_{\beta\delta} + 8 R^{\alpha\beta}R_{\beta\gamma}R^{\gamma}{}_{\alpha} \big] + {\mathcal L}_{\mathrm{matter}} \big\},\label{action non cf}
\end{eqnarray}
where $\varkappa^2 \equiv 16 \pi G = 4 l_{{\mathrm{Pl}}}^2$; $l_{\mathrm{Pl}}$ is the Planck length; $\lambda$, $\mu$ are dimensionless ``gravitational coupling'' constants, while $L$ is a new length scale, which can be chosen as $L = l_{\mathrm{Pl}}$ by an appropriate redefinition of $\lambda$ and $\mu$.
We include the cosmological constant $\Lambda_0>0$ implicitly in the matter Lagrangian ${\mathcal L}_{\mathrm{matter}}$.
The remarkable feature of this cubic extension of the EH action, is that the corresponding equations of motion for all conformally flat metrics, as for example those of domain walls and of flat Friedmann-Robertson-Walker (FRW) space-times:
\begin{eqnarray}
{\mathrm{d}} s^2 = - {\mathrm{d}} t^2 + a^2(t) \, {\mathrm{d}} x^i {\mathrm{d}} x_i \; , \label{FRW metric}
\end{eqnarray}
are of \emph{second order} \cite{Nosso_Paper}, while arbitrary metrics yield, in general, equations of motion of fourth order\footnote{
The particular combination of quadratic terms represents the $d=4$ Gauss-Bonnet topological invariant, and does not contribute to the dynamics.}. This fact, together with the introduction of an appropriate superpotential and the related BPS-like first order system of equations for the cubic QTG-matter model (\ref{action non cf}), derived in Ref.\cite{Nosso_Paper}, provide an efficient method for the analytic construction of a large family of exact flat FRW's solutions, representing asymptotically ${\mathrm{dS}}_4$ space-times.
The most important and universal new property of these higher curvature cosmological models is that, differently from the EH case, the entropy prescribed to the apparent horizons \cite{Sinha_cosmo}
\begin{eqnarray}
& s(t) = \frac{16 \pi^2}{\varkappa^2} \, \frac{1}{ H^{2}} \left( 1 - 2 \lambda L^2 \, H^2 + 3 \mu L^4 \, H^4 \right) \, \label{s(H)}
\end{eqnarray}
with $H \equiv \dot a / a$ denoting the Hubble factor, \emph{is not automatically positive definite and increasing}. As a consequence, the requirement of the thermodynamical consistency of these models: $s(t)\geq 0$ and ${\mathrm{d}} s/ {\mathrm{d}} t > 0$, introduces certain restrictions on the available maximal values $\varrho_{\max}$ of the matter densities $\varrho = \frac{6}{\varkappa^2} H^2 \leq \varrho_{\max}$ and certain minimal scales $L_{\min}$ (related to $\varrho_{\max}$) up to which we can have a physically meaningful description of the Universe evolution within the framework of the cubic QTG cosmologies.
In order to exemplify the effects caused by the higher curvature terms, we choose a particularly simple and yet quite rich cosmological model, representing a QTG extension of the following EH model of a \emph{linear equation of state}:
\begin{eqnarray}
p_0 / \varrho_0 = w_1 - w_2 / \varrho_0 \; . \label{EoS exemplo}
\end{eqnarray}
The matter content is that of a barotropic fluid with constant equation of state parameter $w_1$, together with a dark energy ``fluid'' representing the cosmological constant $\Lambda_0 = \varkappa^2 w_2 / 2 (1 + w_1)$.
This EH cosmological model has been widely studied \cite{Bousso_hepth_0702115, Chavanis_astroph_1208.0801v1, KaloperLinde, Babichev_etal}, with a particularly remarkable result by Bousso et al. \cite{Bousso_hepth_0702115}, who deduce the value of the cosmological constant for a universe dominated by dust through most of its history ($w_1 = 0$). The new QTG features established in the present paper are: The presence of a new (early-time) acceleration period; changes in the duration of the acceleration and deceleration periods, as well as of the future and past event horizon radii; and finally certain very small corrections to the volume of the causal diamond (to be compared with the EH one \cite {Bousso_hepth_0702115}).
\section{Modified FRW Cosmology} \label{Modified FRW Cosmology}
Consider an universe filled with a barotropic fluid with energy density $\varrho_0$ and pressure $p_0$, components of a `bare' energy-momentum matter-tensor $T^{(0)}_{\mu\nu}$.
For the ansatz (\ref{FRW metric}), the QTG equations of motion derived from (\ref{action non cf}) are the modified Friedmann equations:
\begin{subequations}\label{fluid eq QTG all}\begin{eqnarray}
&& \varkappa^2 \varrho_0 = 6 H^2 \left( 1- \mu L^4 \, H^4 \right) \; , \label{fluid eq QTG i}\\
&& \varkappa^2 (\varrho_0 + p_0) = - 4 \dot H \left(1 - 3 \mu L^4 \, H^4 \right) \; ; \label{fluid eq QTG} \\
&&\dot \varrho_0 + 3 H (p_0 + \varrho_0) = 0 \; . \label{cont 0}
\end{eqnarray}\end{subequations}
They reduce to the usual EH-Friedmann equations when $\mu = 0$; otherwise the contributions from the QTG terms may be regarded as separating a ``gravitational energy momentum tensor''
$T^{{\mathrm{QTG}}}_{\mu\nu}$ at the right-hand side of the Einstein equations, thus composing an \emph{effective energy momentum tensor} $T^{\mathrm{eff}}_{\mu\nu}$, viz.
\begin{eqnarray}
G_{\mu\nu} = T^{\mathrm{eff}}_{\mu\nu} \; ; \quad T^{\mathrm{eff}}_{\mu\nu} = T^{(0)}_{\mu\nu} + T^{{\mathrm{QTG}}}_{\mu\nu} , \nonumber
\end{eqnarray}
where $G_{\mu\nu}$ is the Einstein tensor.
Notice that the effective energy-momentum tensor has all the properties of a perfect fluid tensor, i.e. its components, $T^{\mathrm{eff}}_{\mu\nu} = {\mathrm{Diag}} \; (-\varrho , p, p, p)$ satisfy the usual, EH Friedmann equations:
\begin{eqnarray}
& \varrho = \frac{6}{\varkappa^2} H^2 , \quad \varrho + p = - \frac{4}{\varkappa^2} \dot H \; , \label{fluid eq eff}
\end{eqnarray}
as well as the continuity equation,
\begin{eqnarray}
\dot \varrho + 3 H (p + \varrho) = 0 \; , \label{cont eff}
\end{eqnarray}
which is a simple consequence of the Bianchi identities.
Because of its direct connection to the Hubble function, the cosmological observations (of distances and red shifts) should perceive not the bare energy density $\varrho_0$, but rather the effective one, $\varrho$, related to the former via Eq.(\ref{fluid eq QTG i}):
\begin{eqnarray}
& \varrho_0 = \varrho \left( 1- \mu L^4 \frac{\varkappa^4}{36} \varrho^2 \right) \; . \label{vro 0 eff}
\end{eqnarray}
Although such a hydrodynamical interpretation of $T^{\mathrm{eff}}_{\mu\nu}$ is rather formal, we further assume that this ``effective fluid'' obeys the weak energy condition, i.e. $p + \varrho \geq 0$, what assures that $\dot H \leq 0$. Then if the bare fluid also satisfies the weak energy condition, the function
\begin{eqnarray}
& C_0 \equiv 1 - 3 \mu L^4 \, H^4 = 1 - \frac{1}{12} \mu L^4 \varkappa^4 \varrho^2 \label{C0}
\end{eqnarray}
must be positive (or vanishing), as can be seen from Eq.(\ref{fluid eq QTG}).
While this condition holds automatically for $\mu \leq 0$, for positive values of $\mu$ the sign of $C_0$ will depend on the value of the energy density; it vanishes for $\varrho = \frac{2}{L^2 \varkappa^2} \sqrt{3 / \mu}$ and it is indeed \emph{negative} for greater values of $\varrho$. Since near a singularity the value of $\varrho$ grows without bounds, for $\mu > 0$ it is only possible that both the bare and the effective fluids satisfy the weak energy condition in a \emph{nonsingular} universe. This would be the case, for example, in bounce-like models beginning and ending at de Sitter spaces with (asymptotic) densities $\varrho_{{\mathrm{dS}}} \leq \frac{2}{L^2 \varkappa^2} \sqrt{3 / \mu}$. We leave the study of such spaces for a more thorough discussion in \cite{LoveCosmo_tobepublished}, and focus for the remainder of this letter in the singular cases, thus considering only $\mu \leq 0$.
\section{Horizon entropy} \label{sect. horizon entropy}
Killing event horizons are known to posses thermodynamical properties: a temperature $T$ related to the surface gravity, and an entropy $s$ which in EH gravity is given by the Bekenstein-Hawking formula $s = A / 4$ (in geometrized units), $A$ being the area of the horizon \cite{Bardeen:1973gs, Hawking:1974sw, Gibbons:1977mu}. Then the Einstein equations can be rewritten as a Clausius relation \cite{Jacobson1},
${\mathrm{d}} E = T \, {\mathrm{d}} s$, for the flux of energy ${\mathrm{d}} E$ across the horizon%
\footnote{ Remarkably, this equivalence remains valid in a variety of ``higher curvature'' gravitational theories \cite{Jacobson2, Padma, Cai:2005ra, Akbar:2006kj} with the horizon's entropy given then by the Wald formula \cite{Wald:1993nt, Iyer:1994ys}.}.
The lack of time-like Killing vectors in non-stationary space-times -- as for example typical FRW spaces -- represents an obstacle in the definition of a surface gravity for the corresponding \emph{dynamical} apparent horizons. A possible consistent generalization of the ``Thermodynamics/Gravity'' correspondence can nevertheless be achieved by using the Kodama vector to define the horizon's Kodama-Hayward temperature $T_{{\mathrm{KH}}}$ \cite{Hayward}. As it was recently shown by Cai et al. \cite{Cai:2005ra, Akbar:2006kj}, the corresponding Friedmann
equations, for EH gravity and for certain modified theories as well, turn out to be again equivalent to the Clausius relation ${\mathrm{d}} E_{{\mathrm{MS}}} = T_{{\mathrm{KH}}} \, {\mathrm{d}} s_{{\mathrm{KW}}}$, with $E_{{\mathrm{MS}}}$ being the Misner-Sharp energy and $s_{{\mathrm{KW}}}$ an appropriately defined Kodama-Wald entropy, which for the cubic QTG cosmologies is given by Eq.(\ref{s(H)}).%
\footnote{The proof of the equivalence between the QTG modified Friedmann equations (\ref{fluid eq QTG all}) and the above generalization of the Clausius relation is given in our forthcoming paper \cite{alf}.}
Notice that for de Sitter space-times, when $H$ is constant and the apparent horizon coincides with the Killing event horizon, our formula (\ref{s(H)}) reduces to the known static QTG Wald entropy \cite{Sinha_cosmo}.
The consistent interpretation of $s_{{\mathrm{QTG}}}(t)$, given by Eq.(\ref{s(H)}), as an entropy for the apparent horizon in the considered QTG cosmological models requires that it must be a non-negative and non-decreasing function of time. The later is always true if both effective and bare fluids do satisfy the weak energy condition. Then as a consequence we have that $\dot s = - \frac{3}{2 G \varkappa^2} \, \frac{C_0(\varrho)}{\varrho^2} \, \dot \varrho \geq 0$. The restrictions imposed by the positivity condition $s_{{\mathrm{QTG}}}(t)\geq 0$ are slightly more involved: depending on the signs and values of $\lambda$ and $\mu$, they turn out to introduce certain upper bounds on the energy density $\varrho$.
\noindent
\textbf{\textit{ Gauss-Bonnet Gravity:}} The topological nature of the GB term in the action renders the dynamics (i.e. the equations of motion) of GB gravity, for which $\mu = 0$ and $\lambda \neq 0$, identical to that of EH gravity. But the horizon entropy is \emph{not} simply proportional to $H^{-2}$, in fact
\begin{eqnarray}
& s(t) = \frac{1}{4 G} \left( \frac{1}{ H^{2}} - 2 \lambda L^2 \right) \; . \nonumber
\end{eqnarray}
Thus if $\lambda < 0$ the entropy density is always positive, but for $\lambda > 0$ there is a value of $H(t)$ -- or, equivalently, of $\varrho$ -- past which the entropy becomes \emph{negative}. Therefore the assumption of positivity of entropy places as an upper boundary, $\varrho_{\mathrm{GB}}$, on the possible values of the energy density:
\begin{eqnarray}
0 \leq \varrho \leq \varrho_{\mathrm{GB}} \; ; \quad \varrho_{\mathrm{GB}} \equiv \frac{3}{\varkappa^2 L^2 \lambda} \; \label{vro GB}
\end{eqnarray}
\noindent
\textbf{\textit{Quasi-Topological Gravity:}}
Similar considerations applied to the QTG model, for the negative values of the coupling $\mu < 0$ we are interested in, lead us to the conclusion that the apparent horizon entropy is only positive for densities within the \emph{finite} interval:
\begin{eqnarray}
0 \leq \varrho \leq \varrho_{\mathrm{QTG}} \equiv \frac{2}{ \varkappa^2 L^2} \, \frac{1}{ \mu} \left( \lambda - \sqrt{\lambda^2 - 3 \mu} \right) .\label{vro QTG}
\end{eqnarray}
In a singular universe, it is then inevitable that at some instant the (divergent) effective energy density violates the entropic threshold of Eqs.(\ref{vro GB}) or (\ref{vro QTG}) for a finite value of $\varrho
$. Hence in the considered GB gravity (with $\lambda>0$) and QTG models of $\mu<0$, the cosmological singularity lies in a region of space-time which is already \emph{unphysical, for the apparent horizon entropy is negative.}
\section{An example of QTG cosmology}
In order to describe the changes in the evolution of the homogeneous and isotropic Universe caused by the cubic QTG terms, we next address the problem concerning the construction of analytic solutions of the modified Friedmann equations (\ref{fluid eq QTG all}) in the particular example of the matter stress-energy tensor $T^{(0)}_{\mu\nu}$, whose components are related by the following \emph{linear} barotropic equation of state \cite{Bousso_hepth_0702115, Chavanis_astroph_1208.0801v1, KaloperLinde, Babichev_etal}:
\begin{eqnarray}
p_0 / \varrho_0 = \omega_0(\varrho_0) \; ; \quad \omega_0(\varrho_0) = w_1 - w_2 / \varrho_0 \;. \label{EoS exemplo 2}
\end{eqnarray}
The constant $w_2$, if positive, represents an energy density which contributes to the pressure $p_0$ independently of the variable energy density $\varrho_0$ -- thus when the former dominates (i.e. $w_2 / \varrho_0 \gg 1$), the dynamics is driven by a constant energy density with EoS $p_0 = - w_2$, resulting in a de Sitter geometry. In this sense, $w_2$ may be identified with the cosmological constant and (\ref{EoS exemplo 2}) is an example of a simple quintessence model. The constant $w_1$, which may be seen as the ``matter EoS parameter'' (as opposed to the ``cosmological constant parameter'' $w_2$) is equal to the velocity of sound in the fluid: $v_0^2 = \partial p_0 / \partial \varrho_0 = w_1$ (in Plank units, $c=1=\hbar$). The causality condition $w_1 < 1$ excludes superluminal velocities, and if we also assume that the universe \emph{does not have a ``phantom'' phase}, then we have to impose $|w_1| < 1$.
The dynamics of the universe in such QTG cosmology may be found by solving the
differential equation for $H(t)$ obtained by combining Eqs.(\ref{fluid eq QTG all}) with the EoS (\ref{EoS exemplo 2}):
\begin{eqnarray}
\hspace{-0.7 cm} ( 1 - 3 \mu L^4 H^4 ) \dot H = - \frac{3}{2} H^2 ( 1 - \mu L^4 H^4 ) (1 + w_1) + \frac{\varkappa^2}{4} w_2 , \label{before expansion}
\end{eqnarray}
the integration of which yields
\begin{eqnarray}
\hspace{-0.8 cm} &t(H) = - \frac{2}{3 (1+ w_1)} \frac{1}{L^4 \mu} \Bigg\{
2 \upsilon\left[ {\mathrm{arc \, tg}} \left( \frac{H - \xi}{\zeta} \right) +{\mathrm{arc \, tg}} \left( \frac{H + \xi}{\zeta} \right) \right] \nonumber\\
\hspace{-1.2 cm}&-\chi \log \left( \frac{(H - \xi)^2 + \zeta^2}{(H + \xi)^2 + \zeta^2} \right) +
\frac{\alpha}{H_\Lambda} \, {\mathrm{arc \, cth}} \left( H / H_\Lambda \right)
- 2 \pi \upsilon \Bigg\} . \label{t(H)}
\end{eqnarray}
Here $H_\Lambda^2$ is the only real root of the cubic equation (\ref{vro 0 eff}) when written in terms of $H^2 = \varkappa^2 \varrho / 6$ and solved for $H^2$, with $H_0^2 \equiv \varkappa^2 \varrho_0 / 6$ considered known. The real and imaginary parts of the remaining roots, $h^2$ and its complex conjugate $\bar h^2$, are denoted by $\xi$ and $\zeta$, while $\chi$ and $\upsilon$ are the real and imaginary parts of $\alpha /2 \equiv \frac{1 - 3 \mu L^4 h^4}{2 h (h^2 - H_\Lambda^2)(h^2 - \bar{h}^2)}$. Notice that we have chosen one specific singular solution $H (t \to 0) \to \infty$ of Eq.(\ref{before expansion}), representing big-bang space-times with singularity at $t=0$. Depending on the initial conditions imposed on $H(t)$ (or equivalently on $\varrho(t)$) one can construct other non-singular bounce-like solutions (both for QTG or EH models), which are however out of the scope of the problems discussed in the present paper.
The function $t(H)$ (\ref{t(H)}) is not trivially invertible; nevertheless it allows to describe the properties of the different periods of acceleration and deceleration of the QTG corrected Universe evolution, that can be obtained directly from Eqs.(\ref{before expansion}), (\ref{fluid eq QTG}) and (\ref{fluid eq eff}). We next recall that one can also use the \emph{deceleration parameter} $q \equiv - \ddot a \, a / \dot a^2$ (for $\dot a \neq 0$), written in a suggestive form:
\begin{eqnarray}
& q = \frac{1}{2} (1 + 3 \, p / \varrho ) \; ,
\end{eqnarray}
in order to determine whether the universe undergoes accelerated ($q < 0$) or decelerated ($q > 0$) expansion. Thus, the ratio $p / \varrho \equiv \omega_{\mathrm{eff}}$ between the components of the effective energy-momentum tensor plays the role of an `\emph{effective equation of state}'.%
\footnote{Changes in the EoS due to the higher curvature terms arising within the context of $f(R)$-modified gravity have been studied in Refs.\cite{Capozziello:2005mj, Capozziello:2005pa}.}
Its explicit form :
\begin{eqnarray}
\omega_{\mathrm{eff}} (\varrho) = - 1 + \frac{(1 + w_1) \left( 1 - \mu L^4 \varkappa^4 \varrho^2 / 36 \right) \varrho -w_2}{ \varrho \left( 1 - \mu L^4 \varkappa^4 \varrho^2/12 \right) } \; \label{EoS eff}
\end{eqnarray}
is derived by substituting Eq.(\ref{EoS exemplo 2}) into Eqs.(\ref{fluid eq QTG}) and (\ref{fluid eq eff}). As expected, for $\mu = 0$ we get $\omega_{\mathrm{eff}} = \omega_0$. Since $q \gtrless 0$ iff $\omega_{\mathrm{eff}} \gtrless -1/3$, it is convenient to consider only Eq.(\ref{EoS eff}). Observe that as one approaches the initial singularity and $\varrho$ diverges, we can take the zeroth order limit of $1 / (\mu L^4 \varkappa^4 \varrho^2) \ll 1$ in order to show that $1 + \omega_{\mathrm{eff}} \approx \frac{1}{3} (1 + \omega_0)$. Therefore, even if $\omega_0$ is in the ``most decelerated range'' possible, viz. $\omega_0 \lesssim 1$, in the considered QTG cosmology we have an accelerated phase: $\omega_{\mathrm{eff}} \lesssim - 1/3$. Thus, the addition of the cubic QTG terms (\ref{action non cf}) to the EH action results in a \emph{new acceleration period at the beginning of the universe.}
\begin{figure}
\includegraphics{EoS
\caption{ Evolution of the equation of state parameter for $\mu = - 10^{24}$:
the solid line corresponds to the effective EoS of QTG as a function of the effective energy density, Eq.(\ref{EoS eff}); the dashed black line corresponds to the EH case, $\omega_0(\varrho_0)$; the red lines are the entropy densities of the apparent cosmological horizon, Eq.(\ref{s(H)}), for \textit{(i)} $\lambda = -9.00 \times 10^{22}$ ; \textit{(ii)} $\lambda = -2.50 \times 10^{51}$ ; \textit{(iii)} $\lambda = 7.53 \times 10^{69}$.}
\label{fig. EoS}
\end{figure}
This effect may be seen in Fig.\ref{fig. EoS}, where $\omega_0(\varrho_0)$, given by Eq.(\ref{EoS exemplo 2}), is shown as the dashed line, while the continuous black line depicts the effective equation of state (\ref{EoS eff}). Here $w_1 = 0$, and $w_2$ is fixed by the observed value of the cosmological constant (cf. Eq.(\ref{La0 e w2})). One can clearly see that as the energy density increases the plot of $\omega_{\mathrm{eff}}$ sinks beneath the line of $-1/3$, indicating the new period of accelerated expansion. For smaller densities, however, there is very little difference between the EH plot and the QTG one. Although some of the indispensable features of inflation -- slow-roll, for example -- \emph{are not present}, we shall freely nominate this early acceleration period as an ``inflationary''. The duration of such a ``rustic inflation'' evidently depends on the value of $\mu$. By imposing $\omega_{\mathrm{eff}} (\varrho_{\mathrm{acc}}) = -1/3$, we get a cubic equation:
\begin{eqnarray}
& \frac{(w_1 - 1)}{36} \varkappa^4 \, \mu L^4 \; \varrho_{\mathrm{acc}}^3 - \frac{3 w_1 + 1}{3} \varrho_{\mathrm{acc}} + w_2 = 0 \; , \label{cubic acc}
\end{eqnarray}
whose positive real roots give the threshold of the two acceleration periods now present in the dynamics -- the initial one due to QTG and the final due to the cosmological constant.
The number of distinct real solutions depends on the sign of the discriminant of (\ref{cubic acc}) and, for $\mu < 0$ and $w_1 > -1/3$, it determines a critical value
\begin{eqnarray}
|\mu_{{\mathrm{acc}}}| = \frac{16 (3 w_1 + 1)^3}{81 (1 - w_1) \varkappa^4 w_2^2 L^4} \nonumber
\end{eqnarray}
for which the discriminant vanishes. Thus if $|\mu| < |\mu_{{\mathrm{acc}}}|$ there are two positive real roots for (\ref{cubic acc}), corresponding to two distinct periods of acceleration.
But for large enough values of the gravitational coupling, namely $|\mu| \geq |\mu_{{\mathrm{acc}}}|$, there is no positive real root to (\ref{cubic acc}) and as a consequence the initial QTG acceleration period lasts for such a long time that it merges with the final one -- the universe is then never decelerated.
It is worthwhile to remark here that in the QTG counterpart (\ref{EoS eff}) of the EH linear EoS, for $\mu < 0$ the effective speed of sound $v_{\mathrm{eff}}^2 = \partial p / \partial \varrho$ also satisfies the causality conditions $-1 < v_{\mathrm{eff}}^2 < 1$, under the same restrictions on the parameters $w_1$ and $w_2$. On the other hand, for $\mu > 0$, we see that $v_{\mathrm{eff}}^2 \to \infty$ as $\varrho \to \frac{2}{L^2 \varkappa^2} \sqrt{3 / \mu}$. This \emph{non-causal behaviour} of the effective fluid near the points where $C_0(\varrho) = 0$ is yet another reason to consider here only the case of negative values of $\mu$.
Although the form of $t(H)$ given by Eq.(\ref{t(H)}) does not allow to analytically determine the exact form of the Hubble function $H(t)$,
we may invert it in a first order approximation. This is possible when the dimensionless quantity $|\mu| L^4 H^4$ is much smaller than unity. For $L = l_{\mathrm{Pl}}$, such an approximation is valid during most of the universe history, since $H(t)$ is typically of a cosmological order (greater than 1 Mpc $\sim 10^{57} \times l_{\mathrm{Pl}}$). In what follows, we shall refer to this approximation as ``first order in $|\mu|$'':
\begin{eqnarray}
H(t;\mu) = H_0(t) + \mu \, H_1(t) + \cdots ,\nonumber\\
a(t,\mu) = a_0(t) \left[ 1 + \mu \, A_1(t) + \cdots \right],\nonumber
\end{eqnarray}
with the scale factor parametrized as $a(t) = e^{A(t)}$. In zeroth order we have, naturally, the EH solution:
\begin{eqnarray}
& H_0(t) = \varkappa \sqrt{\frac{w_2}{6(1 + w_1)}} \, {\mathrm{cth}} \left[ (t - t_0) / \tau \right] ,\label{H0 t} \\
& a_0(t) = \tilde a_0 \, {\mathrm{sh}}^{\delta} \left[ (t - t_0) / \tau \right] , \;\; \delta = \frac{2}{3(1 + w_1)} \; .\label{a0 t}
\end{eqnarray}
Here $1/\tau = \varkappa \sqrt{3(1 + w_1) \, w_2 / 8}$, and $\tilde a_0$ is a normalization constant. At early times $a_0(t) \sim \tilde a_0 ( t / \tau )^{\delta}$ the observed behaviour is typical of cosmologies with constant EoS: $p_0 / \varrho_0 \approx w_1$. Later, for $t/\tau \gg 1$ the cosmological constant
\begin{eqnarray}
\Lambda_0 = \varkappa^2 w_2 / 8 (1 + w_1) \label{La0 e w2}
\end{eqnarray}
dominates the EoS and the universe enters a final, accelerated, asymptotically de Sitter phase, with an asymptotically constant energy density $\varrho_{\Lambda_0} = w_2 / (1 + w_1)$. Then
\begin{eqnarray}
& a_0(t) \sim \exp \left\{ 2 \sqrt{\frac{\Lambda_0}{3}} \, (t - t_0) \right\} \; . \label{La e tau}
\end{eqnarray}
In particular, by choosing $w_1 = 0$, and thus $\delta = 2/3$, we see that (\ref{EoS exemplo 2}) describes fairly well our observed Universe, neglecting inflation and the radiation dominated era: we begin at $t = 0$ with a dust-filled space-time, which ends at a de Sitter space with $\Lambda_0$ presenting observed value \cite{Bousso_hepth_0702115}
\begin{eqnarray}
\Lambda_0 \approx 3.14 \times 10^{-122} \times l_{\mathrm{Pl}}^{-2} \; ,
\end{eqnarray}
if we choose $w_2$ accordingly, using Eq.(\ref{La0 e w2}).
The first order corrections can be easily calculated from Eq.(\ref{before expansion}):
\begin{eqnarray}
& H_{1}(t) =\frac{\tilde H_1}{ {\mathrm{sh}}^{2} \left( (t-t_0) / \tau \right) }\Big\{ \frac{t - t_0 }{4 \tau} - \frac{1}{8} {\mathrm{sh}} \left( \frac{2 (t - t_0)}{\tau} \right) - \nonumber \\
& - \frac{1}{3} {\mathrm{cth}} \left(\frac{t - t_0}{ \tau} \right) \left[ {\mathrm{sh}}^{-2} \left( \frac{t-t_0}{\tau} \right) + \frac{5}{2} \right] \Big\} ; \label{H1 t} \\
& A_1(t) = \frac{\tilde H_1\tau}{12} \Big\{ {\mathrm{cth}} \left( \frac{t}{\tau} \right) \left[ 5 \, {\mathrm{cth}}\left( \frac{t}{\tau} \right) -\frac{3 t}{\tau} \right] + {\mathrm{sh}}^{-4}\left( \frac{t }{\tau} \right) \Big\} \; , \label{A1 t}
\end{eqnarray}
where $\tilde H_1 = - \varkappa^6 \, w_2^3 \, \tau L^4 / 72(1 + w_1)^2$. The constant $t_0 = 4 \pi \upsilon / 3(1+w_1) \mu L^4$ assures that the singularity is placed in $t = 0$, and as $\mu \to 0$ also $t_0 \to 0$.
From the scale factor and the Hubble function, one can determine all other relevant quantities, and in particular the effective energy density $\varrho(t)$, plotted in Fig.\ref{fig. vro de t}.
\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=0.8]{rho}
\caption{Time evolution of the energy density, for the same parameters of Fig.\ref{fig. EoS}. The black continuous curve gives the exact function $\varrho(t)$, obtained from graphical inversion of $t(\varrho)$ given by Eq.(\ref{t(H)}); the black dashed line gives the first order approximation; the dotted gray line depicts the EH density $\varrho_0(t)$; the horizontal gray line marks the final energy density of the early acceleration period.}
\label{fig. vro de t}
\end{center}
\end{figure}
As one approaches the initial singularity at $t = 0$, Eq.(\ref{t(H)}) shows that $H$ diverges. Eventually we then have $H \gtrsim 1 / l_{\mathrm{Pl}}$ and the first order approximation is bound to fail -- indeed, $H_1(t)$ diverges more rapidly than $H_0(t)$ as $t \to 0$. This can be clearly seen in Fig.\ref{fig. vro de t}: the black continuous line shows the exact function $\varrho(t)$, obtained from graphical inversion of $t(\varrho)$ given by Eq.(\ref{t(H)}); the black dashed line shows the first order approximation $H_0(t) + \mu H_1(t)$. It is clear that the first order approximation is only valid valid for times greater than an instant $t_*$, when the curve has a maximum, but for $t>t_*$ it is in good agreement with the exact solution.
To smallest order in $|\mu|$, we have
\begin{eqnarray}
t_* \approx \left( 2 (1 + w_1)^{3/8} + \pi \right) \frac{\sqrt2}{3 (1 + w_1)} \, L |\mu|^{1/4} \; . \label{t* approx}
\end{eqnarray}
Now, approximating to first order Eq.(\ref{cubic acc}) we find that the initial period ends when the effective energy density decreases to the value
\begin{eqnarray}
&\varrho_{\mathrm{initial}} \approx \sqrt{\frac{1 + 3 w_1}{1 - w_1}} \, l_{\mathrm{Pl}}^{-2} \;( L^4\, |\mu|)^{-1/2} , \label{vro acc init}
\end{eqnarray}
which according to Eq.(\ref{t(H)}) happens at the instant
\begin{eqnarray}
t_{\mathrm{acc}} \approx \frac{(\sqrt3 + \pi) \sqrt2}{3 (1 + w_1)} \; L \, |\mu|^{1/4} \; . \label{t acc approx}
\end{eqnarray}
This shows that $t_*$ is slightly posterior to $t_{\mathrm{acc}}$, hence an approximation to only first order is not sufficient to describe the initial acceleration period created by QTG.
As we have shown above, if $|\mu| \gg |\mu_{\mathrm{acc}}|$ we may have an eternally accelerated expansion.
Such large values of $|\mu|$, therefore, do not correspond reasonably to the observed universe. One might thus pose the question: What are \emph{the restrictions on the values of the gravitational couplings} $\lambda$ and $\mu$, which guarantee the physical consistency of the quasi-topological effects?
Regarding the initial acceleration period as an inflation era, we may assume that it would occur in the range of energies $\varrho_{\mathrm{Pl}} \gtrsim \varrho \gtrsim10^{-12} \times \varrho_{\mathrm{Pl}}$ (see \cite{LindeInflationaryCosmology}),
thus we must have $\mu_{\mathrm{acc}}$ such that the root of (\ref{cubic acc}) lies within this bound. The upper bound of this interval, viz. $\varrho_{\mathrm{acc}} \sim 10^{-12} \times \varrho_{\mathrm{Pl}}$, is indeed the case depicted in Figs.\ref{fig. EoS} and \ref{fig. vro de t}, what serves to demonstrate the validity of the first order approximation.
Another phenomenological restriction stems from the fact the the apparent horizon entropy should not be vanishing for too small values of $\varrho$.
In the GB case, there is no initial acceleration period, and this entropic restriction is in fact the only condition we have on $\lambda$. It is quite evident from Eq.(\ref{vro GB}) that one may choose $\lambda$ to get $\varrho_{\mathrm{GB}}$ as large as one needs -- e.g. for $\lambda = 3/4$ we have $\varrho_{\mathrm{GB}} = \varrho_{\mathrm{Pl}}$. In QTG instead, as it may be easily seen from Eq.(\ref{vro QTG}), for each given value of $\mu$ determining the end of the acceleration period, we can choose $\lambda$ in order to place $\varrho_{\mathrm{QTG}}$: \textit{(i)} before or \textit{(iii)} after $\varrho_{\mathrm{initial}}$, or even to have \textit{(ii)} $\varrho_{\mathrm{QTG}} = \varrho_{\mathrm{initial}}$. This is exemplified in Fig.\ref{fig. EoS}, where the red lines represent the values of $\varrho$ for which $s(\varrho) = 0$. Note that in cases \textit{(ii)} and \textit{(iii)} the whole initial acceleration period is rendered ``unphysical'' on account of the negative horizon entropy there.
\section{On the late Universe QTG effects}
Although the more significant effects of QTG take place when the curvature, as well as the energy density, are big enough -- namely, at early times -- it turns out that the whole evolution of the universe is modified by the QTG terms.
Clearly, at later times, as the curvature diminishes, the cubic and quadratic terms in (\ref{action non cf}) become more and more negligible and the first order approximation made in the last section is then justified.
An example of such changes is given by the fact that the cosmological constant, which characterizes the geometry of the asymptotically ${\mathrm{dS}}_4$ spaces in the limit $t \to \infty$, is not equal to the bare one, $\Lambda_0$, defined by the matter Lagrangian. Indeed, in QTG one observes the \emph{effective} cosmological constant $\Lambda_{\mathrm{eff}}$, related to the Hubble function $H(t)$. To first order in $\mu$, one may determine $\Lambda_{\mathrm{eff}}$ by the approximation (\ref{H1 t}) for $H(t)$, or else by inverting directly the exact equation
\begin{eqnarray}
&\Lambda_0 = \Lambda_{\mathrm{eff}} \left( 1 - \mu L^4 \Lambda_{\mathrm{eff}}^2 /9 \right) \; , \label{La eff e 0}
\end{eqnarray}
obtained from Eq.(\ref{vro 0 eff}): $\Lambda_{\mathrm{eff}} \approx \Lambda_0 + L^4 \mu \, \Lambda_0^3 / 9 \;$.
This is in fact a general result, valid for every asymptotically de Sitter space, regardless of the particular matter EoS leading to the final ${\mathrm{dS}}_4$ vacuum. Notice that for the very small value of the observed cosmological constant, both $\Lambda_0$ and $\Lambda_{\mathrm{eff}}$ are practically equal.
Another feature of asymptotically de Sitter space-times is the presence of a future event horizon.
Its comoving radius is given by the integral $r_f(t) = \int_t^\infty {\mathrm{d}} t / a(t)$ and may be calculated to first order in $\mu$ by using the results (\ref{a0 t}) and (\ref{A1 t}). At zeroth order (i.e. in the EH case) this yields
\begin{eqnarray}
& r^{(0)}_f(t) = \frac{\tau}{\delta \, \tilde a_0} \, \frac{1}{ {\mathrm{ch}}^\delta(t / \tau)} \, {}_2{\mathrm{F}}_1 \left[ \frac{\delta}{2} \, , \, \left(\frac{1 + \delta}{2}\right) \, ; \, \frac{2 + \delta}{2} \, ; \, \frac{1}{{\mathrm{ch}}^2(t/\tau)} \right] , \label{rf EH}
\end{eqnarray}
while the first order QTG correction is given by:
\begin{eqnarray}
& r^{(1)}_f(t) = \frac{\tilde H_1 \tau^2}{12 \tilde a_0} \Bigg\{
\frac{5 / \delta}{{\mathrm{ch}}^\delta (t / \tau)} \, {}_2{\mathrm{F}}_1 \left[ \frac{\delta}{2} , \frac{3 + \delta}{2} ; \frac{2+ \delta}{2} ; \frac{1}{{\mathrm{ch}}^2(t/\tau)} \right] + \nonumber \\
& + \frac{1 / (4+ \delta)}{[{\mathrm{ch}}(t / \tau)]^{(4 + \delta)}} \, {}_2{\mathrm{F}}_1 \left[ \frac{4 + \delta}{2} , \frac{5 + \delta}{2} ; \frac{6 + \delta}{2} ; \frac{1}{{\mathrm{ch}}^2(t/\tau)} \right] - \frac{3 t /(\delta \tau)}{ {\mathrm{sh}}^\delta(t / \tau)} - \nonumber \\
& - \frac{3 / \delta^2}{ {\mathrm{ch}}^\delta(t / \tau)} \, {}_2{\mathrm{F}}_1 \left[ \frac{\delta}{2} , \frac{1 + \delta}{2} ; \frac{2+ \delta}{2} ; \frac{1}{{\mathrm{ch}}^2(t/\tau)} \right] \Bigg\} . \label{r f correction QTG}
\end{eqnarray}
The function $r_f(t)$ describes the past light cone of the (infinite) future of the comoving observer at the origin. The tip of this cone is placed at $\{ r_f = 0 , \, t = \infty \}$.
Then as $t \to \infty$ the \emph{physical radius}, $l_f (t)= a(t) \, r_f(t)$ becomes equal to the (constant) de Sitter radius $1 / H$. The first order approximation to $l_f(t)$ can be easily obtained with the help of Eq.(\ref{A1 t}): for example its value today, at $t = 13.8 \; {\mathrm{Gyrs}}$, is $l_f \approx \left( 4.90 \times 10^3 + \mu \times 9.10 \times 10^{-248} \right) {\mathrm{Mpc}} \; $.
Alternatively, the comoving radius $r_p(t) = \int^t_{\tilde t} {\mathrm{d}} t / a(t)$ describes the future light cone for an observer at the origin, starting from its tip at $\{ r_p = 0, \, t = \tilde t \}$. In a singular universe, if this tip is placed at the beginning of time, $\tilde t = 0$, then $r_p(t)$ is the particle horizon. In practice, the choice of $\tilde t$ determines only a constant, for we may write
\begin{eqnarray}
\hspace{-0.7 cm} r_p(t) = - \int_t^\infty {\mathrm{d}} t / a(t) + \int_{\tilde t}^\infty {\mathrm{d}} t / a = - r_f (t) + r_f (\tilde t) \; . \label{r p e f}
\end{eqnarray}
Thus for example, in the EH case with $\tilde t = 0$, Eq.(\ref{rf EH}) gives
\begin{eqnarray}
\hspace{-1 cm} & r^{(0)}_p(t) = - \frac{\tau / \delta \tilde a_0}{ {\mathrm{ch}}^{\delta}(t / \tau)} \, {}_2{\mathrm{F}}_1 \left[ \frac{\delta}{2} , \frac{1 + \delta}{2} ; \frac{2 + \delta}{2} ; \frac{1}{{\mathrm{ch}}^2(t/\tau)} \right] + \frac{\tau}{2 \tilde a_0} {\mathrm{B}} \left( \frac{\delta}{2} , \frac{1 - \delta}{2} \right) , \label{rp 0}
\end{eqnarray}
and in general Eqs.(\ref{rf EH}) and (\ref{r f correction QTG}) determine also the first order correction for $r_p(t)$, for a given $\tilde t$.
Recall that the first order approximation for the scale factor is only valid for $t \gtrsim t_*$, with $t_*$ denoting the instant where the approximation fails, Eq.(\ref{t* approx}). Therefore in QTG we have the ``technical'' impossibility of placing the tip of the light cone on the initial singularity -- the earlier we may place it is at $\tilde t = t_*$.
Due to the fact that $t_*$ (at our first approximation) is slightly posterior to $t_{\mathrm{acc}}$, we are then technically prevented from describing the increase of the particle horizon during this early ``inflationary'' period. Consequently, we cannot determine its number of $e$-foldings, and whether it solves the usual problems of non-inflationary cosmology -- such as, for example, the horizon problem.
The knowledge of the above expressions for the radii $r_p(t)$ and $r_f(t)$ provides an analytic description of the \emph{causal diamond} \cite{Gibbons1, BoussoNbound} and its comoving volume $V_{{\mathrm{c.d.}}}(t)$, in the QTG cosmological model under investigation. The former is defined as the intersection of the causal past of the ``point'' $\{ r_f = 0 , \, t = \infty \}$ and the causal future of $\{ r_p = 0, \, t = \tilde t \}$. At each instant $t$ the volume is given by $V_{\mathrm{c.d.}}=\frac{4}{3} \pi r^3(t)$ with $r=r_p$ on the upper and $r=r_f$ on the lower half of it. It is easily seen that $V_{\mathrm{c.d.}}$ has a single maximum at $t=t_{\mathrm{edge}}$, when $r_p (t_{\mathrm{edge}})=r_f (t_{\mathrm{edge}})$ \cite{BoussoNbound}. With the aid of Eq.(\ref{r p e f}), the instant $t_{\mathrm{edge}}$ is determined from the equation $r_f(t_{\mathrm{edge}}) = \frac{1}{2} r_f(\tilde t)$, which is exact, i.e. independent from the first order approximation. If $r_f(t)$ is a continuous function, then we conclude that a first order correction to $\tilde t$ must imply a first order change in $t_{\mathrm{edge}}$. Therefore for small $t_* = \tilde t$ in QTG, the edge of the causal diamond occurs at an instant differing not more than at first order from the corresponding value in EH.
In EH gravity with linear EoS (\ref{EoS exemplo 2}) and $w_1 = 0$, describing an early universe dominated by dust\footnote{In which not only the initial inflationary period, but also the radiation-dominated era of the concordance model are absent.}, Bousso et al. \cite{Bousso_hepth_0702115} have calculated $V_{\mathrm{c.d.}} (t)$ and used it to predict the order of magnitude of the observed cosmological constant. Their analysis, based on the rather universal (phenomenological) evaluation of the entropy production rate in our universe, demonstrates that only when $\Lambda_0 \sim 10^{-122} \times l_{\mathrm{Pl}}^{-2}$ \emph{the causal entropic principle (CEP)}, requiring maximal entropic production within the corresponding causal diamond volume, is fulfilled. According to their arguments the main production of bulk entropy occurs during the matter-dominated era. Therefore one can perform a similar analysis for the QTG extension of this linear EoS model, by imposing the $CEP$ conditions for the causal diamond whose inferior tip is placed at $\tilde t = t_*$, thus respecting the restrictions of the considered first approximation. Surely, even if the tips of the causal diamonds in QTG and in EH gravity were placed at the same point -- say, by replacing $t = 0$ with $t = t_*$ in the EH case as well --, still they would not be identical due to the changes in the dynamics given in (\ref{r f correction QTG}). However, as we saw above, the first order QTG corrections we are considering do not change significantly the comoving volume of the causal diamond, and in fact they lead to the same prediction for the magnitude of the effective cosmological constant $\Lambda_{\mathrm{eff}} \approx \Lambda_0 + L^4 \mu \, \Lambda_0^3 / 9 \;\sim 10^{-122} \times l_{\mathrm{Pl}}^{-2}$.
Throughout this discussion, we have not taken into account the entropic bounds derived in Sect.\ref{sect. horizon entropy}. Regardless of our technical restrictions for placing the inferior tip of the causal diamond, in the case of $\mu < 0$, we cannot place it before the instant $t_{\mathrm{QTG}}$ when the apparent horizon's entropy vanishes. The same is true in the GB case, for $\lambda > 0$. We are however assuming that $t_{\mathrm{QTG}}$ is very small, in particular that $t_{\mathrm{QTG}} \lesssim t_*$. This can always be set for an appropriate value of $\lambda$. Either way, the entropic restrictions \emph{do not allow} the inferior tip of the causal diamond to be placed on the singularity.
Let us list in conclusion a few open problems concerning the considered (linear EoS) cosmological model of the cubic Quasi-Topological gravity: (a) The stability conditions for the asymptotic ${\mathrm{dS}}_4$ cosmological QTG solutions, which requires the calculation of the spectrum of the corresponding linear fluctuations at least in the probe approximation; (b) The analysis of the properties of QTG models with more realistic matter content by considering EoS or equivalently (string inspired) matter superpotentials \cite{KKLT} giving rise to early-time inflation with a \emph{desired slow-roll behaviour}, which is under investigation \cite{LoveCosmo_tobepublished}. It is worthwhile to also mention that the methods and some of the results of the present paper seem to have a straightforward ``cosmological'' application to the recently constructed ``higher curvature'' quartic QTG extension \cite{mann} of the EH gravity, as well as to the case of \emph{spatially curved FRW} solutions of the considered four dimensional, cubic QTG model.
\textit{Acknowledgments}. We are grateful to C.P. Constantinidis for his collaboration in the initial stage of this work and for the discussions.
\bibliographystyle{model3-num-names}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,140 |
{"url":"http:\/\/aliceinfo.cern.ch\/ArtSubmission\/node\/3794","text":"# Figure 27\n\n Improvement of the $q\/$\\pt resolution in data when TRD information is included as compared with the performance of tracking without TRD information for various running scenarios. The labels low and high IR indicate interaction rates of 12 and 230~kHz, respectively.","date":"2018-03-19 09:06:14","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.5798829793930054, \"perplexity\": 3435.642000654677}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-13\/segments\/1521257646636.25\/warc\/CC-MAIN-20180319081701-20180319101701-00481.warc.gz\"}"} | null | null |
namespace task_manager {
// Get the current number of GDI handles in use (and peak on >= Win7+).
void GetWinGDIHandles(base::ProcessHandle process,
size_t* current,
size_t* peak);
// Get the current number of USER handles in use (and peak on >= Win7).
void GetWinUSERHandles(base::ProcessHandle process,
size_t* current,
size_t* peak);
} // namespace task_manager
#endif // CHROME_BROWSER_TASK_MANAGER_OS_RESOURCE_WIN_H_
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,078 |
Q: Testing-library fireEvent.change doesn't works with from MUI I have component with element:
<Select
native
role="combobox"
aria-label="select height"
value={ height.toString() }
onChange={ handleChangeHeight }
>
When I try to make a test with changing the value it do nothing:
fireEvent.change(heightSelect, {target: {value: "500"}})
But if I replace element for standard test is working.
<select role="combobox" aria-label="select height" value=... >
How I can fix this problem with testing-library for @mui/material ?
A: fixed:
const heightSelect = screen.getByRole('combobox', { name: 'height select' })
const select = heightSelect.childNodes[0]
fireEvent.change(select, {target: {value: 500}})
const selectedNew = within(heightSelect).getAllByRole('option', {selected: true})[0]
expect(selectedNew.innerHTML).toBe(`height 500 mm`)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,746 |
Q: Proof of Johnsen Lindenstrauss by concentration of measure Question: In Theorem 3 before "..By choosing $t=\sqrt{\frac{k}{5n}}$ we get $m\ge\Omega(\sqrt{\frac{k}{n}})$.." What is this process exactly? Why is an exponential bound critical here? Why wouldn't other type of bounds such as $\frac{1}{n}$ work?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,886 |
And it will rain tomorrow too. So, I made teru teru bozu pouch.
Teru teru bozy is a little doll made of white paper or fabric that we hang outside of window, when we hope good weather.
I like also rainy days, but I want to take pictures of spring flowers.
So I hand embroidered sun on the flower print fabric.
I want someone brings it when he or she hopes sunny day, and the pouch brings smily sun for him or her.
It's a rainy day in The Netherlands, but your sun made me smile. Thank you.
Thank you! Your dog made me smile (* v *)!!!!
You make such gorgeous things!!!
What lovely items you have made.
I like them too! It's originally from China.
I've just made some teru teru bozu too.
Those bags are so pretty~ I love the fabric.
I like to make Teru teru bozu out of paper, but then I realised that I like rain better~ Pretty, anyway!
The little teruterubozu are so cute, I like how you used buttons for their heads.
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My item is on an English craft magazine! | {
"redpajama_set_name": "RedPajamaC4"
} | 3,459 |
Q: How to check how many of my friends like particular page on facebook using PHP SDK I'm workin on an app that would award its users points for each of their friends liking my page.
I need a way to check how many of user's friends like my page. I developed this piece of code to check each my friends for liking a particular page:
$friends = $facebook->api('/me/friends'); //list my friends
$time_start = microtime(true);
echo "<pre>";
$i = 0; //counter of likes
$b = 0; //counter of request in single batch API request
$batch_max = 50 // facebook allows max 50 requests in single batch API call
$page_id = '187941397895831'; //example page ID, i'm checking how many of my friends like this page
$batch = array(); //array used for creating batch API request
$data = array(); //array collecting all API requests results
foreach ($friends['data'] as $friend) {
$req = array(
'method' => 'GET',
'relative_url' => '/'.$friend['id'].'/likes'
);
$batch[] = json_encode($req);
$b++;
if ($b == 50) {
$params = array(
'batch' => '[' . implode(',',$batch) . ']'
);
$data[] = $facebook->api('/', 'POST', $params);
$b = 0;
$batch = array();
}
}
$params = array(
'batch' => '[' . implode(',',$batch) . ']'
);
$data[] = $facebook->api('/', 'POST', $params);
foreach ($data as $data_set) { //iterate through results of each api request
foreach ($data_set as $friend_likes) { //iterate through data of particular friend
$likes_array = json_decode($friend_likes['body'], true);
foreach ($likes_array['data'] as $single_like) { //iterate through all likes of a single friend
if ($single_like['id'] == $page_id) { //if page id found in user's likes increase counter
$i++;
}
}
}
}
$time_end = microtime(true);
$time = $time_end - $time_start;
echo $time."\n";
echo $i;
echo "</pre>";
exit;
In final version I will not be checking my friends but friends of each of my users. My code executes in 14 seconds, if I had to iterate through, let's say, 100 users it'd be 1400 seconds, which is waaaay to long. Is there better way to do that? I'm newbie to facebook API, so I could miss something obvious :)
A: Ok, so here's the working piece of code. You need to know access token for each of users being checked. It executes in ~0.6 seconds instead of 14 seconds for previous code.
$queryResults = array();
$facebook->setAccessToken($user->getAccessToken());
$fql = "SELECT '' FROM page_fan WHERE page_id = 'xxxxxxxxxxxx' AND uid IN (SELECT uid2 FROM friend WHERE uid1 = '".$user->getFbId()."')";
$fql = urlencode($fql);
try {
$queryResults = $facebook->api(
'/fql?q='.$fql
);
} catch (FacebookApiException $e) {
$log->setMessage(print_r($e,true));
$logMapper->save($log);
}
if (!empty($queryResults)) {
$user->setPoints(count($queryResults['data']));
$usersMapper->save($user);
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 655 |
date: 2016-08-05 15:53:56-05:00
embed_url: https://youtu.be/DlwXYY9Ncu4
layout: post
tags:
- culture
- technology
- humor
- music
timestamp: 1470430436
title: 'Emoji: The Musical'
type: video
---
<iframe width="480" height="270" src="https://www.youtube.com/embed/DlwXYY9Ncu4?feature=oembed" frameborder="0" allowfullscreen></iframe>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,516 |
package org.iotp.iothub.server.security;
import org.iotp.infomgt.data.id.DeviceId;
public class DeviceAuthResult {
private final boolean success;
private final DeviceId deviceId;
private final String errorMsg;
public static DeviceAuthResult of(DeviceId deviceId) {
return new DeviceAuthResult(true, deviceId, null);
}
public static DeviceAuthResult of(String errorMsg) {
return new DeviceAuthResult(false, null, errorMsg);
}
private DeviceAuthResult(boolean success, DeviceId deviceId, String errorMsg) {
super();
this.success = success;
this.deviceId = deviceId;
this.errorMsg = errorMsg;
}
public boolean isSuccess() {
return success;
}
public DeviceId getDeviceId() {
return deviceId;
}
public String getErrorMsg() {
return errorMsg;
}
@Override
public String toString() {
return "DeviceAuthResult [success=" + success + ", deviceId=" + deviceId + ", errorMsg=" + errorMsg + "]";
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,355 |
Q: How to delete all duplicate element from an array without using any library or collection As the header said. I want to delete all duplicate element from an array without using any library or collection. I usually use Set or HashMap but it is not possible anymore in this case. I also thought about sort the array and check from the beginning to the end like
If(arr[i]==a[i+1])
delete arr[i]; i--;
Or maybe something like using 2 for loops. But they are not efficient enough. Are there any other more efficiently way to delete duplicates? Thank you!
A: If we sort the array, any duplication between the values will be close to each other.
That way we can remove them
int a[] = { 1,9,55,1,8,9,77,2,5,54,7,10,11 };
Arrays.sort(a);
int j = 0;
for (int i = 0; i < a.length - 1; i++) {
if (a[i] != a[i + 1]) {
a[j] = a[i];
j++;
}
}
a[j] = a[a.length - 1];
return a;
A: If you can use Streams (they are not collections and can be used since Java 8), You can do something like this:
int[] result = Arrays.stream(a).distinct().toArray();
A: This is another possibility. The cost is O(n + m) where m is the max value of the input array.
public static void main(String[] args) {
int arr[] = {23, 56, 78, 92, 44, 3, 3, 3, 23, 11, 10, 10, 10, 10};
// Find the size for the new array to allocate.
int max = 0;
for (int i = 0; i < arr.length; i++) {
if (arr[i] > max) {
max = arr[i];
}
}
// Mark the values stored in the array (hit or miss array)
int[] presence = new int[max + 1];
for (int i = 0; i < arr.length; i++) {
presence[arr[i]] = 1;
}
// Find the size for the new array to allocate
int count = 0;
for (int i = 0; i < presence.length; i++) {
if (presence[i] != 0) {
count++;
}
}
// Store the element in the new array when hit
int[] res = new int[count];
int index = 0;
for (int i = 0; i < presence.length; i++) {
if (presence[i] != 0) {
res[index] = i;
index++;
}
}
for (int i = 0; i < res.length; i++) {
System.out.print(res[i] + ", ");
}
}
I know for sure this can improved significantly , but you may use this as a starting point.
A: We can remove duplicates from the array using the code below without using any collections or streams. Have done it by taking the help of String class. Also the order will be preserved
// Input Array
int a[] = {1, 9, 55, 1, 8, 9, 77, 2, 5, 54, 7, 10, 11};
String s = "";
for (int i = 0; i < a.length; i++) {
String s1 = String.valueOf(a[i]);
if (!s.startsWith(s1 + " ") && !s.contains(" " + s1 + " ")) {
s = s.concat(s1 + " ");
}
}
System.out.println(s);
// output: 1 9 55 8 77 2 5 54 7 10 11
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,475 |
{"url":"https:\/\/dmoj.ca\/problem\/tc19summere","text":"## Solar Power\n\nView as PDF\n\nPoints: 5\nTime limit: 0.1s\nMemory limit: 256M\n\nAuthor:\nProblem type\n\nJoe, ever-efficient, has now turned to another form of green energy: solar power. Joe owns one solar panel which he will use to produce electricity each day. Each day consists of minutes, over each of which the Sun changes position from sunrise at position to sunset at position . The energy collected by the solar panel depends on the distance between its own position and the Sun\u2019s position. Formally, if the solar panel is at a position and the Sun is at a position , the energy collected during that minute is . Joe\u2019s solar panel is an older model, and is rather hard to move. It requires minutes to move it to a new location, during which time it is still collecting power from its current position. Joe would like to know the maximum total amount of energy he can collect, given that his solar panel may initially be at any position. Note that Joe cannot start moving the solar panel before sunrise.\n\n#### Input Format\n\nInput consists of two space-separated integers and on a single line.\n\n#### Output Format\n\nOutput on a single line the greatest amount of energy that Joe can collect on a single day.\n\n#### Sample Input\n\n10 6\n\n#### Sample Output:\n\n87\nSun Panel Value\n1 4 7\n2 4 8\n3 4 9\n4 4 10\n5 4 9\n6 4 8\n7 8 9\n8 8 10\n9 8 9\n10 8 8","date":"2019-08-22 07:52:08","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\": 0.19979624450206757, \"perplexity\": 929.694754152819}, \"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-2019-35\/segments\/1566027316785.68\/warc\/CC-MAIN-20190822064205-20190822090205-00264.warc.gz\"}"} | null | null |
After the update FastCGI is not working anymore when I switch it in ISPConfig3. but when I use CGI it's working fine. Any ideas what could change and how to enable both modes?
PS: Is dotdeb.org a good source to update PHP and Mysql anyway?
So that means the switch in ISPConfig3 will not work anymore? I guess I get now FastCGI when setting in ISPC3 is CGI and when I switch to FastCGI nothing is working. Any ideas how to fix the ISPC3 mappings?
So that means the switch in ISPConfig3 will not work anymore?
I'am sure thats not the case. fcgi and cgi are very different technics and are configured differently, so you can not get fcgi when you selcted cgi.
Which is the exact error message that you get when you use fastcgi?
I don't get anything. Just a 403 error page from ISPC3.
Actually now I was playing with it and i think it's not working on only one domain, but works on all the other domains i add on the server. But, when i do "<?php phpinfo();?>", despite my settings CGI or FastCGI, the result is the same.
Now, Can you tell me what ISPC3 actually does exactly when we switch to CGI and FastCGI. What does it do technically and where can I look to make sure it does what it needs to do?
The error messages are in the error log of the website. Please open the log and post the last error messages.
But, when i do "<?php phpinfo();?>", despite my settings CGI or FastCGI, the result is the same.
Thats always the case as phpinfo is not able to show the differences between the two modes.
[Mon Mar 23 11:57:05 2009] [warn] (104)Connection reset by peer: mod_fcgid: read data from fastcgi server error.
[Mon Mar 23 11:57:19 2009] [warn] (104)Connection reset by peer: mod_fcgid: read data from fastcgi server error.
This looks like a problem with the php binary that you installed, it simply does not seem to support the fastcgi mode. You can either install the php binarys from debian again or you try to compile your own binaries. The php binraies from debian are secure and up to date even if they are not the bleeding edge release, but if you need a stable system it is highly recommended to use the official debian binaries.
The difference of cgi and fcgi is that for cgi a instance of php is started when a page is requested and for fcgi php runs in some kind of daemon mode which is faster when you have a lot of requests.
I'm now even more confused. I found something strange.
I have 3 domains on the Debian Lenny server.
3 domain does not work with neither CGI nor FastCGI.
The domains were added in the order listed.
Could you point me into the right direction. How to find an issue and fix it for new and existing domains?
Take a look at the vhost configuration file as I suggested above.
I did checked the vhost configuration files for domain1 (working with fast-CGI) and domain3 (not working). the vhost files are identical. the only difference is in the urls where one says web1, the other web3.
Any more ideas? What else can I check?
Did you check the error logs of each web site? | {
"redpajama_set_name": "RedPajamaC4"
} | 932 |
Prince in tune with public and independent scientific opinion
1.More on Prince's coments
2.Prince in tune with public and independent scientific opinion
QUOTE: ""¦we [will] end up with millions of small farmers all over the world being driven off their land into unsustainable, unmanageable, degraded and dysfunctional conurbations of unmentionable awfulness." - Prince Charles commenting on the future for small farmers if we stick with GM crops, Daily Telegraph, 13 August 2008.
SUMMARY OF PRINCE'S COMMENTS: Prince Charles has warned that GM crops risk causing the biggest-ever environmental disaster. In an outspoken intervention on the issue of GM food, the Prince said that multinational companies were conducting a "gigantic experiment" with "nature and the whole of humanity which has gone seriously wrong". The Prince went on to say "What we should be talking about is food security not food production - that is what matters"¦".
Daily Telegraph (13 Aug, front page)
http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2008/08/12/eacharles112.x ml
Their readers' comments are well worth looking at:
Full text of the interview with the Prince, conducted by Jeff Randall - the Telegraph's editor-at-large http://www.telegraph.co.uk/portal/main.jhtml?xml=/portal/2008/08/13/ftcharles113 .xml
See a video of the interview with the Prince online
http://www.telegraph.co.uk/telegraph/telegraphtv/tvplayer/?ID=News&bcpid=1452232298&bclid=1452257940&bctid=1726720198
TODAY COVERAGE: BBC Radio 4's Today programme 13 August
7.09am: The Prince of Wales has said GM crops could cause the world's worst environmental disaster. The Daily Telegraph's editor-at-large reveals the depth of Prince Charles's fears.
8.32am: Prince Charles's views on GM have created a stir. Patrick Holden, the director of the Soil Association and Lord Haskins, the Blairite pro-GM former chairman of Northern Foods, discuss the Prince's views.
BBC Radio 4, listen again (13 Aug)
http://news.bbc.co.uk/today/hi/today/newsid_7557000/7557753.stm
2.Prince of Wales in tune with public and independent scientific opinion on GM
Soil Association
PRESS RELEASE, 08/13/2008
The Prince of Wales's views not only reflect the views of 85% of the British public who opposed the commercial growing of GM crops in the UK, but also of an increasing body of independent scientists who question GM company PR claims that GM crops are the answer to world hunger. [1]
Robin Maynard, Soil Association Campaigns Director said: "As so often, the Prince of Wales's views are in tune with public opinion. In questioning the value of GM crops for poor, small-scale farmers in developing countries, his comments also chime with the recent international agricultural assessment by 400 scientists from around the world, which questioned whether GM crops offered any solutions to global poverty, hunger or climate change.
"Even the gung-ho GM US Department of Agriculture accepts that 'currently available GM crops do not increase the yield potential', only PR firms working for the GM industry claim otherwise.[2]
"Agribiz owned and patented GM seeds that only grow 'true' for one season and which need large inputs of chemical fertilisers and pesticides will not deliver greater global food security. They were not designed to meet the needs of poor farmers in developing countries, but to maintain the profits of the vast multinational companies who make both the GM seeds and the chemicals used on them. Prince Charles' previous pithy summary of GM crops, 'as new uses for old herbicides' was spot-on."
[Ends]
Clio Turton, senior press officer, 0117 914 2448 / This email address is being protected from spambots. You need JavaScript enabled to view it.
[1] In April of this year, the report of the International Assessment of Agricultural Science and Technology for Development (IAASTD) chaired by Defra's Chief Scientist, Professor Bob Watson, concluded that GM crop yields were 'highly variable' and the application of GM outside the lab 'contentious'. In contrast it recommended 'agroecological systems', of which organic farming is a practical, proven example.
IAASTD report, published 15 April 2008, London
[2] US Department of Agriculture acknowledges that:
"Currently available GM crops do not increase the yield potential of a hybrid variety. In fact, yield may even decrease if the varieties used to carry the herbicide tolerant or insect-resistant genes are not the highest yielding cultivars."
Fernandez-Cornejo, J. and Caswell, 2006
2.PRINCE CHARLES'S GM CRITICISM WELCOMED BY FRIENDS OF THE EARTH
For immediate release, 13 August 2008
Commenting on Prince Charles's concerns over the impacts of GM crops on the environment and farmers, expressed today, Friends of the Earth's Campaign Director Mike Childs said:
"Prince Charles has hit the nail on the head about the damaging false solution that GM crops present.
"GM crops will not solve the food crisis - and forging ahead with an industrialised farming system will continue to fail people and the environment around the world.
"Global political effort must be channelled into securing long lasting, green farming solutions that put people, not corporations, at their heart - and the UK Government must look at the evidence before falling for GM industry hype."
Earlier this year a UN International Assessment of Agriculture (IAASTD), carried out by 400 scientists and endorsed by 60 countries found no conclusive evidence that GM crops increase crop yields. It concluded that although the green revolution had increased crop yields, this had come at an unacceptable environmental and social cost, degrading soils, contributing to climate change and failing the world's poor. The biotechnology industry pulled out of the process when it became clear that the report would not endorse GM crops. The report stated that "business as usual is not an option" and that science and technology must be combined with traditional knowledge, working with communities on localised farming solutions.
1. Friends of the Earth's briefing on the food crisis:
http://www.foe.co.uk/resource/press_releases/world_leaders_warned_off_p_02062008 .html
2. Prince Charles's comments: http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2008/08/12/eacharles112.x ml
3. UN International Assessment of Agriculture (IAASTD), http://www.agassessment.org/
3.GM Freeze Welcome Prince Charles's Comments on GM Crops
PRESS RELEASE 13th August 2008
Immediate Release
GM Freeze has welcomed Prince Charles's comments on the risks of widespread introduction of GM crops to the environment.
The group supports his view that large scale production of GM crops will not be sustainable and will lead to the destruction of rural communities.
Commenting Pete Riley of GM Freeze said
"Prince Charles's comments are a welcome contribution to the ongoing debate about GM crops around the world. Some of the strongest opposition comes from small and family farmers in South America and India who are already experiencing the social, economic and cultural impacts of GM crop monocultures driven forward by global corporations.
"The Prince has also focused on the environmental impacts of GM crops especially on the soil. Very little research is available on such impacts in South America where there is enormous pressure on farmers to adopt GM crops. In this country the government decided to ban four GM crops because of their impact on wildlife. Until very recently, research has ignored the impacts on soil and consequently our knowledge of how GM crops will impact on life below ground is very limited.
"The debate about GM crops is not only about science and the Prince's comments will enable the wider social, economic, cultural and political issues to get the attention they deserve". | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,123 |
\section{Introduction}\label{sec:intro}
The present work studies flows over dense canopies of filaments of small size. Canopy flows are mainly studied in the context of natural vegetation canopies, but they also encompass engineering flows where the canopy parameters may be very different from those of natural canopies. Many of the key findings from natural canopy studies have been summarised in the reviews by \citet{Finnigan2000}, \citet{Belcher2012} and \citet{Nepf2012}. In engineering applications, filament canopies can, for instance, be used to enhance heat transfer \citep{Fazu1989,Bejan1993} and for energy harvesting \citep{McGarry2011,Elahi2018}. Depending on the geometry and spacing of their elements, canopies can be classified as sparse, dense or transitional \citep{Nepf2012}. Dense canopies typically have small element spacings compared to the lengthscales in the overlying flow, and thus prevent turbulent eddies from penetrating efficiently within the canopy. Sparse canopies, on the other hand, have large element spacings and consequently, turbulent eddies are essentially able to penetrate the full height of the canopy \citep{Poggi2004,Nepf2012,Sharma2018,AS2019}. Transitional, or intermediate, canopies would lie between these two regimes. {In the present study, we assess how the flow within and above dense canopies is affected by canopy parameters, such as the element height and spacing. The canopies considered have spacings $s^+ \approx \mathcal{O}(10)$, which should be small enough to limit the penetration of the overlying turbulence within them. The frontal area density $\lambda_f$ is also a commonly used measure to categorise canopies \citep{Finnigan2000,Poggi2004,Huang2009,Nepf2012}. Canopies with $\lambda \gg 0.1$ are classified as dense, with $\lambda \approx 0.1$ as transitional and with $\lambda \ll 0.1$ as sparse. However, in addition to $\lambda_f$, the lengthscales of the overlying turbulence should also be considered when determining the canopy regime. A given canopy geometry with a fixed $\lambda_f$ may have element spacings much smaller than any overlying turbulent eddy at a particular Reynolds number, thereby not allowing turbulence to penetrate within the canopy. As the Reynolds number is increased, however, the size of these eddies will eventually become comparable to the element spacing, allowing turbulence to penetrate efficiently within the canopy. To assess this effect, we also study canopies with self-similar geometries, which have a fixed $\lambda_f$, but different sizes in friction units.}
{We also place attention on the effect of canopy parameters on the Kelvin--Helmholtz-like, mixing-layer instability characteristic of dense canopy flows \citep{Raupach1996,Finnigan2000,Nepf2012}. This instability originates} from the inflection point in the mean velocity profile at the canopy-tip plane \citep{Raupach1996}. Kelvin--Helmholtz instabilities manifest as spanwise coherent rollers whose streamwise scale is determined by the shear-layer thickness \citep{Michalke1972,Brown1974}. \citet{Ghisalberti2004} noted that, while in free-shear flows the shear-layer thickness, and consequently the instability wavelength, continues to grow downstream, in fully developed canopy flows this thickness is constant and is set by the net canopy drag. Therefore, a fixed instability wavelength is generally associated with dense canopy flows. Several studies have shown that some aspects of this instability can be captured using a mean-flow linear stability analysis \citep{Raupach1996,White2007,Singh2016,Zampogna2016,Luminari2016}. Some studies have also suggested that at the high Reynolds numbers of natural canopy flows these instabilities can be distorted by the ambient turbulence fluctuations and lose their spanwise-coherent nature \citep{Finnigan2009,Bailey2016}. The importance of this instability decreases as the element spacing is increased, and sparse canopies do not exhibit a notable signature \citep{Poggi2004,Pietri2009,Huang2009,AS2019}.
{Based on the observations of previous studies, we would expect that the effect of increasing the canopy height for a fixed element spacing on the instability and the surrounding flow would eventually saturate. \citet{Ghisalberti2009} and \citet{Nepf2012} proposed that the effective canopy height perceived by the overlying flow would be a function of the canopy shear-layer thickness as it determined the extent to which the Kelvin--Helmholtz-like instabilities penetrated within the canopy. In flows over arrays of cuboidal posts, \citet{Sadique2017} found that the mean-velocity profiles over them became independent of the element heights at large element aspect ratios.} They concluded that the overlying flow only interacted with the region near the element tips, and that the height below this `active' region was dormant, and did not have a significant effect on the overlying flow. For their geometries, \citet{Sadique2017} observed the height of this active region to be related to the element width. A similar observation was also made by \citet{Macdonald2018}, who performed direct numerical simulations (DNSs) of flows over spanwise-aligned bars. They found that the gap between the bars was the relevant lengthscale for the overlying flow, and that increasing the height of the bars beyond a certain height-to-gap ratio did not affect the overlying flow, or cause an increase in the drag they produced.
{In the present work, we conduct a systematic range of DNSs changing the canopy height and spacing separately in order to study their individual effects on the surrounding turbulence and on the Kelvin--Helmholtz-like instability. We also consider canopy geometries with constant $\lambda_f$ for which the height and spacing are changed simultaneously in a fixed proportion.} The canopies consist of rigid, prismatic filaments with small element spacings and large height-to-spacing ratios. {The element spacings considered, $s^+ \approx 3$--$50$, are much smaller than those typical of most natural canopy flows and would, for instance, be representative of flows over engineered canopies such as those mentioned previously in this section. We also assess how models based on linear stability analysis capture some of the effects of the canopy parameters on the Kelvin--Helmholtz-like instability.}
The paper is organised as follows. The numerical methods used for the simulations and the canopy parameters are discussed in \S\ref{sec:methodology}. The results from the DNSs, detailing the effect of the canopy parameters on the overlying turbulence and the Kelvin--Helmholtz-like instabilities are discussed in \S\ref{sec:turb_fluct}. The results from linear stability analysis and a model to capture the instabilities are presented in \S\ref{sec:stability_analysis}. The conclusions are summarised in \S\ref{sec:conclusions}.
\section{Methodology}\label{sec:methodology}
We conduct direct numerical simulations of symmetric channels with rigid canopy elements on both walls. The streamwise, wall-normal and spanwise coordinates are $x$, $y$ and $z$, with the associated velocities $u$, $v$ and $w$, {and $p$ is the kinematic pressure}. The wall-normal origin, $y = 0$, is defined at the tip plane of the canopies protruding from the bottom wall. The channel height, $2\delta$, is defined as the distance between the tip planes of the canopies on the top and bottom walls. The canopy elements, therefore, extend below $y = 0$ and above $y = 2\delta$ and have a height $h$. A schematic representation of the channel is portrayed in figure~\ref{fig:channel_schem}. The size of the domain is a standard $2\pi\delta$ in the streamwise direction and $\pi\delta$ in the spanwise direction. {We use the channel half-height as the length scale in outer units, which implies that $\delta = 1$ in outer scaling}. The domain-to-canopy height ratio for most cases considered here is $(\delta+h)/h \approx 3$. We will show in \S\ref{sec:turb_fluct} that the height of the roughness sublayer scales with the canopy spacing rather than their height, as in the configurations of \citet{Sadique2017} and \citet{Macdonald2018}, and that outer-layer similarity is recovered well below the channel half-height. The channel height to element spacing ratio for most canopies considered is $\delta/s \gtrsim 10$, and for the canopy with the largest element spacing is $\delta/s \approx 4$. {The flow is incompressible and the density is always scaled with the fluid density, implying that $\rho = 1$.} The simulations are run at a constant flow rate, with the viscosity, $\nu$, adjusted to obtain a friction Reynolds number $Re_\tau = u_\tau \delta/ \nu \approx 185$ {for most of the cases}, where $u_\tau$ is the friction velocity calculated at the canopy tips. In order to ascertain the effects of the Reynolds number on the flow, a simulation at $\Rey_\tau \approx 405$ was also conducted. The simulation parameters are given in table~\ref{tab:DNS_param} for reference. {Scaling with $u_\tau$ and $\nu$ is referred to as in friction or wall units, and scaling with the channel bulk velocity, $U_b$, and $\delta$ is referred to as in outer units}.
\begin{figure}
\centering
\vspace{0mm} \includegraphics[scale=0.38,trim={0mm 0mm 0mm 0mm},clip]{fig1-eps-converted-to.pdf}%
\mylab{-7.2cm}{0.15cm}{$ -h$}%
\mylab{-6.95cm}{1cm}{$ 0$}%
\mylab{-6.95cm}{2.8cm}{$\delta$}%
\mylab{-5.7cm}{0.9cm}{$ x$}%
\mylab{-6.3cm}{1.5cm}{$ y$}%
\mylab{-7.1cm}{4.6cm}{$2\delta$}%
\mylab{-7.65cm}{5.4cm}{$2\delta+h$}%
\caption{Schematic representation of the domain considered in the present study.}%
\label{fig:channel_schem}
\end{figure}
\begin{table}
\begin{center}
\begin{tabular}{clcccccccc}
&Case &$N_x \times N_z$ &$n_x \times n_z$ &{$u_\tau$} &$\Rey_\tau$ &{$\lambda_f$} & $h^+$ & $s^+$ &{$w^+$} \\
\hline
\multirow{1}{*}{Smooth} &SC &-- &-- &{0.064} &186.3 &-- &-- & -- &-- \\
\hline
&S10 &108$\times$54 &12$\times$12 & {0.071} &176.7 &{4.6} &95.5 &10.3 & {5.2} \\
\multirow{1}{*}{Fixed} &S16(H96) &72$\times$36 &24$\times$24 &{0.088} &187.7 &{3.1} &101.8 &16.4 &{8.2} \\
\multirow{1}{*}{height} &S24 &48$\times$24 &24$\times$24 & {0.102} &187.4 &{2.0} & 101.2 &24.5 &{12.3} \\
\multirow{1}{*}{($h^+ \approx 100$)} &S32 &36$\times$18 &24$\times$24 &{0.112} &186.4 &{1.5} &100.7 &32.5 & {16.3} \\
&S48 &24$\times$12 &24$\times$24 & {0.124} &180.1 &{1.0} &97.0 &47.2 & {23.6} \\
\hline
&H16 &72$\times$36 &24$\times$24 & {0.071} &184.7 &{0.5} &17.2 & 16.1 &{8.1} \\
\multirow{1}{*}{Fixed} &H32 &72$\times$36 &24$\times$24 &{0.080} &188.8 &{1.0} &34.6 &16.5 &{8.3} \\
\multirow{1}{*}{spacing} &H64 &72$\times$36 &24$\times$24 & {0.086} &186.2 &{2.0} &68.1 &16.2 &{8.1} \\
\multirow{1}{*}{($s^+ \approx 16$)} &H96(S16) &72$\times$36 &24$\times$24 &{0.088} &185.7 &{3.1} &101.8 &16.4 & {8.2} \\
&H128 &72$\times$36 &24$\times$24 & {0.086} &184.8 &{4.1} &133.2 &16.4 & {8.2} \\
\hline
&G10 &432$\times$216 &9$\times$9 & {0.064} &175.9 & &10.1 &2.6 & {0.6} \\
\multirow{1}{*}{Self-similar} &G20 &216$\times$108 &9$\times$9 & {0.072} &190.7 & &22.2 &5.6 &{1.2} \\
\multirow{1}{*}{geometry} &G40 &108$\times$54 &18$\times$18 & {0.106} &188.2 &{0.85} &43.4 &11.0 & {2.5} \\
\multirow{1}{*}{($h/s \approx 4$)} &G60 &72$\times$36 &18$\times$18 & {0.127} &183.3 & &64.7 &16.0 & {3.6}\\
&G100 &48$\times$24 &18$\times$18 & {0.147} &185.7 & &97.9 &24.3 &{5.4} \\
\hline
\multirow{2}{*}{Different $\Rey_\tau$} &H32$_{180}$ &72$\times$36 &12$\times$12 & {0.075} &184.6 &\multirow{2}{*}{{1.0}} &33.9 &16.1 &{8.1} \\
&H32$_{400}$ &162$\times$81 &12$\times$12 & {0.066} &399.9 & &32.0 &15.5 &{7.8} \\
\hline
\end{tabular}
\caption{\label{tab:DNS_param} {Simulation parameters. $N_x$ and $N_z$ are the number of rows of canopy elements in the streamwise and spanwise directions, respectively. The number of points used to resolve each period of the canopy in the streamwise and spanwise directions are $n_x$ and $n_z$, respectively. $u_\tau$ is the friction velocity based on the shear at the canopy tips scaled with the channel bulk velocity. $\Rey_\tau$ is the friction Reynolds number based on $u_\tau$ and $\delta$ . The canopy frontal area density, height, spacing and width are $\lambda_f$, $h$, $s$ and $w$, respectively. }}
\end{center}
\end{table}
The numerical method used to solve the three-dimensional Navier--Stokes equations is adapted from \citet{Fairhall2018}. A Fourier spectral discretisation is used in the streamwise and spanwise directions. The wall-normal direction is discretised using a second-order centred difference scheme on a staggered grid. The grid in the wall-normal direction is stretched to give a resolution $\Delta y^+_{min} \approx 0.33$ at the canopy-tip plane, stretching to $\Delta y^+_{max} \approx 3.3$ at the channel centre. The grid within the canopies preserves the resolution of $\Delta y^+_{min} \approx 0.33$ near the canopy-tip plane, and for the tallest canopies considered stretches to $\Delta y^+_{max} \approx 4$ at the base of the canopy, where the flow is quiescent. {The wall-normal grid distribution for a representative canopy simulation is provided in figure~\ref{fig:grid} in appendix~\ref{appA} for reference.} To resolve the element-induced flow while avoiding excessive computational costs, the domain is divided into three blocks in the wall-parallel directions \citep{Garcia-Mayoral2011,Fairhall2018,Abderrahaman2019}. In the central block, the resolutions in the streamwise and spanwise directions are $\Delta x^+ \approx 6$ and $\Delta z^+ \approx 3$, respectively, sufficient to resolve the turbulent eddies. The blocks including the canopy elements and the roughness sublayer have a finer resolution than the central block. In the fine blocks, the limiting resolution is not the one required to resolve the turbulent scales, but that required to resolve the obstacles or the element-induced flow. The resolutions in these blocks are given in table~\ref{tab:DNS_param}. The height of the fine blocks is chosen such that the element-induced flow decays to zero well within the fine-block region, and this is verified a posteriori. The time advancement is carried out using a three-step Runge--Kutta method with a fractional step, pressure correction method to enforce continuity \citep{Le1991}
\begin{eqnarray}
\label{eq:disc_NS}\left[\mathrm{I} - \Delta t \frac{\beta_k}{\Rey} \mathrm{L}\right] \mathbf{u}^n_k & = & \mathbf{u}^n_{k-1} + \Delta t \left[ \frac{\alpha_{k}}{\Rey}\mathrm{L} \mathbf{u}^n_{k-1} - \gamma_{k}\mathrm{N}(\mathbf{u}^n_{k-1}) - \right.\nonumber\\
&&\left. \zeta_k \mathrm{N}(\mathbf{u}^n_{k-2}) - (\alpha_k + \beta_k)\mathrm{G}(p^n_k) \vphantom{ \frac{\alpha_{k}}{\Rey}}\right], k\in[1,3],\\
\mathrm{DG}(\phi^n_k) & = & \frac{1}{(\alpha_k + \beta_k) \Delta t} \mathrm{D}(\mathbf{u}^n_k), \\
\mathbf{u}^n_{k+1} & = & \mathbf{u}^n_k - (\alpha_k + \beta_k)\Delta t G(\phi^n_k),\\
p^n_{k+1} & = & p^n_k + \phi^n_k,
\end{eqnarray}
where $\mathrm{I}$ is the identity matrix and L, D and G are the Laplacian, divergence and gradient operators respectively. N is the advective term which is dealiased using the $2/3$-rule \citep{Canuto2012}. The Runge-Kutta coefficients, $\alpha_k$, $\beta_k$, $\gamma_k$ and $\zeta_k$, for each substep, $k$, are taken from from \citet{Le1991}. The time step is $\Delta t$.
The canopy elements are represented using an immersed-boundary method adapted from \citet{Garcia-Mayoral2011}. {Further details about the immersed boundary method and validation studies are provided in appendix~\ref{appA}.} The parameters of the different simulations conducted are summarised in table~\ref{tab:DNS_param}. The simulation denoted by `SC' is of a turbulent channel flow with smooth walls. The canopy-flow simulations are divided into three groups. The canopy elements studied in each group are prismatic, with a square top-view cross section, and their arrangement is illustrated in figure~\ref{fig:canopy_schem}. The first group, denoted by the prefix `S', consists of canopies with a fixed height, $h^+ \approx 96$, and element spacings ranging from $s^+ \approx 10$ to $48$. The second group, marked by the prefix `H', consists of canopies with a fixed element spacing, $s^+ \approx 16$, and element heights ranging from $h^+ \approx 16$ to $128$. The element width-to-spacing ratio for the canopies of S and H is $w/s = 1/2$. The final group, denoted by the prefix `G', consists of self-similar elements with a fixed height-to-spacing ratio $h/s \approx 4$, and $w/s = 2/9$. The heights for the canopies of G range from $h^+ \approx 10$ to $100$, with the element spacings varying in proportion to their height. {These canopies have a constant $\lambda_f = 0.85$ and are used to study the effect of changing the canopy size for a fixed geometry}. Two additional simulations, H32$_{180}$ and H32$_{400}$, are conducted to check the dependence of the results on the friction Reynolds number. The canopy geometries for both these simulations have $s^+ \approx 16$, $h^+ \approx 32$ and $w/s = 1/2$, with friction Reynolds numbers $\Rey_\tau \approx 180$ and $400$. We also conducted several simulations to assess whether the wall-parallel resolutions used in the simulations are sufficient to resolve the element-induced flow. The simulation S24 was run at resolutions of $12$, $24$ and $36$ points per element spacing, and G100 at $9$, $18$ and $27$ points per element spacing. Different resolution sets are used for the geometries of S and G as they have different element width-to-spacing ratios. The rms velocity fluctuations obtained from these simulations are portrayed in appendix~\ref{appA}. The simulation results are grid independent at a resolution of $24$ points per element spacing for the geometry of case S24, and $18$ points per spacing for that of case G100. The simulations with $9$ and $12$ points per spacing tend to under-predict the fluctuations within the canopies, with the maximum deviation observed in the wall-normal fluctuations of $20\%$ within the canopy. This discrepancy reduces to $4\%$ outside the canopy. These resolutions are only used for the densest canopy cases, where the fluctuations within the canopy are already very small, and therefore, higher resolution simulations would not change the trends observed. The higher Reynolds number simulation, case H32$_{400}$, is also simulated using $12$ points per spacing. For this simulation, using a higher resolution would be computationally restrictive. Note that the same resolutions are used for cases H32$_{180}$ and H32$_{400}$ to avoid grid related discrepancies in the comparison of their results.
\begin{figure}
\centering
\vspace{5mm} \includegraphics[scale=0.59,trim={0mm 0mm 0mm 0mm},clip]{fig2-eps-converted-to.pdf}%
\mylab{-0.4cm}{1.95cm}{$h$}%
\mylab{-1.12cm}{0.45cm}{$w$}%
\mylab{-6.6cm}{-0.15cm}{$s$}%
\mylab{-7.9cm}{0.15cm}{$s$}%
%
\mylab{-9cm}{0.1cm}{$x$}%
\mylab{-9.8cm}{0.9cm}{$y$}%
\mylab{-10.2cm}{0.3cm}{$z$}%
\caption{Schematic of the canopy layouts considered in the present study. The canopies are characterised by their element height, $h$, the element width, $w$, and the element spacing, $s$. Note that the element have a square top-view cross section.}%
\label{fig:canopy_schem}
\end{figure}
\subsection{Reynolds number effect}\label{sec:Rey_effects}
\begin{figure}
\centering
\subfloat{%
\hspace{-2.3mm}\includegraphics[scale=1]{fig3a-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{3mm}\includegraphics[scale=1]{fig3b-eps-converted-to.pdf}
}%
\vspace{0mm}\subfloat{%
\hspace{0mm}\includegraphics[scale=1]{fig3c-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{0mm}\includegraphics[scale=1]{fig3d-eps-converted-to.pdf}
}%
\caption{Rms velocity fluctuations and Reynolds shear stresses for cases H32$_{180}$ in red and H32$_{400}$ in blue. The black lines represent the corresponding smooth-wall cases. The data for the smooth-wall simulations at $\Rey_\tau \approx 400$ is taken from \citet{Moser1999}.}
\label{fig:stats_Re}
\end{figure}
To analyse the influence of the Reynolds number in our subsequent DNSs, we compare the results of cases H32$_{180}$ and H32$_{400}$, which have the same canopy height and spacings in friction units, but different friction Reynolds numbers. The velocity fluctuations and the Reynolds shear stresses within the canopy, and above it up to a height of $y^+\approx 10$, of these simulations essentially collapse, as shown in figure~\ref{fig:stats_Re}. This suggests that the flow in the region near the canopy-tip plane scales in friction units, similar to the near-wall region in smooth-wall flows \citep{Moser1999}. Scaling in friction units over conventional rough surfaces has also been noted by \citet{Chan2015}. Beyond $y^+ \gtrsim 10$, we observe that the magnitude of the peaks in the fluctuations and the Reynolds shear stresses are larger for case H32$_{400}$ compared to case H32$_{180}$. The increase in magnitude of the near-wall peaks in the velocity fluctuations at friction Reynolds numbers larger than $Re_\tau \approx 180$ is consistent with that observed in smooth-wall flows \citep{Moser1999,Sillero2013}, also included in figure~\ref{fig:stats_Re} for reference. Further away from the canopy tips, at $y^+ > 50$, the rms velocity fluctuations from the canopy simulations coincide with those from the smooth-wall simulations at their corresponding Reynolds numbers, which indicates the recovery of outer-layer similarity.
\begin{figure}
\centering
\vspace{6mm} \includegraphics[scale=1.0,trim={8mm 0mm 0mm 0mm},clip]{fig4-eps-converted-to.pdf}%
\mylab{-14.2cm}{3.5cm}{(\textit{a})}%
\mylab{-11.0cm}{3.5cm}{(\textit{b})}%
\mylab{-7.8cm}{3.5cm}{(\textit{c})}%
\mylab{-4.7cm}{3.5cm}{(\textit{d})}%
\mylab{-13.3cm}{4.0cm}{$k_x k_z E_{uu}$}%
\mylab{-10.2cm}{4.0cm}{$k_x k_z E_{vv}$}%
\mylab{-7.0cm}{4.0cm}{$k_x k_z E_{ww}$
\mylab{-3.8cm}{4.0cm}{$k_x k_z E_{uv}$
\caption{Pre-multiplied spectral energy densities for cases H32$_{180}$ (line contours) and H32$_{400}$ (shaded contours), normalised by the respective rms values, at a height $y^+ \approx 15$. Contours from ($a$--$d$) are in increments of $0.075$, $0.06$, $0.07$ and $0.1$, respectively.}%
\label{fig:spectra_h32_Re_var}
\end{figure}
In addition to the rms fluctuations being similar for these simulations, the distribution of energy in different scales is also similar. This is illustrated by the pre-multiplied spectral energy densities at $y^+ \approx 15$, portrayed in figure~\ref{fig:spectra_h32_Re_var}. This height roughly corresponds to the location where the magnitude of the fluctuations peaks in smooth-wall flows \citep{Jimenez1999}. The results of H32$_{180}$ and H32$_{400}$ suggest that the effect of the canopy scales in friction units, and therefore the results presented in the following sections for flows at $\Rey_\tau \approx 180$ should also be relevant for higher Reynolds number flows.
\begin{figure}
\centering
\vspace{2mm}\subfloat{%
\includegraphics[scale=1,trim={20mm 39mm 18mm 22mm},clip]{fig5.pdf}
}%
\caption{Instantaneous realisations of the wall normal velocity at $y \approx 0.1 s$, normalised by $u_\tau$. From top to bottom, the left column represents cases H16 to H128; and the right column, cases G10 to G100. The insets in ($b$) and ($d$) provide a magnified view of the region in the bottom left corner of these panels, marked with a black rectangle. The clearest and darkest colours represent intensity $\pm 0.4$ in the left column and, from top to bottom, $\pm(0.2, 0.4, 0.8, 0.8, 1.0)$ in the right column.}%
\label{fig:v_snap_G}
\end{figure}
\begin{figure}
\centering
\hspace{0.9mm}\subfloat{%
\includegraphics[scale=1]{fig6a-eps-converted-to.pdf}
}%
\hspace{2.7mm}\subfloat{%
\includegraphics[scale=1]{fig6b-eps-converted-to.pdf}
}%
\hspace{1.2mm} \subfloat{%
\includegraphics[scale=1]{fig6c-eps-converted-to.pdf}
}%
\vspace{0mm}\subfloat{%
\includegraphics[scale=1]{fig6d-eps-converted-to.pdf}
}%
\hspace{0mm} \subfloat{%
\includegraphics[scale=1]{fig6e-eps-converted-to.pdf}
}%
\hspace{0.5mm}\subfloat{%
\includegraphics[scale=1]{fig6f-eps-converted-to.pdf}
}%
\vspace{3mm} \hspace{0.4mm}\subfloat{%
\includegraphics[scale=1]{fig6g-eps-converted-to.pdf}
}%
\hspace{-0.3mm} \subfloat{%
\includegraphics[scale=1]{fig6h-eps-converted-to.pdf}
}%
\hspace{-0.9mm} \subfloat{%
\includegraphics[scale=1]{fig6i-eps-converted-to.pdf}
}%
\caption{Root-mean-square velocity fluctuations of the element-induced flow. The lines from red to blue, {indicated by the direction of the arrows}, represent ($a$,$d$,$g$) cases S10 to S48; ($b$,$e$,$h$) cases H16 to H128; and ($c$,$f$,$i$) cases G10 to G100.}
\label{fig:stats_cond}
\end{figure}
\section{Effect of canopy parameters on the surrounding turbulence}\label{sec:turb_fluct}
{In this section, we discuss the results obtained from the DNSs, aiming to characterise the effect of the canopy parameters on both the Kelvin--Helmholtz-like instability and the fluctuating flow within and above the canopies.}
\subsection{{Height of the roughness sublayer}}\label{subsec:RSL}
{Before discussing the effect of the canopy on the overlying flow, we first define the extent of the region affected by the canopy, that is, the height of the roughness sublayer.} Over conventional rough surfaces, with heights comparable to or smaller than their spacings, the height of the roughness sublayer is generally observed to be a function of the roughness height \citep{Raupach1991,Flack2007,Abderrahaman2019}. \citet{Jimenez2004} reviewed the effect of various roughness geometries on turbulent flows and noted that, in flows over closely packed spanwise aligned grooves, the flow within each groove would be isolated from the overlying flow due to the `sheltering' effect of the preceding obstacle. The overlying flow in this case would not interact with the full height of the groove. This sheltering effect was also noted by \citet{Sadique2017} for high-aspect-ratio prismatic roughness and by \citet{Macdonald2018} for spanwise aligned grooves with large spacings, and has been used to model cuboidal roughness by \citet{Yang2016}. As the element spacings of the canopies studied here are small, this sheltering effect should result in the overlying flow only interacting with the region near the canopy-tip plane. In order to determine the height of this region, we examine the element-coherent flow induced by the canopy elements. The footprint of the element-induced flow can be observed in the instantaneous realisations of the velocity above the canopy-tip plane, portrayed for the canopies of families H and G in figure~\ref{fig:v_snap_G}. We isolate the element-induced flow using the standard triple decomposition of \citet{Reynolds1972}
\begin{eqnarray}
\boldsymbol{u} = \boldsymbol{U} + \boldsymbol{u'},\\
\boldsymbol{u'}= \boldsymbol{\widetilde{u}} + \boldsymbol{u''},
\end{eqnarray}
where $\boldsymbol{u}$ is the full velocity, $\boldsymbol{U}$ is the mean velocity obtained by averaging the flow in time and space, and $\boldsymbol{u'}$ is the full space- and time-fluctuating signal. The latter is decomposed into the element-induced, dispersive velocity, $\boldsymbol{\widetilde{u}}$, which is obtained by {ensemble-averaging} the flow in time alone, and the {element-}incoherent fluctuating velocity $\boldsymbol{u''}$, {which includes the contributions from the background-turbulence and the Kelvin--Helmholtz-like instability. The rms fluctuations of $\boldsymbol{\widetilde{u}}$, therefore, result from fluctuations in space alone.}
We observe that the element-induced fluctuations, for all the canopies studied here, decay exponentially above the canopy-tip plane, and become negligible at a height of one element spacing above regardless of the canopy depth, as shown in figure~\ref{fig:stats_cond}. {This suggests that the height of influence of the element-induced flow is determined by the spacing between the elements rather than their height.}
Even though the element-induced fluctuations only extend to one element spacing above the canopy-tip plane, their influence on the background-turbulence extends to a height of approximately $2$--$3$ element spacings, {as can be observed in figure~\ref{fig:stats_all}}. \citet{Abderrahaman2019} observed a similar effect over conventional cubical roughness, where the element-induced fluctuations only extended to $y \approx h$, but the effect of the roughness on the overlying flow extended to $y \approx 3h$ above them. At heights of $y/s > 2$--$3$ above the canopy-tip plane, the full rms velocity fluctuations collapse with those of smooth-wall turbulence, as shown in figure~\ref{fig:stats_all}, which is indicative of the recovery of outer-layer similarity. This is verified by a comparison of the pre-multiplied spectral energy densities of the canopy and smooth-wall cases in figure~\ref{fig:spectra_h90_OLS}, which shows that the energy densities of the canopies of family S collapse with those of the smooth-wall case for $y^+ \gtrsim 90$. This corresponds to a height of about $2s$ for case S48, the canopy with the largest spacing. Although not shown, the pre-multiplied spectral energy densities of the canopies of families H and G collapse with the smooth-wall spectra for $y/s \gtrsim 3$ as well. {Previous canopy studies have proposed that the influence of the canopy elements on the flow above them is set by the wall-normal extent of the Kelvin--Helmholtz-like instability, which is determined by the canopy shear-layer thickness \citep{Ghisalberti2009,GhisalbertiNepf2009,Nepf2012}. It will be demonstrated in \S\ref{sec:stability_analysis} that the shear-layer thickness of the present canopies also depends on the element spacing.}
\begin{figure}
\centering
\subfloat{%
\hspace{-2mm}\includegraphics[scale=1, trim = 0cm 0cm 0cm 0cm,clip]{fig7a-eps-converted-to.pdf}
}%
\hspace{3.5mm}\subfloat{%
\includegraphics[scale=1, trim = 0cm 0cm 0cm -0.07cm,clip]{fig7b-eps-converted-to.pdf}
}%
\hspace{2.2mm} \subfloat{%
\includegraphics[scale=1, trim = 0cm 0cm 0cm -0.07cm,clip]{fig7c-eps-converted-to.pdf}
}%
\vspace{-1.5mm}\subfloat{%
\hspace{-2mm}\includegraphics[scale=1, trim = 0cm 0cm 0cm 0cm,clip]{fig7d-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{3.5mm}\includegraphics[scale=1, trim = 0cm 0cm 0cm -0.07cm,clip]{fig7e-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{3.3mm}\includegraphics[scale=1, trim = 0cm 0cm 0cm -0.07cm,clip]{fig7f-eps-converted-to.pdf}
}%
\vspace{-1.5mm}\subfloat{%
\includegraphics[scale=1, trim = 0cm 0cm 0cm 0cm,clip]{fig7g-eps-converted-to.pdf}
}%
\hspace{0mm} \subfloat{%
\includegraphics[scale=1, trim = 0cm 0cm 0cm -0.07cm,clip]{fig7h-eps-converted-to.pdf}
}%
\hspace{0mm} \subfloat{%
\includegraphics[scale=1, trim = 0cm 0cm 0cm -0.07cm,clip]{fig7i-eps-converted-to.pdf}
}%
\caption{Rms velocity fluctuations within and above the canopies. The lines from red to blue, {indicated by the direction of the arrows}, represent ($a$,$d$,$g$) cases S10 to S48; ($b$,$e$,$h$) cases H16 to H128; and ($c$,$f$,$i$) cases G10 to G100. The black lines represent the smooth-wall case, SC.}
\label{fig:stats_all}
\end{figure}
\begin{figure}
\centering
\vspace*{0.3cm}\includegraphics[scale=1.0,trim={7mm 0mm 0mm 0mm},clip]{fig8-eps-converted-to.pdf}%
\mylab{-14.2cm}{3.5cm}{(\textit{a})}%
\mylab{-11.0cm}{3.5cm}{(\textit{b})}%
\mylab{-7.8cm}{3.5cm}{(\textit{c})}%
\mylab{-4.7cm}{3.5cm}{(\textit{d})}%
\mylab{-13.3cm}{4.0cm}{$k_x k_z E_{uu}$}%
\mylab{-10.2cm}{4.0cm}{$k_x k_z E_{vv}$}%
\mylab{-7.0cm}{4.0cm}{$k_x k_z E_{ww}$
\mylab{-3.8cm}{4.0cm}{$k_x k_z E_{uv}$
\caption{Pre-multiplied spectral energy densities at $y^+ \approx 90$, with line contours from red to blue representing cases S10 to S48, normalised by their respective $u_\tau$. The filled contours represent the smooth-wall case, SC. The contours in ($a$--$d$) are in increments of $0.11$, $0.04$, $0.06$ and $0.04$, respectively.}%
\label{fig:spectra_h90_OLS}
\end{figure}
\begin{figure}
\centering
\subfloat{%
\hspace{-1.2mm}\includegraphics[scale=1, trim=0mm 0mm 0mm 0mm,clip]{fig9a-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{4.5mm}\includegraphics[scale=1, trim=0mm 0mm 0mm -1mm,clip]{fig9b-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{3.5mm} \includegraphics[scale=1, trim=0mm 0mm 0mm -1mm,clip]{fig9c-eps-converted-to.pdf}
}%
\vspace{0mm}\subfloat{%
\includegraphics[scale=1, trim=0mm 0mm 0mm 0mm,clip]{fig9d-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{0mm}\includegraphics[scale=1, trim=0mm 0mm 0mm -0.7mm,clip]{fig9e-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{0mm}\includegraphics[scale=1, trim=0mm 0mm 0mm -0.7mm,clip]{fig9f-eps-converted-to.pdf}
}%
\caption{Profiles of the ($a$--$c$) streamwise mean velocity and ($d$--$f$) Reynolds shear stresses. The lines from red to blue, {indicated by the direction of the arrows}, represent ($a$,$d$) cases S10 to S48; ($b$,$e$) cases H16 to H128; and ($c$,$f$) cases G10 to G100. The black lines represent the smooth-wall case, SC.}
\label{fig:U_uv}
\end{figure}
\subsection{{Effect of element height and spacing}}\label{subsec:fluc}
{In this section, we discuss the effect of the element height and spacing on the element-induced and on the full velocity fluctuations, both within and above the canopy. We observe that the element-induced fluctuations are largest near the canopy-tip plane and decay below it, as shown in figure~\ref{fig:stats_cond}, because they are obstructed by the canopy elements. This effect is more intense for smaller element spacings, and eventually results in the fluctuations vanishing completely well above the canopy floor for the simulations with the smallest spacings in families S and G. For the canopies of family H, which have a constant element spacing, the change in element height does not have a noticeable effect on the element-induced fluctuations, as shown in figures~\ref{fig:stats_cond}($b,e,h$). For the canopies of families S and G, the intensity of the element-induced velocity fluctuations within the canopy increases with element spacing, when scaled using either the friction velocity or the channel bulk velocity. These results suggest that, for canopy elements with a given width, the magnitude of the element-induced fluctuations is governed mainly by the element spacing.}
{As discussed in \S\ref{subsec:RSL},} in canopies with very small element spacing the height of the roughness sublayer is small, and we would expect such canopies not to disrupt the overlying turbulence significantly, regardless of their depth. In the literature on conventional roughness, small roughness elements that have a negligible effect on the overlying turbulent flow are termed `hydraulically-smooth', as the flow over them remains essentially smooth-wall like \citep{Nikuradse1933,Raupach1991}. Roughness elements with a characteristic size of a few wall-units, $h^+ \lesssim 5$, typically fall into the hydraulically smooth category \citep{Raupach1991,Jimenez2004,Flack2007}. Of the canopies studied here, we observe that the overlying flow for canopy G10, which has an element spacing of $s^+ \approx 2.6$, is essentially smooth-wall-like above the canopy-tip plane. This is evidenced by the collapse of the rms velocity fluctuations, Reynolds shear stresses, and the mean velocity profile of this case with those of the smooth-wall case, as shown in figures~\ref{fig:stats_all}($c,f,i$)~and~\ref{fig:U_uv}($c,f$). In addition, the magnitude of the velocity fluctuations below the canopy-tip plane is negligible. This suggests that the overlying turbulent flow essentially perceives the canopy-tip plane as an impermeable wall, and has little or no interaction with the canopy region below this plane.
For canopies with larger element spacings, we begin to observe deviations from smooth-wall-like behaviour in the overlying flow. Above the canopy-tip plane, an increase in the element spacing causes a reduction in the intensity of the streamwise velocity fluctuations and an increase in the intensity of the wall-normal and spanwise ones, as can be observed in figure~\ref{fig:stats_all} for the canopies of families S and G. For canopies with large element spacings, such as those of S48 and G100, the peak in $u'$ typical of smooth-wall flows, is significantly reduced. {These changes in the velocity fluctuations are accompanied by a reduction in the streamwise coherence in the flow with increasing element spacing as can be observed in the instantaneous realisations of the wall-normal velocity for the canopies of family G, portrayed in figure~\ref{fig:v_snap_G}. Near-wall turbulence over smooth walls is characterised by streaks and quasi-streamwise vortices, which are predominantly streamwise-coherent \citep{Kline1967,Jimenez1999}. The decrease in $u'$ and increase in $v'$, $w'$ above the canopy with increasing element size is also commonly reported over conventional rough surfaces \citep{Ligrani1986,Orlandi2006}. Several authors have attributed these changes in the velocity fluctuations and the loss of streamwise coherence to the roughness elements modifying the near-wall cycle and turbulence becoming more `isotropic' \citep{Jimenez2004,Flores2006,Flack2007,Abderrahaman2019}. We also observe an increase in the Reynolds shear stresses above the canopy tip plane with increasing element spacing, shown in figures~\ref{fig:U_uv}($d,f$), with an associated increase in the drag. The drag increase caused by rough surfaces is generally expressed in terms of the downward shift in the logarithmic region of the mean-velocity profile compared to that for a smooth wall \citep{Hama1954}. This shift can be observed for the canopies of families S and G in figures~\ref{fig:U_uv}($a,c$).}
{Focusing now on the flow within the canopy, increasing the element spacing results in an increase in the magnitude of all the components of the full velocity fluctuations, as shown in figure~\ref{fig:stats_all}, which is consistent with the observations of \citet{Green1995}, \citet{Novak2000}, \citet{Poggi2004} and \citet{Pietri2009}}. The wall-parallel velocity fluctuations, $u'$ and $w'$, decay rapidly below the canopy-tip plane, and their magnitude reaches a plateau in the core of the canopy, before dropping again near the canopy base to meet the no-slip condition. {The abrupt changes in the velocity fluctuations near the element tips are typical of textures with perfectly flat and aligned tips and have also been observed over conventional cuboidal rough surfaces \citep{Leonardi2010, Abderrahaman2019} and permeable substrates \citep{Kuwata2017}. However, this effect would likely be smeared out over canopies with irregularly aligned tips.} The height over which the fluctuations decay within the canopy and the magnitude of the fluctuations in the core of the canopy appear to correlate with the element spacing. Note that this plateau in $u'$ and $w'$ within the canopy is asymptotic and requires a sufficiently large canopy depth to occur. Thus, this plateau is essentially absent for the canopy of S48, because of its low canopy height-to-spacing ratio, $h/s \approx 2$. The wall-normal fluctuations within the canopy do not exhibit this plateau and decay gradually below the canopy-tip plane to meet the impermeability condition at the canopy base. {Let us also note here that the element-induced flow accounts for less than $30\%$ of the magnitude of the streamwise velocity fluctuations and less than $10\%$ of the cross-velocity fluctuations within the canopy, which is consistent with the observations of \citet{Poggi2008}. This implies that the velocity fluctuations deep within the canopy result mainly from the penetration of the overlying, element-incoherent velocity fluctuations. This will be discussed further in \S\ref{subsec:KH}.}
{Although, as discussed in the preceding paragraphs, the element spacing has a leading-order effect on the fluctuating flow, their height, $h$, also plays a secondary role. In order to assess the effect of height, we consider the canopies of family H, which have fixed element width and spacing, but different canopy heights.} As noted previously, the differences between the element-induced fluctuations for the fixed-spacing canopies of family H are negligible. However, we do observe changes in the full rms velocity fluctuations for these cases, {implying that the height affects the element-incoherent flow}. Above the canopy tips, we observe a decrease in $u'$ and an increase in $v'$ and $w'$ with increasing canopy height, similar to the effect of increasing element spacing, as shown in figures~\ref{fig:stats_all}($b,e,h$). Within the canopy, $u'$ and $w'$ for all the cases collapse to the same curves, only departing to meet the no-slip condition at the canopy base. The corresponding magnitude of $v'$ within the canopy, however, increases with canopy height up to $h/s \approx 6$, {and saturates for $h/s \gtrsim 6$. This saturation is also observed for the effect of the canopy on the flow in general as} illustrated in figures~\ref{fig:stats_all}($b,e,h$) and \ref{fig:U_uv}($b,e$), which show that the velocity fluctuations, Reynolds shear stresses and the mean velocity profiles for cases H96 and H128, with $h/s \approx 6$--$8$ are essentially the same. {The changes in the element-incoherent flow observed for different element heights likely result from a modulation of the Kelvin--Helmholtz-like instability, discussed in \S\ref{subsec:KH}, which is essentially independent of the element-induced flow.}
\begin{figure}
\centering
\includegraphics[scale=0.99,trim={10.2mm 3mm 0mm 0mm},clip]{fig10-eps-converted-to.pdf}%
\mylab{-11.2cm}{7.5cm}{(\textit{a})}%
\mylab{-8.6cm}{7.5cm}{(\textit{b})}%
\mylab{-6.05cm}{7.5cm}{(\textit{c})}%
\mylab{-3.5cm}{7.5cm}{(\textit{d})}%
\mylab{-0.9cm}{7.5cm}{(\textit{e})}%
%
\mylab{-11.2cm}{5.05cm}{(\textit{f})}%
\mylab{-8.6cm}{5.05cm}{(\textit{g})}%
\mylab{-6.05cm}{5.05cm}{(\textit{h})}%
\mylab{-3.5cm}{5.05cm}{(\textit{i})}%
\mylab{-0.9cm}{5.05cm}{(\textit{j})}%
%
\mylab{-11.2cm}{2.60cm}{(\textit{k})}%
\mylab{-8.6cm}{2.60cm}{(\textit{l})}%
\mylab{-6.15cm}{2.60cm}{(\textit{m})}%
\mylab{-3.5cm}{2.60cm}{(\textit{n})}%
\mylab{-0.9cm}{2.60cm}{(\textit{o})}%
\caption{Pre-multiplied spectral energy densities of the wall-normal velocity, $k_x k_z E_{vv}$, at height $y^+ \approx 15$, normalised by their respective rms values. The line contours represent ($a$--$e$) cases S10 to S48; ($f$--$j$) cases H16 to H128; and ($k$--$o$) cases G10 to G100. The shaded contours represent the smooth-wall case, SC. The contours are in increments of $0.06$ for all the cases. The vertical lines mark the most amplified wavelength predicted by linear stability analysis, discussed in \S\ref{sec:stability_analysis}; \protect\raisebox{2pt}{\tikz{\draw[-,mycolor1,solid,line width = 0.75pt](0,0) -- (5mm,0);}}, DNS mean profiles without drag on fluctuations; \protect\raisebox{2pt}{\tikz{\draw[-,mycolor1,dotted,line width = 0.75pt](0,0) -- (5mm,0);}}, DNS mean profiles with drag on fluctuations; \protect\raisebox{2pt}{\tikz{\draw[-,mycolor1,dashed,line width = 0.75pt](0,0) -- (5mm,0);}}, synthesised mean profiles without drag on fluctuations.}%
\label{fig:spectra_h15_v_all}
\end{figure}
\subsection{{Effect of canopy parameters on the shear-layer instability}}\label{subsec:KH}
The variations observed in the velocity fluctuations for the fixed-element-spacing simulations, discussed above, may result from the growth of the Kelvin--Helmholtz-like, shear-layer instability, typically reported in dense canopy flows \citep{Finnigan2000,Nepf2012}. In order to assess the presence of this instability in the flow, we compare the pre-multiplied spectral energy densities of the wall-normal velocity at $y^+ \approx 15$ in figures~\ref{fig:spectra_h15_v_all}($f$--$j$). For case H16 we observe that the spectral energy densities of the fluctuations above the canopy are similar to those above smooth walls. As the height of the canopy is increased, we observe a progressive increase in the energy in long spanwise wavelengths, $\lambda_z^+ > 100$, for a narrow range of streamwise wavelengths, $\lambda_x^+ \approx 150$--$250$. This range of streamwise wavelengths remains roughly constant for increasing canopy heights. Such a signature in the spectral energy densities has been previously associated with the presence of spanwise-coherent, Kelvin--Helmholtz-like instabilities over riblets \citep{Garcia-Mayoral2011}, transitional roughness \citep{Abderrahaman2019} and permeable substrates \citep{GG2019}. {This signature in the spectral energy densities is also reflected in the instantaneous realisations of the wall-normal velocity, portrayed in figure~\ref{fig:v_snap_G}, which show increased spanwise coherence with increasing element height.} The shear-layer instability is known to generate strong wall-normal fluctuations and, hence, its signature is most clear in the wall-normal spectra \citep{Garcia-Mayoral2011,GG2019}. {\citet{Ghisalberti2009} and \citet{Nepf2012} concluded that canopies only exhibit a shear-layer instability if their height is larger than the wall-normal extent of the instability as otherwise the rollers would be constrained by the lack of canopy depth. Above a short canopy, like that of H16, the proximity of the impermeability condition at the base of the canopy would inhibit the instability by blocking the wall-normal fluctuations. Similarly, \citet{Huerre1983} and \citet{Healey2009} showed that the confinement of a free-shear layer also results in stabilisation of the associated Kelvin--Helmholtz instability.} Increasing the canopy height weakens this effect, leading to a stronger signature of the instability, observed in figures~\ref{fig:spectra_h15_v_all}($f$--$j$). {This enhanced signature of the instability is likely responsible for the increase in the cross-velocity fluctuations for the canopies family H with increasing height, discussed in \S\ref{subsec:fluc}. For $h/s > 6$, the instability no longer perceives the canopy base and the effect of the height on the instability and, consequently, the velocity fluctuations, saturates.} The Kelvin--Helmholtz-like instability has also been reported to cause an increase in the Reynolds shear stresses, with an associated increase in the friction drag, over surfaces such as riblets and permeable substrates \citep{Garcia-Mayoral2011, GG2019}. The increase {and saturation of the Reynolds shear stresses with increasing canopy height can be observed in figure~\ref{fig:U_uv}($e$) for the canopies of family H, and is concurrent with the effect of the element height on the instability, discussed above. This trend in the Reynolds shear stress has a corresponding effect on the drag exerted on the overlying flow, which is illustrated by the downward shift in the mean velocity profiles, portrayed in figure~\ref{fig:U_uv}($b$). The above discussion suggests that the secondary effect that the height has on the full velocity fluctuations within and above the canopy is mainly through its influence on the Kelvin--Helmholtz-like instability.}
The increase in intensity of the Kelvin--Helmholtz-like rollers with increasing canopy height also contributes to the increase in the wall-normal velocity fluctuations within the canopy observed in figure~\ref{fig:stats_all}($e$). This is demonstrated by the wall-normal spectral energy densities of the flow within the canopies, portrayed at $y^+ \approx -10$ for all the canopies of family H, in figures~\ref{fig:spectra_H_can_-10}($a$--$e$). Note that in calculating the spectra for a region with solid obstacles, we have implicitly assumed that the obstacles are fluid regions with zero flow velocity. As discussed in the previous paragraph, for case H16 the instability is inhibited by the proximity of the canopy-base wall, and the flow above shows similarities to a smooth-wall flow. The energy density within the canopy at $y^+\approx -10$ for this case also shows some regions overlapping with the smooth-wall spectra, with additional energy in the wavelengths associated with the Kelvin--Helmholtz-like instability. The smooth-wall spectra displayed for reference are at $y^+ \approx 1$, which is as low as possible while yielding a non-negligible energy, since no direct comparison with $y^+ \approx -10$ is possible. We also observe some energy in the spanwise wavelength corresponding to the canopy spacing and a broad range of streamwise wavelengths. These regions can be attributed to the modulation of the element-induced flow by the larger scale fluctuations induced by the instability or the overlying turbulence \citep{Abderrahaman2019}. This suggests that the fluctuations within a short canopy result mainly from the penetration of the overlying turbulence, with additional contributions from the Kelvin--Helmholtz-like instability and the element-induced flow. As the canopy height is increased, and the instability becomes stronger, the deviations in the spectral energy densities from smooth-wall flow become more prominent. The fluctuations within the canopy in cases H32 to H128 arise mainly from large spanwise wavelengths, likely originating from the Kelvin--Helmholtz-like instability near the canopy-tip plane, along with a contribution of the modulated element-induced flow discussed above. The increasing signature of the instability within the canopy with increasing element height can also be observed in the instantaneous realisations of the wall-normal velocity at $y^+ \approx -10$ portrayed in figure~\ref{fig:v_snap_H_S}. The presence of large spanwise wavelengths deep within the canopy can also be noted for the canopies of family S, whose spectral energy densities and realisations of wall-normal velocity at $y^+ \approx -40$ are portrayed in figures~\ref{fig:spectra_H_can_-10}($f$--$j$) and \ref{fig:v_snap_H_S}, respectively. {This suggests that, in the present dense canopies, the background turbulence is not able to penetrate far below the canopy tips, and that the velocity fluctuations deep within originate mainly from the footprint of the Kelvin--Helmholtz-like rollers above}.
\begin{figure}
\centering
\vspace{2mm}\includegraphics[scale=1.0,trim={8mm 6mm 0mm 0mm},clip]{fig11a-e-eps-converted-to.pdf}%
\mylab{-13.6cm}{2.0cm}{(\textit{a})}%
\mylab{-11.1cm}{2.0cm}{(\textit{b})}%
\mylab{-8.5cm}{2.0cm}{(\textit{c})}%
\mylab{-6.0cm}{2.0cm}{(\textit{d})}%
\mylab{-3.4cm}{2.0cm}{(\textit{e})}%
\vspace{1mm} \includegraphics[scale=1.0,trim={8mm 0mm 0mm 0mm},clip]{fig11f-j-eps-converted-to.pdf}%
\mylab{-13.6cm}{2.6cm}{(\textit{f})}%
\mylab{-11.1cm}{2.6cm}{(\textit{g})}%
\mylab{-8.5cm}{2.6cm}{(\textit{h})}%
\mylab{-6.0cm}{2.6cm}{(\textit{i})}%
\mylab{-3.4cm}{2.6cm}{(\textit{j})}%
\caption{Pre-multiplied spectral energy densities of the wall-normal velocity, $k_x k_z E_{vv}$, for ($a$--$e$) cases H16 to H128 at a height of $y^+ \approx -10$; and ($f$--$j$) cases S10 to S48 at a height of $y^+ \approx -40$. The contours are normalised by the rms values of their respective cases. The shaded contours are of the smooth-wall case, SC at a height of $y^+ \approx 1$, for reference. The contours are in increments of 0.075 for all the cases.}%
\label{fig:spectra_H_can_-10}
\end{figure}
\begin{figure}
\centering
\vspace{2mm}\subfloat{%
\includegraphics[scale=1,trim={20mm 39mm 18mm 22mm},clip]{fig12.pdf}
}%
\caption{Instantaneous realisations of the wall-normal velocity at $y^+ = -10$ (left column) and $y^+ = -40$ (right column), normalised by $u_\tau$. From top to bottom, the left column represents cases H16 to H128; and right column, cases S10 to S48. From top to bottom, the clearest and darkest colours indicate intensities of $\pm(0.1,0.2,0.3,0.3,0.3)$ in the left column and $\pm(0.05,0.2,0.4,0.4,0.5)$ in the right column.}%
\label{fig:v_snap_H_S}
\end{figure}
It is also worth noting that even in canopies with small element spacings, such as that of case S10, although the {fluctuations of the wall-parallel velocities decay rapidly below the canopy-tip plane, the fluctuations of the wall-normal velocity decay more slowly,} as shown in figure~\ref{fig:stats_all}. This is also the case for the velocity fluctuations of the canopies of family H, for which the wall-normal velocity fluctuations within the canopy require larger canopy heights to saturate compared to the wall-parallel fluctuations. The presence of wall-normal fluctuations deep within the canopy are a reflection of the canopy layout being able to obstruct the wall-normal flow less efficiently than the tangential flow. It will be shown in \S\ref{sec:stability_analysis} that, for the present canopies, the effective drag coefficient in the tangential directions can be up to three times larger than in the wall-normal direction. In the core region of a tall canopy, the only mechanism to inhibit the velocity fluctuations is the canopy drag. As the canopy geometries studied here exert more drag on the wall-parallel flow than the wall-normal flow, $u'$ and $w'$ decay faster than $v'$ within the canopy.
{The spacing between the canopy elements affects the excitation of the Kelvin--Helmholtz-like instability through its influence on the canopy drag. \citet{White2007} and \citet{AS2017} have shown that the canopy drag governs the instability through two competing effects, the shear at the canopy tips and the canopy drag. A small element spacing results in a large drag within the canopy, which in turn results in a larger shear at the canopy tips that enhances the instability, but at the same time it also inhibits the fluctuations more strongly, which weakens the instability.} To study this effect, we now compare the pre-multiplied spectral energy densities of the wall-normal velocities for the canopies of family S, which have a constant height and different element spacing. For the canopy with the smallest spacing, S10, {the signature of the Kelvin--Helmholtz-like instability in the energy densities is weak and the distribution of energy in different wavelengths is similar to that over smooth walls, as shown in figure~\ref{fig:spectra_h15_v_all}($a$). This suggests that the large drag exerted on the fluctuations by this canopy inhibits the formation of the shear-layer instability. As the element spacing is increased, the drag on the fluctuations reduces, and there is a progressive increase in the energy in wavelengths associated with the Kelvin--Helmholtz-like instability for the canopies of S16--S48, as can be observed in figures~\ref{fig:spectra_h15_v_all}($b$--$e$). The change in element spacing also has an effect on the instability wavelength, which will be discussed later in this section.} In addition to the increase in the energy associated with the instabilities, the increase in element spacing also results in a progressive decrease in the overlapping regions in the energy densities of the canopy and smooth-wall flows, with a reduction in the energy in wavelengths $\lambda_x^+ \gtrsim 700$, {$\lambda_z^+ \approx 50$--$100$}. If the element spacing was increased further, the Kelvin--Helmholtz-like instability would eventually weaken, and for sparse enough canopies the flow within would begin to resemble smooth-wall flow perturbed by the element-induced flow of the isolated canopy elements. {Such sparse canopies are beyond the scope of the present work, but have been discussed in \citet{AS2019}, as well as in the previous studies of \citet{Poggi2004, Pietri2009} and \citet{Huang2009}.}
Let us now focus on the self-similar canopy geometries of family G. {Although these canopies have the same $\lambda_f$, increasing the size of the canopy elements produces similar effects on the pre-multiplied spectral energy densities as the canopies of family S, discussed in the previous paragraph.} For the densest canopy, G10, the spectral energy densities at $y^+ \approx 15$ collapse with those over a smooth wall, as shown in figures~\ref{fig:spectra_h15_G}($a$--$d$). As the size of the canopy is increased, we observe a stronger signature of the Kelvin--Helmholtz-like instability in the energy densities, {portrayed in figures~\ref{fig:spectra_h15_v_all}($k$--$o$). The associated increase in spanwise coherence in the flow can also be observed in the instantaneous realisations of the wall-normal velocity shown in figure~\ref{fig:v_snap_G}. Note that here, we observe the combined effects of increasing canopy height, as in family H, and increasing spacing, as in family S, on the instability. So far we have mainly discussed the spectral energy densities of the wall-normal velocity fluctuations, as they have the strongest signature of the Kelvin--Helmholtz-like instability. For completeness, we now} use the canopies of family G to illustrate the effect of increasing the canopy size on the spectral energy densities of the streamwise and spanwise fluctuations, and the Reynolds shear stresses, portrayed in figure~\ref{fig:spectra_h15_G}. The distinct region in the wall-normal spectral energy densities associated with the Kelvin--Helmholtz-like instability is not so apparent in the energy densities of the other velocity fluctuations and the Reynolds shear stresses. Nevertheless, as the canopy size increases, we observe an increase in the energy in streamwise wavelengths associated with the instability, along with a general increase in the energy in {shorter and wider} wavelengths compared to smooth-wall flows. {This is consistent with the gradual shortening and widening of the eddies observed in figure~\ref{fig:v_snap_G}.}
\begin{figure}
\centering
\includegraphics[scale=1.0,trim={6mm 5mm 0mm 8mm},clip]{fig13-eps-converted-to.pdf}%
\mylab{-13.9cm}{9.45cm}{(\textit{a})}%
\mylab{-10.8cm}{9.45cm}{(\textit{b})}%
\mylab{-7.7cm}{9.45cm}{(\textit{c})}%
\mylab{-4.6cm}{9.45cm}{(\textit{d})}%
%
\mylab{-13.9cm}{6.35cm}{(\textit{e})}%
\mylab{-10.8cm}{6.35cm}{(\textit{f})}%
\mylab{-7.7cm}{6.35cm}{(\textit{g})}%
\mylab{-4.6cm}{6.35cm}{(\textit{h})}%
%
\mylab{-13.9cm}{3.2cm}{(\textit{i})}%
\mylab{-10.8cm}{3.2cm}{(\textit{j})}%
\mylab{-7.7cm}{3.2cm}{(\textit{k})}%
\mylab{-4.6cm}{3.2cm}{(\textit{l})}%
%
\mylab{-12.9cm}{9.9cm}{$k_x k_z E_{uu}$}%
\mylab{-9.8cm}{9.9cm}{$k_x k_z E_{vv}$}%
\mylab{-6.80cm}{9.9cm}{$k_x k_z E_{ww}$
\mylab{-3.80cm}{9.9cm}{$k_x k_z E_{uv}$
\caption{Pre-multiplied spectral energy densities at $y^+ \approx 15$ normalised by their respective rms value. The line contours represent ($a$--$d$) case G10; ($e$--$h$) case G40; ($i$--$l$) case G100. The filled contours represent the smooth-wall case, SC. The contours in ($a$, $e$, $i$), ($b$, $f$, $j$), ($c$, $g$, $k$) and ($d$, $h$, $l$) are in increments of $0.075$, $0.06$, $0.07$, and $0.1$, respectively.}%
\label{fig:spectra_h15_G}
\end{figure}
The results discussed in this section suggest that the growth of the Kelvin--Helmholtz-like instability depends on both the canopy height and the element spacing. The streamwise wavelength of the instability, however, seems to depend mainly on the element spacing. {We observe that, in the canopies of family H the streamwise wavelength of the instability is roughly constant regardless of the canopy height, $\lambda_x^+ \approx 150$, as can be observed in figures~\ref{fig:spectra_h15_v_all}($f$--$j$). For the canopies of family S, however, the increase in the element spacing results in an increase in the streamwise wavelength of the instability from $\lambda_x^+ \approx 140$ for case S10 to $\lambda_x^+ \approx 280$ for case S48, as shown in figures~\ref{fig:spectra_h15_v_all}($a$--$e$). Similarly, for the canopies of family G there is a progressive increase in the streamwise wavelengths associated with the instability with the increase in canopy size.} The streamwise wavelength of the Kelvin--Helmholtz-like instability is determined by the shear length, {typically defined in the literature as $L_s = U/(dU/dy)$ calculated at the canopy-tip plane \citep{Raupach1996,Finnigan2000,Nepf2012}. Previous studies have shown that the shear length $L_s$ in canopy flows can be determined by the effective streamwise canopy drag coefficient \citep{Finnigan2000,Nepf2007,Ghisalberti2009,Nepf2012}. Intuitively, in tall, dense canopies, we would expect this drag coefficient, and by extension the shear-layer thickness, to be a function of the element spacing. A dependence of the canopy shear-layer thickness on the element spacing was also observed by \citet{Novak2000} in their study of natural canopy flows.} Therefore, the canopies of family H, which have a constant element spacing, have similar mean drag coefficients and, consequently, similar instability wavelengths, as observed in the spectral energy densities of the fixed-spacing canopies. For the canopies of families S and G, increasing the element spacing decreases the canopy drag coefficient, thereby resulting in the larger wavelengths observed {for the shear-layer eddies}. The effect of the canopy spacing on the drag coefficients and the instability wavelengths will be discussed further in \S\ref{sec:stability_analysis}.
{Finally, let us discuss the effect of the Reynolds number on the Kelvin--Helmholtz-like instability.} It was shown in \S\ref{sec:Rey_effects}, that the turbulent fluctuations over dense canopies scale in friction units, and therefore similar results are obtained when simulating canopies with the same height and spacing in friction units at different Reynolds numbers. It can be observed in figure~\ref{fig:spectra_h32_Re_var}($b$) that the signature of this instability in simulations H32$_{180}$ and H32$_{400}$ are essentially the same, and that the associated streamwise wavelength for both cases is roughly $\lambda_x^+ \approx 150$. {As discussed above, the wavelength and amplification of the instability are governed by the shear at the canopy tips. As the canopy parameters for cases H32$_{180}$ and H32$_{400}$ are kept constant in friction units, we can also expect the shear at the canopy tips to also be similar. Therefore, the instability characteristics for both these canopies are essentially the same when scaled in friction units. We have observed similar behaviours for Kelvin--Helmholtz-like instabilities originating over riblets \citep{Garcia-Mayoral2012} and permeable substrates \citep{GG2019}.}
\section{Linear analysis of Kelvin--Helmholtz-like instabilities}\label{sec:stability_analysis}
The results from DNS discussed in \S\ref{sec:turb_fluct} show that the flow in the region near the canopy-tip plane can be dominated by the presence of spanwise-coherent structures originating from a Kelvin--Helmholtz-like instability. This instability can be captured by a two-dimensional, mean-flow linear stability analysis, even in turbulent flows \citep{Jimenez2001,White2007,Garcia-Mayoral2011,Zampogna2016,GG2019}. In this section, we discuss the methodology and results from such an analysis conducted on the velocity profiles obtained from the DNSs. As the Kelvin--Helmholtz-like instability is an inviscid phenomenon, several of the studies just cited use an inviscid analysis to capture it. The inclusion of viscosity, however, inhibits the growth of smaller wavelengths in the flow, and consequently, results in the most amplified wavelength being slightly larger compared to that of an inviscid analysis \citep{Jimenez2001,GG2019}. In this section, we present the results only from viscous analysis. The results from an inviscid analysis are presented in appendix~\ref{appB} for reference. In addition, we show that some of the key features of this instability can be captured by linear analysis performed on velocity profiles modelled a priori, which would not require any information from the DNSs.
For the purpose of the stability analysis, we model the effect of the canopy using a drag force in the Navier--Stokes equations, which results in the following governing equations
\begin{eqnarray}
\frac{\p \mathbf{u}}{\p t} + \mathbf{u}\bcdot\nabla\mathbf{u} & = & -\nabla p + {\nu} \nabla^2 \mathbf{u} - \nu {C_i} \mathbf{u}\label{eq:NS_plus_drag}\\
\nabla\bcdot\mathbf{u} & = & 0,\label{eq:cont}
\end{eqnarray}
where $C_i$ is the effective canopy drag coefficient in each $i^{th}$ direction, {has dimensions of inverse length squared --being essentially the inverse of a permeability--, and is} assumed to be homogeneous over the entire canopy region, as in \citet{Singh2016}. Given the density of the canopies considered, with maximum spacings $s^+ = \mathcal{O}(10)$, we assume that inertial effects in the flow deep within the canopy are small and can be neglected. {In addition, the element width of the canopies is also small, $w^+ \approx 1$--$25$. For such canopies, the canopy drag can be assumed to depend linearly on the velocity \citep{Tanino2005,Tanino2008}.}
In the core of the canopy, away from the shear effects at the canopy base and top, the mean momentum equation would reduce to a balance between the canopy drag and the mean pressure gradient
\begin{equation}
{\nu C_x U = -\frac{\mathrm{d}P}{\mathrm{d} x}.}
\label{eq:canopy_drag_balance}
\end{equation}
Equation~\eqref{eq:canopy_drag_balance} is essentially Darcy's equation for flow within permeable substrates \citep{Darcy1856}, and has been used by \citet{Zampogna2016a} to model flow deep within densely packed, rigid fibres. The streamwise drag coefficient, $C_x$, can be obtained by substituting the values of $U$ and ${\mathrm{d}P}/{\mathrm{d}x}$ obtained from the DNSs into equation~\eqref{eq:canopy_drag_balance}. From dimensional arguments, equation~\eqref{eq:canopy_drag_balance} predicts that the drag coefficient would scale as $C_x \sim 1/s^2$. This scaling is demonstrated in figure~\ref{fig:cd_vs_s}($a$), which suggests that equation~\eqref{eq:canopy_drag_balance} provides a reasonable approximation for the flow deep within the present canopies, excluding the sparsest canopy S48. Although we can expect the flow within the canopy to be Darcy-like in the wall-normal direction as well, we cannot use the DNS results to obtain $C_y$, as there is no mean flow in this direction. In order to obtain $C_y$, we consider separately the Stokes flow along infinitely long canopy elements driven by a constant pressure gradient. The equation for such flow is $\nu (\p^2_x + \p^2_z)v = \mathrm{d}P/\mathrm{d}y$. The wall-normal drag coefficient is then obtained as
\begin{equation}
{\nu C_y \langle v \rangle = -\frac{\mathrm{d}P}{\mathrm{d}y}, }
\label{eq:wall_normal_drag}
\end{equation}
where the angled brackets represent a spatial average. The estimated values of $C_y$ are portrayed in figure~\ref{fig:cd_vs_s}($b$) for reference. It may be noted that the ratio of the streamwise to wall-normal drag coefficients for the present canopies is $C_x/C_y \approx 2$--$3$, which shows that the streamwise flow is more obstructed than the wall-normal flow for the layouts considered. {It is worth noting here that the canopy drag coefficients, $C_x$ and $C_y$, and the ratio between them also depends on significantly on the plan view arrangement and the resulting porosity of the canopy \citep{VanderWest1996,Zampogna2016a}. This is evidenced by the different ratios of the drag lengthscale and the element spacing for the canopies of families S and G, portrayed in figure~\ref{fig:cd_vs_s}, which have width-to-spacing ratios, $w/s = 1/2$ and $2/9$, respectively. The dependence of the $C_x$ on $w/s$ can also be predicted using two-dimensional Stokes flow simulations, as shown in figure~\ref{fig:cd_vs_s}($a$). For more complicated canopy arrangements, such as staggered or random, we would expect the drag to be a function of the planar layout of the elements.}
\begin{figure}
\centering
\vspace{0mm}\subfloat{%
\hspace{0mm}\includegraphics[scale=1]{fig14a-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{4mm}\includegraphics[scale=1]{fig14b-eps-converted-to.pdf}
}%
\caption{Variation of the lengthscales derived from the ($a$) streamwise and ($b$) wall-normal canopy drag coefficients for different element spacings. The symbols represent, \protect\raisebox{0.5pt}{\tikz{\node[draw,scale=0.5,regular polygon, regular polygon sides=4,fill=none](){};}}, cases of S; $+$, cases of H; and \protect\raisebox{0.5pt}{\tikz{\node[draw,scale=0.5,circle,fill=none](){};}}, cases of G. The colours from red to blue represent cases S10 to S48, H16 to H128 and G10 to G100. {The symbols in ($a$) are values obtained from the DNSs, and the dashed and solid lines are predictions from two-dimensional Stokes-flow simulations. Both the symbols and the lines in ($b$) are obtained from Stokes-flow simulations.}}
\label{fig:cd_vs_s}
\end{figure}
{In order to conduct the stability analysis, we linearise} the equations~\eqref{eq:NS_plus_drag} and \eqref{eq:cont} around the mean flow, $U(y)$, {yielding}
\begin{eqnarray}
\frac{\p {u}}{\p t} + U \frac{\p u}{\p x} + v U' & = & -\frac{\p p}{\p x} + {\nu} \nabla^2 u - \nu {C_x} u\\
\frac{\p {v}}{\p t} + U \frac{\p v}{\p x} & = & -\frac{\p p}{\p y} + {\nu} \nabla^2 v - \nu {C_y} v\\
\frac{\p u}{\p x} + \frac{\p v}{\p y} & = & 0.
\label{eq:NS_plus_drag_lin}
\end{eqnarray}
These equations are used to obtain a modified Orr-Sommerfeld equation \citep{Drazin2004,White2007,Singh2016,Zampogna2016},
\begin{eqnarray}
\left(\frac{\p}{\p t} + U \frac{\p}{\p x} + \nu C_y \right)\nabla^2 v - {\nu} \nabla^4 v = U'' \frac{\p v}{\p x} - \nu(C_x - C_y) \frac{\p^2 v}{\p y^2}.
\label{eq:NS_lin_v}
\end{eqnarray}
Assuming wavelike solutions of the form $v = \widetilde{v} e^{i (\alpha x - \omega t)}$, equation~\eqref{eq:NS_lin_v} reduces to the eigenvalue problem
\begin{multline}
(\alpha U - i \nu C_y)(\mathrm{D}^2 - \alpha^2)\widetilde{v}
- \alpha U'' \widetilde{v} - i\nu(C_x - C_y) D^2 \widetilde{v} \\ + {i\nu}(\mathrm{D}^4 - 2\alpha^2 \mathrm{D}^2 + \alpha^4)\widetilde{v}= \omega (\mathrm{D}^2 - \alpha^2) \widetilde{v},
\label{eq:OS}
\end{multline}
where the prime superscript denotes differentiation with respect to $y$, and $\mathrm{D}$ represents the operator $\mathrm{d}/\mathrm{d}y$. Equation~\eqref{eq:OS} is solved to obtain the complex frequency, $\omega$, for real values of the streamwise wavenumber, $\alpha$, subject to no-slip and impermeability boundary conditions at the top and bottom walls. The instability is then amplified for positive values of the imaginary part of $\omega$.
\begin{figure}
\centering
\subfloat{%
\hspace{0mm}\includegraphics[scale=1,trim= 0mm 0mm 0mm 0mm, clip]{fig15a-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{2mm}\includegraphics[scale=1,trim= 0mm 0mm 0mm 0mm, clip]{fig15b-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{2mm}\includegraphics[scale=1,trim= 0mm 0mm 0mm 0mm, clip]{fig15c-eps-converted-to.pdf}
}%
\vspace{0mm}\subfloat{%
\hspace{0mm}\includegraphics[scale=1,trim= 0mm 0mm 0mm 0mm, clip]{fig15d-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{2mm}\includegraphics[scale=1,trim= 0mm 0mm 0mm 0mm, clip]{fig15e-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{2mm}\includegraphics[scale=1,trim= 0mm 0mm 0mm 0mm, clip]{fig15f-eps-converted-to.pdf}
}%
\vspace{0mm}\subfloat{%
\hspace{1.6mm}\includegraphics[scale=1,trim= 0mm 0mm 0mm 0mm, clip]{fig15g-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{0.2mm}\includegraphics[scale=1,trim= 0mm 0mm 0mm 0mm, clip]{fig15h-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{0.2mm}\includegraphics[scale=1,trim= 0mm 0mm 0mm 0mm, clip]{fig15i-eps-converted-to.pdf}
}%
\caption{Growth rates of different perturbation wavelengths obtained from the stability analysis performed on ($a$--$c$) mean profiles obtained from the DNSs, with drag on the perturbations included in the stability analysis; ($d$--$f$) mean profiles obtained from DNSs, with no drag on the perturbations; and ($g$--$i$) mean velocity profiles obtained using equation~\eqref{eq:mean_vel_model}, with no drag on the perturbations. The lines from red to blue, {indicated by the direction of the arrows}, represent ($a$,$d$,$g$) cases S10 to S48; ($b$,$e$,$h$) cases H16 to H128; and ($c$,$f$,$i$) cases G10 to G100.}
\label{fig:amp_vs_lx}
\end{figure}
\begin{table}
\begin{center}
\begin{tabular}{clcccc}
&Case &DNS &SA$_{C0}$ &SAM$_{C0}$ & SA \\
\hline
&S10 &140 &105 &90 &320 \\
\multirow{2}{*}{Fixed}&S16(H96) &160 &115 &105 &385 \\
\multirow{2}{*}{height} &S24 &200 &140 &115 &420 \\
&S32 &230 &152 &130 &465 \\
&S48 &250 & 152 &140 &165 \\
\hline
&H16 &130 &95 &90 &140 \\
\multirow{2}{*}{Fixed} &H32 &150 &105 &95 &200 \\
\multirow{2}{*}{spacing} &H64 &160 &115 &105 &290 \\
&H96(S16) &160 &115 &105 &385 \\
&H128 &160 &115 &105 &560 \\
\hline
&G10 &-- &95 &70 &-- \\
\multirow{2}{*}{Self-similar} &G20 &120 &95 &90 &170 \\
\multirow{2}{*}{geometry} &G40 &140 &140 &115 &240 \\
&G60 &190 &170 &130 &320 \\
&G100 &260 &220 &152 &350 \\
\hline
\multirow{2}{*}{Varying $\Rey_\tau$} &H32$_{180}$ &140 &105 &-- &180 \\
&H32$_{400}$ &140 &105 &-- &180 \\
\hline
\end{tabular}
\caption{\label{tab:instab_wavelengths} Most amplified instability wavelengths observed in the DNSs and predicted by the stability analysis, scaled in friction units. The column labelled `DNS' lists the approximate streamwise wavelength associated with the instability in the wall-normal spectra portrayed in figure~\ref{fig:spectra_h15_v_all}. SA$_{C0}$, most amplified wavelengths from stability analysis on DNS mean profiles without drag on fluctuations; SAM$_{C0}$, on synthesised velocity profiles without drag on fluctuations; and SA, on DNS mean profiles with drag on fluctuations.}
\end{center}
\end{table}
The growth rates for different perturbation wavelengths are portrayed in figures~\ref{fig:amp_vs_lx}($a$--$c$), and the wavelengths with the highest growth rates are summarised in table~\ref{tab:instab_wavelengths}. The most amplified wavelengths predicted by the stability analysis only match those observed in the DNSs for canopies with high values of $\delta/h$. The wavelengths predicted for cases H16, H32, G10, G20 and G40 show reasonable agreement with those observed in the DNSs. For canopies with larger heights, however, the analysis predicts wavelengths larger than those observed in the DNSs. For the fixed-spacing canopies of family H, the predicted instability wavelength also increases with increasing canopy height, whereas the DNSs show that the instability wavelength for these cases is essentially independent of the height. The contours of the instability stream function for case H96 for the most amplified wavelength, $\lambda_x^+ \approx 385$, portrayed in figure~\ref{fig:instab_SF}($a$), show that it has a large wall-normal span, extending up to $y^+\approx 120$. Such an instability was also reported by \citet{Singh2016}, who performed stability analyses similar to the one conducted here, except that the canopy was represented by a drag force depending quadratically on the velocity. \citet{Singh2016} noted that their analysis predicted two instability modes, one similar to the Kelvin--Helmholtz instability and another originating from the canopy drag included in the analysis. They only considered canopies with low $\delta/h$, and observed that the second instability mode, similar to the large-wavelength modes obtained from the present stability analysis, was dominant for canopies with high drag and spanned the entire height of the channel.
\begin{figure}
\centering
\subfloat{%
\includegraphics[scale=1]{fig16a-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{7mm}\includegraphics[scale=1,trim=0mm 0mm 0mm -1.1mm, clip]{fig16b-eps-converted-to.pdf}
}%
\caption{Contours of the stream function for the most amplified mode for case H96 obtained from the stability analysis ($a$) with drag and ($b$) without drag on the perturbations. The blue and red lines correspond to clockwise and counter-clockwise rotation, respectively.}
\label{fig:instab_SF}
\end{figure}
{It is worth noting here, that in the region near the interface between the canopy and the free-flow, the assumption of a constant drag coefficient given by equation~\eqref{eq:canopy_drag_balance} would no longer be valid, as shear and advective effects become stronger. We have conducted some exploratory analyses accounting for this variation in the drag coefficient and these do not provide improved estimates for the instability wavelength compared to the results of the constant-drag analysis presented here. In the present analysis, we have also assumed} that the drag coefficient experienced by the perturbations is the same as that experienced by the mean flow. {However, we have recently reported for sparser canopies that different wavelengths in the flow can perceive drag coefficients different from that for the mean flow \citep{AS2019}. In such a case, the drag coefficient would have to be calculated on a mode-by-mode basis for the different wavelengths. A wavelength dependent drag coefficient would lead to the drag for a given wavelength being dependent on a convolution from all other wavelengths. Such an analysis, however, is beyond the scope of the present work. An alternative approach would be to model the canopy as a permeable substrate, which naturally yields wavelength-dependent equations for the flow within\citep{Zampogna2016,Abderrahaman2017,AS2017,GG2019}. In order to illustrate that applying constant drag coefficient on the perturbations may be a coarse assumption, we also present results from stability analyses with no drag on the perturbations. This is also a rather coarse assumption, but we observe that excluding} the drag on the perturbations in the stability analysis yields better estimates for the instability wavelengths observed in the DNSs, as shown in figure~\ref{fig:spectra_h15_v_all}. For the canopies of family H, the stability analysis without drag on the fluctuations shows that the most amplified wavelength does not vary significantly with the canopy height. For the canopies of families S and G, this analysis shows an increase in the most amplified wavelength with increasing element spacing, owing to the increase in the shear-layer thickness. The results from this analysis are portrayed in figures~\ref{fig:amp_vs_lx}($d$--$f$), and the most amplified wavelength for each case is listed in table~\ref{tab:instab_wavelengths}. While neglecting the drag acting on the fluctuations yields better estimates for the most amplified wavelengths for canopies with small spacings, the predictions for larger spacings differ by up to a factor of two from the DNS observations. This is likely due to the assumption that the mean flow is homogeneous in the tangential directions, implicit in the stability analysis, which breaks down for such cases. {We have not observed any significant signature of the Kelvin--Helmholtz-like instability for the sparser canopies studied in \citet{AS2019} despite the presence of an inflection in the mean velocity profiles.} There may also be some distortion of the instability by the ambient turbulent fluctuations in the DNSs \citep{Rogers1994,Raupach1996}.
\begin{figure}
\centering
\subfloat{%
\includegraphics[scale=1]{fig17a-eps-converted-to.pdf}
}%
\subfloat{%
\hspace{3mm}\includegraphics[scale=1]{fig17b-eps-converted-to.pdf}
}%
\caption{Growth rate for different perturbation wavelengths from the stability analysis for cases \protect\raisebox{2pt}{\tikz{\draw[-,mycolor1,solid,line width = 0.75pt](0,0) -- (5mm,0);}}, H32$_{180}$; and \protect\raisebox{2pt}{\tikz{\draw[-,mycolor1,dashed,line width = 0.75pt](0,0) -- (5mm,0);}}, H32$_{400}$; ($a$) with drag and ($b$) without drag on the perturbations. }
\label{fig:amp_vs_lx_Re}
\end{figure}%
{We have also performed stability analyses on the cases with different Reynolds numbers, H32$_{180}$ and H32$_{400}$. These analyses predict similar instability wavelengths and growth rates in viscous units, as shown in figure~\ref{fig:amp_vs_lx_Re}, which is consistent with the observations in the DNSs, discussed in \S\ref{subsec:KH}. These results emphasize that the strength of inflection in the mean-velocity profile and the shear-layer thickness for both these cases is similar when scaled in friction units and, hence, so is their effect on the instability.}
The results obtained from the DNSs and the stability analysis suggest that there is a dependence on the element spacing of the most amplified wavelength, related to the effect of the spacing on the shear-layer thickness. {The usual definition of the shear-layer thickness, $L_s = U/(dU/dy)$,} misses the contribution of the part of the shear layer above the canopy. {Regarding the latter,} \citet{Garcia-Mayoral2011} studied the formation of Kelvin--Helmholtz-like instabilities over riblets, and noted that the shear-layer thickness above was given by the height at which the vorticity gradient, $\mathrm{d}^2U/\mathrm{d}y^2$, concentrated. In smooth-wall flows, this height is roughly $y_c^+ \approx 5$--$10$. For the present cases, we observe that the instability wavelengths predicted by the stability analysis correlate well with the full shear length $L_s + y_c$, if we take $y_c^+ \approx 5$, as shown in figure~\ref{fig:instab_wavelength_corr}($a$). This suggests that the shear-layer semi-thickness above the canopies, $y_c$, is roughly constant for most of the geometries considered here, and remains close to the smooth-wall value, {while the semi-thickness below has the standard form $L_s = U/(dU/dy)$, measured at the canopy tips plane}. The only notable deviation is for the sparsest canopy studied, S48. For canopies with large element spacings, we observe that the peak in $\mathrm{d}^2U/\mathrm{d}y^2$ moves closer to the canopy-tip plane, so $y_c^+ = 5$ may no longer be a reasonable approximation for the shear-layer semi-thickness above. {Regarding the height of the shear layer within the canopy, $L_s$, we observe that it is set by the mean canopy drag coefficient, $L_s \propto \sqrt{1/C_x}$, as also noted in the studies of aquatic canopy flows by \citet{Nepf2007} and \citet{White2007}. The drag coefficient on the mean flow, in turn, depends on the element spacing and the width-to-spacing ratio}, as shown in figures~\ref{fig:instab_wavelength_corr}($b$) and ($c$). The correlation of $L_s$ with $s$, therefore, explains the dependence of the most amplified wavelength on the element spacing observed in the DNSs and the stability analysis.
\begin{figure}
\centering
\subfloat{%
\hspace{-3mm}\includegraphics[scale=1]{fig18a-eps-converted-to.pdf}
}%
\hspace{-0.4mm}\subfloat{%
\includegraphics[scale=1]{fig18b-eps-converted-to.pdf}
}%
\hspace{0mm} \subfloat{%
\includegraphics[scale=1]{fig18c-eps-converted-to.pdf}
}%
\caption{($a$) Instability wavelength, $\lambda_x^+$, obtained from the linear stability analysis versus the total shear length, $L_s^+ + y_c^+$; ($b$) shear length, $L_s^+$, versus the drag lengthscale; ($c$) shear length versus the element spacing. \protect\raisebox{0.5pt}{\tikz{\node[draw,scale=0.5,regular polygon, regular polygon sides=4,fill=none](){};}}, family S; $+$, family H; \protect\raisebox{0.5pt}{\tikz{\node[draw,scale=0.5,circle,fill=none](){};}}, family G. The colours from red to blue represent cases S10 to S48, H16 to H128 and G10 to G100. {In ($a$) and ($b$), the solid lines are linear regressions with slopes $0.06$ and $1.36$, respectively. In ($c$), the solid and dashed lines are linear regressions with slopes $0.14$ and $0.3$, respectively.}}
\label{fig:instab_wavelength_corr}
\end{figure}
\subsection{Analysis on modelled velocity profiles}
In this section we introduce a simple model for the mean velocity profile in dense canopy flows and discuss the results from their stability analysis. As we only consider canopies with small element spacings, $s^+ = \mathcal{O}(10)$, the magnitude of inertial effects within the canopies are also small and are thus neglected in the model. The results discussed in \S\ref{sec:turb_fluct} also suggest that, for very dense canopies, {turbulence and, consequently, the Reynolds shear} stresses do not penetrate within \citep{Nepf2007}, and are smooth-wall-like above the canopy-tip plane. The mean velocity above the canopy could then be modelled using a smooth-wall eddy viscosity, with the canopy-tip plane acting as the location of the smooth-wall \citep{Jimenez2001,Garcia-Mayoral2011,GG2018,GG2019}. The equation for the mean velocity can then be written as
\begin{equation}
\frac{\mathrm{d}}{\mathrm{d}y}\left( \left[\nu + \nu_T(y)\right] \frac{\mathrm{d}U}{\mathrm{d}y}\right) - {\nu C_x(y)} U - \frac{\mathrm{d} P}{\mathrm{d} x} = 0,
\label{eq:mean_vel_model}
\end{equation}
where $C_x(y)$ is the average streamwise canopy drag coefficient, which is assumed constant within the canopy and zero outside, and $\nu_T(y)$ is the height-dependent eddy viscosity proposed by \citet{Cess1958} to approximate turbulent smooth-channel flow, and is non-zero only outside the canopy. The drag coefficients, $C_x$, used to obtain the velocity profiles are those given by equation~\eqref{eq:canopy_drag_balance} and portrayed in figure~\ref{fig:cd_vs_s}($a$). These have been obtained using the data from the direct numerical simulations, but can {also be obtained from Stokes-flow simulations as shown in figure~\ref{fig:cd_vs_s}($a$), which are significantly less computationally intensive.}
The most amplified wavelengths predicted by the stability analysis conducted on these modelled velocity profiles, with no drag applied on the fluctuations, are in reasonable agreement with those {obtained from the same no-drag analysis} on profiles obtained from the DNSs. The growth rates predicted are portrayed in figures~\ref{fig:amp_vs_lx}($g$--$i$). The wavelengths with maximum growth rates are also summarised in table~\ref{tab:instab_wavelengths}. We have also conducted stability analyses on these modelled velocity profiles including the effect of the eddy viscosity. The results are portrayed in appendix~\ref{appB}, and they are essentially the same as the ones obtained using molecular viscosity alone, apart from a slight reduction in the instability growth rates, {which suggests that although $\nu_T$ is important for setting the shape of the mean velocity profile, its effect on the fluctuations is not significant. This is likely because the Kelvin--Helmholtz-like rollers occur near the canopy tips, where $\nu_T$ is small and the molecular viscosity, $\nu$, dominates}. It is worth noting that even though this model is able to capture the instability wavelength, the velocity profiles obtained using this model do not match those from the DNSs, apart from those of S10 and G10. This is most likely due to our assumption that the turbulent stresses do not penetrate within the canopy {and remain smooth-like}, which fails as the element spacing is increased. As discussed previously, the wavelength of the instability is set by the shear length. The shear-layer semi thickness within the canopy, $L_s$, is set by the canopy drag coefficient, $C_x$. As this drag coefficient is the same both from the DNSs and for the modelled velocity profiles, we expect $L_s$ to be similar as well. The shear length above the canopy, however, could differ, as the profiles from DNS would include the effect of the turbulent stresses penetrating into the canopy and deviating from their smooth-wall values, while the modelled velocity profiles do not. The similarity in the instability wavelengths between these analyses therefore suggest that, for most of the dense canopies considered in this work, turbulence is essentially precluded from penetrating into the canopy, and that the shear length above does not vary significantly from its smooth-wall value.
\section{Conclusions}\label{sec:conclusions}
In the present work, we have examined the effect of the canopy layout on turbulent flows over canopies of densely packed filaments of small size. Three families of simulations have been conducted, the first with the element height in friction units fixed, the second with the element spacing fixed, and the third with the height-to-spacing ratio fixed. {The layouts considered had height-to-spacing ratios greater than one, and elements spacings in the range $s^+ \approx 3$--$50$. The penetration of turbulent fluctuations within such canopies was limited by their small element spacings. Consequently, the height of the roughness sublayer was also determined by the element spacing, rather than their height, extending up to $y \approx 2$--$3s$ above the canopy tips. The canopy drag coefficient was also found to be determined by the element spacing, $C_x \sim 1/s^2$. Canopies with small spacings were, therefore, found to suppress the velocity fluctuations within them owing to the large drag exerted, and the fluctuations became more intense as the spacing increased. The intensity of the characteristic Kelvin--Helmholtz-like instability over canopies was observed to be governed by two competing effects resulting from the canopy drag, the inflection at the canopy tips and the drag on the fluctuations. Canopies with large drag had a large shear at the canopy tips, and thus a stronger inflection, which enhanced the instability, but also exerted a large drag on the velocity fluctuations, which suppressed the instability. The instability was found to be inhibited in canopies with $s^+ \lesssim 10$ and, for the range of canopy spacings considered here, a stronger signature of the instability was observed as the spacing was increased. We also showed that the main contribution to the velocity fluctuations deep within the canopy was the footprint of the Kelvin--Helmholtz-like instability, and that the contribution of the element-induced dispersive flow was negligible. Short canopies with $h/s \sim 1$ were also found to inhibit the instability, owing to the blocking effect of the wall at the canopy base. For height to spacing ratios $h/s \gtrsim 6$, the instability was no longer influenced by the bottom wall, and the effect of the canopy height on the flow within and above the canopy saturated. Increasing the canopy height for a fixed spacing did not change the element-induced velocity fluctuations, and instead affected the surrounding flow through the influence of height on the instability.}
{Linear stability analysis conducted on the mean velocity profiles obtained from the DNSs is} able to capture the approximate wavelength of the instability observed in the DNSs for canopies with small element spacings. The analysis fails for larger element spacings, for which the assumption of the flow perceiving the canopy in a homogenised fashion breaks down. We showed that the shear-layer thickness, which determines the instability wavelength, {has two components, one within the canopy and the other above. The latter is set by the height above the canopy tips at which the vorticity gradient concentrates, and is essentially constant for the present canopies, $y_c^+ \approx 5$. The shear layer thickness within the canopy follows the conventional definition, $L_s = U/(dU/dy)$, and is determined by the canopy drag, thus depending linearly on the canopy spacing. We have also proposed a simplified model to capture the most amplified instability wavelength over dense canopies.} The model assumes that the turbulence above the canopy does not penetrate within and remains smooth-wall-like, and uses the mean streamwise drag coefficient of the canopies to synthesise an approximate mean-flow profile. The stability analysis conducted using these synthesised profiles yields similar results to those conducted using the mean profiles from DNS.
\bigskip
A.S. was supported by an award from the Cambridge Commonwealth, European and International Trust. Computational resources were provided by the ``Cambridge Service for Data Driven Discovery" operated by the University of Cambridge Research Computing Service and funded by EPSRC Tier-2 grant EP/P020259/1. The authors report no conflicts of interest.
\bigskip
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\section{#1}}
\title{Mixingales on Riesz spaces\footnote{{\bf Keywords:} Riesz spaces, Vector lattices, mixingales,
martingales, independence, dependent processes, laws of large numbers,\
{\em Mathematics subject classification (2000):} 47B60; 60G42; 60G20; 46G40.}}
\author{
Wen-Chi Kuo\footnote{Funded by an FRC short term postdoctoral fellowship and by NRF Scarce Skills Postdoctoral Fellowship 82395}\\
School of Computational and Applied Mathematics\\
University of the Witwatersrand\\
Private Bag 3, P O WITS 2050, South Africa \\ \\
Jessica Vardy\footnote{Funded in part by the FRC} \&
Bruce A. Watson\footnote{Funded in part by NRF grant IFR2011032400120 and the Centre for Applicable
Analysis and Number Theory} \\
School of Mathematics\\
University of the Witwatersrand\\
Private Bag 3, P O WITS 2050, South Africa }
\maketitle
\abstract{ \noindent
A mixingale is a stochastic process which combines properties of martingales and mixing sequences.
McLeish introduced the term mixingale at the $4^{th}$ Conference on Stochastic Processes and
Application, at York University, Toronto, 1974, in the context of $L^2$.
In this paper we generalize the concept of a mixingale to the measure-free Riesz space setting
(this generalizes all of the $L^p, 1\le p\le \infty$ variants) and prove that a weak law of large
numbers holds for Riesz space mixingales. In the process we also generalize the concept of
uniform integrability to the Riesz space setting.
}
\parindent=0cm
\parskip=0.5cm
\newsection{Introduction}
Mixingales were first introduced by D.L. McLeish in \cite{mcleish1}.
Mixingales are a generalization of martingales and mixing sequences. McLeish
defines mixingales using the $L^2$-norm. In \cite{mcleish1} McLeish proves
invariance principles under strong mixing conditions. In \cite{mcleish}
a strong law for large numbers is given using mixingales with restrictions
on the mixingale numbers.
In 1988, Donald W. K. Andrews used mixingales to present $L^1$ and weak laws
of large numbers, \cite{andrews}. Andrews used an analogue of McLeish's mixingale
condition to define $L^1$-mixingales. The $L^1$-mixingale condition is
weaker than McLeish's mixingale condition. Furthermore, Andrews makes no restriction
on the decay rate of the mixingale numbers, as was assumed by McLeish. The proofs presented
in Andrews are remarkably simple and self-contained. Mixingales have also been considered in a
general $L^p, 1\le p<\infty$, by, amongst others de Jong, in \cite{dejong-1, dejong-2}
and more recently by Hu, see \cite{hu}.
In this paper we define mixingales in a Riesz space and prove a weak law of large numbers for
mixingales in this setting. This generalizes the results in the $L^p$ setting to a measure free
setting. In our approach the proofs rely on the order structure of the Riesz spaces which
highlights the underlying mechanisms of the theory. This develops on the work of Kuo, Labuschagne,
Vardy and Watson, see \cite{ klw-indag, klw-exp, vw-1, vw-2}, in formulating the theory of stochastic
processes in Riesz spaces. Other closely related generalizations were given by Stoica \cite{stoica-4}
and Troitsky \cite{troitsky}.
In Section 2 we give a summary of the Riesz space concepts needed as well as the essentials of the
formulation of stochastic processes in Riesz spaces. Analogous concepts in the classical probability
setting can be found in \cite{billingsley}. Mixingales in Riesz spaces are defined in Section 3 and
some of their basic properties derived. The main result, the weak law of large number for
mixingales, Theorem \ref{WLLN}, is proved in Section 4 along with a result on the Ces\`aro
summability of martingale difference sequences.
We thank the referees for their valuable suggestions.
\newsection{Riesz Space Preliminaries}
In this section we present the essential aspects of Riesz spaces required for this paper,
further details can be found in \cite{A-B} or \cite{zaanen}.
The foundations of stochastic processes in Riesz spaces will also given.
These will form the framework in which mixingales will
be studied in later sections.
A Riesz space, $E$, is a vector space over ${\mathbb R}$, with an order structure that is compatible
with the algebraic structure on it, i.e. if $f,g\in E$ with $f\le g$ then $f+h\le g+h$ and
$\alpha f\le \alpha g$ for $h\in E$ and $\alpha \ge 0, \alpha \in {\mathbb R}$.
A Riesz space, $E$, is Dedekind complete if every non-empty upwards directed subset of $E$
which is bounded above has a supremum.
A Riesz space, $E$, is Archimedean if for each
$u \in E_+ := \{ f\in E | f\geq 0\}$, the positive cone of $E$, the sequence
$(nu)_{n\in{\mathbb N}}$ is bounded if and only if $u=0$.
We note that every Dedekind complete Riesz space is Archimedean, \cite[page 63]{zaanen}.
We recall from \cite[page 323]{A-B}, for the convenience of the reader, the definition of order
convergence of an order bounded net $(f_\alpha)_{\alpha\in\Lambda}$
in a Dedekind complete Riesz space:
$(f_\alpha)$ is order convergent if and only if
$$\lim\sup_{\alpha} f_\alpha=\lim\inf_{\alpha} f_\alpha.$$
Here
\begin{eqnarray*}
\lim\sup_{\alpha} f_\alpha&=&\inf\{ \sup\{ f_\alpha\,|\, \alpha\ge \beta\}\,|\,\beta\in\Lambda\},\\
\lim\inf_{\alpha} f_\alpha&=&\sup\{ \inf\{ f_\alpha\,|\, \alpha\ge \beta\}\,|\,\beta\in\Lambda\}.
\end{eqnarray*}
Bands and band projections are fundamental to the methods used in our study.
A non-empty linear subspace $B$ of $E$ is a band if the following conditions are satisfied:
\begin{description}
\item[(i)]
the order interval $[-|f|, |f|]$ is in $B$ for each $f\in B$;
\item[(ii)]
for each $D\subset B$ with $\sup D\in E$ we have $\sup D \in B$.
\end{description}
The above definition is equivalent to saying that a band is a solid order closed
vector subspace of $E$.
The band generated by a non-empty subset $D$ of $E$ is the
intersection of all bands of $E$ containing $D$, i.e. the minimal band containing $D$.
A principal band is a band generated by a
single element. If $e\in E_+$ and the band generated by $e$ is $E$, then $e$ is called a weak order
unit of $E$ and we denote the space of $e$ bounded elements of $E$ by
$$E^e=\{ f\in E\,:\, |f|\le ke \mbox{ for some } k\in {\mathbb R}_+\}.$$
In a Dedekind complete Riesz space with weak order unit every band is a principal band
and, for each band $B$ and $u \in E^+$,
\[P_Bu: = \sup\{v\,:\, 0\leq v \leq u, v\in B\}\]
exists.
The above map $P_B$ can be extended to $E$ by setting $P_Bu=P_Bu^+-P_Bu^-$ for $u\in E$.
With this extension, $P_B$ is a positive linear projection which commutes with the operations
of supremum and infimum in that $P(u\vee v)=Pu\vee Pv$ and $P(u\wedge v)=Pu\wedge Pv$.
Moreover $0\le P_Bu\le u$ for all $u\in E_+$ and the range of $P_B$ is $B$.
In order to study stochastic processes on Riesz spaces, we need to recall the definition of
a conditional expectation operator on a Riesz space from \cite{klw-indag}.
As only linear operators between Riesz spaces will be considered, we use the term operator
to denote a linear operator between Riesz spaces. Let $T: E \to F$ be an operator
where $E$ and $F$ are Riesz spaces. We say that $T$ is a positive operator if $T$ maps the
positive cone of $E$ to the positive cone of $F$, denoted $T\ge 0$.
In this paper we are concerned with order continuous positive operators between Riesz spaces.
\begin{defs}
Let $E$ and $F$ be Riesz spaces and $T$ be a positive operator between $E$ and $F$.
We say that $T$ is order continuous if for each directed set
$D \subset E$ with $f \downarrow_{f\in D} 0$ in $E$ we have that $Tf \downarrow_{f\in D} 0$.
Here a set $D$ in $E$ is said to be downwards directed if for $f,g\in D$ there exists $h\in D$
with $h\le f \wedge g$. In this case we write $D\downarrow$ or $f \downarrow_{f\in D}$.
If, in addition, $g=\inf D$ in $E$,
we write $D\downarrow g$ or $f \downarrow_{f\in D} g$.
\end{defs}
Note that if $T$ is a positive order continuous operator with $0\leq S \leq T$ (i.e.
$0\le Sg\le Tg$ for all $g\in E$)
then $S$ is order continuous. In particular band projections are order continuous.
\begin{defs}
Let $E$ be a Dedekind complete Riesz space with weak order unit, $e$.
We say that $T$ is a conditional expectation operator in $E$ if
$T$ is a postive order continuous projection which maps weak order units to weak order units
and has range, ${\cal R}(T)$, a Dedekind complete Riesz subspace of $E$.
\end{defs}
If $T$ is a conditional expectation operator on $E$, as $T$ is a projection it is easy to verify that
at least one of the weak order units of $E$ is invariant under $T$. Various authors have studied
stochastic processes and conditional expectation type operators in terms of order (i.e. in Riesz
spaces and Banach lattices), see for example \cite{LdP, stoica-4, troitsky}.
To access the averaging properties of conditional expectation operators a multiplicative structure is
needed. In the Riesz space setting the most natural multiplicative structure is that of
an $f$-algebra. This gives a multiplicative structure that is compatible with
the order and additive structures on the space. The space $E^e$, where $e$ is a weak order
unit of $E$ and $E$ is Dedekind complete, has a natural $f$-algebra structure generated by setting
$(Pe)\cdot (Qe)=PQe=(Qe)\cdot (Pe)$ for band projections $P$ and $Q$.
Now using Freudenthal's Theorem this multilpication can be extended to the whole of $E^e$
and in fact to the universal completion $E^u$. Here $e$ becomes the multiplicative unit.
This multiplication is associative,
distributive and is positive in the sense that if $x,y\in E_+$ then $xy\ge 0$.
If $T$ is a conditional expectation operator on the Dedekind complete Riesz space $E$ with weak
order unit $e = Te$, then restricting our attention to the $f$-algebra $E^e$
$T$ is an averaging operator, i.e. $T(fg)=fTg$ for $f,g\in E^e$ and $f\in R(T).$
In fact $E$ is an $E^e$ module which allows the extension of the averaging
property, above, to $f,g\in E$ with at least one of them in $E^e$.
For more information about $f$-algebras and the averaging properties of conditional
expecation operators we refer the reader to \cite{BBT, BvR, dodds, grobler, klw-exp}.
\begin{defs}
Let $E$ be a Dedekind complete Riesz space with weak order unit and $T$ be a strictly positive conditional expectation on $E$.
The space $E$ is universally complete with respect to $T$, i.e. $T$-universally complete,
if for each increasing net $(f_\alpha)$ in $E_+$
with $(Tf_\alpha)$ order bounded, we have that $(f_\alpha)$ is order convergent.
\end{defs}
If $E$ is a Dedekind complete Riesz space and $T$ is a strictly positive conditional
expectation operator on $E$, then $E$
has a $T$-universal completion, see \cite{klw-exp}, which is
the natural domain of $T$, denoted ${\rm dom}(T)$ in the universal completion, $E^u$, of $E$,
also see \cite{dodds, grobler}.
Here ${\rm dom}(T)=D-D$ and $Tx:=Tx^+-Tx^-$ for $x\in {\rm dom}(T)$ where
$$D=\{ x\in E^u_+ | \exists(x_\alpha)\subset E_+, x_\alpha\uparrow x, (Tx_\alpha)
\ \mbox{order bounded in}\ E^u\},$$
and $Tx:=\sup_\alpha Tx_\alpha$, for $x\in D$, where $(x_\alpha)$ is an increasing net in $E_+$
with $(x_\alpha)\subset E_+$, $(Tx_\alpha)$ order bounded in $E^u$.
Building on the concept of a conditional expectation, if $(T_i)$ is a sequence of conditional
expectations on $E$ indexed by either ${\mathbb N}$ or ${\mathbb Z}$, we say that $(T_i)$
is a filtration on $E$ if
$$T_iT_j=T_i=T_jT_i,\quad \mbox{for all}\quad i\le j.$$
If $(T_i)$ is a filtration and $T$ is a conditional expectation with $T_iT=T=TT_i$ for all $i$,
then we say that the filtration is compatible with $T$.
The sequence $(T_i)$ of conditional expectations in $E$ being a filtration
is equivalent to ${\cal R}(T_i)\subset {\cal R}(T_j)$ for $i\le j$.
If $(T_i)$ is a filtration on $E$ and $(f_i)$ is a sequence in $E$, we say that
$(f_i)$ is adapted to the filtration $(T_i)$ if $f_i\in{\cal R}(T_i)$ for all $i$ in the
index set of the sequence $(f_i)$. The double sequence $(f_i,T_i)$ is called a martingale
if $(f_i)$ is adapted to the filtration $(T_i)$ and in addition
$$f_i=T_if_j,\quad\mbox{for}\quad i\le j.$$
The double sequence $(g_i,T_i)$ is called a martingale difference sequence
if $(g_i)$ is adapted to the filtration $(T_i)$ and
$$T_i g_{i+1}=0.$$
We observe that if $(f_i)$ is adapted to the filtration $(T_i)$ then $(f_i-T_{i-1}f_i,T_i)$
is a martingale difference sequence. Conversely, if $(g_i,T_i)$ is a martingale difference
sequence, then $(s_n,T_n)$ is a martingale, where
$$s_n=\sum_{i=1}^n g_i, \quad n\ge 1,$$
and the martingale difference sequence generated from $(s_n,T_n)$ is
precisely $(g_n,T_n)$.
We now give some basic aspects of independence in Riesz spaces.
An in depth discussion of independence in the context of Markov processes in
Riesz spaces can be found in \cite{vw-1, vw-2}.
\begin{defs}
Let $E$ be a Dedekind complete Riesz space with conditional expectation $T$ and weak order unit $e=Te$.
Let $P$ and $Q$ be band projections on $E$, we say that $P$ and $Q$ are $T$-conditionally independent with respect to $T$ if
\begin{eqnarray}
TPTQe=TPQe=TQTPe.\label{indep-e}
\end{eqnarray}
We say that two Riesz subspaces $E_1$ and $E_2$ of $E$ containing ${\cal R}(T)$,
are $T$-conditionally independent with respect to $T$ if
all band projections $P_i, i=1,2,$ in $E$ with $P_ie\in E_i, i=1,2,$
are $T$-conditionally independent with respect to $T$.
\end{defs}
\begin{cor}
Let $E$ be a Dedekind complete Riesz space with conditional expectation $T$ and let $e$
be a weak order unit which is invariant under $T$.
Let $P_i, i=1,2,$ be band projections on $E$. Then $P_i, i=1,2,$ are $T$-conditionally independent
if and only if the closed Riesz subspaces
$E_i=\left< P_ie, \mathcal{R}(T)\right>, i=1,2,$ are $T$-conditionally independent.
\end{cor}
If $(\Omega, {\cal A}, \mu)$ is a probability space and $f_\alpha, \alpha\in\Lambda,$
is a family in
$L^1(\Omega, {\cal A}, \mu)$, indexed by $\Lambda$,
the family is said to be uniformly integrable if
for each $\epsilon>0$ there is $c>0$ so that
$$\int_{\Omega_\alpha (c)} |f_\alpha|\,d\mu\le \epsilon,\quad\mbox{for all}\quad \alpha\in\Lambda,$$
where $\Omega_\alpha (c)=\{ x\in\Omega \,:\, |f_\alpha (x)| > c\}.$
This concept can be extended to the Riesz space setting as
$T$-uniformity,
see the definition below,
where $T$ is a conditional expectation operator.
In the case of the Riesz space being $L^1(\Omega, {\cal A}, \mu)$ and $T$ being the
expectation operator, the two concepts coincide.
\begin{defs}
Let $E$ be a Dedekind complete Riesz space with conditional expectation operator
$T$ and weak order unit $e=Te$.
Let $f_\alpha,\alpha\in\Lambda,$ be a family in $E$, where $\Lambda$ is some index set.
We say that $f_\alpha,\alpha\in\Lambda,$ is $T$-uniform if
\begin{eqnarray}
\sup\{ TP_{(|f_\alpha|-ce)^+}|f_\alpha| \,:\, \alpha\in\Lambda\} \to 0 \quad \text{ as } \quad c\to \infty.
\label{ui}
\end{eqnarray}
\end{defs}
\begin{lem}\label{UI}
Let $E$ be a Dedekind complete Riesz space with conditional expectation $T$ and let $e$
be a weak order unit which is invariant under $T$.
If $f_\alpha\in E, \alpha\in\Lambda,$ is a $T$-uniform family, then
the set $\{ T|f_\alpha|\,:\, \alpha\in\Lambda\}$ is bounded in $E$.
\end{lem}
\noindent{\em Proof:\ }
As the sequence $f_\alpha,\alpha\in\Lambda,$ is $T$-uniform
\begin{eqnarray*}
J_c:=\sup\{ TP_{(|f_\alpha|-ce)^+}|f_i|\, :\, \alpha\in\Lambda\}
\to 0 \quad \text{ as } \quad c\to \infty.
\end{eqnarray*}
In particular this implies that $J_c$ exists for $c>0$ large and that, for sufficiently large $K>0$,
the set $\{J_c\,:\, c\ge K\}$ is bounded in $E$.
Hence there is $g\in E_+$ so that
\begin{eqnarray*}
TP_{(|f_\alpha|-ce)^+}|f_\alpha|\le g,\quad\mbox{for all}\quad \alpha\in\Lambda, c\ge K,
\end{eqnarray*}
By the definition of $P_{(|f_\alpha| -ce)^+}$,
$$(I-P_{(|f_\alpha| - ce)^+})|f_\alpha|\le ce,\quad\mbox{for} \quad \alpha\in\Lambda, c>0.$$
Combining the above for $c=K$ gives
\begin{eqnarray*}
T|f_\alpha| =TP_{(|f_\alpha| - Ke)^+}|f_\alpha| + T(I-P_{(|f_\alpha| - Ke)^+})|f_\alpha|
\leq g + Ke,
\end{eqnarray*}
for all $\alpha\in\Lambda$.
\hskip 5mm \rule{2.5mm}{2.5mm}\vskip 10pt
\newsection{Mixingales in Riesz Spaces}
In terms of classical probability theory $((f_i)_{i\in{\mathbb N}},({\cal A}_i)_{i\in {\mathbb Z}})$ is a mixingale in the
probability space $(\Omega,{\cal A},\mu)$ if $({\cal A}_i)_{i\in {\mathbb Z}}$ is an increasing sequence of
sub-$\sigma$-algebras of ${\cal A}$ and $(f_i)_{i\in {\mathbb N}}$ is a sequence of
${\cal A}$ measurable functions with
${\mathbb E}[|{\mathbb E}[f_i|{\cal A}_{i-m}]|]$ and ${\mathbb E}[|f_i-{\mathbb E}[f_i|{\cal A}_{i+m}]|]$ existing and
${\mathbb E}[|{\mathbb E}[f_i|{\cal A}_{i-m}]|]\le c_i\Phi_m$ and ${\mathbb E}[|f_i-{\mathbb E}[f_i|{\cal A}_{i+m}]|]\le c_i\Phi_{m+1}$
for some sequences $(c_i), (\Phi_i)\subset {\mathbb R}_+$ with $\Phi_i\to 0$ as $i\to\infty$.
They were first introduced, in \cite{mcleish}, with the additional assumption that
$(f_i)\subset L^2(\Omega,{\cal A},\mu)$, this was later generalized, in \cite{andrews}, to
$(f_i)\subset L^1(\Omega,{\cal A},\mu)$. We now formulate a measure free abstract
definition of a mixingale in the setting of Riesz spaces with conditional expectation operator.
This generalizes the above classical definitions.
\begin{defs}\label{mixing}
Let $E$ be a Dedekind complete Riesz space with conditional expectation operator, $T$,
and weak order unit $e = Te$.
Let $(T_i)_{i\in {\mathbb Z}}$ be a filtration on $E$ compatible
with $T$ in that $T_iT=T=TT_i$ for all $i\in{\mathbb Z}$.
Let $(f_i)_{i\in{\mathbb N}}$ be a sequence in $E$.
We say that $(f_i, T_i)$ is a
mixingale in $E$ compatible with $T$
if there exist $(c_i)_{i\in{\mathbb N}}\subset E_+$ and $(\Phi_m)_{m\in{\mathbb N}}\subset {\mathbb R}_+$
such that $\Phi_m \to 0$ as $m \to \infty$ and for all $i,m\in{\mathbb N}$ we have
\begin{itemize}
\item[(i)] $T|T_{i-m}f_i|\leq\Phi_m c_i$,
\item[(ii)] $T|f_i - T_{i+m}f_i| \leq \Phi_{m+1}c_i$.
\end{itemize}
\end{defs}
The numbers $\Phi_m, m\in{\mathbb N},$ are referred to as the mixingale numbers.
These numbers give a measure of the temporal dependence of the sequence $(f_i)$.
The constants $(c_i)$ are chosen to index the \lq magnitude\rq \ of the the
random variables $(f_i)$.
In many applications the sequence $(f_i)$ is adapted to the filtration $(T_i)$.
The following theorem sheds more light on the structure of mixingales for this special case.
We recall that if $T$ is a conditional expectation operator on a Riesz space $E$
then $T|g|\ge |Tg|$.
\begin{lem}
Let $E$ be a Dedekind complete Riesz space with
conditional expectation operator, $T$,
and weak order unit $e = Te$.
Let $(f_i, T_i)_{i\geq 1}$ be a mixingale in $E$ compatible with $T$.
\begin{itemize}
\item[(a)]{The sequence $(f_i)$ has $T$-mean zero, i.e. $Tf_i=0$ for all $i\in{\mathbb N}$.}
\item[(b)]{If in addition $(f_i)_{i\in{\mathbb N}}$ is $T$-conditionally independent and
${\cal R}(T_i) = \left< f_1, \dots, f_{i-1}, {\cal R}(T)\right>$
then the mixingale numbers may be taken as zero, where
$\left<f_1,\dots,f_{i-1},{\cal R}(T)\right>$ is the order closed Riesz subspace of $E$ generated
by $f_1,\dots,f_{i-1}$ and ${\cal R}(T)$.}
\end{itemize}
\end{lem}
\noindent{\em Proof:\ }
{\bf (a)} Here we observe that the index set for the filtration $(T_i)$ is ${\mathbb Z}$, thus
\begin{eqnarray*}
|Tf_i| &=& |TT_{i-m}f_i|\\
&\leq & T|T_{i-m} f_i|\\
&\leq & \Phi_m c_i\\
&\to& 0 \quad \text{ as } m \to \infty
\end{eqnarray*}
giving $Tf_i=0$ for all $i\ge 0$.
{\bf (b)} As $f_i \in {\cal R}(T_{i+1}) \subset {\cal R}(T_{i+m})$, it follows that
$$f_i- T_{i+m}f_i = 0,\quad\mbox{ for all }\quad i,m\in{\mathbb N}.$$
We recall from \cite{vw-1} that two closed Riesz spaces, say $E_1$ and $E_2$, are
$T$-conditionally independent if and only if $T_if = Tf$ for all $f \in E_{3-i},\ i =1,2$. As $(f_i)$ is $T$-conditionally
independent and
as $(f_i)$ has $T$-mean zero (from (a)), we have that
$$T_{i-m}f_i=Tf_i=0,$$
for $i,m\in{\mathbb N}$
Thus we can choose $\Phi_m = 0$ for all $m \in{\mathbb N}$.
\hskip 5mm \rule{2.5mm}{2.5mm}\vskip 10pt
\newsection{The Weak Law of Large Numbers}
We now show that the above generalization of mixingales to the measure free Riesz
space setting admits a weak law of large numbers. For a sequence
$(f_i)$, we shall denote its Cez\`{a}ro mean by
\[\overline{f}_n = \frac1n\sum_{i=1}^n f_i.\]
\begin{lem}\label{the-lemma}
Let $E$ be a Dedekind complete Riesz space with conditional expectation operator $T$,
weak order unit $e= Te$ and filtration $(T_i)_{i\in {\mathbb N}}$ compatible with $T$.
Let $(f_i)$ be an $e$-uniformly bounded sequence adapted to the filtration $(T_i)$,
and $g_i:=f_i-T_{i-1}f_i$,
then $(g_i,T_i)$ is a martingale difference sequence with
\[T|\overline{g}_n| \to 0 \quad \text{ as } n\to \infty.\]
\end{lem}
\noindent{\em Proof:\ }
Clearly
$$T_ig_{i+1}=T_if_{i+1}-T^2_if_{i+1}=0$$
and $(g_i)$ is adapted to $(T_i)$ so indeed $(g_i,T_i)$ is a martingale difference sequence.
Let $B>0$ be such that $|f_i|\le Be$, for all $i\in{\mathbb N}$.
For $j>i$, as $T_jT_i=T_i$ and $T_if_i=f_i$ it follows that $T_ig_i=g_i$ and
$$T_{i}g_j=T_{i}f_j-T_{i}T_{j-1}f_j=T_{i}f_j-T_{i}f_j=0.$$
In addition,
$$|g_i|\le |f_i|+|T_{i-1}f_i|\le |f_i|+T_{i-1}|f_i|\le 2Be,\quad\mbox{for all}\quad i\in{\mathbb N}.$$
Set
$$s_n=\sum_{i=1}^n g_i.$$
As $|g_i|\le 2Be$ we have that $g_i$ is in the $f$-algebra $E^e$. Hence the product
$g_ig_j$ is defined in $E^e$.
Now as $T_j$ is an averaging operator, see \cite{klw-exp}, and $g_j\in{\cal R}(T_j)$ we have
$$T_i(g_ig_j)=g_iT_ig_j=0,\quad \mbox{for}\quad j>i.$$
Combining these results gives
\begin{eqnarray*}
T(s_n^2)&=&\sum_{i,j=1}^n T(g_ig_j)\\
&=& \sum_{i=1}^n T(g_i^2)+2\sum_{i<j} T(g_ig_j)\\
&=& \sum_{i=1}^n T(g_i^2)+2\sum_{i<j} TT_i(g_ig_j)\\
&=& \sum_{i=1}^n T(g_i^2)+0.
\end{eqnarray*}
Thus
$$T(s_n^2)=\sum_{i=1}^n T(g_i^2).$$
But
$$g^2_i=|g_i|^2\le 4B^2e$$
as $e$ is the algebraic identity of the $f$-algebra $E^e$ and $|g_i|\le 2Be$. Thus
\begin{eqnarray}
T(s_n^2)\le 4nB^2e.\label{square}
\end{eqnarray}
Now let
$$J_n=P_{s_n^+}-(I-P_{s_n^+})$$
where $P_{s_n^+}$ is the band projection on the band in $E$ generated by $s_n^+$.
From the definition of the $f$-algebra structure on $E^e$, if $P$ and $Q$ are band projections
then $(Pe)(Qe)=PQe$ which together with Freudenthal's Theorem \cite[page 216]{zaanen}
enables us to conclude $$|s_n|=J_ns_n=(J_ne)s_n$$
and $(J_ne)^2=e$, as $J_n^2=I$. But
\begin{eqnarray*}
0&\le&\left(\frac{J_ne}{n^{1/4}}-\frac{s_n}{n^{3/4}}\right)^2\\
&=&\left(\frac{J_ne}{n^{1/4}}\right)^2 +
\left(\frac{s_n}{n^{3/4}}\right)^2
-2\frac{J_ne}{n^{1/4}}\frac{s_n}{n^{3/4}}\\
&=&\frac{e}{n^{1/2}} +
\frac{s_n^2}{n^{3/2}}
-2\frac{|s_n|}{n}
\end{eqnarray*}
giving
$$\frac{e}{n^{1/2}} + \frac{s_n^2}{n^{3/2}}\ge 2\frac{|s_n|}{n}.$$
Applying $T$ to this inequality gives
$$\frac{e}{n^{1/2}} +
\frac{T(s_n^2)}{n^{3/2}}
\ge 2\frac{T|s_n|}{n}$$
Combining the above inequality with (\ref{square}) gives
\begin{eqnarray*}
2\frac{T|s_n|}{n}&\le&\frac{e}{n^{1/2}} + \frac{T(s_n^2)}{n^{3/2}}\\
&\le&\frac{e}{n^{1/2}} + \frac{4nB^2e}{n^{3/2}}\\
&=&\frac{1 + 4B^2}{n^{1/2}} e,
\end{eqnarray*}
and thus
\begin{eqnarray}
T|\overline{g}_n|
&\le&\frac{1 + 4B^2}{2n^{1/2}} e.\label{g-bound}
\end{eqnarray}
Since $E$ is an Archimedean Riesz space letting $n\to\infty$ in (\ref{g-bound}) gives
$T|\overline{g}_n|\to 0$ as $n\to\infty$.
\hskip 5mm \rule{2.5mm}{2.5mm}\vskip 10pt
We are now able to prove an analogue to the weak law of large numbers for
mixingales in Riesz spaces.
\begin{thm}\label{WLLN}{\rm\bf [Weak Law of Large Numbers]}
Let $E$ be a Dedekind complete Riesz space with conditional expectation operator $T$,
weak order unit $e= Te$ and filtration $(T_i)_{i\in {\mathbb Z}}$. Let $(f_i, T_i)_{i\geq 1}$ be a
$T$-uniform mixingale with $c_i$ and $\Phi_i$ as defined in Definition \ref{mixing}.
\begin{itemize}
\item[(a)]
If $\displaystyle{\left( \frac{1}{n} \sum_{i=1}^n c_i \right)_{n\in {\mathbb N}}}$ is bounded in $E$ then
\[ T|\overline{f}_n| = T\left|\frac{1}{n}\sum_{i=1}^n f_i\right| \to 0 \quad \text{ as } n \to \infty.\]
\item[(b)]
If $c_i = T|f_i|$ for each $i\geq 1$ then
\[ T|\overline{f}_n| = T\left|\frac{1}{n}\sum_{i=1}^n f_i\right| \to 0 \quad \text{ as } n \to \infty.\]
\end{itemize}
\end{thm}
\noindent{\em Proof:\ }
{\bf (a)}
Let $$y_{m,i} = T_{i+m}f_i - T_{i+m - 1}f_i,\quad\mbox{for}\quad i \geq 1, m \in {\mathbb Z}.$$
Let $B> 0$. Let $h_i=(I-P_{(|f_i|-Be)^+})f_i$ and $d_i=P_{(|f_i|-Be)^+}f_i, i\in {\mathbb N}$ then
$f_i=h_i+d_i$.
Now $(T_{i+m}h_i)_{i\in{\mathbb N}}$ is $e$-bounded and adapted to $(T_{i+m})_{i\in{\mathbb N}}$, so
from Lemma \ref{the-lemma}
$(T_{i+m}h_i-T_{i+m-1}h_i,T_{i+m})_{i\in{\mathbb N}}$
is a martingale difference sequence with
$$T\left|\frac{1}{n}\sum_{i=1}^n (T_{i+m}h_i-T_{i+m-1}h_i)\right|\to 0$$
as $n\to\infty$.
Using the $T$-uniformity of $(f_i)$ we have
\begin{eqnarray*}
T\left|\frac{1}{n}\sum_{i=1}^n (T_{i+m}d_i-T_{i+m-1}d_i)\right|
&\le& T\frac{1}{n}\sum_{i=1}^n |T_{i+m}d_i-T_{i+m-1}d_i|\\
&\le& \frac{1}{n}\sum_{i=1}^n (TT_{i+m}|d_i|+TT_{i+m-1}|d_i|)\\
&=& \frac{2}{n}\sum_{i=1}^n T|d_i|\\
&\le& 2\sup\{ T|d_i|\,:\, i=1,\dots,n\}.
\end{eqnarray*}
Thus
\begin{eqnarray*}
T\left|\frac{1}{n}\sum_{i=1}^n (T_{i+m}d_i-T_{i+m-1}d_i)\right|
&\le& 2\sup\{ T|P_{(|f_i|-Be)^+}f_i|\,:\, i\in{\mathbb N}\}.
\end{eqnarray*}
Combining the above results gives
\begin{eqnarray*}
\limsup_{n\to\infty}T\left|\frac{1}{n}\sum_{i=1}^n (T_{i+m}f_i-T_{i+m-1}f_i)\right|
&\le& 2\sup\{ TP_{(|f_i|-Be)^+}|f_i|\,:\,i\in{\mathbb N}\}\\
&\to&0
\end{eqnarray*}
as $B\to\infty$ by the $T$-uniformity of $(f_i)$.
Thus $T|\overline{y}_{m,n}| \to 0$ as $ n\to \infty$.
We now make use of a telescoping series to expand $\overline{f}_n$,
\begin{eqnarray*}
\overline{f}_n &=& \frac1n \sum_{i=1}^n f_i\\
&=& \frac{1}{n} \sum_{i=1}^n\left(f_i - T_{i+M}f_i
+ \sum_{m = -M +1}^M (T_{i+m}f_i - T_{i+m-1}f_i)
+ T_{i-M}f_i\right) \\
&=& \frac1n \sum_{i=1}^n(f_i - T_{i+M}f_i) + \sum_{m = -M +1}^M \frac1n\sum_{i=1}^n(T_{i+m}f_i - T_{i+m-1}f_i)
+ \frac1n\sum_{i=1}^nT_{i-M}f_i\\
&=& \frac1n \sum_{i=1}^n(f_i - T_{i+M}f_i) + \sum_{m = -M +1}^M \overline{y}_{m,n} + \frac1n\sum_{i=1}^nT_{i-M}f_i\\
\end{eqnarray*}
Applying $T$ to the above expression we can bound $T|\overline{f}_n|$ by means of the
defining properties of a mixingales as follows
\begin{eqnarray*}
T|\overline{f}_n|
&\leq & \frac1n \sum_{i=1}^nT|f_i - T_{i+M}f_i| + \sum_{m = -M +1}^MT|\overline{y}_{m,n}|
+ \frac1n\sum_{i=1}^nT|T_{i-M}f_i|\\
&\leq & \frac1n \sum_{i=1}^n \Phi_{M+1}c_i + \sum_{m = -M +1}^MT|\overline{y}_{m,n}|+
\frac1n \sum_{i=1}^n \Phi_M c_i.
\end{eqnarray*}
Since
$\displaystyle{\left(\frac1n\sum_{i=1}^{n} c_i \right)_{n\in{\mathbb N}}}$ is bounded in $E$ there is
$q\in E_+$ so that
$\displaystyle{\frac1n\sum_{i=1}^{n} c_i \le q,}$ for all $n\in{\mathbb N}$, which when combined with the
above display yields
\begin{eqnarray*}
T|\overline{f}_n|
&\leq & (\Phi_{M+1}+\Phi_M)q + \sum_{m = -M +1}^MT|\overline{y}_{m,n}|.
\end{eqnarray*}
Letting $n\to\infty$ gives
\begin{eqnarray*}
\limsup_{n\to\infty}T|\overline{f}_n|
&\leq & (\Phi_{M+1}+\Phi_M)q.
\end{eqnarray*}
Now taking $M\to\infty$ gives
\begin{eqnarray*}
\limsup_{n\to\infty}T|\overline{f}_n|=0,
\end{eqnarray*}
completing the proof of (a).
{\bf (b)} By Lemma \ref{UI}, $(T|f_i|)$ is bounded, say by $q\in E_+$, so
\begin{eqnarray*}
\limsup_{n\to\infty} \frac{1}{n}\sum_{i=1}^n c_i
= \limsup_{n\to\infty} \frac{1}{n}\sum_{i=1}^n T|f_i|\le q,
\end{eqnarray*}
making (a) applicable.
\hskip 5mm \rule{2.5mm}{2.5mm}\vskip 10pt
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,350 |
import React, { useState } from "react";
import { SketchPicker } from "react-color";
const App = () => {
const [color, setColor] = useState();
const handleChange = color => setColor(color);
return (
<div className="App">
<SketchPicker color={color} onChangeComplete={handleChange} />
</div>
);
};
export default App;
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,672 |
Die Gedenkstätte Geschlossener Jugendwerkhof Torgau ist eine Gedenkstätte in der sächsischen Stadt Torgau, die an das Unrecht im Geschlossenen Jugendwerkhof Torgau als Gipfelung der repressiven Heimerziehung in der DDR, ihre Auswirkungen und Opfer erinnert.
Lage
Die Gedenkstätte befindet sich auf dem Gelände des ehemaligen Geschlossenen Jugendwerkhofs, der von 1964 bis zur Wende und friedlichen Revolution 1989 Gebäude und Außenflächen des vormaligen Gefängnisses nutzte. Während 1996 der überwiegende Teil der Gebäude privatisiert und zu Wohnungen umgebaut wurde, wurde 1998 in dem verbliebenen Verwaltungsgebäude die Gedenkstätte eingerichtet. Besichtigt werden können außerdem die Dunkelarrestzellen sowie der ursprüngliche Innenhof und Reste der Außenmauern.
Inhalte der Ausstellung
Die Ausstellung befasst sich mit dem repressiven Erziehungssystem und der Struktur der DDR-Jugendhilfe und der Spezialheime der DDR, darunter Spezialkinderheime und Jugendwerkhöfe. Ideologisch galt es, eine sozialistische Persönlichkeit durch Umerziehung herauszubilden, die sich in das systemkonforme Kollektiv einordnete. Unerwünschte abweichende politische Meinungen oder prowestliche Einflüsse waren ebenso Ausgangspunkt der Heimeinweisung (siehe z. B. Punk in der DDR) wie fragwürdige Diagnosen aus der Psychologie oder zum Sozialverhalten. Ungeschultes Personal und unmenschliche Behandlungsmethoden, darunter massive Gewaltanwendung, Folter und Misshandlungen, führten schließlich in Torgau zu einem katastrophalen Unrechtssystem. 4000 Jugendliche haben diesen Jugendwerkhof durchlaufen. Die Einweisung erfolgte direkt über das Ministerium für Volksbildung und ohne Gerichtsbeschluss. In der Ausstellung kommen medial Zeitzeugen zu Wort und Teile der Akten können eingesehen werden. Ausstellungsstücke und veranschaulichtes Alltagshandeln verdeutlichen den repressiven Charakter des Jugendwerkhofs. Einzelne jugendliche Heimbewohner begingen Suizid, andere versuchten durch Selbstverletzungen dem täglichen Drill zu entkommen. Viele ehemalige Betroffene leiden bis heute unter körperlichen und psychischen Folgeschäden. Neben der Dauerausstellung finden in der Gedenkstätte Führungen, Zeitzeugengespräche und Projekttage statt. Wanderausstellungen ergänzen die gezeigten Inhalte.
Verantwortlich für den Aufbau des Jugendwerkhofs war Eberhard Mannschatz, in einem Raum der Gedenkstätte hängt sein Porträt zusammen mit denen der anderen Verantwortlichen: Heimleiter Horst Kretzschmar und Margot Honecker.
Das Theaterstück Wer sich umdreht oder lacht … von Ulrike Schanko wurde 2011 in der Gedenkstätte uraufgeführt. Neben der geschichtlichen Aufarbeitung forscht die Gedenkstätte bezüglich aktueller Missstände und Tendenzen zu repressiven Erziehungsmodellen. Zum wissenschaftlichen Beirat gehören u. a. Rainer Eckert und Christian Sachse.
Siehe auch
Gedenkstätte Mümliswil
Filme
INVICTUS - In Erinnerung an die rund 500.000 ehemaligen Heimkinder in der DDR von 1949 - 1990, Kurzfilm
Weblinks
Gedenkstätte Jugendwerkhof Torgau
Einzelnachweise
Bauwerk in Torgau
Aufarbeitung der SED-Diktatur
Jugend (DDR)
Torgau
Gegründet 1998
Bildung in der DDR
Kulturdenkmal in Torgau
Bildung im Landkreis Nordsachsen | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,265 |
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\section{Introduction}
There is increasing evidence from recent cosmic observations of Type Ia Supernovae\cite{Riess, Perlmutter}, Large Scale Structure (LSS)\cite{Tegmark1, Tegmark2, Tegmark3, Seljak, Adelman, Abazajian} and Cosmic Microwave Background(CMB)\cite{Spergel1, Page, Hinshaw, Jarosik} that the universe is undergoing an accelerated expansion at the present stage. This phenomenon indicates that the universe at present is dominated by a smooth energy component, dubbed ``dark energy'', with a negative pressure that counteracts the gravitational forces produced by ordinary matter species, such as baryons and radiation, leading then to an accelerated expansion of the universe. Despite many years of research and much progress, the nature and the origin of dark energy have not been confirmed yet.
Obviously, the best and simplest candidate for such dark energy is the so-called cosmological constant (CC) $\Lambda$ which was introduced by Einstein into his gravitational field equations in an \emph{ad hoc} fashion. However, CC explanation for dark energy usually faces some fundamental problems in physics, namely the fine-tuning problem and notably the cosmic coincidence puzzles \cite{Weinberg, Copeland, Amendola1}. In particle physics, the CC is often interpreted as the energy, $\rho_{vac}$, of the quantum vacuum, which is close to the Planck density $M_{P}^{4}$ ($M_{P}=1/\sqrt{8\pi G}$ is the reduced Planck mass) in magnitude. The observed value of the dark energy density is much less than that of the quantum vacuum, $\rho_{obs} \approx 10^{-123}\rho_{vac}$. Suppressing this great difference of about 123 orders of magnitude between the observed value of dark energy and that estimated from quantum field theory requires some severe fine-tuning mechanisms to work\cite{Hawking, Kachru, Tye, Yokoyama, Mukohyama, Kane, Dolgov}. On the other hand, even if this fine-tuning problem could be evaded, the non-dynamical behaviour of the quantum vacuum energy renders the coincidence problem unsolved. Attempting to alleviate these two fundamental problems and to explain the late-time cosmic acceleration, many plausible dynamical models, such as quintessence \cite{Ratra}, phantom \cite{Onemli, Caldwell}, k-essence \cite{Armendariz}, tachyon \cite{Padmanabhan}, holographic \cite{Li, Limiao}, agegraphic \cite{Cai}, hessence \cite{Wei}, Chaplygin gas \cite{Kamenshchik}, Yang-Mills condensate \cite{Zhang}, etc., have been proposed (see also Review article \cite{Copeland} and references therein).
A different approach to explain the observed accelerating universe with models involving only the standard matter is a plausible modification of the Einstein gravitational field equations . Such a modification can arise, either by extending the Einstein-Hilbert action to a more fundamental theory ($f(R)$ theories of gravity \cite{Kerner, Capozziello, Nojiri, Capozziello1, Nojiri1}) or by modifying the Riemannian geometry. In the latter case, a Lyra's geometry \cite{Lyra, Sen1, Sen2}, which bears a close similarity to Weyl's geometry \cite{Weyl} and is propounded in order to unify gravitation and electromagnetism into a single space-time geometry, got lots of interest. Indeed, in contrast to Weyl's geometry, the connection in Lyra's geometry is metric preserving, as in Riemannian geometry, and length transfers are also integrable. In addition, theories of gravitation, that have been constructed in the framework of Lyra's geometry with both a constant and a time-dependent displacement vector field, involve scalar fields and tensors that are all intrinsic to the geometry \cite{Sen1, Sen2, Sen3, Sen4, Scheibe, Halford, Halford1, Soleng, Soleng1, Hudgin, Beesham, Beesham1, Manoukian, Matyjasek, Anirudh, Mohanty, Rahaman, Katore, Gad, Shchigolev}. On the other hand, as shown in \cite{Sen1, Halford1} these theories predict the same effects within observations limits, as far as the classical Solar System, as well as tests based on the linearised form of the field equations, and are free of the Big-Bang singularity and solve the entropy and horizon problems, which beset the standard models based on Riemannian geometry.
In the present work, we consider a pressureless matter in interaction with the displacement vector field. As pointed out in \cite{Shchigolev}, we will see that, in the absence of a pressureless matter the displacement vector field alone could not be considered as a cosmological constant (term) but rather a stiff fluid, because the associated equation of state is $\omega_{\phi}=+1$ and not $\omega_{\textsc{cc}}=-1$. Meanwhile, interacting with the pressureless matter, the displacement vector can play the same role as a cosmological constant (term), establishing therefore the intrinsic geometrical origin of the cosmological term. Subsequently, it is shown that the observed accelerating universe can occur without considering an alien energy component with a negative pressure.
The outline of the paper is as follows. In Sect. II, firstly we derive the $\Lambda$CDM model from a model containing the standard matter and a constant displacement vector field, and secondly we focus on a time-dependent vector field that yields a variable cosmological term and drives then an accelerating universe. A summary of the results and the conclusions are presented in Sect. III. Throughout the paper we adopt the Planck units $c=\hbar=\kappa^{2}=1$ and use the \textit{space-like metric signature} $(-,+,+,+)$.
\section{Cosmic Acceleration in Normal-Gauge Lyra manifold}
The Einstein gravitational field equations in normal gauge for a four-dimensional Lyra manifold, as obtained by Sen \cite{Sen1} are
\begin{equation}
\label{h}
G_{\mu\nu}=T_{\mu\nu}+{\cal T}_{\mu\nu},
\end{equation}
where
\begin{equation}
{\cal T}_{\mu\nu}=-\frac{3}{2}\left(\phi_{\mu}\phi_{\nu}-\dfrac{1}{2}g_{\mu\nu}\phi_{\lambda}\phi^{\lambda} \right),
\end{equation}
is the stress-energy tensor associated with the displacement vector field $\phi_{\mu}$, i.e., arising as an intrinsic geometrical energy-momentum tensor, whereas $T_{\mu\nu}$ represents a perfect fluid energy-momentum tensor defined by
\begin{equation}
T_{\mu\nu}=\left( p+\rho\right)u_{\mu}u_{\nu} +pg_{\mu\nu}.
\end{equation}
$u_{\mu}=(1,0,0,0)$ is the 4-velocity of the comoving observer, satisfying $u^{\mu}u_{\mu}=-1$, $\rho$ and $p=\omega_{b}\rho$ with $0\le \omega_{b}< 1$ are the background energy density and pressure, respectively. In this paper we shall consider a homogeneous time-depending time-like displacement vector
\begin{equation}
\phi_{\mu}=\left(\phi(t),0,0,0 \right)
\end{equation}
With these assumptions the $(0,0) $ and $(i,j)$-components of Eq. (\ref{h}), in the flat \textit{Friedmann-Lema\^{i}tre-Robertson-Walker} background $ds^{2}=-dt^2+a^{2}d\vec{x}^{2}$, where $a=a(t)$ is the scale factor of an expanding universe, may be written
\begin{eqnarray}
\label{2}
3H^{2}=\rho-\frac{3}{4}\phi^{2}(t)=\rho_{eff},\\
\label{3}
-\left( 2\dot{H}+3H^{2}\right) =\omega_{b}\rho-\frac{3}{4}\phi^{2}(t)=p_{eff},
\end{eqnarray}
where an overdot denotes differentiation with respect to the time coordinate $t$ and $H=\dot{a}/a$ is the Hubble parameter. In the above equations we can recast the pressure and energy density of the displacement vector in the forms $p_{\phi}=\rho_{\phi}=-\frac{3}{4}\phi^{2}(t)$, giving a constant equation of state, $\omega_{\phi}=+1$, of a stiff matter. This proves that the displacement vector alone cannot be considered as a cosmological constant which, by contrast, has an equation of state $\omega_{\textsc{cc}}=-1$. In the following, we set $\theta\equiv \phi^{2}$ and refer to $\theta$ as \textit{displacement field}. Thus, arguing the displacement field is a geometrical energy component contributing to the total energy and interacting with the standard matter, we will show that the displacement vector can play the role of a cosmological constant (term). In this context we consider both a constant and time-dependent displacement vector field.
\subsection{Constant Vector Field and Cosmological Constant}
Considering a constant vector field $\phi^{2}=\phi^{2}_{0}=\theta_{0}$ and starting with a background fluid with a constant equation of state $\omega_{b}$ the Friedmann equations translate into
\begin{eqnarray}
\label{2.1}
3H^{2}=\rho-\frac{3}{4}\theta_{0}=\rho_{eff},\\
\label{2.2}
2\dot{H}+3H^{2}=-\omega_{b}\rho+\frac{3}{4}\theta_{0}=-p_{eff}.
\end{eqnarray}
Resolving the continuity equation of the effective energy density, $d\rho_{eff}/dx+3(\rho_{eff}+p_{eff})=0$ where $x=\ln a$ is the e-folding number, one obtains
\begin{eqnarray}
\label{11}
\rho=ke^{-3(1+\omega_{b})x} +\frac{3}{2(1+\omega_{b})}\theta_{0},\\
\label{11a}
3H^{2}=\rho_{eff}=ke^{-3(1+\omega_{b})x} +\frac{3}{4}\dfrac{1-\omega_{b}}{1+\omega_{b}}\theta_{0},\\
\label{11b}
p_{eff}=\omega_{b}ke^{-3(1+\omega_{b})x}-\frac{3}{4}\dfrac{1-\omega_{b}}{1+\omega_{b}}\theta_{0},
\end{eqnarray}
whence we can compute the effective equation of state as follows
\begin{equation}
\omega_{eff}=-1+\dfrac{1+\omega_{b}}{1+n_{0}e^{3(1+\omega_{b})x}}
\end{equation}
with
\begin{equation}
n_{0}=\frac{3}{4}\dfrac{1-\omega_{b}}{1+\omega_{b}}\dfrac{\theta_{0}}{k}.
\end{equation}
Hence the effective equation of state varies from $\omega_{b}$ at $x\to-\infty$ to $\omega_{\textsc{cc}}=-1$ at $x\to+\infty$.
Considering now a pressureless matter $\omega_{b}=0$, Eqs. (\ref{11})-(\ref{11b}) reduce to the $\Lambda$CDM-like model
\begin{eqnarray}
\label{matter}
\rho=ke^{-3x} +\frac{3}{2}\theta_{0},\\
\label{2.3}
3H^{2}=\rho_{eff}=ke^{-3x} +\frac{3}{4}\theta_{0},\\
\label{press}
p_{eff}=-\frac{3}{4}\theta_{0}.
\end{eqnarray}
From Eq. (\ref{matter}) we say that the pressureless background fluid $\rho$ is the contribution of two terms: the cold dark matter (CDM) and a gain of energy $\varepsilon=\frac{3}{2}\theta_{0}$ from a modification of the Riemannian manifold by the presence of a vector field in the geometrically structureless manifold. On the other hand, Eq. (\ref{2.3}) shows that the effective energy density is also a sum of two terms, namely the CDM and a contribution from the displacement field, $\tilde{\epsilon}=\frac{3}{4}\theta_{0}$. Since the effective pressure (\ref{press}) is the contribution of the displacement field only, one finds that through the conservation of the total energy density the equation of state for the displacement field becomes $\omega_{\phi_{int}}=p_{eff}/\tilde{\epsilon}=-1$. In this case the displacement field (vector) plays the same role as the cosmological constant $\Lambda$.
The effective equation of state and the fractional Hubble parameter $E\equiv H/H_{0}$ are therefore given by
\begin{equation}
\omega_{eff}=-\frac{1}{1+\lambda(1+z)^{3}},
\end{equation}
\begin{equation}
E^{2}(z)=\Omega_{m}(1+z)^{3}+(1-\Omega_{m}),
\end{equation}
where $z=a^{-1}-1$ is the redshift, $\lambda=\frac{4k}{3\theta_{0}}=\dfrac{\Omega_{m}}{1-\Omega_{m}}$, $\Omega_{m}\equiv \dfrac{k}{3H_{0}^{2}}$ is the matter density parameter. Thus, at present time ($x=0$) acceleration occurs for $\lambda<2$ or $\Omega_{m}<2/3$. A model involving a pressureless background fluid in normal gauge for Lyra manifold is therefore equivalent to the $\Lambda$CDM model if one sets $\Lambda=\frac{3}{4}\theta_{0}$. We conclude that this model shows the intrinsic geometrical origin of the cosmological constant with $\omega_{\textsc{cc}}=\omega_{\phi_{int}}=-1$, and the constant displacement vector field arises therefore as the origin of the late time accelerated expansion of the universe.
\subsection{Time-Dependent Vector Field}
The vector field $\phi_{\mu}$ now depending on time interacts mutually with the background fluid $\rho$. And the effective energy conservation equation can be written as
\begin{equation}
\label{2.5}
\frac{d\rho}{dx}+3(1+\omega_{b})\rho-\frac{3}{4}\left(\frac{d\theta}{dx}+6\theta \right)=0,
\end{equation}
Eq. (\ref{2.5}) involves two unknown functions $\rho$ and $\theta$, that means in addition to the Hubble parameter we have three unknown functions to be determined with only two independent equations. In what follows we construct the cosmological consequences of these equations, under some conditions that significantly simplify the search for solutions, but nevertheless show the richness of the cosmological dynamics of the present model. We can thus encode the interaction between $\rho$ and $\theta$ into the conservation equations \cite{Amendola1, Limiao}
\begin{eqnarray}
\label{2.7}
\frac{d\rho}{dx}+3(1+\omega_{b})\rho=\gamma(x),\\
\label{2.8}
\frac{3}{4}\left(\frac{d\theta}{dx}+6\theta \right)=\gamma(x),
\end{eqnarray}
where $\gamma$ denotes the phenomenological interaction term. Owing to the lack of the knowledge of micro-origin of the interaction and following other works \cite{Limiao} we simply parametrize the interaction term in the form:
\begin{equation}
\label{2.9}
\gamma=3b\rho+\frac{9}{2}\tilde{b}\theta~,
\end{equation}
where both $b$ and $\tilde{b}$ are dimensionless coupling constants, and the factors $3$ and $9/2$ before $b$ and $\tilde{b}$ are for convenience in the following calculations. We emphasize here that $\gamma$ does not contain explicitly the Hubble parameter $H$, because we are using the e-folding number $x=\ln a$. However, once we are dealing with the cosmological time $t$, we instead use $\tilde{\gamma}=H\gamma=\Gamma\rho+\tilde{\Gamma}\theta$, where $\Gamma$ and $\tilde{\Gamma}$ characterize the strength of the coupling. Without loss of generality and in order to reduce, furthermore, the number of parameters we shall consider in this section a pressureless matter and then set $\omega_{b}=0$. In the following we shall study the cases: $i)$ $b\ne 0$ and $\tilde{b}=0$, $ii)$ $b=0$ and $\tilde{b}\ne 0$ and $iii)$ $b\ne 0$ and $\tilde{b}\ne 0$, respectively.
\subsubsection*{Case $i$:~~ $b\ne 0$ and $\tilde{b}=0$}
Solving (\ref{2.7}) and (\ref{2.8}) we find
\begin{eqnarray}
\theta= -M_{1}e^{-6x}+\frac{4bC_{1}}{3(1+b)}e^{-3(1-b)x},\\
\rho= C_{1}e^{-3(1-b)x},\\
\label{2.11}
3H^{2}=\rho_{eff}=\frac{C_{1}}{1+b}e^{-3(1-b)x}+\frac{3 M_{1}}{4}e^{-6x},\\
\label{2.12}
p_{eff}=\frac{3 M_{1}}{4}e^{-6x}-\frac{b C_{1}}{1+b}e^{-3(1-b)x},
\end{eqnarray}
where $C_{1}$ and $M_{1}$ are integration constants. We realize that, with this choice of $\gamma$ and for $M_{1}>0$, the pressureless fluid energy and the effective energy density are always positive and monotonically decreasing for $C_{1}>0$ and $-1<b<1$ during the evolution of the universe. Meanwhile the effective pressure could be either positive in early times (the pressureless matter dominates over the displacement field) or negative at the present stage (vector field dominance epoch). We can now evaluate the dynamically varying effective equation
\begin{equation}
\omega_{eff}=\frac{1-b\xi e^{3(1+b)x}}{1+\xi e^{3(1+b)x}}~,
\end{equation}
where $\xi=\frac{4C_{1}}{3M_{1}(1+b)}$ is a positive dimensionless constant for $b>-1$. Assuming a monotonically decreasing effective energy density and positive $\xi$, the coupling constant $b$ needs to range in the region $-1<b<1$. The effective equation of state then lies in the range $\omega_{eff}^{+\infty}=-b<\omega_{eff}<\omega_{eff}^{-\infty}=1$. At the present stage we have
\begin{equation}
\omega^{0}_{eff}=-b+\dfrac{1+b}{1+\xi},
\end{equation}
which is less than $\omega_{acc}=-1/3$ for $\xi>\dfrac{4}{3b-1}$. For example, $\omega^{0}_{eff}=-0.9$ if $\xi=\dfrac{1.9}{b-0.9}$.
\subsubsection*{Case $ii$:~~ $b=0$ and $\tilde{b}\ne 0$}
In this case the different quantities, previously considered, become
\begin{eqnarray}
\theta=M_{2}e^{-6(1-\tilde{b})x},\\
\label{rho}
\rho=C_{2}e^{-3x}+\frac{3\tilde{b}M_{2}}{2(2\tilde{b}-1)}e^{-6(1-\tilde{b})x},\\
3H^{2}=\rho_{eff}=C_{2}e^{-3x}+\frac{3M_{2}}{4(2\tilde{b}-1)}e^{-6(1-\tilde{b})x},\\
\label{2.16}
p_{eff}=-\frac{3M_{2}}{4}e^{-6(1-\tilde{b})x},
\end{eqnarray}
where $C_{2}$ and $M_{2}$ are integration constants. For $\tilde{b}>1/2$ both effective energy and pressureless background energy densities are positive-defined. The former is the sum of two terms: CDM and a dynamically variable quantity, $\Lambda(x)$, that could be thought of as a \textit{variable cosmological-type term} associated with the vector field:
\begin{equation}
\label{2.17}
\Lambda(x)=\frac{3\varpi_{1}H_{0}^{2}}{2\tilde{b}-1}e^{-6(1-\tilde{b})x}~~\mbox{with}~~ \varpi_{1}=\dfrac{M_{2}}{4H_{0}^{2}}>0.
\end{equation}
For $\tilde{b}<1$ the cosmological term is large during the early stages of the universe and has decayed to its low value at present, explaining readily the fine-tuning and coincidence puzzles (see fig.(\ref{fig30.eps}) where we plot both the pressureless energy density $\rho$ and the cosmological term $\Lambda$). On the other hand, the pressureless background fluid is also a sum of two terms, corresponding to CDM energy and an energy, $\rho_{geo-gained}$, geometrically gained as the universe evolves, that is,
\begin{equation}
\rho=\rho_{\textsc{cdm}}+\rho_{geo-gained},
\end{equation}
where
\begin{equation}
\rho_{geo-gained}=\frac{6\varpi_{1}H_{0}^{2}}{2\tilde{b}-1}e^{-6(1-\tilde{b})x}
\end{equation}
is proportional to the cosmological term $\Lambda(x)$.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=5in,height=3in,angle=0]{fig30.eps}
\caption[\emph{Evolution of $\rho/3H^{2}_{0}$ and $\Lambda/3H^{2}_{0}$ versus the e-folding number $x$}]{Evolution of $\rho/3H^{2}_{0}$ (dash-dotted curve) and $\Lambda/3H^{2}_{0}$ (solid curve) versus the e-folding number $x$ for $\varpi_{1}=0.3$ and $\tilde{b}=0.7$. In early times the cosmological term was negligible, compared to the pressureless energy density, while at the present stage they are of the same order. Hence, this model seems to solve both the fine-tuning and the coincidence problems.}
\label{fig30.eps}
\end{center}
\end{figure}
Since the effective pressure is the sum of the CDM pressure, $p_{\textsc{cdm}}=0$ and that of the variable cosmological term $\Lambda(x)$, from ({\ref{2.16}}) and ({\ref{2.17}}) one can determine the equation of state for the variable cosmological term: \[\omega_{\Lambda}\equiv\frac{p_{eff}}{\Lambda},\]\\
or
\begin{equation}
\omega_{\Lambda}=1-2\tilde{b},
\end{equation}
which, for $\tilde{b}\neq 1$, is different from the equation of state of the usual cosmological constant $\omega_{\textsc{cc}}=-1$. For example, for $\tilde{b}=0.9$, $\omega_{\Lambda}=-0.8$, and for $\tilde{b}=0.99$, $\omega_{\Lambda}=-0.98$. However, the choice $\tilde{b}>1$ will lead to dark energy behaving as phantom, i.e., $\omega_{\Lambda}$ being less than $-1$ \cite{Onemli, Caldwell, Kunz, Alam}, and the variable cosmological term will increase exponentially from $0$ at $x\to -\infty$ to $+\infty$ at $x+\infty$. The ratio of the effective pressure over the effective energy density furnishes the effective equation of state in the form
\begin{equation}
\omega_{eff}=\frac{\omega_{\Lambda}}{1-\omega_{\Lambda}f_{0}e^{3\omega_{\Lambda}x}},
\end{equation}
where
\begin{eqnarray}
f_{0}&=&\frac{4C_{2}}{3M_{2}}\nonumber\\
&=&\dfrac{1}{\varpi_{1}}+\dfrac{1}{\omega_{\Lambda}}
\end{eqnarray}
is supposed to be a positive constant, unlike $\omega_{\Lambda}$ which is always assumed negative. One thus has
\begin{equation}
\omega^{-\infty}_{eff}=0,~~~~ \omega^{0}_{eff}=-\varpi_{1},~~~\omega^{+\infty}_{eff}=\omega_{\Lambda}.
\end{equation}
As we have pointed out, a positive $f_{0}$ implies $\omega^{+\infty}_{eff}<\omega^{0}_{eff}$. Hence, $\varpi_{1}>1/3$ can drive an accelerated expansion. For example, taking $\varpi_{1}$ as the present fractional density of dark energy, $\omega^{0}_{eff}\approx -0.73$.
\subsubsection*{Case $iii$:~~ $b\ne 0$ and $\tilde{b}\ne 0$}
Combining (\ref{2.7}) and (\ref{2.8}) and after some algebra it is shown that the effective energy density $\rho_{eff}$, the background fluid energy $\rho$ and the displacement field $\theta$ satisfy the same ordinary differential equation of second order under the form
\begin{equation}
\frac{d^{2}Q}{dx^{2}}+3(3-b-2\tilde{b})\frac{dQ}{dx}+18(1-b-\tilde{b} )Q=0,
\end{equation}
where $Q\in \left\lbrace \rho; \theta; \rho_{eff}\right\rbrace $. We will now consider some special cases where $b$ is explicitly related to $\tilde{b}$.
\begin{description}
\item[A/]~~$\tilde{b}=1-b$ ($b\ne 1$ or $\tilde{b}\ne 0$ ), one then obtains
\begin{equation}
\rho_{eff}(x)=N_{1}+\dfrac{N_{2}}{1+b}e^{-3(1+b)x},
\end{equation}
\end{description}
and the effective equation of state in this case takes for $b>-1$ the values $\omega_{eff}^{-\infty}=b$,~ $\omega_{eff}^{0}=-1+\varpi$ and $\omega_{eff}^{+\infty}=\omega_{\textsc{cc}}=-1$, where $\varpi=N_{2}/3H_{0}^{2}$. Acceleration thus occurs if $\varpi<2/3$.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\
\begin{description}
\item[B/]~~$\tilde{b}=\dfrac{3-b}{2}$ ($b\ne 3$ or $\tilde{b}\ne 0$ ), $\rho_{eff}(x)$ takes the form
\end{description}
\begin{equation}
\rho_{eff}(x)=N_{3}e^{3\sqrt{1+b}~x}+N_{4}e^{-3\sqrt{1+b}~x},
\end{equation}
$N_{3}$ and $N_{4}$ being constants and $b>-1$. For monotonically decreasing $\rho_{eff}(x)$ as suggested observations we will set $N_{3}=0$, hence the effective equation of state is a constant, given by $\omega_{eff}=-1+\sqrt{1+b}$, which is less than $\omega_{acc}=-1/3$ and greater than $\omega_{\textsc{cc}}=-1$ for $-1<b<-5/9$.\\
~~~~~~~~~~~~~~~~~~~~~~~~~~\\
On the other hand, considering a nonzero $N_{3}$ but setting instead $N_{3}=N_{4}=r/2$, the effective energy density transforms according to
\begin{equation}
\label{spec}
\rho_{eff}(x)=r\cosh\left(3\sqrt{1+b}~x \right)
\end{equation}
and
\begin{equation}
\label{spec1}
\omega_{eff}=-1-\sqrt{1+b}\tanh\left(3\sqrt{1+b}~x \right).
\end{equation}
The effective equation of state $\omega_{eff}$ (\ref{spec1}) varies from $\omega^{-\infty}_{eff}=-1+\sqrt{1+b}$, crosses $\omega_{\textsc{cc}}=-1$ at $x=0$ and tends to $\omega^{+\infty}_{eff}=-1-\sqrt{1+b}$. That thus leads to \emph{quintom} dark energy with the equation of state crossing the cosmological constant boundary $\omega_{\textsc{cc}}=-1$ \cite{Guo}.\\
\begin{description}
\item[C/]~~Now, considering the cases where $\tilde{b}\ne 1-b$ and $\tilde{b}\ne\dfrac{3-b}{2}$ the general solution is given by
\begin{equation}
Q(x)=Q_{1}\exp\left[ -\frac{3}{2}\left(3-b-2\tilde{b}+\sqrt{\zeta} \right)x\right]
+\tilde{Q}_{1}\exp\left[ -\frac{3}{2}\left(3-b-2\tilde{b}-\sqrt{\zeta}\right)x\right],
\end{equation}
\end{description}
where $Q_{1}\in \left\lbrace \rho_{1}; \theta_{1}; \rho^{1}_{eff}\right\rbrace $ and $\tilde{Q}_{1}\in \left\lbrace \tilde{\rho}_{1}; \tilde{\theta}_{1}; \tilde{\rho}^{1}_{eff}\right\rbrace $ are integration constants, and
\begin{equation}
\zeta=(3-b-2\tilde{b})^{2}-8(1-b-\tilde{b}).
\end{equation}
The effective energy density reads then:
\begin{subequations}
\begin{eqnarray}
\label{special}
3H^{2}=\rho_{eff}&=&Q_{2}\exp\left[ -\frac{3}{2}\left(3-b-2\tilde{b}+\sqrt{\zeta} \right)x\right]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~\nonumber\\
&&+\tilde{Q}_{2}\exp\left[ -\frac{3}{2}\left(3-b-2\tilde{b}-\sqrt{\zeta}\right)x\right] ,\\
\end{eqnarray}
where
\begin{equation}
Q_{2}=\rho^{1}_{eff}=\rho_{1}-\dfrac{3}{4}\theta_{1},~~~~\tilde{Q}_{2}=\tilde{\rho}^{1}_{eff}=\tilde{\rho}_{1}-\dfrac{3}{4}\tilde{\theta}_{1},
\end{equation}
\end{subequations}
When $\zeta=0$ or $b_{\pm}=-1\pm 2\sqrt{2\tilde{b}}-2\tilde{b}$, and looking only for solutions leading to an accelerated expansion (which corresponds here to the value $b_{+}=-1+2\sqrt{2\tilde{b}}-2\tilde{b}$ ), $\rho_{eff}$ and $\omega_{eff}$ become
\begin{equation}
\rho_{eff}=\left(Q_{2}+\tilde{Q}_{2} \right)e^{-3\left(2-\sqrt{2\tilde{b}} \right)x}~~\mbox{and}~~\omega_{eff}=1-\sqrt{2\tilde{b}}.
\end{equation}
$\rho_{eff}$ decreases for $x\le 0$ and acceleration then occurs if $8/9<\tilde{b}<2$. On the other hand, $\rho_{eff}$ reduces to the cosmological constant with $\omega_{eff}=\omega_{\textsc{cc}}=-1$ for $\tilde{b}=2$.\\
~~~~~~~~~~~~~~~~~~~\\
Now, taking $\zeta\ne 0$ and assuming furthermore a monotonically decreasing effective density during the evolution of the universe the coupling $b$ and $\tilde{b}$ have to satisfy one of the following constraints:
\begin{equation}
\label{con}
\begin{array}{rlll}
\alpha_{1}) &&\tilde{b}< 0 \Longrightarrow b<1-\tilde{b},\\
\alpha_{2})&& 0<\tilde{b}\leq 2 \Longrightarrow b\leq -1-2\sqrt{2\tilde{b}}-2\tilde{b}~~~~~~~~~~~~~\\
&&~~~~~~~~~~~~~~\mbox{or}~-1+2\sqrt{2\tilde{b}}-2\tilde{b}\leq b<1-\tilde{b},\\
\alpha_{3})&& \tilde{b}>2 \Longrightarrow b\leq -1-2\sqrt{2\tilde{b}}-2\tilde{b},
\end{array}
\end{equation}
where we considered both positive and negative values for $b$ and $\tilde{b}$, and assumed that the integrations constants $Q_{1}$ and $\tilde{Q}_{1}$ are all nonzero and positive. The effective equation of state may be written as
\begin{equation}
\label{specc}
\omega_{eff}(x)=\dfrac{1}{2}\left[1-b-2\tilde{b}+\sqrt{\zeta}~\dfrac{1-\chi e^{3\sqrt{\zeta}x}}{1+\chi e^{3\sqrt{\zeta}x}} \right],
\end{equation}
with $\chi=\dfrac{\varpi_{2}}{1-\varpi_{2}}$ and $\varpi_{2}=\dfrac{\tilde{Q}_{2}}{3H_{0}^{2}}$.
Taking $b=\tilde{b}=1/3$ we obtain $\omega_{eff}^{-\infty}=\sqrt{3}/3$,~ $\omega_{eff}^{+\infty}=-\sqrt{3}/3<-1/3$ and $\omega_{eff}^{0}=(1-2\varpi_{2})\sqrt{3}/3$ which is less than $-1/3$ if $\varpi_{2}>1/2+\sqrt{2}/6\approx 0.78$.
The Figure (\ref{fig31.eps}) shows the plot of $\omega_{eff}$ in (\ref{specc}) versus $x$ for different values of $(b, \tilde{b}, \chi)$: $b=1/3,~ \tilde{b}=1/3,~ \chi=9$ (dashed curve, $\omega_{eff}\approx -0.46$);~ $b=0.66,~ \tilde{b}=1/3,~ \chi=4$ (dash-dotted curve, $\omega_{eff}\approx -0.66$) and $b=0.66,~ \tilde{b}=1/3,~ \chi=9$ (solid curve, $\omega_{eff}\approx -0.83$), and the dotted line represents $\omega_{acc}=-1/3$.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=5in,height=3in,angle=0]{fig31.eps}
\caption[\emph{$\omega_{eff}$ versus x}]{$\omega_{eff}$ (\ref{specc}) versus $x$ for $b=1/3,~ \tilde{b}=1/3,~ \chi=9$ (dashed curve, $\omega_{eff}\approx -0.46$);~ $b=0.66,~ \tilde{b}=1/3,~ \chi=4$ (dash-dotted curve, $\omega_{eff}\approx -0.66$) and $b=0.66,~ \tilde{b}=1/3,~ \chi=9$ (solid curve, $\omega_{eff}\approx -0.83$), the dotted line represents $\omega_{acc}=-1/3$.}
\label{fig31.eps}
\end{center}
\end{figure}
Notice that in the special case where $Q_{2}=\tilde{Q}_{2}=\dfrac{q}{2}$, Eq. (\ref{special}) becomes
\begin{equation}
\rho_{eff}=q\cosh\left(\dfrac{3}{2}\sqrt{\zeta}x \right)\exp\left[ -\frac{3}{2}\left(3-b-2\tilde{b} \right)x\right]
\end{equation}
which decreases monotonically when $x\le 0$.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\
~~~~~~~~~~~~~~~~~~~~~~~\\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\
~~~~~~~~~~~~~~~~~~~~~~~\\
\subsection{Concluding Remarks}
We have constructed, in normal gauge for a four-dimensional Lyra manifold, a dark energy model containing only the standard matter that interacts with the vector field $\phi_{\mu}$. Assuming a constant displacement vector field, the model mimics the $\Lambda$CDM model, indicating that the constant displacement field, considered as an energy component of the total energy, plays the role of a cosmological constant with $\omega_{\textsc{cc}}=\omega_{\phi_{int}}=-1$. Introduced in general relativity in an ad hoc fashion, the cosmological constant arises in Lyra's geometry as a result of the presence of a vector field in the affine structure and has then an intrinsic geometrical significance. On the other hand, considering a time-dependent displacement vector field mutually interacting with the pressureless matter and without an alien energy component with a negative pressure, we have alleviated the fine-tuning and coincidence puzzles and shown that the universe could recently enter an accelerating phase, with even an equation of state crossing the cosmological constant boundary $\omega_{\textsc{cc}}=-1$. In fact, the geometrical contribution to the effective energy density, resulting from the modification of the Riemann manifold is endowed with a negative pressure that counteracts the gravitational forces produced by the ordinary matter and therefore favours the acceleration of the universe. In contrast to several models that consider an alien energy component in the universe, this work ensures that dark energy responsible for the late time acceleration of the universe has an intrinsic geometrical origin.
\section*{Acknowledgements}
I would like to thank Dr. K. Ayenagbo for valuable discussions
\section*{References}
\providecommand{\href}[2]{#2}\begingroup\raggedright
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,783 |
El Frente de Liberación Nacional de Córcega (en corso: Fronte di Liberazione Naziunale Corsu, FLNC) es una organización terrorista corsa que preconiza la formación de un Estado independiente en la isla de Córcega. Desde junio de 2014 la organización se encuentra inmersa en un proceso de desarme y abandono del terrorismo.
Nació de la unión de Ghjustizia Paolina y Fronte Paesanu Corsu di Liberazione.
Presente sobre todo en Córcega y algo menos en el resto de Francia, en su período de actividad armada llevó a cabo aproximadamente un millar de asaltos, además de atentados con dinamita y robos a mano armada contra bancos, edificios públicos civiles y militares, estructuras turísticas y todo lo que estaba relacionado con el Gobierno francés en la isla.
Fundación y Objetivos
El FLNC se creó a partir de una fusión de "Ghjustizia Paolina" y "Fronte Paesanu Corsu di Liberazione", las dos organizaciones armadas más grandes en Córcega. Es una rama del partido político A Cuncolta Independentista que tenía miembros en la Asamblea de Córcega y algo de apoyo entre los locales.
El FLNC llevó a cabo sus primeros ataques la noche del 4 de mayo de 1976 con 21 bombas explotando en Ajaccio, Bastia, Sartène, Porto-Vecchio y otras ciudades de Córcega.
La mayoría de los objetivos eran edificios públicos y oficinas de agentes inmobiliarios. El 5 de mayo, el FLNC anunció formalmente su existencia cuando emitió un manifiesto bilingüe que también se atribuía la responsabilidad de los ataques de la noche anterior.
El manifiesto contenía seis demandas:
El reconocimiento del derecho nacional del pueblo corso.
La eliminación de todos los instrumentos del colonialismo francés, incluidos el Ejército francés y los "colonos" (continentales franceses que viven en la isla).
La creación de un gobierno democrático popular que exprese la voluntad y las necesidades del pueblo corso.
La confiscación de fincas "coloniales".
Reforma agraria para cumplir las aspiraciones de los agricultores, trabajadores e intelectuales y librar al país de todas las formas de explotación.
El derecho a la autodeterminación del pueblo corso
En la década de 1990 comenzaron los conflictos y las disputas internas en el FLNC. Las distintas corrientes dentro de la organización llegaron incluso a enfrentarse en una "guerra abierta" en 1995, que acabó con 15 muertos y varios heridos.
Abandono de la lucha armada
El 25 de junio de 2014, mediante un comunicado de 14 páginas, el FLNC anunció a varios medios de comunicación de Córcega su intención de abandonar la práctica de la lucha armada y el inicio de un "proceso de desmilitarización", así como una "salida progresiva de la clandestinidad".
El 1 de octubre de 2019 un video fue lanzado donde se muestran cinco presuntos militantes, donde leen un manifisto con la finalidad de "querer reconstruir al FLNC", se descubrieron en Brando folletos similares al que anunciaba la reactivación del grupo. La Fiscalía anti terrorista ha abierto una investigación por "asociación delictiva terrorista" e "infracción de la legislación de armas en relación con una actividad terrorista".
Referencias
Nacionalismo corso
Organizaciones terroristas en Francia
Antiguas organizaciones terroristas
Movimientos de liberación nacional | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,768 |
'
' +---------------------------------------------------------------------+
' | AjGenesis - Code and Artifacts Generator in .NET |
' +---------------------------------------------------------------------+
' | Copyright (c) 2003-2011 Angel J. Lopez. All rights reserved. |
' | http://www.ajlopez.com |
' | http://www.ajlopez.net |
' +---------------------------------------------------------------------+
' | This source file is subject to the ajgenesis Software License, |
' | Version 1.0, that is bundled with this package in the file LICENSE. |
' | If you did not receive a copy of this file, you may read it online |
' | at http://www.ajlopez.net/ajgenesis/license.php. |
' +---------------------------------------------------------------------+
'
'
Imports System.IO
Imports AjGenesis.Core
Class TransformerManager
Public Sub Transform(ByVal input As TextReader, ByVal output As TextWriter, ByVal env As Environment)
Dim cmp As New TemplateCompiler(input)
Dim pgm As Program = cmp.Compile
pgm.Output = output
pgm.Execute(env)
End Sub
Public Sub Transform(ByVal inputfile As String, ByVal outputfile As String, ByVal env As Environment)
inputfile = GetFileName(inputfile)
PushFilePath(inputfile)
Try
Dim input As New StreamReader(inputfile)
Dim output As New StreamWriter(outputfile, False, System.Text.Encoding.Default)
Transform(input, output, env)
input.Close()
output.Close()
Finally
PopFilePath()
End Try
End Sub
Public Sub Transform(ByVal inputfile As String, ByVal outputfile As String, ByVal env As Environment, ByVal preservemark As String)
inputfile = GetFileName(inputfile)
PushFilePath(inputfile)
Try
If String.IsNullOrEmpty(preservemark) Then
Transform(inputfile, outputfile, env)
Return
End If
If Not File.Exists(outputfile) Then
Transform(inputfile, outputfile, env)
Return
End If
Dim tempfile As String = outputfile & ".tmp"
Transform(inputfile, tempfile, env)
Dim mergefile As String = outputfile & ".merge"
Dim merger As New FileMerger
merger.Merge(tempfile, outputfile, mergefile, preservemark)
File.Delete(tempfile)
File.Delete(outputfile)
File.Move(mergefile, outputfile)
Finally
PopFilePath()
End Try
End Sub
End Class
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,620 |
Q: Windows Phone Store localized app title is always displayed in English I tried to localize my app title using the WP7 AppResLib DLL Generator and it partially work. After installing, the application title in the application list adjust well to the phone's language. For now two languages are supported: Polish and English.
Unfortunately, the application title in the Windows Phone Store is always displayed in English (no matter which language is set as a phone language or which version of the Store's website I visit).
In the root folder of the project I have the following files:
*
*AppResLib.dll
*AppResLib.dll.0409.mui (0409 - English (United States))
*AppResLib.dll.0415.mui (0415 - Polish (Poland))
And that's how my WMAppManifest.xml file looks like:
<?xml version="1.0" encoding="utf-8"?>
<Deployment xmlns="http://schemas.microsoft.com/windowsphone/2012/deployment" AppPlatformVersion="8.0">
<DefaultLanguage xmlns="" code="en-US" />
<Languages xmlns="">
<Language code="en-US" />
<Language code="pl-PL" />
</Languages>
...
</Deployment>
Can anyone tell me why it doesn't work as expected?
Remark:
Solution provided in the Microsoft's article How to localize an app title for Windows Phone 8 didn't worked for me, since I had problems with compiling the resource project both in VS2012 Express for Windows Phone or VS2013 for Windows.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,622 |
Дрізд кордильєрський (Turdus fulviventris) — вид горобцеподібних птахів родини дроздових (Turdidae). Мешкає в Андах.
Опис
Довжина птаха становить 25 см. У самців голова і горло чорні, горло поцятковане білими смужками. Спина темно-сіра. крила і хвіст більш темні. Верхня частина грудей блідо-сіра, нижня частина грудей і живіт руді. Дзьоб жовтий, навколо очей оранжеві кільця. Лапи тьмяно-жовті. Самиці мають більш тьмяне забарвлення.
Поширення і екологія
Кордильєрські дрозди мешкають у Венесуелі (Кордильєра-де-Мерида), Колумбії (зокрема в горах Сьєрра-де-Періха), Еквадорі і північному Перу (Кахамарка). Вони живуть в кронах вологих гірських тропічних лісів Анд і на узліссях. Зустрічаються поодинці або парами, переважно на висоті від 1300 до 2700 м над рівнем моря. Не приєднуються до змішаних зграй птахів.
Примітки
Дроздові
Птахи, описані 1858
Птахи Венесуели
Птахи Колумбії
Птахи Еквадору
Птахи Перу | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,777 |
{"url":"https:\/\/www.physicsforums.com\/threads\/showing-that-the-virial-theorem-holds.63306\/","text":"# Showing that the Virial Theorem holds\n\n1. Feb 9, 2005\n\n### Ed Quanta\n\nSo I have already calculated correctly that the expectation of the interaction potential for hydrogenic atoms is\n\n<nlm|V(r)|nlm>=-(uZ^2e^4)\/((hbar^2)*n^2)\n\nNote that u= mass,and V(r)=-Ze^2\/r\n\nI now have to calculate <nlm|T|nlm> where T is the kinetic energy operator, and\n\nT=p^2\/(2u) + L^2\/(2ur^2)\n\nNote that p is the radial momentum operator and L is the angular momentum operator\n\nI know hbar^2l(l+1)=L^2 and I know (pretty sure) that <1\/r^2>=e^2\/(2n^3hbar^2).\n\nHowever, I am unsure how to find the expectation value of the p^2\/(2u) term, and don't see how <T> is going to equal <V> which the book hints at being true since <T> and <V> are said to satisfy the Virial Theorem.\n\nHelp anyone?\n\n2. Feb 9, 2005\n\n### Tom Mattson\n\nStaff Emeritus\nYou can do it by brute force (that's what I call working in function space). Insert the differential operator for p into the expression for T, sandwich it between ψn'l'm'* and ψnlm, and integrate.\n\n3. Feb 9, 2005\n\n### dextercioby\n\nThere's a piece of genius on my behalf:\n\n$$\\hat{H}=\\hat{T}+\\hat{V}$$ (1)\n\n$$\\langle nlm|\\hat{H}|nlm\\rangle = E_{n} =-\\frac{Z^{2}\\mu e^{4}}{2\\hbar^{2}(4\\pi\\epsilon_{0})} \\frac{1}{n^{2}}$$ (2)\n\n$$\\langle nlm|\\hat{V}|nlm\\rangle =-\\frac{Ze^{2}}{(4\\pi\\epsilon_{0})}\\langle \\frac{1}{r}\\rangle _{|nlm\\rangle}$$ (3)\n\nCompute (3) using the average of 1\/r.\n\nThen:\n\n$$\\langle nlm|\\hat{T}|nlm\\rangle =\\langle nlm|\\hat{H}-\\hat{V}|nlm\\rangle=E_{n}+\\frac{Ze^{2}}{(4\\pi\\epsilon_{0})}\\langle \\frac{1}{r}\\rangle _{|nlm\\rangle}$$ (4)\n\nTell where u get stuck.\n\nDaniel.\n\nLast edited: Feb 9, 2005\n4. Feb 9, 2005\n\n### Ed Quanta\n\nMy book seems to leave out the 4pi*epsilon term in the denominator for some reason. But yeah thanks, I am cool now. I was missing the expectation value for the Hamiltonian. Thanks for your genius my man.\n\n5. Feb 9, 2005\n\n### kanato\n\nIt must use the cgs unit system.. in cgs a factor of $$( 4 \\pi \\epsilon_0 )^{\\frac{1}2}$$ is \"absorbed\" into the unit of charge, so that Coulomb's law can be written as $$\\vec{F} = \\frac{e^2}{r^2}\\hat{r}$$\n\nKnow someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook\n\nHave something to add?","date":"2016-05-24 09:57:50","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 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\": 0.8241561651229858, \"perplexity\": 2511.7426138432434}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-22\/segments\/1464049270527.3\/warc\/CC-MAIN-20160524002110-00103-ip-10-185-217-139.ec2.internal.warc.gz\"}"} | null | null |
export const PaperState = {
accepted: 'accepted',
rejected: 'rejected',
submitted: 'submitted',
to_be_corrected: 'to_be_corrected',
};
export const CommentVisibility = {
judges: 'judges',
reviewers: 'reviewers',
contributors: 'contributors',
};
| {
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} | 8,556 |
{"url":"http:\/\/jmlr.csail.mit.edu\/papers\/v16\/bellec15a.html","text":"## Sharp Oracle Bounds for Monotone and Convex Regression Through Aggregation\n\nPierre C. Bellec, Alexandre B. Tsybakov; 16(Sep):1879\u22121892, 2015.\n\n### Abstract\n\nWe derive oracle inequalities for the problems of isotonic and convex regression using the combination of $Q$-aggregation procedure and sparsity pattern aggregation. This improves upon the previous results including the oracle inequalities for the constrained least squares estimator. One of the improvements is that our oracle inequalities are sharp, i.e., with leading constant 1. It allows us to obtain bounds for the minimax regret thus accounting for model misspecification, which was not possible based on the previous results. Another improvement is that we obtain oracle inequalities both with high probability and in expectation.\n\n[abs][pdf][bib]","date":"2017-07-21 12:42:23","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\": 0.7469019889831543, \"perplexity\": 834.7688796067721}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-30\/segments\/1500549423774.37\/warc\/CC-MAIN-20170721122327-20170721142327-00396.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.daniweb.com\/programming\/web-development\/threads\/341678\/machine-config-in-visual-studio-2005","text":"## mgonzalezwec\n\nHow do I specify the default SMTP host within Visual Studio 2005 or within a web project in Visual Studio 2005? I realize this can be done in the web.config file, however I don't want to do it at that level (I would rather it be done at the machine level). I can set the default SMTP host on IIS 7.0 so that I do not have to specify it in all of my applications, but I cannot find where to specify this in Visual Studio 2005. Is there a machine.config file somewhere that I can change to add this default host? When I debug my web project within Visual Studio, I get run-time errors because I have not specified the SMTP host, but this is not needed on the IIS server so I don't want to code it in. I appreciate your help.\n\n## Ramesh S 129\n\nHi,\n\nThe machine.config file can be located in the following folder in the server\/PC.\ndrive:\\<windows>\\Microsoft.NET\\Framework\\<version>\\config\\machine.config\n\nYou can open it using notepad or VS 2005.\n\n## mgonzalezwec\n\nPerfect. Thank you.","date":"2018-10-21 03:26:45","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8191893100738525, \"perplexity\": 1337.4859662573704}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-43\/segments\/1539583513686.3\/warc\/CC-MAIN-20181021031444-20181021052944-00232.warc.gz\"}"} | null | null |
{"url":"http:\/\/www.komal.hu\/verseny\/feladat.cgi?a=feladat&f=P4662&l=en","text":"Mathematical and Physical Journal\nfor High Schools\nIssued by the MATFUND Foundation\n Already signed up? New to K\u00f6MaL?\n\n# Problem P. 4662. (October 2014)\n\nP.\u00a04662. The goal-keeper is just about to kick off the ball. The kick lasts for $\\displaystyle \\Delta t=0.01$ s, during which the goalkeeper exerts an average force of $\\displaystyle F=850$ N on the ball lying on the ground. If there is no air drag, the kicked ball would reach the ground in $\\displaystyle t=3$ s and it would be $\\displaystyle \\ell=45$ m further.\n\n$\\displaystyle a)$ What is the greatest height that the ball could reach?\n\n$\\displaystyle b)$ According to the official rules of association football the mass of the ball must be between 410 g and 450 g. Is the match played according to the rules?\n\n(4\u00a0pont)\n\nDeadline expired on November 10, 2014.\n\n### Statistics:\n\n 154\u00a0students\u00a0sent\u00a0a\u00a0solution. 4\u00a0points: 122\u00a0students. 3\u00a0points: 10\u00a0students. 2\u00a0points: 13\u00a0students. 1\u00a0point: 6\u00a0students. 0\u00a0point: 3\u00a0students.\n\nProblems in Physics of K\u00f6MaL, October 2014","date":"2018-01-19 05:40:40","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\": 0.3803730607032776, \"perplexity\": 1003.8012995424519}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-05\/segments\/1516084887746.35\/warc\/CC-MAIN-20180119045937-20180119065937-00156.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.enotes.com\/homework-help\/cylindrical-can-with-height-h-radius-r-made-hold-464749","text":"# A cylindrical can with height h and radius r is to be made to hold 1L (i.e. 1000cm3)of oil. Find the dimensions that will minimize the cost of the metal to manufacture\u00a0the can.\n\nFormula for the volume of the cylinder is `V=r^2 pi h`\u00a0which is equal to 1. From that we conclude that\n\n`h=V\/(r^2pi)=1\/(r^2pi) `\u00a0 \u00a0 (1)\n\nSurface area of the cylinder (which we must minimize) is given by formula\u00a0`S=2r^2pi+2rpih` ` `\n\nNow we plug formula (1) into formula for surface area to get\n\n`S=2r^2pi+2rpi*1\/(r^2pi)=2r^2pi+2\/r`\n\nTo get minimum value of surface area we need to find minimum of function\u00a0`S(r)=2r^2pi+2\/r`\n\nFor that we first find where it's derivative is equal to 0.\n\n`S'(r)=0`\n\n` ` `4rpi-2\/r^2=0`\n\nMultiply by `r^2.`\n\n`4r^3pi-2=0`\n\n`r=root(3)(1\/(2pi))`\n\nNow we check to see that it is truly minimum by taking second derivation.\n\n`S''(r)=4pi+4\/r^3`\n\nSince `S''(r)>0`\u00a0(`4pi>0`\u00a0and\u00a0`4\/r^3>0`\u00a0because radius must be positive)we conclude that\u00a0`r=root(3)(1\/(2pi))`\u00a0is indeed minimum value. If we plug that value of `r`\u00a0into (1) we get `h=2root(3)(1\/(2pi)).`\u00a0i.e. height is twice as big as the radius.\n\nSolution: `r=root(3)(1\/(2pi)),` `h=2root(3)(1\/(2pi))`\n\nApproved by eNotes Editorial Team","date":"2023-02-07 12:47:35","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9241448044776917, \"perplexity\": 761.9481707630496}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764500456.61\/warc\/CC-MAIN-20230207102930-20230207132930-00300.warc.gz\"}"} | null | null |
Q: Share sessions between laravel subdomains I have two laravel 7 projects, blog1 and blog2, I want when a user signs in using blog1 and when he/she visits blog2 is already logged in.
My valuables;
Blog1 (config.php)
'driver' => env('SESSION_DRIVER', 'database'),
'domain' => env('SESSION_DOMAIN', '.blog.com'),
Blog1 (.env)
APP_KEY=base64:jiiuuiuriuriurj
APP_URL=http://blog.com
My valuables;
Blog2 (.env)
APP_KEY=base64:jiiuuiuriuriurj
APP_URL=http://blog2.blog.com
| {
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import libvirt
import sys
conn = libvirt.open("xen+ssh://vmx-administrator@213.127.142.245:1920")
if conn == None:
print('Failed to open connection to the hypervisor')
sys.exit(1)
mem = conn.getFreeMemory()
print("Free memory on the node (host) is " + str(mem) + " bytes.")
conn.close()
exit(0) | {
"redpajama_set_name": "RedPajamaGithub"
} | 8,343 |
{"url":"https:\/\/www.cheenta.com\/digits-and-order-aime-i-1992-question-2\/","text":"Categories\n\nDigits and Order | AIME I, 1992 | Question 2\n\nTry this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Order.\n\nTry this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Order.\n\nDigits and order \u2013 AIME I, 1992\n\nA positive integer is called ascending if, in its decimal representation, there are at least two digits and each digit is less than any digit to its right. Find number of ascending positive integers are there.\n\n\u2022 is 107\n\u2022 is 502\n\u2022 is 840\n\u2022 cannot be determined from the given information\n\nKey Concepts\n\nIntegers\n\nDigits\n\nOrder\n\nBut try the problem first\u2026\n\nSource\n\nAIME I, 1992, Question 2\n\nElementary Number Theory by\u00a0David Burton\n\nTry with Hints\n\nFirst hint\n\nThere are nine digits that we use 1,2,3,4,5,6,7,8,9.\n\nSecond Hint\n\nHere each digit may or may not be present.\n\n$$\\Rightarrow 2^{9}$$=512 potential ascending numbers, one for subset of {1,2,3,4,5,6,7,8,9}\n\nFinal Step\n\nSubtracting empty set and single digit set\n\n=512-10\n\n=502.","date":"2020-09-26 19:08:25","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 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\": 0.1759529560804367, \"perplexity\": 4529.380972732899}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-40\/segments\/1600400244353.70\/warc\/CC-MAIN-20200926165308-20200926195308-00698.warc.gz\"}"} | null | null |
Псевдотензор (в частном случае — псевдовектор, псевдоскаляр) — тензорная (а в частности и векторная или скалярная) величина, получающая дополнительный множитель (-1) по сравнению с истинными тензорами соответствующего ранга (истинными векторами, истинными скалярами) в случае преобразований координат с отрицательным детерминантом матрицы преобразования, то есть при преобразовании, меняющем ориентацию базиса. В остальном же псевдотензор (псевдовектор, псевдоскаляр) преобразуется как истинный тензор (вектор, скаляр), а при положительном детерминанте матрицы преобразования координат — в точности как истинный тензор (вектор, скаляр).
С математической, свободной от координат точки зрения, псевдотензор на гладком многообразии есть тензор с коэффициентами в старшей внешней степени кокасательного расслоения. Так, псевдоскаляр есть просто сечение этого расслоения, иными словами, форма старшей степени или плотность. Таким образом, тензор типа на -мерном многообразии является тензором типа , кососимметричным по последним входам.
Другое значение термину псевдотензор придавал, например, Эйнштейн, называя так нетензорную величину, которая дает тензор после интегрирования по 4-мерному объему. Такое употребление также общепринято, по крайней мере по отношению к тем конкретным объектам, к которым их применял Эйнштейн.
Ссылки
Д. Мэтьюз, Р. Уокер, «Математические методы физики», 1972 г.
М. Г. Иванов Введение в тензоры в теории поля
Примечания
Тензорное исчисление
Тензоры в ОТО | {
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Panno, Samuel V.; Hackley, Keith C.; Kelly, Walton R.; Luman, Donald E.
Author(s): Panno, Samuel V.; Hackley, Keith C.; Kelly, Walton R.; Luman, Donald E.
"Sponsored by: P.E. LaMoreaux & Associates, Inc. ..."
Table of Contents: Abstract. -- Introduction. -- Guide to the route. -- Stop descriptions. -- Acknowledgments. -- References. -- Appendix: aerial photographs.
Copyright 2011 Board of Trustees University of Illinois. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,618 |
Paramita was a pop rock act in the Philippines that played their own brand of music from 2005 to 2013. Paramita was made up of Marco De Leon on guitars (replacing Norman Dellosa), Alsey Cortez on bass, and Ria Bautista on drums and vocals. Paramita have released three several albums in its career.
History
In 2005, they released their first single "Hiling" under Vicor Records which placed them on the map. It was included in the 10-track full-length album entitled Tala. Six of the album's songs are written in English while four are in Tagalog. Their second album was self-titled Paramita which was released in 2008 under Terno Recordings.
Despite being such a young band, Paramita has already been featured in several media sources, such as MTV Ink magazine, the Philippine Daily Inquirer, NU 107's In The Raw radio program and the ABS-CBN morning show Breakfast. Paramita is fast becoming one of the most solid independent acts in the scene today, enlightened by music and strengthened by a belief in their own unique talents. By 2010, they decided to go fully independent under Blaster Music (an independent music organization) and launched their third album named Liyab. Their song "Turbulence" was on NU107.7 Stairway to Seven and was no. 1 for 12 weeks on UR105.9 Underground Radio. Their songs "Sulyap" and "Nightingale" received airplay on local stations.
Paramita is now with Blaster Music along with Reklamo and upcoming artists Odat, Penguin, Trapeze, and Eleyn.
Break-up
In the 10th day of October 2013, Paramita announced its disbanding and their future plans as individual artists and musicians on the group's Facebook page.
Band members
Marco De Leon – rhythm guitar
Alsey Cortez – co-vocals, bass guitar
Ria Bautista – drums, lead vocals
Former members
Norman Dellosa – lead guitar
Jeremy Lacorte - rhythm guitar
Paolo Legaspi - bass
Discography
Studio albums
Tala – 2005 Vicor Music Corporation
Paramita – 2008 Terno Recordings
Liyab – 2010 Blaster Records
Collaboration albums
Kami nAPO Muna Ulit (2007, Universal)
Awards and nominations
References
Notes
Bibliography
Paramita on Soundclick.com
Filipino rock music groups
Musical groups established in 2002
Musical groups disestablished in 2013
Musical groups from Manila | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,914 |
Akroním (: ākron – konica + : ōnyma – ime) je po SSKJ ustaljena okrajšava večbesednih imen, po navadi sestavljena iz začetnih črk ali zlogov. Je posebna vrsta kratice, tvorjena iz začetnih komponent v frazi ali besedi. Te komponente so lahko posamezne črke (kot npr. v laser) ali deli besed (kot npr. v Beneluks in Ameslan). O točni definiciji različnih imen za takšne kratice ni splošnega soglasja, kot tudi ne o pisni rabi. V mnogih jezikih imajo takšne kratice omejeno rabo, bolj razširjene pa so postale v 20. stoletju. Akronim je vrsta besedotvornega procesa, imamo pa ga lahko za podvrsto kontaminacije – nastanka novega jezikovnega elementa iz dveh ali več različnih elementov.
Izrazje
Izraz akronim je ime za besedo iz prvih črk vsake besede v nizu besed, kot npr. sonar, tvorjeno iz angleškega izraza SOund Navigation And Ranging). Prvič se je beseda »Akronym« v nemščini pojavila leta 1921, beseda »acronym« v angleščini pa leta 1940.
Medtem ko je kratica okrajšana oblika kakšne začetnice, zloga ali dela fraze ali besed, se inicializem (oziroma manj splošno alfabetizem) nanaša na okrajšano tvorjeno obliko in se rabi preprosto kot niz začetnic. Čeprav se izraz akronim širše rabi kot kratica, tvorjena iz začetnic, nekateri slovarji definirajo akronim kot »besedo« v njenem izvirnem smislu, drugi pa vključujejo dodatne pomene, in pripisujejo akronimom enak pomen kot inicializem. Kadar se rabi, je razlika odvisna od tega ali se kratica izgovarja kot beseda ali kot niz črk. V takšnih primerih so zgledi iz slovarjev npr.: NATO, scuba in radar za akronime, ter HTML, FBI in KGB za inicializme.
Ni soglasja kako naj se imenujejo kratice, katerih izgovorjava obsega kombinacijo črkovnih imen in besed, kot npr. JPEG in MS-DOS.
Tudi ni soglasja kako naj se imenujejo kratice, ki jih nekateri izgovarjajo kot črke, drugi pa kot besede. Izraza URL in IRA se na primer lahko izgovarjata kot posamezne črke, ali kot posamezni besedi. Takšne konstrukcije, če so tvorjene iz začetnic, lahko ne glede na to kako se izgovarjajo, označimo kot inicializmi.
Črkovana oblika akronima ali inicializma (to je kar dejansko pomeni) se imenuje njegova razširitev.
Zgledi akronimov
ABBA – švedska pop skupina, ime tvorjeno iz prvih črk njenih članov: Agnetha, Björn, Benny, Anni-Frid,
Agfa – Aktiengesellschaft für Anilinfabrikation [nemško],
AMEX – American Stock Exchange [angleško],
BETI – BElokranjska TrIkotaža,
bit – binary digit [angleško], dvojiška števka,
DINOS – Dajmo Industriji Nazaj Odpadne Surovine,
KOMET – KOnfekcija METlika,
modem – modulator demodulator [angleško],
NAPROZA – NArodno PROdajna ZAdruga,
NATO – North Atlantic Treaty Organization [angleško],
parsek – paralaksa ene kotne sekunde [angleško parsec – parallax of one arcsecond],
SKOJ – Savez komunističke omladine Jugoslavije [srbohrvaško], Zveza komunistične mladine Jugoslavije,
Tosama – Tovarna sanitetnega materiala,
Zgledi inicializmov
AMZS – Avto-moto zveza Slovenije,
CD – Compact disc [angleško], zgoščenka,
OZN – Organizacija združenih narodov,
ppm – število delcev na milijon [angleško – parts per million],
SPQR – Senātus Populusque Rōmānus [latinsko], Senat in Rimljani,
ZDA – Združene države Amerike,
ZK – Zveza Komunistov.
Glej tudi
abreviatura
psevdonim
eponim
Opombe in sklici
Viri
Jezikoslovje | {
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\section{Introduction}
FBS~0107-082 (also known as Cet 7, and designated FBS0107 in this paper)
was found in the First Byurakan Survey (FBS)
for objects with UV excesses. Based on spectra obtained with the 6-m
telescope at the Special Astronomical Observatory, Kopylov et al. (1988)
provided a preliminary classification as a nova-like (NL) cataclysmic
variable (CV). FBS0107 was subsequently listed as a CV in SIMBAD and in
the Downes, Webbink, \& Shara (1997) CV catalog, but has received very little
attention since the initial discovery paper. We obtained spectra of FBS0107
in 2005 as part of a survey for winds in NL CVs, finding that the spectrum
resembles that of a symbiotic star or planetary nebulae. We have complemented
these initial spectra with multi-epoch photometry and with an analysis of
archival ESO spectra.
In this paper we report on our spectroscopic and photometric findings and
discuss the most likely kinds of objects that fit these findings.
The star appears to be an unusual symbiotic binary. Symbiotic stars
(Kenyon 1986) have evidence for
a hot component in the near UV plus a cool component in the near-IR.
In most cases the hot component is judged to be a white dwarf or
evolved subdwarf, and the
companion to be an M giant with a strong wind. Nebular emission lines are
produced by the action of the radiation field of the hot component on the
surrounding plasma from the wind. Symbiotic stars are not a particularly
homogeneous group and the evolutionary state of the hot component (e.g.
subdwarf or white dwarf) is often uncertain. Our observations are not
a perfect fit to the symbiotic classification, but this identification
seems to best match the properties of FBS0107.
\section{Data Acquisition and Reduction}
\subsection{Photometry}
V-band photometry was obtained over a 1.5 month interval in 2005 on the 0.8-m
telescope of Tenagra Observatory\footnote{http://www.tenagraobservatories.com/}.
There were typically 1-4 exposures on most clear nights,
but on two nights we obtained nearly continuous coverage for several
hours. These data were reduced using a custom pipeline consisting of
IRAF\footnote{IRAF is distributed by the National Optical Astronomy
Observatories, which are operated by the Association of Universities for
Research in Astronomy, Inc., under cooperative agreement with the National
Science Foundation.}
routines for detector calibrations, followed by the application of
SExtractor\footnote{SEextractor is a source detection and photomery package
described by Bertin and Arnouts 1996. It is available from
http://terapix.iap.fr/soft/sextractor/.}. The light curves were then generated
using the incomplete ensemble photometry technique contained in
Astrovar\footnote{ASTROVAR is a custom Indiana
University package based on the technique described in Honeycutt 1992, but
with the addition of a graphical user interface.}.
FBS0107 was also placed on the
long-term monitoring program of the Indiana University (IU) 1.25-m autonomous
telescope\footnote{This facility is located 20 km north of Bloomington IN,
in the Morgan-Monroe State Forest}
for $\sim$ 16 months in 2007/2008. The useable data are comprised of 122
exposures on $\sim$113 different nights. The 1.25-m data were also reduced using
the IRAF/SExtractor/Astrovar pipeline. Table 1 is a log of our photometric
data. Column 1 assigns a number to identify each data set, column 2 gives
the UT dates, column 3 the telescope used, column 4 the exposure time in sec,
column 5 the number of useable exposures, column
6 the duration of the sequence, and column 7 the typical spacing of the
exposures.
Both the Tenagra exposures and the IU 1.25-m exposures were compromised
by various circumstances, and did not reach the desired (and expected) level of
precision. The Tenagra calibration data is acquired automatically, with
no user control of the process. In our case the twilight flats, acquired
on most evenings, were very underexposed; we ended up using a median
combination of all the twilight flats over the $\sim$1.5 months of the
FBS0107 Tenagra exposures. Furthermore the Tenagra bias levels were unstable,
sometimes leading to negative sky counts. The IU 1.25-m data and calibrations were
also acquired in unattended fashion, during commissioning of the telescope and
detector systems. Few
twilight flats were acquired, and the nightly dome flats gave poor results.
Therefore we used median sky flats constructed from all the exposures on a
given (or adjacent) night. Also, we had significant dark current from the
thermoelectically-cooled system that was in service on the IU 1.25-m at this time,
which further degraded the S/N. Fortunately Astrovar has sufficient tools to
evaluate errors
that might result from these difficulties (such as non-linearity, or field errors),
and Astrovar also robustly estimates external errors based on the repeatability
of all constant stars in the field.
In the end the average error for stars with
brightness similar to FBS0107 was $\sim$0.02 mag for the Tenagra data
and $\sim$0.025 mag for the IU 1.25-m data. These errors are for differential
magnitudes with respect to the ensemble. There are no secondary standards
available for this field (although the AAVSO is in the process of establishing
such standards) so we used USNO-B1 magnitudes\footnote{The USNOFS Image and
Catalogue Archive is operated by the United States Naval Observatory, Flagstaff
Station (http://www.nofs.navy.mil/data/fchpix/).}
to establish a somewhat crude, but nevertheless realistic, zeropoint.
The average of the B2 and R2
USNO-B1.0 magnitudes for several stars near FBS0107 were compared to the Astrovar
differential V magnitudes of those same stars, separately for the Tenagra and
for the IU 1.25-m data, to find the
correction from Astrovar magnitude to V. This process has a formal
uncertainty of 0.06 (sdm) mag, but the zeropoint error could be as large as 0.15 mag
considering possible systematic errors in USNO-B1.0, plus errors introduced by
our averaging of B and R to estimate the V magnitude.
\subsection{Spectroscopy}
Five spectra over $\sim$1 hr were obtained in 2005 using MOS/Hydra multiple
object spectrograph on the
WIYN\footnote{The WIYN Observatory is a joint facility of the University of
Wisconsin-Madison, Indiana University, Yale University, and the National
Optical Astronomy Observatory}
telescope. Grating 600 was used in first order, providing
coverage $\sim$5300-8200\AA. The ``red'' 2$\arcsec$ fiber bundle was employed,
yielding $\sim$3\AA\ resolution; numerous other fibers were used for sky
subtraction. Also, a single spectrum
was obtained in 2006 using the RC slit spectrograph on the Kitt Peak
4-m telescope\footnote{The Mayall 4-m telescope is at
Kitt Peak National Observatory, a division of the National Optical Astronomy
Observatory, which is operated by the Association of Universities for Research
in Astronomy, Inc., under cooperative agreement with the National Science
Foundation}.
Grating KPC-007 was used in first order, providing coverage $\sim$5600-7900\AA\
at $\sim$3\AA\ resolution. Finally, the archives of the ESO
Observatory\footnote{
Based on observations made with the European Southern Observatory
telescopes obtained from the ESO/ST-ECF Science Archive Facility.}
were found to contain spectra of FBS017 acquired during a single night in 2004
using the EFOSC-2 spectrograph on the 3.6-m telescope at La Silla. Eighteen
spectra were available using grism \#18, covering $\sim$4700-6700\AA\, along
with 5 spectra using grism \#7, with useable coverage 3700-5240\AA. A 1$\arcsec$
slit was used, and the instrument manual gives a resolution of
7.4\AA\ for these settups. However, we find that the narrowest emission lines
in the FBS0107 spectra have FWHM $\sim$5-6\AA.
For detector calibrations we used standard IRAF
procedures, and for spectral extractions and wavelength calibrations we used
IRAF's onedspec/twodspec packages. No spectrophotometric calibrations were
applied for any of the spectra, and the continua in the reduced WIYN and
Mayall spectra were nomalized to unity. Also, no corrections were made for
telluric spectral features in the near-IR. Table 1 is a log of the
spectrographic observations.
\section{Analysis}
\subsection{Photometry}
Figure 1 plots the results from the two nights of nearly continuous
monitoring (Sets 1 and 2 in Table 1). The top plot appears to contain a small
outburst of amplitude
$\sim$0.07 mag, while the bottom plot shows a decline of $\sim$0.04 mag
over 5 hours. The Astrovar light curves of several field stars of similar
brightness to FBS0107 were examined and did not show such
features. The features are therefore probably real, but since they
barely exceed the errors in the light curves we are reluctant to draw
any conclusions from them. The variability over a night is
smaller than expected from CV-like flickering from accretion.
Figure 2 shows the longer-term light curve of FBS0107. The top panel contains
all the data in Sets 1, 2, and 3 of Table 1, while the middle and lower
panels contain the data for the two observing seasons in Set 4.
It seems clear from Figure 2 that there is no systematic long-term trend over
these 4 years. Nevertheless the scatter generally exceeds the individual
error bars by 3-4$\times$, at least for the points having smaller errors.
To further illustrate this effect, Figure 3 is like Figure 2 except that
data points having errors $>$0.035 mag are excluded (these were obtained
under partly cloudy conditions). Also, the
two sequences over single nights have been averaged to one data point each
for Figure 3. One can find in Figure~3 a number of instances of systematic drifts
in both directions amounting to $\sim$0.1 mag over 15-20 days.
There is an indication of much longer time-scale variability from the
magnitudes in USNO-B1.0. The average of the B and R magnitudes in USNO-B1.0
for FBS0107 is 14.72 (epoch 1951-1954). This is 0.33 mag brighter than our
average magnitude of 15.05 in 2005-2008. One might question this result
because of the
uncertain effect of averaging B and R to estimate V. However, the
exercise is robust in the following sense: The magnitude differences between
our Astrovar instrumental magnitudes and the B,R average for our secondary
standards are consistent to within 0.1 mag (s.d.s.o.), whereas the similar
magnitude difference of FBS0107 is off by 0.33 mag from the mean of the
other field stars. In other words, if one tries to treat FBS0107 as a secondary
standard, it deviates from the field stars by more than 3-sigma, probably because
it is variable. FBS0107 has a B-R color that is similar to that of the
secondary standards, so we conclude that FSB is now fainter by $\sim$0.3 mag in
V compared to when the Palomar plates were exposed $\sim$55 years earlier.
To summarize the photometry, we find that FBS0107 is a variable, but a
puny one. We see changes of a
few hundredths of a mag during a night and perhaps 2-3$\times$ that amount
over a few weeks, but with no systematic trends exceeding 0.05 mag over our
4 year interval of photometry.
These variations do not exceed our observational errors by much, and
we are therefore unable to characterize the changes very well. No flickering
was detected, nor any indication of an eclipse.
\subsection{Spectroscopy}
No exposure-to-exposure changes were apparent in the line strengths of the
reduced spectra from any given night. Furthermore we did not detect any
radial velocity variations during these sequences, to within
$\sim\pm$10 km s$^{-1}$ for 5 WIYN spectra, and to within
$\sim\pm$15 km s$^{-1}$ for the ESO spectral sequences.
Therefore we median-combined the 5 WIYN spectra, the 18 ESO red spectra,
and the 5 ESO blue spectra, for further analysis.
First we compare the WIYN and KPNO 4-m spectra. These are separated by
2 months but have similar resolutions and wavelength ranges.
Figure~4 shows the average of the 5 WIYN spectra of FBS0107 along with an
inset plot of the H$\alpha$ line on an expanded scale, while Figure~5 is a
similar plot for the KPNO 4-m spectrum. In each case H$\alpha$ dominates
the spectrum, seen at a rather spectacular $\gtrsim$50$\times$ the continuum
level, at this resolution. The H$\alpha$ line is steeper on the red side,
with this
asymmetry being more pronounced in the KPNO 4-m spectrum. The weaker
lines are shown in Figures~6 and 7, for two adjacent spectral regions in
common to the WIYN and the 4-m spectra. Except for higher S/N in the
WIYN spectra (due to having combined 5 exposures), the pairs of spectra in
Figures~6 and 7 (separated by 2 months) appear identical. Most of the lines
are due to HeI and OI. There is one absorption feature
near 7772\AA\, which we assign to OI.
Figure~8 shows the median-combined ESO spectra (both red and blue). The
identifications of the strongest lines are given in Table 3, where the
equivalent width measures (EW) have a typical error of $\sim\pm$0.5\AA.
The lines are mostly emission lines of Hydrogen and HeI, plus
forbidden emission lines of oxygen and iron. We also see weak absorption
features at Ca H/K and at NaD. The inset shows the Balmer discontinuity
in strong absorption. In order to preserve information about the Balmer
discontinuity, the continua of the ESO spectra have not been normalized
to unity as was done for the WIYN and KPNO spectra. A broad emission feature
near 6160-6170\AA in Figs. 6 and 8 is assigned to FeI 6164, likely blended
with an unidentified contributor which increases the breadth.
\section{Discussion}
The 1984 spectrum of FBS0107 in Kopylov et al. (1988) covers the range
3240-5040\AA\ at a resolution of 4.5\AA. It shows narrow Balmer emission
lines with a steep decrement. HeII 4686 is weak, but [OIII] 5959, 5007,
and [FeII] are strong. The Balmer discontinuity is not apparent in the
Kopylov et al. spectrum. Their detector response is apparently weak
below 3650\AA\ but a Balmer discontinuity in emission can be ruled out.
Overall, the 1984 spectrum appears very similar
to the ESO 2004 spectrum, indicating little variability in the spectrum of the
star over those 20 years.
We discuss below a number of kinds of emission line objects as
candidates for the nature of FBS0107, noting the similarities and
and differences to the currently-known properties of FBS0107. We begin
with symbiotic stars.
\subsection{Symbiotic systems}
Symbiotic stars (Friedjung \& Viotti 1982; Kenyon 1986; Allen 1988;
Mikolajewska et al. 1988)
are interacting binaries with orbital periods of hundreds of days, consisting of
a late-type giant doner star transfering gas (generally via a wind) to a much
hotter compact companion. The hot object appears to most often be a
white dwarf or hot subdwarf, but may be a main sequence star or neutron star in some
instances. The hot star photoionizes the wind, giving rise
to a nebular spectrum with emission lines due to species such as
HI, He I, He II, [OIII], [Fe II], etc. Symbiotic stars are a rather hetrogeneous
group, and might better be considered as a common phenomenon rather
than a particular configuration and/or evolutionary state. The FBS0107 emission
lines seen in Kopylov et al. (1988) and in Figures~4-8 of this paper
are generally consistent with those of a symbiotic star, albeit having somewhat
lower ionization level than average. The Balmer decrement in FBS0107
is quite steep, as is often found in symbiotic stars. However, because
our spectra are not on a flux scale we cannot reliably quantify the decrement.
Apart from the emission lines, the spectrum of FBS0107 differs significantly
from that of a classical
symbiotic star. In the near-IR, the spectra of symbiotic stars show features
from the late type companion. This is typically an M giant, but can be
as early as G5 (Belczy\'{n}ski et al. 2000); no such features are seen in
FBS0107. The few absorption features we see in FBS0107 do not belong
to a late-type star. Using the plots and tables in Jaschek \& Jaschek (1995)
for the variations of the EWs of absorption features with spectral type,
we find the following constraints on the absorption line spectral class for
FBS0107: EW = 0.9\AA\ for CaII 3934 is most consistent with A0-A5;
EW = $\sim$0.5\AA\ for NaD is most consistent with
A5-G5, and EW = 1.2\AA\ for OI 7772\AA\ is most consistent with
A0-F0 III-I. (This OI line is strongly luminosity sensitive,
reaching EW$\sim$2\AA\ in supergiants (Parsons 1964)).
Overall the results show that a late A to early F photospheric absorption
spectrum is present in FBS0107.
Also, the Balmer continuum is in absorption
in FBS0107. In nearly all other cases in which the Balmer discontinuity is
visible in a symbiotic, the jump is part of the nebular spectrum and appears
in emission (see the compilations of spectra of symbiotics in Allen (1983) and
in Munari \& Zwitter (2002)).
The Barbier \& Chalonge system of spectrophotometric
classification uses the parameter D to measure strength of the Balmer jump,
where D is the log of the ratio of the fluxes on the red and blue sides of
the discontinuity. From the spectrum in Figure~9 we measure D = 0.30. A
convenient calibration of D with spectral
type can be found in Golay (1974). For giants, D = 0.3 corresponds to
either B5 or F1, and F1 is consistent with our earlier deduction of a late A to
early F spectrum in FBS0107.
We also note that two emission features at $\lambda\lambda$6825
and $\lambda\lambda$7082 are not present in our spectra. These two features
are probably due to Raman scattering of OIII resonance lines by neutral
hydrogen (Schmid 1989) and appear in most high excitation symbiotics.
This distinction may not be compelling however, because FBS0107 has a
quite low excitation emisson line spectrum.
IR photometry can potentially be used to discriminate between symbiotic binaries
and other sources such as planetary nebulae and CVs, as well as between
S-type and D-type symbiotics. Using 2MASS photometry, Figure~9 is a plot of
J-H vs H-K$_{S}$ for CVs (Hoard et al. 2002), symbiotics (Phillips 2007),
and PN (Ramos-Larios \& Phillips 2005).
We see that the location of FBS0107 falls firmly among the
PN, not the symbiotics, mostly because the J-H color is bluer than for
most symbiotics. Most symbiotics contain an M giant, which contributes
to making the J-H color redder. If FSB0107 is a symbiotic, then either
the M star is heavily dust-obscured in the optical, or the M star is
otherwise hidden.
Proga, Mikolajewska \& Kenyon (1994) found that the ratio of the strengths
of the He~I emission lines $\lambda$6678/$\lambda$5876 fall in the
range 0.15-0.3 for D-type (dusty) symbiotics, and 0.3-2.0 for S-type, which is
attributed to a systematic difference in densities for the line forming
regions in the two types. This ratio is $\sim$0.4 in FBS0107 (see Table 3).
This value is an upper limit because there has been no correction for
differential extinction between the wavelengths of the two lines. If
FBS0107 is a symbiotic star, it appears
that this ratio is consistent with either D or S-type.
The variability properties of FBS0107 seem consistent with FBS0107
being a symbiotic star, but offer no particular evidence in favor. The lack
of detectable radial velocity variations is not surprising given the
long orbital periods and relatively small amplitudes of the radial velocities
in symbiotic binaries. The variability in the H$\alpha$ profile seen
in FBS0107 is also common in symbiotic binaries, but not uniformly present.
Likewise flickering (not seen in FBS0107) is common (Belczy\'{n}ski et al. 2000)
but has not been reported for all symbiotics.
Finally, symbiotic stars are often associated with a resolved nebula.
The raw long-slit KPNO 4-m spectra were carefully examined for any
extension of the emission lines along the slit, with negative results.
The forbidden lines in FBS0107 indicate that a nebular emission line emission
region is present in FBS0107, but the angular size of the nebula must be
quite small.
The emission line species seen in FBS0107 require
photons with energies $\sim$35 ev for ionization, which in turn
requires temperatures of $\gtrsim$10$^{5}$ $\arcdeg$K. The early F star
seen in the spectrum
cannot be the source of this ionizing radiation, instead requiring the presence of
a white dwarf or hot subdwarf. In principle the F star could be the
mass doner and supplier of the nebular gas (via a wind), but this would
require considerable extension of the definitions and mechanisms of symbiotic
binaries.
A substantial fraction of symbiotic binaries undergo outbursts lasting weeks to
decades, with a brightness increase of 2-7 mag. These are thought to be due
to thermonuclear burning of hydrogen in the white dwarf envelope, analogous to
the outbursts of ordinary novae, but much slower. Like ordinary novae, these
symbiotic novae often display a A-F absorption spectrum during the early outburst stages,
due to an optically thick envelope that
develops around the erupting star. AG~Peg, RT~Ser, and RR~Tel (see discussions and
refs in Kenyon 1986) are examples of symbiotic novae with A-F absorption line spectra
at maximum. The outbursts can sometimes last for decades, and for more than a century
in the case of AG~Peg. In each of these three systems, near outburst maximum, the M star
spectrum is not seen in the near-IR. Emission lines appear during
the decline from maximum, with the emission lines evolving to higher excitation as the
decline progresses. (The AG~Peg emission lines also showed P~Cygni profiles
and multiple velocity components, behaviors similar to that of ordinary novae.) Our
spectra of FBS0107 are mostly consistent with that of the three symbiotic nova mentioned
above, as displayed during the early portion of the decline
from maximum. At this stage they have retained
some of the absorption lines from near maximum, and have developed a relatively
low excitation emission line spectrum, prior to the development of high-excitation
emission lines and the emergence of the spectrum of the M star during late decline.
All three of the symbiotic novae mentioned above showed the Raman emission feature at
$\lambda\lambda$6825, which is not present in FBS0107; this could be due to FBS0107
having not yet developed a high excitation emission line spectrum.
The photometry of FBS0107 raises two difficulties with the symbiotic nova
interpretation. The first is the almost total lack of variability, at least by
symbiotic star standards. All symbiotic systems (including symbiotic novae) seem to have
significant photometric variability on many time scales, with many different origins
(e.g. Skopal 2003), while conspicious variability seems to be missing in FBS0107.
The second issue concerns the time scale of the conjectured FBS0107 outburst.
The slowest symbiotic nova, AG Peg, has a mean decline of 2.3 mag per century (Kenyon
1986). We cannot rule out the possibility that the 1951-54 Palomar Schmidt exposures
were acquired during a separate earlier outburst. But if FBS0107 has remained bright
since 1951-54, then
the decline was only $\lesssim$0.3 mag over 50 years. If FBS0107
is indeed a symbiotic nova in a prolonged outburst, then this outburst is extremely slow
and the photometric stability during outburst is very high.
\subsection{Other Possibilities}
The optical emission lines in FBS0107 resemble that of a high N$_e$ planetary nebulae (PN),
as is true for many symbiotics. However, compared to the template PN spectra in Munari \&
Zwitter (2002), the ratios Balmer /[OIII] and [OIII]/[OI] are each much larger in FBS0107
than in a PN.
Guti\'{e}rrez-Moreno, Moreno \& Cortes (1995) provide a diagositic
diagram to separate PN from symbiotic stars, using the line ratios
R1 = [OIII]4363/H$\gamma$ vs R2 = [OIII]5007/H$\beta$. The [OIII]
line strengths are ratioed to a nearby Balmer line partly to minimize
the effects of differential extinction, which varies slowly with
wavelength. In our case it is also important to use such ratios
because they are nearly independent of the spectrophotometric calibration.
This unknown calibration, which is normally critical in
using emission line ratios for quantitative purposes, is also slowly varying
with wavelength. Therefore we should still be able to apply R1 and R2 to FBS0107.
Note that it is not safe for us to use the ratio R3 = [OIII]5007/[OIII]4363
as described in Guti\'{e}rrez-Moreno et al. (1995) because of the larger wavelength
separation of the two features.
Guti\'{e}rrez-Moreno et al. (1995) find that in a plot of R1 vs R2
(their Figure~1) the region divides into 3 wedges emanating from the origin. The
lower wedge (Region A) contains only PN, while the upper wedge (Region C) contains only
symbiotic stars. The middle wedge (Region B) is lightly populated with young
PN. From Table 3 we find R1 = 0.06 and R2 = 0.36 for FBS-0107. This point
falls very close to the origin of the diagnostic diagram, in a region where the demarcation
wedges are converging and there are very few objects. This is because the Balmer lines
in FBS0107 are very strong compared to [OIII], pushing the values of R1 and R2 to
very small values. It is the normalization process using nearby Balmer
lines (which we need to retain) that is causing the difficulty; the ratio of the
two [OIII] lines is the important variable, and that ratio is within range of the plot.
Therefore we characterize the two dividing lines for the three wedges as
R4 $\equiv$ R1/R2 = 0.17 for the upper line and R4 = 0.075 for the lower line.
For FBS0107, R4 = 0.17. This places FBS0107 on the dividing line
between symbiotics and young PN, and quite some distance from the wedge containing
PN.
A major difficulty in associating FBS0107 with PN is that the photospheric features
in FBS0107 are not that of a PN central star (hot subdwarf), but rather of an early F giant.
Furthermore we detect no nebulosity around FBS0107.
B[e] stars (Zickgraf 1998) are early-type emission line stars with low-excitation permitted
and forbidden emission lines, plus the IR signature of hot dust. They have similarities to
both symbiotic stars and to compact PN. As in symbiotics, the group is not
homogeneous and may represent more of a common phenomenon than a group having a
common physical nature. Unlike symbiotics, they are not required to have a composite
spectrum, and may mostly be single stars. The observational similarities between
B[e] stars and symbiotic binaries in outburst are strong because the
M star in symbiotics is often hidden from view during eruption. It seems likely that
there is cross-contamination between lists of symbiotics and B[e] stars, awaiting
clarification based on the binary nature of the object.
B[e] stars are mostly B stars, so the late A/early F spectrum in FBS0107 is not a good
fit to the B[e] grouping. Another distinction may be between the ``hot dust'' in
B[e] stars and the cooler dust in D type symbiotic stars. The 2MASS colors of
FBS0107 are J-H = 0.27 and H-K$_S$ = 0.65. Gummersbach et al. (1995) show
the location of B[e] stars in the two-color diagram J-H vs H-K. (The difference
between H-K and H-K$_S$ (Carpenter 2001) is unimportant for our purposes.)
FBS0107 falls just outside the blue edge (in both colors) of the B[e] star grouping,
which is an inconclusive result.
Finally, one other object in the Kopylov et al. (1988) list has similarities
to FBS0107. This object (FBS0022-021 = Psc 3) has a blue continuum
and numerous emission lines, some being forbidden. Zharikov et al.
(2004) suggested that this might be an $\eta$~Car-type object, partly
due to the Fe-rich nature of the spectrum. However, unlike FBS0022-021,
the Fe lines in FBS0107 are not particularly strong or numererous.
\section{Conclusions}
Although our conclusion is not as rugged as desired, our opinion is that
FBS0107 is most likely a symbiotic nova, seen in prolonged outburst. This judgement is
partly due to the shortcomings of various competing identifications, but is mostly
based on the presence of the early-F photosphere in the spectrum of FBS0107. The
presence of this absorption spectrum is quite secure and is difficult to explain
without invoking the outburst phase of a nova event. The fact that FBS0107 deviates
somewhat from the properties of most symbiotic stars insofar as IR colors and emission line
ratios is tentatively attributed to the fact that FBS0107 is in prolonged
outburst, and therefore not representative of the majority of symbiotic binaries
which are found in quiesence.
A somewhat worrisome implication of our interpretation is that FBS0107
must be an extreme member of the small class of symbiotic novae, having an outburst
time scale perhaps as long as that of AG Peg, and changing so slowly at present
that photometric variations are barely detectable.
Symbiotic binaries have been considered as progenitors of Type Ia supernovae
(e.g. Munari \& Renzini 1982; Kenyon et al. 1993; Hachisu et al. 1999), especially the
subclasses of recurrent novae (Mikolajewska 2008) and symbiotic novae, (e.g. Hernanz \&
Jos\'{e} 2008). Note however that there are considered arguments against symbiotic
binaries being a significant channel for SNIa (e.g. Hillebrandt \& Niemeyer
2000; Iben \& Fujimoto 2008). In any case, this aspect of symbiotic binaries may lend
additional motivation to understanding the nature of FBS0107, especially if FBS0107 is
able to remain in very protracted thermonuclear outburst, as we are suggesting.
Fortunately our symbiotic outburst hypothesis has fairly straightforward tests. If
FBS0107 is currently in symbiotic outburst, then photographic plate archives may provide
a record of the pre-outburst
state. Also, narrow-band imaging at high angular resolution may reveal nebulosity.
Non-optical observations can further discriminate among the possible candidates for
the nature of FBS0107; for example, it would be most interesting to know if FBS0107 is (or has
been) a supersoft x-ray source, indicative of steady nuclear burning. Overall, it seems that
one of our more definite conclusions is the all-too-common ending to observational papers
that ``more observations are needed''.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,262 |
Q: ASP.NET / Active Directory - Supporting auto login for domain users I am developing a simple ASP.NET website that will run on the intranet on a WS2008(IIS7) box and respond to users running XP/IE8. Everything is domain connected and I am trying to automatically login the users much like SharePoint does.
On my dev machine (XP), when running the site through VS, everything works. I can pickup on the user perfectly. I am using the following settings:
<authentication mode="Windows"/>
<identity impersonate="true"/>
<anonymousIdentification enabled="false"/>
<authorization>
<allow users="*"/>
<deny users="?"/>
</authorization>
However, when I publish to the WS2008 box, it doesn't work. Clearly I am missing a setting in IIS7 to support this.
I have the following set for Authentication on the site:
Anon Auth - Enabled
ASP.NET Impersonation - Enabled
Basic Auth - Disabled
Forms Auth - Disabled
Windows Auth - Disabled
What am I missing?
Thanks
A: Try disabling anonymous login from the iis. Go to the security options for the site on IIS and uncheck the Enable Anonymous login. Make sure that windows authentication is checked.
Edit:: If the login box appears when trying to login with IE, there is a setting that you can set so that IE sends the username when used in the intranet sites. Go to tools > internet options > security and in the security settings select the option Automatic Logon with current username and password or Automatic Logon only in intranet Zone You have to make sure that the site you are trying to use is added in the intranet zone.
There is a similar setting with firefox and chrome I believe but I am not sure how to set it up
A: You need to enable "Windows Authentication" in IIS and disable "Anon Auth"
Here are the settings, you should be using:
Anon Auth - Disabled
ASP.NET Impersonation - Enabled
Basic Auth - Disabled
Forms Auth - Disabled
Windows Auth - Enabled
A: Consider also the intranet zone settings for the browser, as well as the security settings. Try adding other flavors/variations of the URL to the intranet sites zone in IE. My understanding is this is how IE determines if it should automatically submit credentials instead of prompting.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,900 |
Q: I have a question about using extended_image in flutter Hi I ran into a problem while using flutter's extended image.
The image is rendered by putting the url in the getExtendedImage method, but if the url is newly updated, it is not reflected immediately, and the image is updated and rendered only when hot reload or other page is visited.
As soon as the url is modified, how do I get it reflected?
AnimationController extendedController;
void initState() {
// TODO: implement initState
NameController.text = GlobalProfile.loggedInUser.name;
NickNameController.text = GlobalProfile.loggedInUser.nickName;
PhoneNumController.text = GlobalProfile.loggedInUser.phone;
// extendedController = AnimationController();
super.initState();
extendedController = AnimationController(
vsync: this,
duration: const Duration(seconds: 1),
lowerBound: 0.0,
upperBound: 1.0);
}
//get_resize_image_name(GlobalProfile.loggedInUser.profileUrlList,120) returns url
getExtendedImage(get_resize_image_name(GlobalProfile.loggedInUser.profileUrlList,120), 0,extendedController),
A: Use setState(){} to update your widgets
https://api.flutter.dev/flutter/widgets/State/setState.html
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Frank Deford, Longtime Sports Writer, Dies At 78
Doug Mataconis · Wednesday, May 31, 2017 · 1 comment
Frank Deford, who was among the best sports reporters in the business, has died at the age of 78:
Frank Deford, who mined the sports world for human stories and told them with literary grace over six decades in Sports Illustrated, a shelf of books and many years of radio and television commentary, died on Sunday at his home in Key West, Fla. He was 78.
His wife, Carol, confirmed his death on Monday but said she did not yet know the cause.
Mr. Deford retired from NPR's "Morning Edition" on May 3, signing off with what the radio network said was his 1,656th weekly commentary since 1980. He also appeared on HBO's "Real Sports With Bryant Gumbel" for 22 years and wrote for Sports Illustrated for more than 30 years.
At Sports Illustrated, he became a leader in a form of literary sports journalism nurtured by its managing editor, André Laguerre, who recruited him as one of a blue-ribbon roster of writers that included Mark Kram, Dan Jenkins and Roy Blount Jr. Together they made the magazine one of the most successful at Time Inc.
Mr. Deford was a six-time Sportswriter of the Year, a National Magazine Award recipient, a member of the National Sportscasters and Sportswriters Hall of Fame and the first sportswriter to be given a National Humanities Medal, presented by President Barack Obama in a White House ceremony in 2013.
He wrote more than a dozen books, including fiction and nonfiction. In a memoir, "Alex: The Life of a Child" (1983), he wrote about a daughter who died of cystic fibrosis when she was 8. The book was later the basis of a 1986 television movie. He was national chairman of the Cystic Fibrosis Foundation for 16 years.
In another memoir, "Over Time: My Life as a Sportswriter," published in 2012, Mr. Deford said he had written about his daughter "to make her short life mean something."
Benjamin Franklin Deford III was born on Dec. 16, 1938, in Baltimore and attended the Calvert and Gilman schools there before enrolling at Princeton, from which he graduated in 1962. He began his career at Sports Illustrated as a researcher.
In 1980, having become one of the magazine's top writers, he was recruited for what he thought would be a temporary stint, delivering weekly sports commentary on NPR's "Morning Edition."
There he spoke to an audience less obsessed with box scores, statistics and injury updates and more interested in the cultural impact of sports and the people behind the games.
"Nothing made me happier than to hear from literally hundreds of listeners, who would tell me how much the commentaries revealed about a subject they otherwise had never cared much for," NPR quoted him as saying in May.
In 1990, he was recruited to be the founding editor in chief of The National Sports Daily, also known as The National, a short-lived tabloid newspaper that assembled a murderers' row of writers and editors, including John Feinstein and Mike Lupica. Some said they had been drawn there by Mr. Deford's presence.
"I'd follow Frank Deford into any foxhole," Peter Richmond, a sportswriter, told Grantland in 2011. "To this day, I would. If he started this sucker up again and said, 'Except this time we've only got $10,000 and four writers, and you'll have to walk to every city,' I'd do it."
The paper went out of business in less than two years, having lost $150 million.
Besides his wife, Carol, whom he married in 1965, Mr. Deford is survived by his son, Christian; another daughter, Scarlet Crawford; and two grandchildren.
Deford was also a frequent guest on several networks over the years to discuss sports-related issues. His insights, and his prose, will be missed.
FILED UNDER: Obituaries, Sports, Baltimore, Barack Obama, HBO, journalism, NPR, Princeton, television
Guarneri says:
Friday, 2 June 2017 at 09:32
Always sad to see the end of a life. Especially a meaningful one. He was a great sportswriter.
Sports Leagues File Suit To Stop Sports Gambling In New Jersey
Federal Judge Blocks New Jersey Sports Betting, But N.B.A. Commissioner Says 'Legalize It'
Sports Illustrated Ends Print-Only Subscriptions
Supreme Court Justices Appear Skeptical Of Law Barring Legalization Of Sports Gambling
But What About the Most Vulnerable? | {
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{"url":"https:\/\/web2.0calc.com\/questions\/please-help-on-time-constraint-would-really-appreciate-it","text":"+0\n\n0\n132\n2\n\nIf someone could help me with this htat would mean a lot, please and thank you\n\nLet\u00a0$$z = 2 e^{10 \\pi i\/21}$$\u00a0and\u00a0$$w = e^{\\pi i\/7}$$\u00a0then what is\n\n$$$|(z+w)^6|,$$$\n\nthe magnitude of\n\n$(z+w)^6$? ?\n\nSorry for the awful format I am still getting used to this.\n\nJun 28, 2020\n\n#1\n0\n\nThe answer works out to (7*sqrt(2))^2 = 98.\n\nJun 28, 2020\n#2\n0\n\nThank you for the response, but I don't believe that is correct. is there any way you can show me how you got there, so we can figure out, where it went wrong :)\n\nGuest\u00a0Jun 28, 2020","date":"2021-01-19 12:22:13","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 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\": 0.5662966370582581, \"perplexity\": 507.4918558467818}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-04\/segments\/1610703518240.40\/warc\/CC-MAIN-20210119103923-20210119133923-00114.warc.gz\"}"} | null | null |
Transistor has joined the revolutionary nicotine salt trend with their new #BabyClouds Salt E-Liquid by Transistor. Often times high nicotine levels in vape juice can give a harsh throat hit, especially for those just getting into the lifestyle. Nicotine salt provides a much smoother draw so you can enjoy great flavor while still getting your nicotine fix. #BabyClouds Salt offers up a tasty blend of some of the best flavors on the market. Experience subtle undertones of savory Vanilla amidst an array of Nuts from all over the world. The flavor profile comes into full-fruition with an unforgettable Strawberry Custard sensation. #BabyClouds Salt E-Liquid by Transistor has the same great taste as the original #BabyClouds that can now be enjoyed with higher levels of nicotine and still provide an enjoyable throat hit. | {
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A legacy of passion
Granddaughter of the jeweler FRED Samuel, representing the 4th generation of a line of jewelers, Géraldine Samuel grew up between Paris and Provence, in the world of high jewelry. Very early on, she developed a passion for creation: "As a child, I drew princess dresses, like all little girls do, but with the jewels that went with them". Her grandfather advised her, shared the secrets of the trade with her, created the first jewels she designed:
"He trusted my taste and my imagination". And gave her his first watch "A Tigress, by FRED of course!" ».
Today Géraldine perpetuates the family jewelry tradition, an heritage that allows her to display her creations with her own influences by drawing inspiration from tradition to better break out of the mold and reinvent the art of jewelry.
The essence of Géraldine's creations is her imagination, what surrounds her, what she feels, even if it means going against the current of traditional institutions: "I never do jewelry catalogs, I never go to Place Vendôme. I draw inspiration from everything I love, like this mouth pendant I created when I was pregnant with my daughter ". Thus, Géraldine revisits luxury jewelry by drawing inspiration from sensations, childhood memories, images captured on the fly: landscapes, a cloud, a butterfly, scents of lavender, the color of a peony... Her creativity, sublimated by her great sensitivity, gives birth to creations with an unique design, elegant and glamorous, sometimes daring or full of humor, always evoking the sweetness of life. Another look at jewelry where childhood is never far away: "Everything I do for men or women, I decline for children".
BROOKE SHIELD AS AN AMBASSADOR
"Since childhood , I have jewel creation in my skin" admits Géraldine. This is how, after studying business in Paris, determined to make a name for herself in the world of jewelry, she decided to fly to the United States where she obtained her diploma at Carlsbad's GIA. It was the beginning of a career that saw her collaborate with big names in jewelry, Martin Katz, Lorenz Baümer, JEY... Then, with FRED, she created her own "ready-to-wear" jewelry collection in Los Angeles and Miami, "Gery by Géraldine Samuel", which seduced Brooke Shield so much that she became its ambassador.
"… Geraldine, my cousin, also became a very talented jeweler. For their part, my brother and my cousins, in finance, real estate, natural gas transport or trade, also perpetuate the entrepreneurial spirit and the sense of family inherited from our grandfather. »
"And the 4th generation? When we were children, my cousins and I played in the vault of the rue Royale, which seemed to be a magic chest sheltering fabulous treasures. »
"Monsieur Fred", as his relations, his clients, and his collaborators called him, could really have been a hero on the big screen. But for his wife Thérèse, his sons Henri and Jean, his grandchildren Jérôme, Anthony, Gregory, Géraldine and myself, he was above all a loving husband, an affectionate father and grandfather who had unconditional love for his family. »
DESTINATION OF HIGH-END JEWELRY
Imagining, drawing, creating, choosing precious stones, pearls… such is Géraldine's playground. A tremendous space of freedom which allows her all the audacity, all the freedoms. Today, it is on her native land, in France, that she has returned to exercise her passion for fine jewelry and is developing a new high-end collection, imagined and designed by her. Expert in gemmology, Géraldine has also chosen the most beautiful pieces of jewelery to make her new collection a collection of exceptional jewelery intended for a demanding clientele.
We use cookies on our website to provide you with the most relevant experience by remembering your preferences and repeat visits. By clicking "Accept", you consent to the use of ALL cookies. | {
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Celebración del Centenario
Sigma Delta Pi, the National Collegiate Hispanic Honor Society, was founded on November 14, 1919, at the University of California, Berkeley by a junior undergraduate student named Ruth Helen Barnes. Later that same academic year, on May 1, 1920, the first formal induction ceremony was conducted. On January 1, 2019, Sigma Delta Pi launched a centennial commemoration that concluded on July 29, 2020 with the Society's first-ever virtual awards reception held via Zoom. The 19-month centennial celebration featured numerous initiatives and projects that highlighted Sigma Delta Pi's 100-year history.
Each new member initiated during the 2019 calendar year received a special commemorative membership pin of the design posted above. Existing members of Sigma Delta Pi may also purchase this same pin, while supplies last, for the cost of $10 through their home chapters.
During the entire year of 2020, and to commemorate Sigma Delta Pi's first formal induction ceremony on May 1, 1920 in Berkeley, CA, all new members receive the Ruth Barnes' commemorative pin that replicates the original presented to founding members. Existing members may also purchase this same replica, while supplies last, for the cost of $10 through their home chapters.
In April 2020 and to commemorate the Society's first 100 years, the College of Charleston's Mark P. Del Mastro published an updated history of the organization: Sigma Delta Pi: Rediscovering a Century, 1919-2019 with Juan de la Cuesta Hispanic Monographs. Although the book is available directly through Amazon, special signed copies may be purchased from Sigma Delta Pi's national headquarters (click here to order). If you missed the May 1, 2020 Facebook Live reading by the author of select chapters from this book, the recording is found at "Reading from Sigma Delta Pi's New History Book"(click here).
While preparing this tome, Del Mastro also published multiple notes that highlight select aspects of Sigma Delta Pi's collaboration during its history:
"Reflections on a Common Past: MIFLA and Sigma Delta Pi,"
MIFLC Review 9 (Fall 2018-2019): 1-5.
"Sigma Delta Pi y la ANLE: Historias y protagonistas,"
Glosas 9.7 (September 2019): 63-66.
"Sigma Delta Pi and the AATSP: A Shared Century of Leadership and Collaboration,"
Hispania 102.1 (March 2019): 5-7.
"Sigma Delta Pi, La Sociedad Nacional Honoraria Hispánica: El Centenario 1919-2019,"
The 2nd World Conference on University Researchers (WCUR).
The Vellum Page & Downhill Publishing, 2019, 15-18.
The University of Maine published a brief article about Del Mastro's research for this book:
"The Missing Volumes,"
Raymond E. Fogler Library Magazine, 2019, 17-18.
Also to commemorate Sigma Delta Pi's centennial, Del Mastro organized a "Sigma Delta Pi History Panel" that was accepted and scheduled for presentation at the AATSP's 102nd Annual Conference in Puerto Rico in July 2020. Because of the conference's postponement due to COVID-19, in early June 2020 participants recorded their respective presentations (click here to view the virtual panel).
Sigma Delta Pi's History
Ruth Helen Barnes | {
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Bradley Curry
For a Good Time, Listen to Midland's Boot Scootin' Single "Mr. Lonely"
Bradley Curry Raised Rowdy Contributor
Trio Mark Wystrach, Jess Carson, and Cameron Duddy, otherwise known as Midland, have helped revive the honky tonk sound that many country fans have been longing to hear the past couple decades and they're continuing to do so with their latest single "Mr. Lonely."
Photo by Harper Smith
On the group's Instagram, they said that this new single "pays homage to some of our musical heroes with it's scootin' rhythm and guitar driven "Friday Night" dancehall sound. It's balls to the wall country, honky tonk rock 'n' roll that's serious bout getting you off your barstool and up on the dance floor." The initial guitar riff will remind many of Dwight Yoakam's 1993 single "Fast As You," giving fans hope that real honky tonk music is still out there. To promote the new single, they created an Instagram profile ran by Mr. Lonely himself and even gave him a phone number. Fans can of course call or text the one and only Mr. Lonely at 512-648-6364 for a surprise. (seriously, do it. It's cool).
Midland will be traveling all over the country on their Electric Rodeo tour as well as opening for the king himself, George Strait on June 8th in Columbus, Ohio. Follow Midland on Instagram (@Midland) and Twitter (@MidlandOfficial). Download "Mr. Lonely" on anywhere music is streamed! | {
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Paul Brunton Philosophic Foundation homepage > Notebooks of Paul Brunton > Category 19: The Reign of Relativity > Chapter 2: The Double Standpoint
The Double Standpoint
All experience may be regarded from either the practical or the philosophical standpoint, but best of all from the double standpoint.
We use a twofold standpoint in this quest. This is because it is the minimum possible. Yet even this would seem to contradict and negate itself. But each serves a purpose of its own. It is possible, because of the reign of relativity in the universe, even to trace a sevenfold standpoint, all the levels coexisting.
Mentalism says we can make sense of our experiences only if we apply to them, and to our understanding of them, the double standpoint: Immediate and Ultimate, or Appearance and Reality, or Relative and Absolute. The ordinary, normal point of view takes the world as the five senses find it--that is, as it appears to be. This is easy for everyone to understand and accept. But the deepest possible examination and analysis by philosophic intelligence, as well as the highest possible insight of mystic experience, presents a totally different result: The One, That which IS, has undergone no change at all.
Can we ever escape from the relativity which affects everything from an ant to an aeon? In a universe where everything is in process of continuous change and is ever becoming something else, where nothing has a self-existence that is really enduring, where every ephemeral change seems the only reality at the moment, can we hope to find something that exists by its own right and forever exists unchanged in itself? Reality that IS? The answer is provided by philosophy. Our intellects and senses may misapprehend it and perceive form without perceiving its essence. Nevertheless, reality interpenetrates everything and goes out into all things. There is nothing here in this space-time without its share in reality. Hence philosophy bids us see through the multitudinous forms of the world into the unity upon which they are grounded, without, however, letting our consciousness lose, as the mystic loses, the forms themselves. And this unitary substance is none other than Mind-essence itself.
If we think, "I strive to become one with God," or, "I am one with God," we have unconsciously denied the statement itself because we have unconsciously set up and retained two things, the "I" and "God." If these two ultimately exist as separate things they will always exist as such. If, however, they really enter into union, then they must always have been in union and never apart. In that case, the quest of the underself for the Overself is unnecessary. How can these two opposed situations be resolved? The answer is that relativity has taught us the need of a double standpoint, the one relative and practical and constantly shifting, the other absolute and philosophical and forever unchanged. From the first standpoint we see the necessity and must obey the urge of undertaking this quest in all its practical details and successive stages. From the second one, however, we see that all existence, inclusive of our own and whether we are aware of it or not, dwells in a timeless, motionless Now, a changeless, actionless Here, a thing-less, egoless Void. The first bids us work and work hard at self-development in meditation, metaphysics, and altruistic activity, but the second informs us that nothing we do or abstain from doing can raise us to a region where we already are and forever shall be in any case. And because we are what we are, because we are Sphinxes with angelic heads and animal bodies, we are forced to hold both these standpoints side by side. If we wish to think truthfully and not merely half-truthfully, we must make both these extremes meet one another. That is, neither may be asserted alone and neither may be denied alone. It is easier to experience this quality than to understand it.
This is puzzling indeed and can never be easy, but then, were life simple and less paradoxical than it is, all its major problems would not have worried the wisest men from the remotest antiquity until today. Such is the paradox of life and we had better accept it. That is, we must not hold one standpoint to the detriment of the other. These two views need not oppose themselves against each other but can exist in a state of reconciliation and harmony when their mutual necessity is understood. We have to remember both that which is ever-becoming and that which is ever in being. We are already as eternal, as immortal, as divine as we ever shall be. But if we want to become aware of it, why then we must climb down to the lower standpoint and pursue the quest in travail and limitation.
It would be an error to believe that the two standpoints are in conflict with each other; they are not because they cannot be. They can never produce a logical antimony; they are different readings of the same thing, a difference rendered inevitable because referring to different levels of knowledge, experience, and position.
One of the helpful notions which philosophy contributes to those who not only seek Truth through the intellect alone, but also seek to know how they are to live with that Truth in the active world itself, is the idea of the twofold view. There is the immediate view and there is the ultimate viewpoint. The first offers us a convenient way of looking at our activities in the world and of dealing with them whilst yet holding firmly to the Truth. The first tells us to act as if the world is real in the absolute sense. The second viewpoint, the ultimate, tells us that there can be only one true way of looking at everything, because there is only one Reality. Since it deals with the Absolute, where time and space disappear and there is no subject to view, no object to be viewed, there is no thought or complex of thoughts which can hold it; it transcends intellect. Therefore it could be said that philosophy uses duality for its practical viewpoint, but it stays in nonduality for its basic one, thus reconciling both.
What is the practical value of the teaching about time? The full answer to this question would embrace many fields, but here is one of the most important. Philosophy teaches its student to apply the double point of view to the outward happenings of his life as it does to the inward contents of his sense-experience. From the ordinary point of view, the nature of an event determines whether it is a good or an evil one; from the philosophic point of view, the way he thinks about the event will determine whether it is good or evil for him. He should always put the two points of view together and never separate them, always balance the short-range one by the long-range one.
The higher point of view enables him to escape some of the suffering which the lower one would impose upon him. An event which to the worldly man seems staggeringly important and evil from the point of view of the moment, becomes smaller and smaller as the years recede and, consequently, less and less hurtful. Twenty years later it will have lost some of its power to shake him; fifty years later it will have lost still more--indeed, it may have lost so much as to cause him no further pain; one incarnation later it will not trouble him at all. When the student adopts the long-range point of view he achieves the same result in advance and by anticipation of time. It is said that time heals all sorrows; if we seek the reason why, we shall find it is because it insensibly gives a more philosophic point of view to the sorrowful. The taste of water in a jar will be strongly sweetened by a cupful of sugar; the taste of water in a bucket will be moderately sweetened by it; the taste of water in a bathtub will be only slightly sweetened by it; and water in a lake will be apparently quite unmodified by it at all. In exactly the same way, the stream of happenings which makes up time for human consciousness gradually dilutes the suffering which each individual event may bring us.
The student is not content, however, to wait for such a slow process in order to reduce his suffering. By bringing the philosophic attitude to bear upon each event, as and when it occurs, he immediately reduces his suffering and fortifies his peace. Every calamity which is seen from this standpoint becomes a means whereby he may ascend, if he will, to a higher level of understanding, a purer form of being. What he thinks about it and what he learns from it will be its real legacy to him. In his first fresh anguish the unawakened man may deny this; in the mental captivity which gives reality to the Present and drops it from the Past, he may see no meaning and no use in the calamity; but either by time or by philosophy he will one day be placed at the point of view where the significance of suffering will be revealed to him and where the necessity of suffering will be understood by him. This, indeed, is one of the great paradoxes of the human development: that suffering leads him step by step from the false self to the acceptance of the true self, and that the true self leads him step by step back to the acceptance of suffering.
If the worldly man agitatedly sees the event against the background of a moment, if the philosophic student calmly sees it against the background of an entire lifetime, the sage, while fully aware of both these points of view, offsets them altogether by adding a third one which does not depend on any dimension of time at all. From this third point of view, he sees both the event itself and the ego to whom it happens as illusory. He feels the sense of time and the sense of personality as unreal. Deep within his mind he holds unshakeably to the timeless character of true being, to the eternal life of the kingdom of heaven. In this mysterious state time cannot heal, for there are no wounds present whereof to be healed. So soon as we can take the reality out of time, so soon can we take the sting out of suffering. For the false self lives like a slave, bound to every passing sensation, whereas the true self lives in the timeless peace of the kingdom of heaven. As soon as we put ourselves into harmony with the true self, we put ourselves into harmony with the whole universe; we put ourselves beyond the reach of calamity. It may still happen, but it does not happen to nor is it felt by our real self. There is a sense of absolute security, a feeling that no harm can come to us. The philosophic student discovers the mission of time; it heals sorrows and, under karma or through evolution, cures evils. The sage solves the mystery of timelessness, which redeems man.
Philosophy would not be worthwhile if it did not take the view that for the practical purposes of life, it must turn around and adopt a non-metaphysical approach. Thus a twofold attitude is the only complete and therefore correct one which it may approve. We have the right and bear the duty to ask ourselves in what way is a teaching related to everyday living; in what way is it connected with the world we know? If both relation and connection are absent, it is fair to say that the teaching is inadequate and lacks the necessary balance of interests.
Metaphysically, every thing and every thought contains in itself the form of its opposite. We must try not to be attached to one opposite and not to be repelled by the other in a personal way. This does not mean that we may ignore them--indeed we cannot do so, for practical life requires that we attempt at least to negotiate them--but that we deal with them in an equable and impersonal way. Thus we keep free of the bonds of possessiveness. If we try to cling to one of the opposites alone whilst rejecting the other, we are doomed to frustration. To accept what is inherent in the nature of things is therefore a wise act. If, through being personally hurt by it, we are unwilling to do so, if we rebel against it, then we shall succeed only in hurting ourselves all the more. To run away from one of the opposites and to run after the other is an unwise act. We must find a balance between them; we must walk between the two extremes; we must ascend the terrace above the standpoint which affirms and above that which negates: for the entire truth is never caught by either and is often missed by both. For the way in which our consciousness works shuts us up, as it were, in a prison house of relativistic experiences which are the seeming real but never the actually real. To accept both and yet to transcend both, is to become a philosopher. To transcend the opposites we have to cease thinking about what effect they will have upon us personally. We have to drop the endless "I" reference which blinds us to the truth about them. We must refuse to set up our personal preferences as absolute standards, our relative standpoints as eternal ones. To do this is to cease worrying over events on the one hand, to cease grabbing at things on the other. It is indeed to rise to an impersonal point of view and enter into harmony with what Nature is seeking to do in us and in our environment. We have to find a new and higher set of values. For so long as we cling to a personal standpoint we are enslaved by time and emotion, whereas as soon as we drop it for the philosophic one, we are liberated into a serene timeless life.
All concepts are dualistic; each implies its contrary concept. We cannot think them without silently posing their counterparts: the Void and the All, the "I" and the not-Self. This is why we have to abandon dualism in the end for nondualism if we want truth. We cannot have one foot in each camp.
Once the double viewpoint is understood and set up as the necessary starting point, the timed measure and the timeless order fall into his scheme of things. Practical experience carries him through the ordinary existence, and divine experience--the eternal Now--is not displaced by it. Success in living the philosophic life and maturing the mentality it requires makes this possible.
Only by accepting the double standpoint concurrently, rejecting neither the Real nor the Illusory, can we achieve Truth's wholeness.
Unless one looks at life from this double point of view, one can get only an inadequate unbalanced and incomplete perspective. It is needful for the everyday practical routine of living to regard it only at the point of personal contact. Here one sees its momentary, transitory, and finite form. But it is also needful for the satisfaction of the higher interests of mind and heart to regard the living universe as a whole. Here one sees an eternal and infinite movement, cored and surrounded by mystery.
That which IS is not moved, affected, or changed by events or things, by cosmic calamities or human thoughts. For these are all in time, THAT is out of it, has always been out of it and must therefore always be out of it. To us, all is happening in successive moments, but that is the timed view.
Hegel in Germany and the Jains in India taught the relativity of truth. They showed that by taking up different positions different aspects of truth would be revealed. But where the Jains put forward seven positions as covering the range, Hegel put forward three. Any relative truth is limited, one-sided, incomplete, and may even contradict the others. While philosophy endorses the truth of relativity present in both positions, it cannot endorse their exclusive character. It paradoxically adopts a positionless position free from their rigidity and limitations. It comes into no conflict with any sect, system, or religion, with any fixed dogmatism or free-thinking scepticism. It is a rival to none, competes with none. It reconciles the varied expressions of human thought and belief, accommodates them all by refusing their one-sidedness, bias, prejudice, but avoids their errors and incompleteness. It knows what it teaches, the final incontrovertible truth that there is nothing beyond Mind. It experiences the final uncontradictable reality where no distorting ego is present.
Science has pushed forward its exploration and operation into the immense distances of the cosmos without being able to conceive an end to them, as it has penetrated the unbelievably tiny world of the atom with a similar result. This is the mathematical infinite. But there is another. No instruments and no apparatus can be applied to objects of thought which imply its existence, for measurement and quantity are not concerned. That is the metaphysical infinite.
(a) "The one without a second" reappears in the universe as "no two things alike." (b) Nonduality, not two, means mentalism; the world is my idea, in my consciousness, hence not separate from me. There are not two--me plus world.
The World-Mind itself dwells in the Timeless Present, the Eternal Now. But for human beings all things happen, are experienced and observed, in succession.
Why did Emerson remark when he had to examine a quantity of wood he had ordered: "We must see to these things, you know, as if they were real"?
Unless these two standpoints are recognized as necessary, only bewildered minds, confused thinking, and false conclusions will follow. The immediate must be distinguished from the ultimate, the obvious from the profound.
Just as The Hidden Teaching Beyond Yoga defines Reality as that which is always real and never changing, so Truth is that which is always and everywhere true and not necessarily under certain conditions.
Consciousness can assume different forms, can operate on different space and time levels, so that it is relative. But it can also remain itself and assume no form; it is then what has been called absolute, not relative. But to reject the possible existence of all these other forms, however temporary they may be, as do those Indians who limit themselves solely to the doctrine of nonduality--fascinated as they are by the reality of the Real and the illusoriness of the unreal, so that they forget whether they are real or unreal--is to forget that he who holds the doctrine is himself a human being. He who comes back from the mystic experience of universality comes back to a human form, is himself a human being, however divine in his inmost essence. The Absolute is not a human being and can have no possible point of view, but the human being must have a humanized philosophy and can have a point of view. What is he to do after recognizing the opposition between the absolute and the relative consciousnesses, between the real and the unreal? The answer is and must be the double point of view. Not, mind you, the double nature of Truth, but the double point of view for us, humans: the one being empirical, practical, earthly and rational, the other being ultimate, divine, intuitive.
The enigma of existence cannot be solved on the single basis of the Void alone, nor on the basis of manifestation alone. Both must be taken into account together and at the same time in order to constitute existence for human entities as incarnate individuals.
This recognition of the dual principle governing all manifested existence does not cancel recognition of the Unmanifest as being the Final, the Unique, the Real. For the two are derived from it; into it their appearance and working vanish at last, but they themselves, as part of the World-Idea, never. Each universe follows the Divine Order of Yin-Yang.
The attempt to reduce truth to a single focal point fixed at the highest possible level suffices for the meditator and the dreamer. But it is too limited to suffice for life itself: thought and action, insight and practice, require two distinct points of view--the immediate and the ultimate.
The way out of the to-and-fro wanderings of his moods, to spirit and then away from it, is to accept the double nature of his being and the double polarity of Nature, the double viewpoint of truth and the double aspects of God. Then struggles cease and harmony prevails. There is then no warlike confrontation within himself, but peaceful reconciliation.
We have learned that time is but the succession of our thoughts. We have learned also that in all our experience of time and irrespective of the particular series to which it belongs, whether it run with the rapidity peculiar to dream or with the slowness peculiar to wakefulness, there must exist in us a background of rest, of stillness, against which we unconsciously measure our time-sense. The problem is how to bring this background into the field of consciousness. The answer is partly provided for us by this brief analysis. If the thought-succession were stopped--if awareness were determinedly pinned down to a single immobile point--then we would become enfranchised in the kingdom of Infinite Duration. This, however wonderful it be, could nevertheless only be a temporary process because life itself demands that we return to world-consciousness, to the knowledge of experience in space-time. It is indeed the condition which the successful mystic evidently arrives at, the condition of sublime trance which is regarded by him as the perfection of his quest.
The ultimate truth refers to the essence of a thing, its real nature. The immediate truth refers to its shifting conditions or passing states, the thing as it appears at the moment of perception.
Paradox is the only way to view both the immediate and the ultimate at the same time.
Philosophy says that its highest teaching is necessarily paradoxical because the one is in the many and the many, too, are one, because nonduality is allied to duality, because the worldly and limited points to the Absolute and Unbounded: hence the doctrine of two Truths.
Paradox is the only proper way to look at things and situations, at life and the cosmos, at man and God. This must be so if as full and complete a truth as mind can reach is desired. To express that truth there are two ways because of its own double nature: there is what the thing seems to be and what it really is. The difference is often as great as that yielded by an electronic microscope with five thousand-fold magnification when it is focused on an ant, compared to the view yielded by the naked eye.
If we question time and matter--those foundations of all our worldly experience--for their real nature, we come up against paradox and contradiction, against irrationality and logical absurdity. The only proposition which can properly be affirmed about them is that they exist and do not exist at the same time.
You cannot put It into any symbol without falsifying what It really is. Yet you cannot even mention It in any way whatsoever without putting It into a symbol. What then are you to do? If mystics declare, as they so often do, that you should keep silent, ask them why so many of them have failed to obey this rule themselves? In their answer you will find its own insufficiency and incompleteness. For although, like everyone else, they too have to function on two separate and distinct levels, yet the truths pertaining to one level must in the end be coupled with those pertaining to the other.
Paradox is the bringing together of two elements which are antagonistic yet complementary.
The worship of God in the ordinary and personal sense is quite valid for those who wish to practise it, and for the masses who cannot rise to the highest nondual conception of God. If it involves this phenomenal world, and keeps the worshipper in duality and relativity, he is not wasting his time. As soon as the human mind insists on indulging its imagination or its thinking capacity and tries to understand where it ought to stop and let go of its egoistic effort, it must accept such a paradoxical situation as the double standpoint. The sixth-century Chinese philosopher Chi Tsang, in his "Essay on the Double Truth," which accepted both the immediate or relative and the ultimate or absolute standpoints, felt the difficulty but could do no other than accept it.
Its cultivation and application
The necessity of employing the double viewpoint leads to the acceptance of paradox as being the nature of truth. The practising philosopher finds that he must live in time as well as simultaneity, extension as well as infinity, mind as well as MIND. Were he to be simplistic he would create confusion.
He has to practise living on two different planes of being at once, the immediate and ultimate, the short-range and long-range, the relative and the Absolute, not as if they were in eternal contradiction but as if they were one and indivisible.
We have to cope with the world and the problems it brings us with the body and its needs. There is no evading them. Yet on the other hand, we have to recognize that in Absolute Truth there is no world, no body, no problems--only the one infinite timeless Being. How can we meet this enigmatic dilemma? Christian Science denies the dilemma in theory, but is untrue to its denial in practice. This is why so many have passed into its portals only to emerge again in later years. Philosophy counsels us to admit the plain fact, to cultivate a bifocal vision, and to see the relative truth where and when we want it but always fitted into the larger absolute truth.
There are two viewpoints: a qualified truth for the lower stage of aspirants which admits duality; and the complete viewpoint of nonduality for the highest student; thus for practical life, when dealing with other people or when engaged in some activity, those in the first stage must accept the notion of the world being real, because of expediency; yet even so, when they are alone or when keeping quiet, inactive, they ought to revert back to regarding the world, which includes one's own body as a part of it, as idea. Only for the sage is the truth always present, no matter whether he is with others, whether he is working, or whether he is in trance, and this truth is continuous awareness of one Reality alone and one Self alone.
Two simultaneous states of awareness are present in him.
We must perceive unity in diversity, and diversity in unity.
There is no loftier metaphysical standpoint than that of nonduality, but man cannot live by metaphysics alone. He is in the body, which in its turn is in the world. He needs a second standpoint to deal with both body and world. He needs the relative, the finite, the immediate one of personal experience. Metaphysics may tell him that the world, when examined and analysed, is but an appearance, and not even that when it is taken into the deepest meditation; but the five senses tell him that he must come to terms with it.
The world exists in precisely the same way for both the simpleton and the sage, but whereas it exists only as it appears in the first case it exists both as it appears and as it really is in the other.
In order to remember that we are godlike in essence we do not need to forget that we are human in existence.
We exist as beings in time and space, but as Being in the Timeless and Spaceless. For an Advaitin to deny the first statement is as futile as for a materialist to deny the second one.
Does this double standpoint mean that there is a constant oscillation between the two aspects, a mind which flutters from one to the other over and over again? Of course not! Just as the small circle can be contained within a larger circle, so the mind can be at once in the practical and the metaphysical yet able to concentrate on the one needed at any moment.
He has a double existence, with the frontal part of his consciousness in time and the real part out of it. All the miseries and misfortunes which may enter into the one part will make no difference to the blessed tranquillity which permanently reigns in the other.
He is to be not only an actor in the world's drama taking part in the events, but also a member of the audience watching them, not only in the very midst of the happenings but also their detached observer. This sounds too contradictory: are the two roles irreconcilable?
His awareness of the relativity of things relieves the philosopher of any compulsion to identify himself with any particular viewpoint. His liberation from dogma enables him to take the viewpoint which best suits the circumstances. This does not at all mean that chaos will enter into his affairs, insincerity into his attitudes, and anarchy into his morals. He is safeguarded from such perils by the link he has established with the Overself's infinite wisdom and immeasurable goodness.
The knowledge of its essence thrusts itself up between him and the world so that the physical sensed-envelope is seen for what it is.
Only by having a philosophic perspective on whatever happens to him, by balancing the day's events against the timelessness of Reality, can he find and keep peace of mind.
He lives in this fixity of consciousness deep within his heart, a fixity which makes the passage of time seem illusory and which makes the happenings of time seem appearances.
Live among men as if the world-appearance is what they feel it to be--the reality--but know for yourself the inner truth about it and about yourself.
Coming down here into the body of flesh and blood is our confusion. Experiencing the sufferings and distresses which we do is our fate. The satisfactions are there also, yes, and induce us to cling to life and return anew after each reincarnation. We need always remember that all this experience which a human undergoes is relative to time and place and must pass on and away. To what? To that higher order of the universe where we are with God as higher creatures.
With this larger outlook comes a larger acceptance of the past, of bygone deeds and thoughts, however one may regret actions or feel guilty or embarrassed about emotions. For if there is to be a forgiveness of others, there must also be forgiveness of one's self. And if one has outgrown one's past self, it should be as if one were looking upon another being, a stranger being.
This duality of his life will go on until he is ready for the Great Truth which displaces all the lesser ones but which he cannot grasp while clinging to them. If he persists in doing so, he will never be able to make the transition to understanding that there is only the One Infinite Life-Power, the One Ever-Existent Mind, and that all else is mere illusion, idea, or dream.
We hear from the East that the world is unreal and that the ego is unreal, or that the world does not exist and that the ego does not exist. It is here that semantics as developed by Western minds may perhaps be of some service in clarifying confused thinking leading to confused statements. The body is a part of the world. Do we or do we not dwell in a body? If we do not then we should stop feeding it and stop taking it to the physician when it gets sick. Yet even those people who make such extraordinary statements do continue to eat, to fall sick, and to visit a doctor. Surely that disposes immediately of the question whether or not the body exists. In the same way and by the same pattern of reasoning we can discover that the world also exists. What then has led these Indian teachers to proclaim otherwise? Here we begin to intrude upon the field of mentalism and as a necessary part of the key to mentalism we must turn to the dream state. If we dream of a world around us and of a body in which we live in this dream world and of other bodies of other persons moving in it, the Indians say that these dream persons and this dream world is seen to be non-existent when we wake up and hence they deny its reality. But the experience did happen, so let us scrutinize it. There was no such thing as this world, true, but something was there; what was there? Thoughts. All this world and all these persons about whom we dream pass through consciousness as thoughts, so the thoughts were there. Whether we consider dream or hallucination, the pictures are there in the person's mind; they exist there, but they exist there only as mental creations. But when we say they are merely mental creations, we are bringing in an attempt to judge them, to judge their nature, what they really are. The statement that they are unreal is therefore a judgement and is acceptable only on the basis of a particular standpoint, the standpoint of the observer who is outside the dream, outside the hallucination. It is not acceptable on the basis of the person who is having the experience at that moment. Thus we see that the existence of the ego, the body, and the world need not be denied; it is there, it is part of our experience, but what we have to do is to examine it more closely and attempt a judgement of its nature. And this judgement does not alter the fact that they are being experienced. This is a fact of our own, of everyone's experience, including the highest sage, only the sage and the common man each has his own judgement from his point of view, from his knowledge. In all these topics we can see how much easier it is to pick our way if we adopt the attitude which was proclaimed in The Hidden Teaching Beyond Yoga that there is a double viewpoint and a double standard in this teaching in order that we may be clear about our experiences and about our ideas and not get them mixed up. These two standpoints, the immediate and the ultimate, the common and the philosophic, are absolutely necessary in all talk and study about such metaphysical topics. Otherwise we get lost in mere verbiage, words, words, words.
The illumined person must conform to the double action of nature in him, that is, to the outgoing and incoming breaths. So his illumination must be there in the mind, and here in the body. It is the two together which form the equilibrium of the double life we are called upon to live--being in the world and yet not of it. In the prolongation of the expiring breath, we not only get rid of negative thought, but also of the worldliness, the materialism of keeping to the physical alone. With the incoming breath we draw positive inspiring remembrance of the divine hidden in the void. Hence we are there in the mind and here in the body. We recognize the truth of eternity yet act in time. We see the reality of the Void, yet know that the entire universe comes forth from it.
The exterior reality being Maya, our universe becomes both an enigma and a paradox until nonduality is accepted as the final and only solution.
The difficulty in accommodating the practical and philosophical views of existence is understandable. However, these dual views should not be mistaken for contrasting and opposing ones. The ultimate insight synthesizes them although it cannot prevent the continuance of their seeming variations. It is as though the foreground of the mind must hold the practical view while the background simultaneously holds a philosophical view. This is true for the developed aspirant, but in the adept there arrives, after long practice and profound experience, a condition of illumination which treats all experience for the idea that it is and at the same time keeps bright the light of the ever-burning lamp of reality--Pure Mind.
The idea of illusion is a necessary discovery for the beginner, but with deeper knowledge he discovers that the illusion is also the real because it is not apart from reality. The truth is that reality is attainable.
The philosophic view does not depose the empiric everyday view of the world. For practical purposes, the rules of the latter will always remain dominant.
To live in the ego is to live in time, to live in the Overself is to live in timelessness. But because man must live in both to live on earth at all, let him learn the art of resting in the eternal Now, the continuing moment which opens on to eternity.
The double viewpoint doctrine is as useful as it is convenient, for it enables the philosopher to live among the ignorant who believe they inhabit a totally real world as if he shared their belief. Otherwise they might segregate him from his fellows on a charge of insanity and put him in the special institutions built for such cases.
We live in the limitations of relativity but pursue the freedoms of divinity. Only later do we discover both are counterpart ideas--to be transcended.
The statement "to be" is to be "in time" or "in timelessness." Most limit its meaning to the first phrase only. But the more enlightened know that the higher possibility has been realized by some.
Where time is dismissed as unreal, attention to historic change must necessarily wane, and where form is regarded as illusory, the need of a cosmogony will not be felt. The correctness of this position cannot be argued away but its one-sidedness can. For we still have to live in time and form, with our bodies at least.
So long as you think there is variety, as in dream you feel the differences are real, you are in the illusory plane. In the unenquired stage, when you don't enquire into the reality of your experience (as in dream) you hold the illusive view.
The practical standpoint cannot be dispensed with because it is not humanly possible to find time to gather all the facts and so we have to take many matters on trust or on authority. We use it with confidence because it is based on a fairly uniform experience. The fact remains, however, that the knowledge it affords is not true but only probable knowledge.
World-Mind has truly made an image of itself in man who has his pure Mind state in sleep and his active state in waking. Hence space-time relations are introduced only with manifestation and not in Mind. The eternal stillness of Mind is broken by the birth of a cosmos, but it is broken only from the low standpoint of human ignorance. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,886 |
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"redpajama_set_name": "RedPajamaC4"
} | 9,568 |
Q: Bluetooth HC-05 Won't Get Paired To Android So, recently I follow these series of tutorial http://www.youtube.com/playlist?list=PL2cK5QO_pN1gfEcWZ8tCWUb-WyxAiMyIK
To connect Arduino with Android using Bluetooth module HC-05
I did exactly on his scheme, the bluetooth module detected as HC-05 on my android, but won't get paired. The red LED keep blinking.
as http://mcuoneclipse.com/2013/06/19/using-the-hc-06-bluetooth-module/ said the red LED on the module indicates the status:
blinking: ready to pair
steady on: paired
here is the code that I should get output "(Paired)" beside my device name
receiver = new BroadcastReceiver(){
@Override
public void onReceive(Context context, Intent intent) {
String action = intent.getAction();
if (BluetoothDevice.ACTION_FOUND.equals(action)){
BluetoothDevice device = intent.getParcelableExtra(BluetoothDevice.EXTRA_DEVICE);
devices.add(device);
String s = "";
for(int a=0;a<pairedDevices.size();a++){
if (device.getName().equals(pairedDevices.get(a))){
//append
s = "(Paired)";
break;
}
}
listAdapter.add(device.getName()+" "+s+" "+"\n"+device.getAddress());
}else if (BluetoothAdapter.ACTION_DISCOVERY_STARTED.equals(action)){
}else if (BluetoothAdapter.ACTION_DISCOVERY_FINISHED.equals(action)){
}else if (BluetoothAdapter.ACTION_STATE_CHANGED.equals(action)){
if (btAdapter.getState() == btAdapter.STATE_OFF){
turnOnBT();
}
}
}
};
instead i got a toast saying that the device is not paired
@Override
public void onItemClick(AdapterView<?> arg0, View arg1, int arg2, long arg3) {
// TODO Auto-generated method stub
if (btAdapter.isDiscovering()){
btAdapter.cancelDiscovery();
}
if (listAdapter.getItem(arg2).contains("(Paired)")){
BluetoothDevice selectedDevice = devices.get(arg2);
ConnectThread connect = new ConnectThread(selectedDevice);
connect.start();
}else {
Toast.makeText(getApplicationContext(), "device is not paired", 0).show();
}
}
what did I miss?
note:
I am using,
external power supply
Module HC-05 with two chip (on video there is only one chip)
Arduino UNO (on videos used Android Pro Mini)
A: i find my own answer,
before connecting using our own apps in android, we have to pair it first from system settings>bluetooth> input password of our bluetooth module (in my case 1234)
A: You can also make your hc 05 to be connected by your code instead of pairing it from settings.
You just made one mistake in your code:
Inside onItemClick method you are checking if devices is already paired then you call connect thread and if not paired you are showing toast saying device not paired , but it does not make any sense ..
You should connect it if it does not contain "paired" else you make an object of connectThread and call connect method.
Hope this works!
Let me know if it does not.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,969 |
\section{Introduction}
\setcounter{equation}{0}
Define the Fourier transform ${\mathcal F}\! f$ (or $\hat f$ for brevity) of an integrable function $f$ on the $d$-dimensional Euclidean space ${\mathbb{R}}^d$
by
\begin{equation}\label{fouriertransform.def}
{\mathcal F}\! f(\xi):=\int_{{\mathbb{R}}^d} e^{-i \langle {\bf x}, \xi\rangle} f({\bf x}) d{\bf x},\end{equation}
and extend the above definition to all tempered distributions as usual.
Here we denote by
$\langle \cdot, \cdot\rangle$ and $\|\cdot\|$ the standard inner product and norm on ${\mathbb{R}}^d$ respectively.
Let ${\mathcal S}:={\mathcal S}({\mathbb{R}}^d)$ be the space of all Schwartz functions on ${\mathbb{R}}^d$ and ${\mathcal S}':={\mathcal S}'({\mathbb{R}}^d)$
the space of all tempered distributions on ${\mathbb{R}}^d$.
For $\gamma>0$, define the {\em fractional Laplacian} $(-\triangle)^{\gamma/2}$
by
\begin{equation}\label{fractionallaplacian.def}
{\mathcal F}((-\triangle)^{\gamma/2}f)(\xi):=\|\xi\|^\gamma \ {\mathcal F} f(\xi),\quad f\in {\mathcal S}.
\end{equation}
The fractional Laplacian has the remarkable property of being dilation-invariant. It plays a crucial role in the definition of thin plate splines \cite{duchon1977},
is intimately tied to fractal stochastic processes (e.g., fractional Brownian fields) \cite{mandelbrot1968,tafti2009} and
stable Levy processes \cite{chen10}, and has been used in the study of singular obstacle problems
\cite{caffarelli08, silvestre06}.
In this paper, we present a detailed mathematical investigation of the functional properties of dilation-invariant differential operators together with a characterization of their inverses.
Our primary motivation is to provide a rigorous operator framework for solving the
stochastic partial differential equation
\begin{equation}\label{randompde.def}
(-\triangle)^{\gamma/2} \Phi=w\end{equation}
with white noise $w$ as its driving term. We will show that this is feasible via the specification of a novel family of dilation-invariant left-inverses
of the fractional Laplacian $(-\triangle)^{\gamma/2}$ which have appropriate $L^p$-boundedness properties.
We say that a continuous linear operator $I$ from ${\mathcal S}$ to
${\mathcal S}'$ is {\em dilation-invariant}
if there exists a real number $\gamma$ such that
\begin{equation}
I (\delta_t f)= t^\gamma \delta_t (If)\quad{\rm for\ all} \ f\in {\mathcal S}\ {\rm and} \ t>0,
\end{equation}
and {\em translation-invariant} if
\begin{equation}I (\tau_{{\bf x}_0} f)= \tau_{{\bf x}_0} (If)\quad {\rm for\ all} \ f\in {\mathcal S}\ {\rm and} \ {\bf x}_0\in {\mathbb{R}}^d, \end{equation}
where the {\em dilation operator} $\delta_t, t>0$ and the {\em translation operator} $\tau_{{\bf x}_0}, {\bf x}_0\in {\mathbb R}^d$ are defined by
$(\delta_t f) ({\bf x})= f(t {\bf x})$ and
$\tau_{{\bf x}_0} f({\bf x})= f({\bf x}-{\bf x}_0), f\in {\mathcal S}$, respectively.
One may verify that the fractional Laplacian $(-\triangle)^{\gamma/2}, \gamma>0$, is dilation-invariant
and translation-invariant, a central property used in the definition of thin plate splines \cite{duchon1977}.
Next, we define the {\em Riesz potential} $I_\gamma$ (\cite{riesz49}) by
\begin{equation} \label{rieszpotential.eq1}
I_\gamma f({\bf x})=\pi^{-d/2} 2^{-\gamma} \frac{\Gamma((d-\gamma)/2)}{\Gamma(\gamma/2)}\int_{{\mathbb R}^d} \|{\bf x}-{\bf y}\|^{\gamma-d} f({\bf y}) d{\bf y}, \quad f\in {\mathcal S},
\end{equation}
where $0<\gamma<d$.
Here the Gamma function $\Gamma$ is given by
$\Gamma(z)=\int_0^\infty t^{z-1} e^{-t} dt$ when the real part ${\rm Re}\ z$ is
positive, and is extended analytically to a meromorphic function
on the complex plane. For any Schwartz function $f$, $I_\gamma f$ is continuous and satisfies
\begin{equation} \label{rieszpotential.eq2}
|I_\gamma f({\bf x})|\le C_\epsilon \Big(\sup_{{\bf z}\in {\mathbb R}^d} |f({\bf z})| (1+\|{\bf z}\|)^{d+\epsilon}\Big) (1+\|{\bf x}\|)^{\gamma-d}\quad {\rm for \ all}\ {\bf x}\in {\mathbb R}^d,
\end{equation}
where $\epsilon>0$ and $C_\epsilon$ is a positive constant, see also Theorem \ref{generalizedrieszomega1.tm}. Then the Riesz potential $I_\gamma$ is a continuous linear operator from ${\mathcal S}$ to ${\mathcal S}'$.
Moreover one may verify that $I_\gamma$ is dilation-invariant and translation-invariant, and also
that $I_\gamma, 0<\gamma<d$, is the inverse of the fractional Laplacian $(-\triangle)^{\gamma/2}$; i.e.,
\begin{equation}\label{rieszpotential.eq3}
I_\gamma (-\triangle)^{\gamma/2} f=(-\triangle)^{\gamma/2} I_\gamma f=f\quad {\rm for\ all} \ f\in {\mathcal S}
\end{equation}
because
\begin{equation}\label{rieszpotential.eq4}
{\mathcal F}(I_\gamma f)(\xi)= \|\xi\|^{-\gamma} {\mathcal F}f (\xi), \ f\in {\mathcal S}.
\end{equation}
A natural question then is as follows:
{\bf Question 1}: {\em For any $\gamma>0$, is there a continuous linear operator $I$ from ${\mathcal S}$ to ${\mathcal S}'$
that is translation-invariant and dilation-invariant, and that is an inverse of the fractional Laplacian $(-\triangle)^{\gamma/2}$?}
In the first result of this paper (Theorem \ref{generalizedriesz.tm}), we give an affirmative answer to
the above existence question for
all positive non-integer numbers $\gamma$ with the invertibility replaced by the left-invertibility, and further prove the uniqueness
of such a continuous linear operator.
To state that result, we recall some notation and definitions.
Denote the dual pair between a Schwartz function and a tempered
distribution using angle bracket $\langle \cdot, \cdot\rangle$, which is given by
$\langle f, g\rangle=\int_{{\mathbb R}^d} f({\bf x}) {g({\bf x})} d{\bf x}$ when $f, g\in {\mathcal S}$
(we remark that the dual pair between two complex-valued square-integrable functions
is different from their standard inner product).
A tempered distribution $f$ is said to be {\em homogeneous of degree $\gamma$} if
$\langle f, \delta_t g\rangle= t^{-\gamma-d} \langle f, g\rangle$ for all Schwartz functions $g$
and all positive numbers $t$. We notice that the multiplier $\|\xi\|^{-\gamma}$ in the Riesz potential $I_\gamma$, see \eqref{rieszpotential.eq4},
is a homogenous function of degree $-\gamma\in (-d, 0)$.
This observation inspires us to follow the definition of homogeneous tempered distribution in \cite{hormanderbook} and then to extend the definition of the Riesz potential $I_\gamma$ to any non-integer number $\gamma>d$ as follows:
\begin{eqnarray}\label{generalizedriesz.def}
I_\gamma f({\bf x})& := & \frac{(2\pi)^{-d}\Gamma(d-\gamma)}{ \Gamma(d+k_0-\gamma)} \int_{S^{d-1}} \int_0^\infty r^{k_0-\gamma+d-1}\nonumber \\
& &
\times \Big(-\frac{d}{dr}\Big)^{k_0} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi')\Big) dr d\sigma(\xi'),
\quad f\in {\mathcal S},
\end{eqnarray}
where $S^{n-1}=\{\xi'\in {\mathbb{R}}^d: \ \|\xi'\|=1\}$ is the unit
sphere in ${{\mathbb{R}}}^d$, $d\sigma$ is the area element on $S^{n-1}$, and
$k_0$ is a nonnegative integer larger than $\gamma-d$.
Integration by parts shows that the above definition \eqref{generalizedriesz.def}
of $I_\gamma f$ is independent on the nonnegative integer $k_0$ as long as it is larger than $\gamma-d$, and
also that it coincides with the classical Riesz potential when $0<\gamma<d$ by letting $k_0=0$
and recalling that
the inverse Fourier transform ${\mathcal F}^{-1} f$ of an integrable function $f$ is given by
\begin{equation}\label{inversefouriertransform.def}
{\mathcal F}^{-1} f({\bf x}):=(2\pi)^{-d} \int_{{\mathbb{R}}^d} e^{i \langle {\bf x}, \xi\rangle} f(\xi) d\xi.\end{equation}
Because of the above consistency of definition, we call
the continuous linear operator $I_\gamma, \gamma\in (0, \infty)\backslash ({\mathbb{Z}}_++d)$ in \eqref{generalizedriesz.def} the {\em generalized Riesz potential}, where ${\mathbb{Z}}_+$ is the set of all nonnegative integers.
\begin{Tm} \label{generalizedriesz.tm}
Let $\gamma$ be a positive number with $\gamma-d\not\in {\mathbb{Z}}_+$, and let $I_\gamma$ be
the linear operator defined by \eqref{generalizedriesz.def}.
Then $I_\gamma$ is the {\bf unique} continuous linear operator from ${\mathcal S}$ to ${\mathcal S}'$ that
is dilation-invariant and translation-invariant, and that is a left inverse of the fractional Laplacian $(-\triangle)^{\gamma/2}$.
\end{Tm}
Let $L^p:=L^p({\mathbb R}^d), 1\le p\le \infty$, be the space of all $p$-integrable functions on ${\mathbb R}^d$ with
the standard norm $\|\cdot\|_p$. The Hardy-Littlewood-Sobolev fractional integration theorem (\cite{steinbook})
says that the Riesz potential $I_\gamma$ is a bounded linear operator from $L^q$ to $L^p$ when $1<p\le \infty, 0<\gamma<d(1-1/p)$
and $q=pd/(d+\gamma p)$. Hence
$I_\gamma f\in L^p$ for any Schwartz function $f$
when $0<\gamma<d(1-1/p)$.
We observe that for any non-integer number $\gamma$ larger than or equal to $d(1-1/p)$,
there exists a Schwartz function $f$ such that $I_\gamma f\not\in L^p$, see Corollary \ref{nonintegrable.cr}.
An implication of this negative result, which will become clearer in the sequel (cf. Section 4), is that we cannot generally use the translation-invariant inverse $I_\gamma$ to solve
the stochastic partial differential
equation \eqref{randompde.def}.
What is required instead is a special left-inverse of the fractional Laplacian
that is dilation-invariant and $p$-integrable. Square-integrability in particular ($p=2$) is a strict requirement when the driving noise is Gaussian and has been considered in prior work \cite{tafti2009}; it leads to a fractional Brownian field solution, which is the multi-dimensional extension of Mandelbrot's celebrated fractional Brownian motion \cite{blu, mandelbrot1968}.
Our desire to extend this method of solution for non-Gaussian brands of noise leads to the second question.
{\bf Question 2}: {\em Let $1\le p\le \infty$ and $\gamma>0$.
Is there a continuous linear operator $I$ from ${\mathcal S}$ to ${\mathcal S}'$
that is dilation-invariant and a left-inverse of the fractional Laplacian $(-\triangle)^{\gamma/2}$ such that $If\in L^p$ for all Schwartz functions $f$?}
In the second result of this paper (Theorem \ref{integrablefractionalderivative.tm}), we give an affirmative answer to the above question when both $\gamma$ and $\gamma-d(1-1/p)$
are not integers, and show the uniqueness of such a continuous linear operator.
To
state that result, we introduce some additional multi-integer notation.
For ${\bf x}=(x_1, \ldots, x_d)\in {\mathbb R}^d$ and
${\bf j}=(j_1, \ldots, j_d)\in {\mathbb Z}_+^d$ (the $d$-copies of the set ${\mathbb Z}_+$),
we set
$|{\bf j}|:=|j_1|+\cdots+|j_d|$, ${\bf j}!:=j_1!\cdots j_d!$ with $0!:=1$,
${\bf x}^{\bf j}:=x_1^{j_1}\cdots x_d^{j_d}$ and $\partial^{\bf j} f({\bf x}):=\partial^{j_1}_{x_1}\cdots\partial^{j_d}_{x_d} f({\bf x})$.
For $1\le p\le \infty$ and $\gamma>0$, we define the linear operator $I_{\gamma, p}$
from ${\mathcal S}$ to ${\mathcal S}'$ with the help of the Fourier transform:
\begin{equation}\label{fractionalderivative.veryolddef}
{\mathcal F}(I_{\gamma, p} f)(\xi)=\Big({\mathcal F} f(\xi)-\sum_{|{\bf j}|\le \gamma-d(1-1/p)}
\frac{\partial^{\bf j} ({\mathcal F} f)({\bf 0})}{{\bf j}!} \xi^{\bf j}\Big) \|\xi\|^{-\gamma}, \quad f\in {\mathcal S},
\end{equation}
which is the natural $L^p$ extension of the fractional integral operator that was introduced in \cite{blu, tafti2009,taftu2010} for $p=2$ and $\gamma\not\in {\mathbb{Z}}/2$.
We call $I_{\gamma, p}$ the {\em $p$-integrable Riesz potential of degree $\gamma$}, or the
{\em integrable Riesz potential} for brevity. Indeed,
when both $\gamma$ and $\gamma-d(1-1/p)$ are non-integers, the linear operator
$I_{\gamma, p}$ is the unique
left-inverse of the fractional Laplacian $(-\triangle)^{\gamma/2}$ that enjoys the
following dilation-invariance and stability properties.
\begin{Tm}\label{integrablefractionalderivative.tm}
Let $1\le p\le \infty$, and $\gamma$ is a positive number such that
both $\gamma$ and $\gamma-d+d/p$ are not nonnegative integers.
Then $I_{\gamma, p}$ in \eqref{fractionalderivative.veryolddef} is the {\bf unique} dilation-invariant left-inverse of the fractional Laplacian $(-\triangle)^{\gamma/2}$ such that
its image of the Schwartz space ${\mathcal S}$ is contained in $L^p$.
\end{Tm}
One of the primary application of the $p$-integrable Riesz potentials
is the construction of generalized random processes by suitable functional integration of white noise \cite{tafti2009, taftu2010, Unser2009}.
These processes are defined by the
stochastic partial differential equation \eqref{randompde.def}, the motivation being that the solution should essentially display the same invariance properties as the defining operator (fractional Laplacian).
In particular, these processes will exhibit some level of self-similarity (fractality) because $I_{\gamma, p}$ is dilation-invariant. However, they will in general not be stationary because the requirement for a stable inverse excludes translation invariance. It is this last aspect that deviates from the classical theory of stochastic processes and requires the type of mathematical safeguards that are provided in this paper. While the case of a white Gaussian noise excitation is fairly well understood \cite{tafti2009}, it is not yet so when the driving term is impulse Poisson noise which leads to the specification of sparse stochastic processes with a finite rate of innovation. The current status has been to use the operator $I_{\gamma,2}$ to specify sparse processes with the restriction that the impulse amplitude distribution must be symmetric \cite[Theorem 2]{Unser2009}. Our present contribution is to show that one can lift this restriction by considering the operator $I_{\gamma,1}$, which is the proper inverse to handle general impulsive Poisson noise.
To state our third result,
we recall some concepts about generalized random processes and Poisson noises.
Let ${\mathcal D}$ be the space of all compactly supported $C^\infty$ functions with standard topology.
A {\em generalized random process}
is a random functional $\Phi$ defined on ${\mathcal D}$
(i.e., a random variable $\Phi(f)$ associated with every $f\in {\mathcal D}$)
which is linear, continuous and compatible \cite{gelfandbook}.
The white Poisson noise
\begin{equation}\label{whitepoisson.def}
w({\bf x}):=\sum_{k\in {\mathbb Z}} a_k \delta({\bf x}-{\bf x}_k)\end{equation}
is a generalized random process such that the random variable associated with a function $f\in {\mathcal D}$ is given by
\begin{equation}w(f):=\sum_{k\in {\mathbb{Z}}} a_k f({\bf x}_{k}),\end{equation}
where the $a_k$'s are i.i.d. random variables with probability distribution $P(a)$, and where the ${\bf x}_k$'s
are random point locations in ${\mathbb R}^n$ which are mutually independent and follow a spatial Poisson distribution
with Poisson parameter $\lambda>0$.
The
random point locations ${\bf x}_k$ in ${\mathbb R}^n$ follow a {\em spatial Poisson distribution}
with Poisson parameter $\lambda>0$ meaning that for any measurable set $E$ with finite Lebesgue measure $|E|$,
the probability of observing $n$ events in $E$
(i.e., the cardinality of the set $\{k| \ {\bf x}_k\in E\}$ is equal to $n$)
is $\exp(-\lambda |E|) (\lambda |E|)^n/ n!$. Thus, the Poisson parameter $\lambda$
represents the average number of random impulses per unit.
As the white Poisson noise $w$ is a generalized random process, the stochastic partial differential equation \eqref{randompde.def}
can be interpreted as the following:
\begin{equation}\label{randompde.def2}
\langle \Phi, (-\triangle)^{\gamma/2} f\rangle=\langle w, f\rangle\quad {\rm for\ all} \ f\in {\mathcal D}.
\end{equation}
So if $I$ is a left-inverse of the fractional Laplacian operator $(-\triangle)^{\gamma/2}$, then
\begin{equation}\Phi=I^* w\end{equation} is
{\em literally} the solution of the stochastic partial differential equation \eqref{randompde.def} as
\begin{equation}
\langle I^*w, (-\triangle)^{\gamma/2} f\rangle=\langle w, I(-\triangle)^{\gamma/2} f\rangle=\langle w, f\rangle \quad {\rm for \ all} \ f\in {\mathcal D},
\end{equation}
where $I^*$ is the conjugate operator of the continuous linear operator $I$ from ${\mathcal S}$ to ${\mathcal S}'$
defined by $$\langle I^*f, g\rangle:=\langle f, Ig\rangle\quad {\rm for\ all} \ f, g\in {\mathcal S}.$$
The above observation is usable only if we can specify a left-inverse (or equivalently we can impose appropriate boundary condition)
so that $I^*w$ defines a bona fide generalized random process in the sense of Gelfand and Vilenkin; mathematically, the latter is equivalent to providing its characteristic functional by the Minlos-Bochner Theorem (cf. Section 4).
The following result establishes
that $P_\gamma w:=I_{\gamma, 1}^*w$ is a proper
solution of the stochastic partial differential equation
\eqref{randompde.def}, where $w$ is the
Poisson noise defined by (\ref{whitepoisson.def}).
\begin{Tm}\label{generalizedpoisson.tm}
Let $\gamma$ be a positive non-integer number, $\lambda$ be a positive number,
$P(a)$ be a probability distribution with $\int_{{\mathbb{R}}} |a| dP(a)<\infty$, and $I_{\gamma, 1}$ be defined as in \eqref{fractionalderivative.veryolddef}.
For any $f\in {\mathcal D}$, define the random variable $P_\gamma w$ associated with $f$ by
\begin{equation}\label{generalizedpoisson.tm.eq1}
P_\gamma w (f):=\sum_{k} a_k I_{\gamma, 1}(f)({\bf x}_k)
\end{equation}
where
the $a_k$'s are i.i.d. random variables with probability distribution $P(a)$, and the ${\bf x}_k$'s
are random point locations in ${\mathbb R}^n$ which are mutually independent and follow a
spatial Poisson distribution with Poisson parameter $\lambda$.
Then $P_{\gamma} w$ is
the generalized random process associated with the characteristic
functional
\begin{equation}\label{generalizedpoisson.tm.eq2}
{\mathcal Z}_{P_\gamma w}(f)= \exp\Big(\lambda \int_{{\mathbb{R}}^d}\int_{{\mathbb{R}}} \big(e^{-ia (I_{\gamma, 1}f)({\bf x})}-1\big) dP(a)d{\bf x}\Big),
\quad f\in {\mathcal D}.
\end{equation}
\end{Tm}
\bigskip
The organization of the paper is as follows. In Section \ref{grp.section}, we first introduce
a linear operator $J_\Omega$ for any
homogeneous function $\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ of degree $-\gamma$, where $\gamma-d\not\in {\mathbb{Z}}_+$.
The linear operator $J_\Omega$
becomes the generalized Riesz potential $I_\gamma$ in \eqref{generalizedriesz.def} when $\Omega(\xi)=\|\xi\|^{-\gamma}$;
conversely, any derivative of the generalized Riesz potential $I_\gamma$
is a linear operator $J_\Omega$ associated with some homogeneous function $\Omega$:
$$\partial^{\bf j} I_\gamma f= J_{\Omega_{\bf j}} f\quad {\rm for\ all} \ f\in {\mathcal S}\ {\rm and} \ {\bf j}\in {\mathbb{Z}}_+^d,$$ where $\Omega_{\bf j}(\xi)=(i\xi)^{\bf j} \|\xi\|^{-\gamma}$.
We then study various properties of the above linear operator $J_\Omega$, such as polynomial decay property, dilation-invariance,
translation-invariance, left-invertibility, and non-integrability in the spatial domain and in the Fourier domain.
The proof of Theorem \ref{generalizedriesz.tm} is given at the end of Section \ref{grp.section}.
In Section \ref{irp.section}, we introduce a linear operator $U_{\Omega,p}$ for any homogeneous function
$\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ of degree $-\gamma$, where $1\le p\le \infty$. The above linear operator $U_{\Omega, p}$ becomes
the operator $I_{\gamma,p}$ in \eqref{fractionalderivative.veryolddef} when $\Omega(\xi)=\|\xi\|^{-\gamma}$, and
the operator $J_\Omega$ in \eqref{fractionalderivative.def} when $0<\gamma<d(1-1/p)$.
We show
that the linear operator $U_{\Omega,p}$ is dilation-invariant, translation-variant and $p$-integrable, and
is a left-inverse of the fractional Laplacian $(-\triangle)^{\gamma/2}$ when $\Omega(\xi)=\|\xi\|^{-\gamma}$.
The proof of Theorem \ref{integrablefractionalderivative.tm} is given at the end of Section \ref{irp.section}.
In Section \ref{poisson.section}, we give the proof of Theorem \ref{generalizedpoisson.tm} and show that the generalized
random process $P_\gamma w$ can be evaluated pointwise in the sense that
we can replace
the function $f$ in \eqref{generalizedpoisson.tm.eq1} by the delta functional $\delta$.
In this paper, the capital letter $C$ denotes an absolute positive constant which may vary depending on the occurrence.
\section{Generalized Riesz Potentials}\label{grp.section}
Let $\gamma$ be a real number such that $\gamma-d\not\in {\mathbb{Z}}_+$, and let
$\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be a homogeneous function of degree $-\gamma$.
Following the definition of homogenous tempered distributions in \cite{hormanderbook},
we define the linear operator $J_\Omega$ from ${\mathcal S}$ to ${\mathcal S}'$
by
\begin{eqnarray}\label{fractionalderivative.def}
J_\Omega f({\bf x})\!\! & := & \!\! \frac{(2\pi)^{-d}\Gamma(d-\gamma)}{ \Gamma(d+k_0-\gamma)} \int_{S^{d-1}} \int_0^\infty \Omega(\xi')r^{k_0-\gamma+d-1}\nonumber \\
& &
\times \Big(-\frac{d}{dr}\Big)^{k_0} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi')\Big) dr d\sigma(\xi'), \quad f\in {\mathcal S},
\end{eqnarray}
where $S^{n-1}=\{\xi'\in {\mathbb{R}}^d: \ \|\xi'\|=1\}$ is the unit
sphere in ${{\mathbb{R}}}^d$, $d\sigma$ is the area element on $S^{n-1}$, and
$k_0$ is a nonnegative integer larger than $\gamma-d$.
Note that the linear operator $J_\Omega$ in \eqref{fractionalderivative.def}
becomes the generalized Riesz potential $I_\gamma$ in \eqref{generalizedriesz.def}
when $\Omega(\xi)=\|\xi\|^{-\gamma}$ and $\gamma>0$.
Therefore we call the linear operator $J_\Omega$ in \eqref{fractionalderivative.def} {\em the generalized Riesz potential associated with
the homogeneous function $\Omega$ of degree $-\gamma$}, or {\em the generalized Riesz potential} for brevity.
The above definition
of the generalized Riesz potential $J_\Omega$ is independent on the nonnegative integer $k_0$ as long as it satisfies $k_0>\gamma-d$,
that can be shown by integration by parts.
Then, for $\gamma \in (-\infty, d)$, we may take $k_0=0$ and reformulate \eqref{fractionalderivative.def} as
follows:
\begin{equation}\label{fractionalderivative.neweq2}
J_\Omega f({\bf x})=(2\pi)^{-d} \int_{{\mathbb{R}}^d} e^{i\langle {\bf x}, \xi\rangle} \Omega(\xi) \hat f(\xi) d\xi
\quad {\rm for \ all} \ f\in {\mathcal S},
\end{equation}
or equivalently
\begin{equation}
\widehat{J_\Omega f}(\xi)= \Omega(\xi) \hat f(\xi)\quad {\rm for \ all} \ f\in {\mathcal S},\end{equation}
so that the role of the homogeneous function $\Omega(\xi)$ in \eqref{fractionalderivative.def}
is essentially that of the Fourier symbol for a conventional translation-invariant operator.
Let ${\mathcal S}_\infty$ be the space of all Schwartz functions $f$ such that
$ \partial^{\bf i}\hat f({\bf 0})=0$ for all ${\bf i}\in {\mathbb{Z}}_+^d$, or equivalently that
$\int_{{\mathbb R}^d} {\bf x}^{\bf j} f({\bf x}) d{\bf x}=0$ for all ${\bf j}\in {\mathbb{Z}}_+^d$.
Given a homogenous function $\Omega\in C^\infty({\mathbb R}^d\backslash \{{\bf 0}\})$, define
the linear operator $i_\Omega$ on ${\mathcal S}_\infty$
by
\begin{equation}\label{fractionalderivative.def1}
\widehat{i_\Omega f}(\xi)= \Omega(\xi) \hat f(\xi),\quad f \in {\mathcal S}_\infty.
\end{equation}
Clearly $i_\Omega$ is a continuous linear operator on the closed linear subspace ${\mathcal S}_\infty$
of ${\mathcal S}$.
For any function $f\in {\mathcal S}_\infty$, applying the integration-by-parts technique $k_0$ times and noticing that
$\lim_{\epsilon\to 0}
\epsilon^{-\gamma} |\partial^{\bf i} \hat f(\epsilon \xi')|=0$ for all $\xi'\in S^{d-1}$ and ${\bf i}\in {\mathbb{Z}}_+^d$,
we obtain that
\begin{eqnarray}\label{extension.eq}
J_\Omega f({\bf x}) & = & \frac{(2\pi)^{-d}\Gamma(d-\gamma)}{ \Gamma(d+k_0-\gamma)}
\lim_{\epsilon\to 0}\int_{S^{d-1}} \int_\epsilon^\infty r^{k_0+d-\gamma-1}\Omega(\xi')\nonumber \\
& &
\quad \times \Big(-\frac{d}{dr}\Big)^{k_0} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi')\Big) dr d\sigma(\xi')\nonumber\\
& = & (2\pi)^{-d} \lim_{\epsilon\to 0}
\int_{S^{d-1}} \int_\epsilon^\infty \Omega(\xi')r^{d-\gamma-1} e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi') dr d\sigma(\xi')\nonumber\\
& = & (2\pi)^{-d}\int_{{\mathbb{R}}^d} e^{i\langle {\bf x}, \xi\rangle} \Omega(\xi) \hat f(\xi) d\xi= i_\Omega f({\bf x}).
\end{eqnarray}
Hence the generalized Riesz potential $J_\Omega$ is the extension of the linear operator $i_\Omega$ from the closed
subspace ${\mathcal S}_\infty$ to the whole space ${\mathcal S}$.
In the sequel, we will study further properties of the generalized Riesz
potential $J_\Omega$, such as the polynomial decay property
(Theorem \ref{generalizedrieszomega1.tm}),
the continuity as a linear operator from ${\mathcal S}$ to ${\mathcal S}'$ (Corollary \ref{generalizedrieszomega1.cr}),
the translation-invariance and dilation-invariance (Theorem \ref{maintheorem.iomega1}),
the composition and left-inverse property (Theorem \ref{composition.tm} and Corollary \ref{composition.cr}),
the uniqueness of various extensions
of the linear operator $i_\Omega$ from the closed
subspace ${\mathcal S}_\infty$ to the whole space ${\mathcal S}$ (Theorems \ref{iomega2.tm}
and \ref{iomega4.tm}),
the non-integrability in the spatial domain (Theorem \ref{time1.tm}), and the non-integrability in the Fourier domain (Theorem \ref{frequency.tm1}).
Some of those properties will be used to prove Theorem \ref{generalizedriesz.tm}, which is included at
the end of this section.
\subsection{Polynomial decay property and continuity}
\begin{Tm} \label{generalizedrieszomega1.tm} Let $\gamma$ be a positive number with $\gamma-d\not\in {\mathbb{Z}}_+$,
$k_0$ be the smallest nonnegative integer larger than $\gamma-d$,
and let $\Omega\in C^\infty ({\mathbb{R}}^d\backslash \{\bf 0\})$ be a homogeneous function of degree $-\gamma$.
If there exist positive constants $\epsilon$ and $C_\epsilon$ such that
\begin{equation}\label{generalizedrieszomega1.tm.eq1}
|f({\bf x})|\le C_\epsilon (1+\|{\bf x}\|)^{-k_0-d-\epsilon} \ {\rm for \ all} \ {\bf x}\in {\mathbb R}^d,
\end{equation}
then there exists a positive constant $C$ such that
\begin{eqnarray}\label{generalizedrieszomega1.tm.eq2}
|J_\Omega f({\bf x})| \le
C \Big(\sup_{{\bf z}\in {\mathbb R}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_0+d+\epsilon}\Big) (1+\|{\bf x}\|)^{\gamma-d},
\ \ {\bf x}\in {\mathbb R}^d.
\end{eqnarray}
\end{Tm}
\begin{proof}
Noting that
$ \big(\frac{d}{dr}\big)^{s} e^{ir\langle {\bf x}, \xi'\rangle}
=
s! \Big(\sum_{|{\bf i}|=s} \frac{(i{\bf x})^{\bf i} \xi'^{\bf i}}{ {\bf i}!} \Big)e^{ir\langle {\bf x}, \xi'\rangle}$
and
$\big(\frac{d}{dr}\big)^{k_0-s} \hat f(r\xi')= (k_0-s)! \sum_{|{\bf j}|=k_0-s} \frac{ (\xi')^{\bf j} \partial^{\bf j} \hat f(r\xi')}{{\bf j}!}
$ for all $0\le s\le k_0$, we obtain from the Leibniz rule that
\begin{eqnarray*}
\Big(\frac{d}{dr}\Big)^{k_0} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi')\Big)
& = & \sum_{s=0}^{k_0}\binom{k_0}{s}
\Big\{\Big(\frac{d}{dr}\Big)^{k_0-s} e^{ir\langle {\bf x}, \xi'\rangle}\Big\}\cdot
\Big\{\Big(\frac{d}{dr}\Big)^{k_0} \hat f(r\xi')\Big\}\nonumber\\
& = &
\Big(\sum_{|{\bf i}|+|{\bf j}|=k_0}\frac{k_0!}{{\bf i}!{\bf j}!}
{ (i{\bf x})}^{\bf i} (\xi')^{{\bf i}+{\bf j}}
\partial^{\bf j} \hat f(r\xi')\Big)e^{ir\langle {\bf x}, \xi'\rangle}.
\end{eqnarray*}
Substituting the above expression into \eqref{fractionalderivative.def}
we get
\begin{eqnarray}\label{generalizedrieszomega1.tm.pf.eq1}
J_\Omega f({\bf x}
& = & (-1)^{k_0}\sum_{|{\bf i}|+|{\bf j}|=k_0}\frac{k_0!}{{\bf i}!{\bf j}!} (i{\bf x})^{\bf i}
\Big\{\frac{(2\pi)^{-d}\Gamma(d-\gamma)}{ \Gamma(d+k_0-\gamma)}\nonumber\\
& & \times
\int_{{\mathbb{R}}^d} e^{i\langle {\bf x}, \xi\rangle} \big(\xi^{{\bf i}+{\bf j}}\Omega(\xi)\big)
\partial^{\bf j}\hat f(\xi)d\xi\Big\}\nonumber\\
& = & \frac{\Gamma(d-\gamma)}{\Gamma(d+k_0-\gamma)} \sum_{|{\bf i}|+|{\bf j}|=k_0}\frac{k_0! }{{\bf i}!{\bf j}!} (-{\bf x})^{\bf i} J_{\Omega_{{\bf i}+{\bf j}}} (f_{\bf j})({\bf x}),
\end{eqnarray}
where $\Omega_{{\bf i}+{\bf j}}(\xi)= (i\xi)^{{\bf i}+{\bf j}}\Omega(\xi)$
and $f_{\bf j}({\bf x})= {\bf x}^{\bf j} f({\bf x})$. Denote the inverse Fourier transform
of $\Omega_{{\bf k}}, |{\bf k}|=k_0$, by $K_{{\bf k}}$. Then $K_{{\bf k}}\in C^\infty({\mathbb R}^d\backslash \{{\bf 0}\})$ is a homogeneous function of degree $\gamma-k_0-d$ (\cite[Theorems 7.1.16 and 7.1.18]{hormanderbook}), and hence
there exists a positive constant $C$ such that
\begin{equation}\label{generalizedrieszomega1.tm.pf.eq2}
|K_{\bf k}({\bf x})|\le C \|{\bf x}\|^{\gamma-k_0-d} \quad {\rm for \ all} \ {\bf x}\in {\mathbb R}^d\backslash \{{\bf 0}\}.
\end{equation}
For any $\epsilon>0$ and $\beta\in (0, d)$, we have
\begin{eqnarray}\label{generalizedrieszomega1.tm.pf.eq3}
& & \int_{{\mathbb R}^d} \|{\bf x}-{\bf y}\|^{-\beta} (1+\|{\bf y}\|)^{-d-\epsilon} d{\bf y}\nonumber\\
& \le &
\Big( \int_{\|{\bf y}\|\le (\|{\bf x}\|+1)/2}+\int_{(\|{\bf x}\|+1)/2\le \|{\bf y}\|\le 2(\|{\bf x}\|+1)}+
\int_{\|{\bf y}\|\ge 2(\|{\bf x}\|+1)} \Big) \nonumber\\
& & \qquad \|{\bf x}-{\bf y}\|^{-\beta} (1+\|{\bf y}\|)^{-d-\epsilon} d{\bf y}\nonumber\\
& \le & C (1+\|{\bf x}\|)^{-\beta}.
\end{eqnarray}
Combining \eqref{generalizedrieszomega1.tm.pf.eq1},
\eqref{generalizedrieszomega1.tm.pf.eq2} and \eqref{generalizedrieszomega1.tm.pf.eq3} yields
\begin{eqnarray*}
|J_\Omega f({\bf x})| & \le & C \sum_{|{\bf i}|+|{\bf j}|=k_0}
|{\bf x}|^{|{\bf i}|} \Big|\int_{{\mathbb R}^d} K_{{\bf i}+{\bf j}}({\bf x}-{\bf y}) {\bf y}^{\bf j} f({\bf y}) \Big| d{\bf y}\nonumber\\
& \le & C (1+\|{\bf x}\|)^{k_0} \int_{{\mathbb R}^d}
\|{\bf x}-{\bf y}\|^{\gamma-k_0-d}
(1+\|{\bf y}\|)^{k_0} |f({\bf y})| d{\bf y}\nonumber\\
& \le & C \Big(\sup_{{\bf z}\in {\mathbb R}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_0+d+\epsilon}\Big) (1+\|{\bf x}\|)^{\gamma-d}.\end{eqnarray*}
This proves the desired polynomial decay estimate \eqref{generalizedrieszomega1.tm.eq2}.
\end{proof}
For any $f\in {\mathcal S}$ and ${\bf j}\in {\mathbb{Z}}_+^d$ with $|{\bf j}|=1$, it follows from \eqref{fractionalderivative.def} that
\begin{eqnarray*}
\partial^{\bf j}(J_\Omega f) ({\bf x}) &= & J_\Omega(\partial^{\bf j} f) ({\bf x})\nonumber\\
& = &
\frac{(2\pi)^{-d}\Gamma(d-\gamma)}{ \Gamma(d+k_0-\gamma)} \int_{S^{d-1}} \int_0^\infty \Omega(\xi') (i\xi')^{\bf j} r^{k_0+d-\gamma-1}\nonumber \\
& &
\times \Big(-\frac{d}{dr}\Big)^{k_0} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi') r \Big) dr d\sigma(\xi')\nonumber\\
& = &
\frac{(2\pi)^{-d}\Gamma(d-\gamma)}{ \Gamma(d+k_0-\gamma)} \int_{S^{d-1}} \int_0^\infty \Omega(\xi') (i\xi')^{\bf j} r^{k_0+d-\gamma-1}\nonumber \\
& &
\times \Big\{ r \Big(-\frac{d}{dr}\Big)^{k_0} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi') \Big)
\nonumber\\
& & \quad -{k_0}\Big(-\frac{d}{dr}\Big)^{k_0-1} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi') \Big)\Big\} dr d\sigma(\xi')\nonumber\\
& = & \Big(\frac{d+k_0-\gamma}{d-\gamma}-k_0\frac{1}{d-\gamma}\Big) J_{\Omega_{\bf j}} f({\bf x})=
J_{\Omega_{\bf j}} f({\bf x}),
\end{eqnarray*}
where $\Omega_{\bf j}(\xi)=(i\xi)^{\bf j} \Omega(\xi) $.
Applying the argument inductively leads to
\begin{equation} \label{fractionalderivative.eq00}
\partial^{\bf j} (J_\Omega f)= J_\Omega(\partial^{\bf j} f) = J_{\Omega_{\bf j}} f \quad {\rm for \ all} \ f\in {\mathcal S} \ {\rm and} \ {\bf j}\in {\mathbb{Z}}_+^d,
\end{equation}
where $\Omega_{\bf j}(\xi)= (i\xi)^{\bf j}\Omega(\xi)$. This together with Theorem \ref{generalizedrieszomega1.tm} shows that
$J_\Omega f$ is a smooth function on ${\mathbb R}^d$ for any Schwartz function $f$.
\begin{Cr} \label{generalizedrieszomega1.cr0} Let $\gamma, k_0$ and $\Omega$ be as
in Theorem \ref{generalizedrieszomega1.tm}.
If $f$ satisfies \eqref{generalizedrieszomega1.tm.eq1} for some positive constants $\epsilon$ and $C_\epsilon$,
then for any ${\bf j}\in {\mathbb{Z}}_+^d$ with $|{\bf j}|<\gamma$ there exists a positive constant $C_{\bf j}$ such that
\begin{equation}\label{generalizedrieszomega1.cr0.eq2}
|\partial^{\bf j} (J_\Omega f)({\bf x})| \le
C_{\bf j} \Big(\sup_{{\bf z}\in {\mathbb R}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_0+d+\epsilon}\Big) (1+\|{\bf x}\|)^{\gamma-|{\bf j}|-d}, \ {\bf x}\in {\mathbb{R}}^d.
\end{equation}
\end{Cr}
An easy consequence of the above smoothness result about $J_\Omega f$ is the
continuity of the generalized Riesz potential $J_\Omega$ from ${\mathcal S}$ to ${\mathcal S}'$.
\begin{Cr}\label{generalizedrieszomega1.cr}
Let $\gamma$ be a positive number with $\gamma-d\not\in {\mathbb{Z}}_+$,
and let $\Omega\in C^{\infty} ({\mathbb{R}}^d\backslash \{\bf 0\})$ be a homogeneous function of degree $-\gamma$.
Then the generalized Riesz potential $J_\Omega $ associated with the homogeneous function $\Omega$ is
a continuous linear operator from ${\mathcal S}$ to ${\mathcal S}'$.
\end{Cr}
Now consider the generalized Riesz potential $J_\Omega$ when $\Omega$ is a homogeneous function of positive degree $\alpha$.
In this case,
$$ J_\Omega f({\bf x}) = (2\pi)^{-d} \int_{{\mathbb{R}}^d} e^{i\langle {\bf x}, \xi\rangle}
\Omega(\xi)\hat f(\xi) d\xi\quad {\rm for \ all} \ f\in {\mathcal S}$$
by \eqref{fractionalderivative.neweq2}.
Applying the integration-by-parts technique then gives
$$
J_\Omega f({\bf x})
= (2\pi)^{-d} (-i {\bf x}^{\bf i})^{-1} \sum_{{\bf j}+{\bf k}={\bf i}}
\frac{{\bf i}!}{{\bf j}!{\bf k}!}
\int_{{\mathbb{R}}^d}
e^{i\langle {\bf x}, \xi\rangle}
\partial^{\bf j} \Omega(\xi) \partial^{\bf k}\hat f(\xi) d\xi
$$
for any ${\bf i}\in {\mathbb{Z}}_+^d$.
This, together with the identity
$$1=\sum_{|{\bf l}|=\lceil \alpha\rceil-|{\bf j}|} \frac{(\lceil \alpha \rceil-|{\bf j}|)!}{{\bf l}!}
\Big(\frac{i\xi}{\|{\bf \xi}\|^2}\Big)^{\bf l}
(-i\xi)^{\bf l},\quad |{\bf j}|\le \lceil \alpha\rceil,$$
leads to the following estimate of $J_\Omega f({\bf x})$:
\begin{eqnarray*}
|J_\Omega f({\bf x})|\!\! & \le & \!\! C (1+\|{\bf x}\|)^{-\lceil \alpha\rceil}
\sum_{|{\bf j}|+|{\bf k}|\le \lceil \alpha\rceil, |{\bf l}|=\lceil \alpha\rceil-|{\bf j}|}
\Big|\int_{{{\mathbb{R}}}^d} e^{i\langle {\bf x}, \xi\rangle}
\Omega_{{\bf j}, {\bf l}}(\xi) \xi^{\bf l} \partial^{\bf k} \hat f(\xi) d\xi\Big| \nonumber\\
\!\! & \le & \!\!
C (1+\|{\bf x}\|)^{-\lceil \alpha\rceil}
\sum_{|{\bf j}|+|{\bf k}|\le \lceil \alpha\rceil, |{\bf l}|+|{\bf j}|=\lceil \alpha\rceil} |I_{\Omega_{{\bf j}, {\bf l}}} f_{{\bf l}, {\bf k}}({\bf x})|,
\end{eqnarray*}
where $\lceil \alpha\rceil$ is the smallest integer larger than $\alpha$, $\Omega_{{\bf j}, {\bf l}}(\xi)=\partial^{\bf j}\Omega(\xi) (i\xi/\|\xi\|^2)^{\bf l}$, and
$\widehat{ f_{{\bf l}, {\bf k}}} (\xi)=(-i\xi)^{\bf l} \partial^{{\bf k}} \hat f(\xi)$.
Note that $\Omega_{{\bf j}, {\bf l}}\in C^\infty({\mathbb{R}}^d\backslash \{{\bf 0}\})$ is a homogeneous function of degree $\alpha-\lceil \alpha\rceil<0$
when $|{\bf j}|+|{\bf l}|=\lceil \alpha\rceil$, and also that functions
$f_{{\bf l}, {\bf k}}({\bf x}), |{\bf k}|, |{\bf l}|\le \lceil \alpha\rceil$ are linear combinations of
${\bf x}^{\bf i} \partial^{\bf j} f({\bf x}), |{\bf i}|, |{\bf j}|\le \lceil \alpha\rceil$.
We then apply Theorem \ref{generalizedrieszomega1.tm} to obtain the following polynomial decay estimate of $J_\Omega f$ when $\Omega$ is
a homogeneous function of positive degree:
\begin{pr}\label{positivegeneralizedrieszomega1.cr}
Let $\alpha$ be a positive non-integer number, and
$\Omega\in C^\infty ({\mathbb{R}}^d\backslash \{\bf 0\})$ be a homogeneous function of degree $\alpha$.
If there exist positive constants $\epsilon$ and $C_\epsilon$ such that
\begin{equation*}\label{positivegeneralizedrieszomega1.cr.eq1}
\sum_{|{\bf i}|\le \lceil \alpha\rceil}
|\partial^{\bf i} f({\bf x})|\le C_\epsilon (1+\|{\bf x}\|)^{-\lceil \alpha\rceil-d-\epsilon} \ {\rm for \ all} \ {\bf x}\in {\mathbb R}^d,
\end{equation*}
then there exists a positive constant $C$ such that
\begin{equation}
\label{positivegeneralizedrieszomega1.cr.eq2}
|J_\Omega f({\bf x})| \le
C \Big(\sum_{|{\bf i}|\le \lceil \alpha\rceil} \sup_{{\bf z}\in {\mathbb R}^d} |\partial^{\bf i} f({\bf z})| (1+\|{\bf z}\|)^{\lceil \alpha\rceil+d+\epsilon}\Big) (1+\|{\bf x}\|)^{-\alpha-d}
\end{equation}
for all ${\bf x}\in {\mathbb R}^d$.
\end{pr}
The estimates in \eqref{generalizedrieszomega1.tm.eq2} and
\eqref{positivegeneralizedrieszomega1.cr.eq2} indicate that the generalized Riesz potential $J_\Omega f$ has faster polynomial
decay at infinity when the degree of the homogeneous function $\Omega$ becomes larger.
Next, we show that the generalized Riesz potential $J_\Omega f$ has faster polynomial decay at infinity
when $f$ has vanishing moments up to some order; i.e.,
\begin{equation}\label{momentcondition}
\int_{{\mathbb{R}}^d} {\bf x}^{\bf i} f({\bf x}) d{\bf x}=0,\ |{\bf i}|\le m_0
\end{equation}
where $m_0\ge 0$.
In this case, $\partial^{\bf i}\hat f({\bf 0})=0$ for all $|{\bf i}|\le m_0$, and hence
\begin{equation}
\hat f(\xi)= \sum_{|{\bf k}|=m_0+1}\frac{m_0+1}{{\bf k}!} \int_0^1 \xi^{\bf k} \partial^{\bf k} \hat f(t\xi) (1-t)^{m_0} dt
\end{equation}
by the Taylor expansion to $\hat f$ at the origin.
Now we assume that $\Omega\in C^\infty({\mathbb{R}}^d\backslash\{{\bf 0}\})$ is a homogeneous function of degree
$\alpha\in (-m_0-1, \infty)\backslash {\mathbb{Z}} $.
Then
\begin{eqnarray}\label{momentgeneralizedrieszomega1.pr.pf1}
|J_\Omega f({\bf x})|\!\! \!& \le &\!\!
C \sum_{|{\bf k}|=m_0+1}\int_0^1\int_{\|\xi\|\le 1} |\xi|^{\alpha+m_0+1} |\partial^{\bf k} \hat f(t\xi)| d\xi dt+
C \int_{|\xi|\ge 1} |\xi|^{\alpha} |\hat f(\xi)|d\xi\nonumber\\
& \le & C \sum_{|{\bf i}|\le m_0+1} \sup_{\xi \in {\mathbb{R}}^d}
\big((1+\|\xi\|)^{\lceil \alpha\rceil +d} |\partial^{\bf i}\hat f(\xi)|\big)
\end{eqnarray}
for all ${\bf x}\in {\mathbb{R}}^d$ with $\|{\bf x}\|\le 1$, and
\begin{eqnarray}\label{momentgeneralizedrieszomega1.pr.pf2}
|J_\Omega f({\bf x})|\!\! &\le &\!\! C \sum_{|{\bf k}|=m_0+1}
\int_0^1
\Big|\int_{{\mathbb{R}}^d} e^{-i\langle {\bf x}, \xi\rangle} \phi(\|{\bf x}\| \xi) \xi^{\bf k} \Omega(\xi) \partial^{\bf k} \hat f(t\xi) d\xi\Big| dt\nonumber\\
\!\! & & \!\!
+C\sum_{|{\bf k}|=m_0+1}
\int_0^1 \Big|\int_{{\mathbb{R}}^d} e^{-i\langle {\bf x}, \xi\rangle} \big(\phi(\xi)-\phi(\|{\bf x}\| \xi)\big)\xi^{\bf k} \Omega(\xi)
\partial^{\bf k} \hat f(t\xi) d\xi\Big|dt\nonumber
\\
\!\!& &\!\! + C
\Big|\int_{{\mathbb{R}}^d} e^{-i\langle {\bf x}, \xi\rangle} \big(1-\phi(\xi)\big) \Omega(\xi) \hat f(\xi) d\xi\Big|\nonumber\\
\!\!&\le & \!\!
C (1+\|{\bf x}\|)^{-\lceil \alpha\rceil-m_0-d}
\Big\{\sum_{|{\bf k}|=m_0+1, |{\bf j}|\le \lceil \alpha\rceil+m_0+d}\nonumber\\
\!\!& &\!\!
\quad \int_0^1\int_{{\mathbb{R}}^d} \Big|\partial^{\bf j} \big(\phi(\|{\bf x}\|\xi) \xi^{\bf k} \Omega(\xi) \partial^{\bf k}\hat f(t\xi)\big)\Big| d\xi dt\Big\}
\nonumber\\
\!\!& &\!\!
+
C (1+\|{\bf x}\|)^{-\lceil \alpha\rceil-m_0-d-1} \Big\{\sum_{|{\bf k}|=m_0+1, |{\bf j}|\le \lceil \alpha\rceil+m_0+d+1}\nonumber\\
\!\!& &\!\! \quad \int_0^1\int_{{\mathbb{R}}^d} \Big|\partial^{\bf j}\big( (\phi(\xi)-\phi(\|{\bf x}\|\xi)) \xi^{\bf k} \Omega(\xi) \partial^{\bf k}\hat f(t\xi)\big)\Big| d\xi dt\Big\}\nonumber\\
\!\!& &\!\! +
C (1+\|{\bf x}\|)^{-\lceil \alpha\rceil-m_0-d-1} \nonumber\\
& & \quad \times \Big\{\sum_{|{\bf j}|\le \lceil \alpha\rceil+m_0+d+1}
\int_{{\mathbb{R}}^d} \Big|\partial^{\bf j}\big( (1-\phi(\xi)) \Omega(\xi) \hat f(\xi)\big)\Big| d\xi\Big\} \nonumber\\
\!\!& \le & \!\!
C \Big(\sum_{|{\bf i}|\le \lceil \alpha\rceil+2m_0+d+2} \sup_{\xi\in {\mathbb{R}}^d} (1+\|\xi\|)^{\lceil \alpha\rceil+d} |\partial^{\bf i} \hat f(\xi)|\Big) (1+\|{\bf x}\|)^{-\alpha-m_0-d-1}
\end{eqnarray}
for all ${\bf x}\in {\mathbb{R}}^d$ with $\|{\bf x}\|\ge 1$, where $\phi$ is a $C^\infty$ function such that
$\phi(\xi)=1$ for all $\xi$ in the unit ball $B({\bf 0}, 1)$ centered at the origin, and
$\phi(\xi)=0$ for all $\xi$ not in the ball $B({\bf 0}, 2)$ with radius 2 and center at the origin.
This proves the following result about the generalized Riesz potential $J_\Omega f$ when $f$ has vanishing moments upto some order.
\begin{pr}\label{momentgeneralizedrieszomega1.pr}
Let $m_0\ge 0, \alpha\in (-m_0-1, \infty)\backslash {\mathbb{Z}}$, and $\Omega\in C^\infty({\mathbb{R}}^d\backslash\{{\bf 0}\})$ be a homogeneous function of degree $\alpha$. Then the following statements hold.
\begin{itemize}
\item [{(i)}] If $f$ satisfies \eqref{momentcondition} and
\begin{equation}
\sum_{|{\bf i}|\le\lceil \alpha\rceil+2m_0+d+2} \sup_{\xi\in {\mathbb{R}}^d} (1+\|\xi\|)^{\lceil \alpha\rceil+d} |\partial^{\bf i} \hat f(\xi)|<\infty,
\end{equation}
then there exists a positive constant $C$ such that
\begin{eqnarray}
|J_\Omega f({\bf x})| & \le & C \Big(\sum_{|{\bf i}|\le\lceil \alpha\rceil+2m_0+d+2} \sup_{\xi\in {\mathbb{R}}^d} (1+\|\xi\|)^{\lceil \alpha\rceil+d} |\partial^{\bf i} \hat f(\xi)|\Big)
\nonumber\\
& & \quad \times (1+\|{\bf x}\|)^{-\alpha-m_0-d-1} \quad {\rm for \ all} \ {\bf x}\in {\mathbb{R}}^d.
\end{eqnarray}
\item[{(ii)}] If $f$ satisfies \eqref{momentcondition} and
\begin{equation}
\sum_{|{\bf i}|\le \max(\lceil \alpha\rceil +d, 0)}
\sup_{{\bf z}\in {\mathbb{R}}^d} \big( (1+\|{\bf z}\|)^{\lceil \alpha\rceil+2m_0+2d+2+\epsilon} |\partial^{\bf i} f({\bf z})|\big)<\infty
\end{equation}
for some $\epsilon>0$, then
\begin{eqnarray}
|J_\Omega f({\bf x})| & \le & C \Big( \sum_{|{\bf i}|\le \max(\lceil \alpha\rceil +d, 0)}
\sup_{{\bf z}\in {\mathbb{R}}^d} \big( (1+\|{\bf z}\|)^{\lceil \alpha\rceil+2m_0+2d+2+\epsilon} |\partial^{\bf i} f({\bf z})|
\Big)
\nonumber\\
& & \quad \times (1+\|{\bf x}\|)^{-\alpha-m_0-d-1} \quad {\rm for \ all} \ {\bf x}\in {\mathbb{R}}^d.
\end{eqnarray}
\end{itemize}
\end{pr}
The conclusions in Proposition \ref{momentgeneralizedrieszomega1.pr} do not apply to the generalized Riesz potential $J_\Omega f$
where $\Omega\in C^\infty({\mathbb{R}}^d\backslash \{{\bf 0}\})$ is a homogeneous function of degree zero.
In this case, applying the argument used to establish
\eqref{momentgeneralizedrieszomega1.pr.pf1} and \eqref{momentgeneralizedrieszomega1.pr.pf2}, we have
that
\begin{eqnarray}\label{momentgeneralizedrieszomega2.pr.pf1}
|J_\Omega f({\bf x})
& \le & C \sum_{|{\bf i}|\le m_0+1} \sup_{\xi \in {\mathbb{R}}^d}
\big((1+\|\xi\|)^{d+\epsilon} |\partial^{\bf i}\hat f(\xi)|\big)
\end{eqnarray}
for all ${\bf x}\in {\mathbb{R}}^d$ with $\|{\bf x}\|\le 1$, and
\begin{eqnarray}\label{momentgeneralizedrieszomega2.pr.pf2}
|J_\Omega f({\bf x})
\!\!&\le & \!\!
C (1+\|{\bf x}\|)^{-m_0-d} \nonumber\\
& & \times \Big\{
\sum_{|{\bf k}|=m_0+1, |{\bf j}|\le m_0+d} \int_0^1\int_{{\mathbb{R}}^d} \big|\partial^{\bf j} \big(\phi(\|{\bf x}\|\xi) \xi^{\bf k} \Omega(\xi) \partial^{\bf k}\hat f(t\xi)\big)\big| d\xi dt\Big\}
\nonumber\\
\!\!& &\!\!
+
C (1+\|{\bf x}\|)^{-m_0-d-1} \sum_{|{\bf k}|=m_0+1, |{\bf j}|+|{\bf l}|\le m_0+d+1, |{\bf j}|\le m_0+d}\nonumber\\
\!\!& &\!\! \quad \int_0^1\int_{{\mathbb{R}}^d} \big|\partial^{\bf j}\big( (\phi(\xi)-\phi(\|{\bf x}\|\xi)) \xi^{\bf k} \Omega(\xi)\big)\big|\times
\big| \partial^{{\bf k}+{\bf l}}\hat f(t\xi)\big)\big| d\xi dt\Big\}\nonumber\\
\!\!& &\!\!
+
C (1+\|{\bf x}\|)^{-m_0-d-2} \sum_{|{\bf k}|=m_0+1, |{\bf j}|+|{\bf l}|\le m_0+d+2, |{\bf l}|\le 1}\nonumber\\
\!\!& &\!\! \quad \int_0^1\int_{{\mathbb{R}}^d} \big|\partial^{\bf j}\big( (\phi(\xi)-\phi(\|{\bf x}\|\xi)) \xi^{\bf k} \Omega(\xi)\big)\big|\times
\big| \partial^{{\bf k}+{\bf l}}\hat f(t\xi)\big)\big| d\xi dt\Big\}\nonumber\\
\!\!& &\!\! +
C (1+\|{\bf x}\|)^{-m_0-d-1}
\sum_{|{\bf j}|\le m_0+d+1}
\int_{{\mathbb{R}}^d} \big|\partial^{\bf j}\big( (1-\phi(\xi)) \Omega(\xi) \hat f(\xi)\big)\big| d\xi \nonumber\\
\!\!& \le & \!\!
C \Big(\sum_{|{\bf i}|\le 2m_0+d+2} \sup_{\xi\in {\mathbb{R}}^d} (1+\|\xi\|)^{d+\epsilon} |\partial^{\bf i} \hat f(\xi)|\Big) (1+\|{\bf x}\|)^{-m_0-d-1}
\end{eqnarray}
for all ${\bf x}\in {\mathbb{R}}^d$ with $\|{\bf x}\|\ge 1$, where $\epsilon\in (0,1)$.
Therefore
\begin{pr}\label{momentgeneralizedrieszomega2.pr}
Let $\Omega\in C^\infty({\mathbb{R}}^d\backslash\{{\bf 0}\})$ be a homogeneous function of degree zero. Then the following statements hold.
\begin{itemize}
\item [{(i)}] If $f$ satisfies \eqref{momentcondition} for some $m_0\ge 0$ and
$$ \sum_{|{\bf i}|\le 2m_0+d+2} \sup_{\xi\in {\mathbb{R}}^d} (1+\|\xi\|)^{d+\epsilon} |\partial^{\bf i} \hat f(\xi)|<\infty$$ for some $\epsilon>0,$
then there exists a positive constant $C$ such that
$$
|J_\Omega f({\bf x})| \le C \Big(\sum_{|{\bf i}|\le 2m_0+d+2} \sup_{\xi\in {\mathbb{R}}^d} (1+\|\xi\|)^{d+\epsilon} |\partial^{\bf i} \hat f(\xi)|\Big)
(1+\|{\bf x}\|)^{-m_0-d-1}
\quad {\rm for \ all} \ {\bf x}\in {\mathbb{R}}^d.
$$
\item[{(ii)}] If $f$ satisfies \eqref{momentcondition} for some $m_0\ge 0$ and
$$
\sum_{|{\bf i}|\le d+1}
\sup_{{\bf z}\in {\mathbb{R}}^d} \big( (1+\|{\bf z}\|)^{2m_0+2d+2+\epsilon} |\partial^{\bf i} f({\bf z})|\big)<\infty
$$
for some $\epsilon>0$, then
\begin{eqnarray*}
|J_\Omega f({\bf x})| & \le & C \Big( \sum_{|{\bf i}|\le d+1}
\sup_{{\bf z}\in {\mathbb{R}}^d} \big( (1+\|{\bf z}\|)^{2m_0+2d+2+\epsilon} |\partial^{\bf i} f({\bf z})|
\Big)
\nonumber\\
& & \quad \times (1+\|{\bf x}\|)^{-m_0-d-1} \quad {\rm for \ all} \ {\bf x}\in {\mathbb{R}}^d.
\end{eqnarray*}
\end{itemize}
\end{pr}
\subsection{Translation-invariance and dilation-invariance}
In this subsection, we show that
the generalized Riesz potential $J_\Omega$ from ${\mathcal S}$ to ${\mathcal S}'$
is dilation-invariant and translation-invariant, and that its restriction on the closed subspace ${\mathcal S}_\infty$
of ${\mathcal S}$ is the same as the linear
operator $i_\Omega$ on ${\mathcal S}_\infty$.
\begin{Tm}\label{maintheorem.iomega1}
Let $\gamma\in {\mathbb{R}}$ with $\gamma-d\not \in {\mathbb{Z}}_+$,
$\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be a homogeneous function of degree $-\gamma$,
and let $J_\Omega$ be defined by \eqref{fractionalderivative.def}. Then
\begin{itemize}
\item[{(i)}] $J_\Omega$ is dilation-invariant;
\item[{(ii)}] $J_\Omega$ is translation-invariant; and
\item[{(iii)}] $\widehat{J_\Omega f}(\xi)= \Omega(\xi) \hat f(\xi)$ for any function $f\in {\mathcal S}_\infty$.
\end{itemize}
\end{Tm}
\begin{proof} {\em (i)}\quad
For any $f\in {\mathcal S}$ and any $t>0$,
\begin{eqnarray*}
J_\Omega (\delta_t f) ({\bf x}) & = & \frac{(2\pi t)^{-d}\Gamma(d-\gamma)}{ \Gamma(d+k_0-\gamma)}
\int_{S^{d-1}} \int_0^\infty \Omega(\xi')r^{k_0-\gamma+d-1}\nonumber \\
& &
\times \Big(-\frac{d}{dr}\Big)^{k_0} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi'/t)\Big) dr d\sigma(\xi')
= t^{-\gamma} \delta_t(J_\Omega f)({\bf x}),
\end{eqnarray*}
where the first equality follows from $\widehat {\delta_t f}(\xi)=t^{-d} \hat f(\xi/t)$
and the second equality is obtained by change of variables.
This leads to the dilation-invariance of the generalized Riesz potential $J_\Omega$.
{\em (ii)}\quad
For any $f\in {\mathcal S}$ and a vector ${\bf x}_0\in {\mathbb{R}}^d$,
we obtain from \eqref{fractionalderivative.def} that
\begin{eqnarray*}
J_\Omega (\tau_{{\bf x}_0}f)({\bf x})
& = & \frac{(2\pi)^{-d}\Gamma(d-\gamma)}{ \Gamma(d+k_0-\gamma)} \int_{S^{d-1}} \int_0^\infty r^{k_0-\gamma+d-1} \Omega(\xi') \nonumber \\
& & \times
\big(-\frac{d}{dr}\big)^{k_0} \Big(e^{ir\langle {\bf x}-{\bf x}_0, \xi'\rangle} \hat f(r\xi')\Big) dr d\sigma(\xi')= J_\Omega f( {\bf x}-{\bf x}_0),
\end{eqnarray*}
where $k_0$ is a nonnegative integer larger than $\gamma-d$. This shows that
the generalized Riesz potential $J_\Omega$
is translation-invariant.
{\em (iii)}\quad
The third conclusion follows by taking Fourier transform of the equation \eqref{extension.eq} on both sides.
\end{proof}
\subsection{Composition and left-inverse}
In this subsection, we consider the composition and left-inverse properties of generalized Riesz potentials.
\begin{Tm}\label{composition.tm}
Let $\gamma_1$ and $\gamma_2\in {\mathbb{R}}$ satisfy
$\gamma_2<d, \gamma_1+\gamma_2<d$ and $\gamma_1-d\not\in {\mathbb{Z}}_+$,
and let $\Omega_1, \Omega_2\in C^\infty({\mathbb{R}}^d\backslash\{{\bf 0}\})$
be homogeneous functions of degree $-\gamma_1$ and $-\gamma_2$ respectively.
Then
\begin{equation}\label{composition.tm.eq1}
J_{\Omega_1}(J_{\Omega_2} f)=J_{\Omega_1\Omega_2} f \quad {\rm for\ all} \ f\in {\mathcal S}.
\end{equation}
\end{Tm}
As a consequence of Theorem \ref{composition.tm}, we have the following result about left-invertibility
of the generalized Riesz potential $J_\Omega$.
\begin{Cr}\label{composition.cr}
Let $\gamma\in (-d, \infty)$ with $\gamma-d\not\in {\mathbb{Z}}_+$ and
$\Omega\in C^\infty({\mathbb{R}}^d\backslash\{{\bf 0}\})$
be homogeneous of degree $-\gamma$ with $\Omega(\xi)\ne 0$ for all $\xi\in S^{d-1}$.
Then $J_{\Omega}J_{\Omega^{-1}}$ is an identity operator on ${\mathcal S}$.
If we further assume that $\gamma\in (-d, d)$, then both
$J_{\Omega^{-1}}J_\Omega$ and $J_{\Omega}J_{\Omega^{-1}}$ are identity operators on ${\mathcal S}$.
\end{Cr}
Taking $\Omega(\xi)=\|\xi\|^{-\gamma}$ in the above corollary yields that the linear operator $I_\gamma$ in \eqref{generalizedriesz.def} is a left-inverse of the fractional Laplacian $(-\triangle)^{\gamma/2}$.
\begin{Cr}\label{invariantleftinverse.cr}
Let $\gamma$ be a positive number with $\gamma-d\not\in {\mathbb{Z}}_+$. Then $I_\gamma$ is a left-inverse
of the fractional Laplacian $(-\triangle)^{\gamma/2}$.
\end{Cr}
\begin{proof}[Proof of Theorem \ref{composition.tm}]
Let $k_0$ be the smallest nonnegative integer such that $k_0-\gamma_1+d>0$, and set $\Omega(\xi)=\Omega_1(\xi)\Omega_2(\xi)$.
If $k_0=0$, then
the conclusion \eqref{composition.tm.eq1} follows from
\eqref{fractionalderivative.neweq2}. Now we assume that $k_0\ge 1$.
Then
\begin{eqnarray*}\label{composition.tm.pf.eq2}
J_{\Omega_1}(J_{\Omega_2} f)({\bf x})
\!\!
& = &
\frac{(2\pi)^d\Gamma(d-\gamma_1)}{ \Gamma(d+k_0-\gamma_1)} \lim_{\epsilon\to 0} \int_{S^{d-1}} \int_\epsilon^\infty \Omega(\xi')
r^{k_0+d-\gamma_1-1} \nonumber \\
& &\times
\Big\{ r \Big(-\frac{d}{dr}\Big)^{k_0} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi') r^{-\gamma_2-1} \Big)\nonumber\\
& & -k_0 \Big(-\frac{d}{dr}\Big)^{k_0-1} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi') r^{-\gamma_2-1} \Big)\Big\}
dr d\sigma(\xi')\nonumber\\
& = & \frac{(2\pi)^d\Gamma(d+1-\gamma_1)}{ \Gamma(d+k_0-\gamma_1)} \lim_{\epsilon\to 0} \int_{S^{d-1}} \int_\epsilon^\infty \Omega(\xi')
r^{k_0+d-\gamma_1-1} \nonumber \\
& &\times
\Big(-\frac{d}{dr}\Big)^{k_0-1} \Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi') r^{-\gamma_2-1} \Big) dr d\sigma(\xi')\nonumber\\
& = & \cdots\nonumber\\
& = &
\frac{ (2\pi)^{-d}\Gamma(d+k_0-\gamma_1)}{ \Gamma(d+k_0-\gamma_1)} \lim_{\epsilon\to 0} \int_{S^{d-1}} \int_\epsilon^\infty \Omega(\xi')
r^{k_0+d-\gamma_1-1} \nonumber \\
& &\times
\Big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi') r^{-\gamma_2-k_0} \Big) dr d\sigma(\xi')\nonumber\\
& = & J_{\Omega_1\Omega_2} f({\bf x})\quad {\rm for\ all} \ {\bf x}\in {\mathbb{R}}^d,
\end{eqnarray*}
where the second equality is obtained by applying the integration-by-parts technique and using the fact that
$ \epsilon^{k_0+d-\gamma_1} \big(\frac{d}{dr}\big)^{k_0-1} \big(e^{ir\langle {\bf x}, \xi'\rangle} \hat f(r\xi') r^{-\gamma_2-1} \big)\big|_{r=\epsilon}$ converges to zero uniformly on $\ \xi\in S^{d-1}$ under the assumption that $\gamma_1+\gamma_2<d$.
The conclusion
\eqref{composition.tm.eq1} then follows.
\end{proof}
\subsection{Translation-invariant and dilation-invariant extensions of the linear operator $i_\Omega$}
In this subsection, we show that the generalized Riesz potential $J_\Omega$ in \eqref{fractionalderivative.def} is the {\bf only}
continuous linear operator from ${\mathcal S}$ to ${\mathcal S}'$ that is translation-invariant and dilation-invariant, and
that is an extension of the linear operator $i_\Omega$ in \eqref{fractionalderivative.def1} from the closed subspace ${\mathcal S}_\infty$ to the whole space ${\mathcal S}$.
\begin{Tm}\label{iomega2.tm}
Let $\gamma$ be a positive number with $\gamma-d\not\in {\mathbb{Z}}_+$,
$\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be a nonzero homogeneous function of degree $-\gamma$,
and let $J_\Omega$ be defined by \eqref{fractionalderivative.def}. Then
$I$ is a continuous linear operator from ${\mathcal S}$ to ${\mathcal S}'$ such that
$I$ is dilation-invariant and translation-invariant, and that the restriction of $I$
on ${\mathcal S}_\infty$ is
the same as the linear operator $i_\Omega$ in
\eqref{fractionalderivative.def1} if and only if $I=J_\Omega$.
\end{Tm}
To prove Theorem \ref{iomega2.tm}, we need two technical lemmas about extensions of the linear operator $i_\Omega$ on ${\mathcal S}_\infty$.
\begin{Lm}\label{homogeneous1.lm}
Let $\gamma$ be a positive number with $\gamma-d\not\in {\mathbb{Z}}_+$,
$\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be a homogeneous function of degree $-\gamma$,
and let $J_\Omega$ be defined by \eqref{fractionalderivative.def}.
Then
a continuous linear operator $I$ from ${\mathcal S}$ to ${\mathcal S}'$ is an extension of the linear operator $i_\Omega$ on ${\mathcal S}_\infty$ if and only if
\begin{equation}\label{homogeneous1.lm.eq1}
If= J_\Omega f+\sum_{|{\bf i}|\le N} \frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} H_{\bf i}
\end{equation}
for some integer $N$ and tempered distributions $H_{\bf i}, {\bf i}\in {\mathbb{Z}}_+^d$ with $|{\bf i}|\le N$.
\end{Lm}
\begin{proof} The sufficiency follows from Theorem \ref{maintheorem.iomega1} and the assumption that $H_{\bf i}, |{\bf i}|\le N$, in \eqref{homogeneous1.lm.eq1}
are tempered distributions.
Now the necessity. By Corollary \ref{generalizedrieszomega1.cr} and Theorem \ref{maintheorem.iomega1}, $I-J_\Omega$
is a continuous linear operator from ${\mathcal S}$ to ${\mathcal S}'$ that satisfies that
$(I-J_\Omega)f=0$ for all $f\in {\mathcal S}_\infty$.
This implies that the inverse Fourier transform of the tempered distribution $(I-J_\Omega)^* g$
is supported on the origin for any Schwartz function $g$.
Hence there exist an integer $N$ and tempered distribution $H_{\bf i}, |{\bf i}|\le N$,
such that
${\mathcal F}^{-1}((I-J_\Omega)^* g)=\sum_{|{\bf i}|\le N} \langle g, H_{\bf i}\rangle \delta^{({\bf i})}/{{\bf i}!}$,
where the tempered distributions $\delta^{({\bf i})}, {\bf i}\in {\mathbb{Z}}_+^d$, are
defined by $\langle \delta^{({\bf i})}, f\rangle=\partial^{\bf i} f({\bf 0})$ \cite[Theorem 2.3.4]{hormanderbook}.
Then
$\langle (I-J_\Omega)f, g\rangle=
\langle \hat f, {\mathcal F}^{-1}(I-J_\Omega)^*g\rangle= \sum_{|{\bf i}|\le N} \langle H_{\bf i}, g\rangle {\partial^{\bf i} \hat f({\bf 0})}/{{\bf i}!}
$ for all Schwartz functions $f$ and $g$, and hence \eqref{homogeneous1.lm.eq1} is established.
\end{proof}
\begin{Lm}\label{homogeneous2.lm}
Let $\gamma$ be a positive number with $\gamma-d\not\in {\mathbb{Z}}_+$,
and consider the continuous linear operator $K$ from ${\mathcal S}$ to ${\mathcal S}'$:
\begin{equation}\label{homogeneous2.lm.eq-1}
Kf=\sum_{|{\bf i}|\le N} \frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} H_{\bf i}, \quad f\in {\mathcal S}\end{equation}
where $N\in {\mathbb Z}_+$ and $H_{\bf i}, |{\bf i}|\le N$, are tempered distributions,
Then the following statements hold.
\begin{itemize}
\item[{(i)}] The equation
\begin{equation} \label{homogeneous2.lm.eq0} K (\delta_t f)= t^{-\gamma} \delta_t (Kf)\end{equation}
holds for any $f\in {\mathcal S}$ and $t>0$
if and only if for every ${\bf i}\in {\mathbb{Z}}_+^d$ with $|{\bf i}|\le N$,
$H_{\bf i}$ is homogeneous of degree $\gamma-d-|{\bf i}|$.
\item[{(ii)}]
The linear operator $K$ is translation-invariant if and only if
there exists a polynomial $P$ of degree at most $N$ such that
$H_{\bf i}=(-i\partial)^{\bf i} P$ for all ${\bf i}\in {\mathbb{Z}}_+^d$ with $|{\bf i}|\le N$.
\item[{(iii)}] The linear operator $K$
is translation-invariant and satisfies \eqref{homogeneous2.lm.eq0}
if and only if $H_{\bf i}=0$ for all
${\bf i}\in {\mathbb{Z}}_+^d$ with $|{\bf i}|\le N$.
\end{itemize}
\end{Lm}
\begin{proof}
{\em (i)}\quad
The sufficiency follows from the homogeneous assumption on $H_{\bf i}, |{\bf i}|\le N$, and
the observation that
\begin{equation}\label{homogeneous2.lm.pf.eq1}
\partial^{\bf i} \widehat {\delta_t f}({\bf 0})=t^{-d-|{\bf i}|} \partial^{\bf i} \hat f({\bf 0})\quad
{\rm for\ all}\ f\in {\mathcal S} \ {\rm and} \ {\bf i}\in {\mathbb{Z}}_+^d.\end{equation}
Now the necessity.
Let $\phi$ be a $C^\infty$ function such that
$\phi(\xi)=1$ for all $\xi\in B({\bf 0}, 1)$ and
$\phi(\xi)=0$ for all $\xi\not\in B({\bf 0}, 2)$, where $B({\bf x}, r)$ is the ball with center ${\bf x}\in {\mathbb{R}}^d$ and radius $r>0$.
Define $\psi_{\bf i}\in {\mathcal S}, {\bf i}\in {\mathbb{Z}}_+^d,$ with the help of the Fourier transform by
\begin{equation}\label{homogeneous2.lm.pf.eq7}
\widehat {\psi_{\bf i}}(\xi)=\frac{\xi^{\bf i}}{{\bf i} !} \phi(\xi). \end{equation}
One may verify that
\begin{equation}\label{homogeneous2.lm.pf.eq8}
\partial^{{\bf i}'} \widehat{\psi_{\bf i}}({\bf 0})=\left\{\begin{array}{ll} 1 & {\rm if} \ {\bf i}'={\bf i},\\
0 & {\rm if} \ {\bf i}'\ne {\bf i}.\end{array}\right.
\end{equation}
For any ${\bf i}\in {\mathbb{Z}}_+^d$ with $|{\bf i}|\le N$,
the homogeneous property of the tempered distribution $H_{\bf i}$ follows by replacing $f$ in \eqref{homogeneous2.lm.eq0} by $\psi_{\bf i}$ and using \eqref{homogeneous2.lm.pf.eq8}.
{\em (ii)}\quad ($\Longleftarrow$) Given $f\in {\mathcal S}$ and ${\bf x}_0\in {\mathbb{R}}^d$,
\begin{eqnarray} \label{homogeneous2.lm.pf.eq10}
K(\tau_{{\bf x}_0}f) ({\bf x}) & = & \sum_{|{\bf i}|\le N}
\sum_{{\bf j}+{\bf k}= {\bf i}}
\frac{ (-i{\bf x}_0)^{{\bf k}}}{{\bf k}!} \frac{\partial^{\bf j} \hat f({\bf 0})}{{\bf j}!}
(-i\partial)^{\bf i}P({\bf x})\nonumber\\
&= & \sum_{|{\bf j}|\le N}
\frac{(-i)^{\bf j}\partial^{\bf j} \hat f({\bf 0})}{{\bf j}!}
\Big(\sum_{|{\bf k}|\le N-|{\bf j}|}\frac{\partial^{{\bf j}+{\bf k}} P({\bf x})}{{\bf k}!} (-{\bf x}_0)^{\bf k}\Big)
\nonumber\\
& = & \sum_{|{\bf j}|\le N}
\frac{(-i)^{\bf j}\partial^{\bf j} \hat f({\bf 0})}{{\bf j}!}\partial^{{\bf j}} P({\bf x}-{\bf x}_0)=Kf({\bf x}-{\bf x}_0),
\end{eqnarray}
where the first equality follows from
\begin{equation} \label{homogeneous2.lm.pf.eq11}
\partial^{\bf i} \widehat {\tau_{{\bf x}_0}f}({\bf 0})=\sum_{{\bf j}\le {\bf i}}
\binom{{\bf i}}{{\bf j}} (-i{\bf x}_0)^{{\bf i}-{\bf j}} \partial^{\bf j} \hat f({\bf 0}),
\end{equation}
and the third equality is deducted from the Taylor expression of the polynomial $\partial^{\bf j} P$
of degree at most $N-|{\bf j}|$.
($\Longrightarrow$)
By \eqref{homogeneous2.lm.pf.eq11} and the translation-invariance of the linear operator $K$,
\begin{equation} \label{homogeneous2.lm.pf.eq12}
\sum_{|{\bf i}|\le N}
\sum_{{\bf j}+{\bf k}= {\bf i}}
\frac{ (-i{\bf x}_0)^{{\bf k}}}{{\bf k}!} \frac{\partial^{\bf j} \hat f({\bf 0})}{{\bf j}!}
H_{\bf i}= \sum_{|{\bf i}|\le N}
\frac{\partial^{\bf j} \hat f({\bf 0})}{{\bf j}!} \tau_{ {\bf x}_0}H_{\bf j}
\end{equation}
holds for any Schwartz function $f$ and ${\bf x}_0\in {\mathbb{R}}^d$.
Replacing $f$ in the above equation by the function $\psi_{\bf 0}$ in \eqref{homogeneous2.lm.pf.eq7}
and then using \eqref{homogeneous2.lm.pf.eq8}, we get
\begin{equation} \label{homogeneous2.lm.pf.eq13}
\tau_{{\bf x}_0} H_{\bf 0} =
\sum_{|{\bf i}|\le N}
\frac{ (-i{\bf x}_0)^{{\bf i}}}{{\bf i}!}
H_{\bf i}.
\end{equation}
This implies that
$
\langle H_{{\bf 0}}, g(\cdot+{\bf x}_0)\rangle=
\sum_{ |{\bf i}|\le N} \frac{ (-i{\bf x}_0)^{{\bf i}}}{{\bf i}!}
\langle H_{{\bf i}}, g\rangle
$
for any Schwartz function $g$. By taking partial derivatives $\partial^{\bf k}, |{\bf k}|=N+1$, with respect to ${\bf x}_0$
of both sides of the above equation,
using the fact that $\partial^{{\bf k}} {\bf x}^{{\bf i}}=0$ for all ${\bf k}\in {\mathbb{Z}}_+$ with $|{\bf k}|=N+1$,
and then letting ${\bf x}_0={\bf 0}$, we obtain that
$\langle H_{{\bf 0}}, \partial^{\bf k} g\rangle =0
$ holds
for any $g\in {\mathcal S}$ and ${\bf k}\in {\mathbb{Z}}_+$ with $|{\bf k}|=N+1$.
Hence $H_{\bf 0}=P$ for some polynomial $P$ of degree at most $N$.
The desired conclusion about $H_{\bf i}, |{\bf i}|\le N$,
then follows from \eqref{homogeneous2.lm.pf.eq13} and
$\tau_{{\bf x}_0}H_{\bf 0}({\bf x})=\sum_{|{\bf i}|\le N} \frac{ (-{\bf x}_0)^{\bf i}}{{\bf i}!} \partial^{\bf i} P({\bf x})
$ by the Taylor expansion of the polynomial $P$.
{\em (iii)} \quad Clearly if $H_{\bf i}=0$ for all $|{\bf i}|\le N$, then $Kf=0$
for all $f\in {\mathcal S}$ and hence $K$ is translation-invariant and satisfies \eqref{homogeneous2.lm.eq0}.
Conversely, if $K$ is translation-invariant and satisfies \eqref{homogeneous2.lm.eq0}, it follow from
the conclusions (i) and (ii) that for every ${\bf i}\in {\mathbb{Z}}_+^d$ with $|{\bf i}|\le N$,
$H_{\bf i}$ is homogeneous of degree $\gamma-d-|{\bf i}|\not\in {\mathbb{Z}}$ and also a polynomial of degree at most $N-|{\bf i}|$.
Then $H_{\bf i}=0$ for all $ {\bf i}\in {\mathbb{Z}}_+^d$ with $|{\bf i}|\le N$ because
the homogeneous degree of any nonzero polynomial is a nonnegative integer if it is
homogeneous.
\end{proof}
We now have all of ingredients to prove Theorem \ref{iomega2.tm}.
\begin{proof}[Proof of Theorem \ref{iomega2.tm}] The sufficiency follows from Corollary \ref{generalizedrieszomega1.cr} and Theorem \ref{maintheorem.iomega1}. Now the necessity.
By Lemma \ref{homogeneous1.lm}, there exist
an integer $N$ and tempered distributions $H_{\bf i}, |{\bf i}|\le N$,
such that \eqref{homogeneous1.lm.eq1} holds.
Define
$Kf=\sum_{|{\bf i}|\le N} \frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} H_{\bf i}$ for any $f\in {\mathcal S}$. Then
$Kf $ is a continuous linear operator from ${\mathcal S}$ to ${\mathcal S}'$ and
\begin{equation}\label{iomega2.tm.pf.eq1}
If=J_\Omega f+Kf, \quad \ f\in {\mathcal S}.\end{equation}
Moreover the linear operator $K$ satisfies \eqref{homogeneous2.lm.eq0} and is translation-invariant by \eqref{iomega2.tm.pf.eq1},
Theorem \ref{maintheorem.iomega1} and the assumption on $I$.
Then $Kf=0$ for all $f\in {\mathcal S}$ by Lemma \ref{homogeneous2.lm}. This together with
\eqref{iomega2.tm.pf.eq1} proves the desired conclusion that $I=J_\Omega$.
%
\end{proof}
\subsection{Translation-invariant extensions of the linear operator $i_\Omega$ with additional localization in the Fourier domain}
Given a nonzero homogeneous function $\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ of degree
$-\gamma$, we recall from \eqref{fractionalderivative.neweq2} and
Theorem \ref{maintheorem.iomega1} that $J_\Omega$ is translation-invariant and
the Fourier transform of $J_\Omega f$ belongs to $K_1$ when $\gamma\in (0, d)$,
where
\begin{equation}
K_1=\Big\{h:\ \int_{{\mathbb{R}}^d} |h(\xi)| (1+\|\xi\|)^{-N} d\xi<\infty \ \ {\rm for \ some} \ N\ge 1\Big\}.\end{equation}
In fact, the generalized Riesz potential $J_\Omega$ is the {\bf only} extension
of the linear operator $i_\Omega$ on ${\mathcal S}_\infty$ to the whole space ${\mathcal S}$ with the above two properties.
\begin{Tm}\label{iomega4.tm}
Let $\gamma>0$ with $\gamma-d\not\in {\mathbb{Z}}_+$, $\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be
a nonzero homogeneous function of degree $-\gamma$,
and the continuous linear operator $I$ from ${\mathcal S}$ to ${\mathcal S}'$
be an extension of the linear operator $i_\Omega$ on ${\mathcal S}_\infty$
such that the Fourier transform
of $If$ belongs to $K_1$ for all $f\in {\mathcal S}$.
Then $I$ is translation-invariant if and only if $I=J_\Omega$ and $\gamma\in (0, d)$.
\end{Tm}
\begin{proof} The sufficiency follows from \eqref{fractionalderivative.neweq2} and
Theorem \ref{maintheorem.iomega1}. Now we prove the necessity.
By the assumption on the linear operator $I$, applying an argument similar to the proof of
Lemma \ref{homogeneous1.lm}, we can find a family of functions $g_{\bf i}\in K_1, |{\bf i}|\le N$,
such that
\begin{eqnarray}\label{iomega4.tm.pf.eq0}
\widehat{If}(\xi) & = & \Big(\hat f(\xi)-
\sum_{|{\bf i}|\le \gamma-d} \frac{\partial^{{\bf i}} \hat f({\bf 0})}{ {\bf i}!} \xi^{\bf i}\Big)
\Omega(\xi) +\sum_{|{\bf i}|\le N} \frac{\partial^{{\bf i}} \hat f({\bf 0})}{ {\bf i}!} g_{\bf i}(\xi)
\end{eqnarray}
for any Schwartz function $f$.
This together with \eqref{homogeneous2.lm.pf.eq11} and the translation-invariance of the linear operator $I$
implies that
\begin{eqnarray*}\label{iomega4.tm.pf.eq1}
& & -
\sum_{ |{\bf i}|\le \gamma-d} \sum_{{\bf j}+{\bf k}={\bf i}}
\frac{\partial^{\bf j}\hat f({\bf 0})}{{\bf k}! {\bf j}!} (-i{\bf x}_0)^{{\bf k}} \xi^{\bf i}\Omega(\xi) +
\sum_{ |{\bf i}|\le N} \sum_{{\bf j}+{\bf k}= {\bf i}}
\frac{\partial^{\bf j}\hat f({\bf 0})}{{\bf k}! {\bf j}!} (-i{\bf x}_0)^{{\bf k}} g_{\bf i}(\xi)\nonumber\\
& = & \
e^{i{\bf x}_0\xi}
\Big(-\sum_{|{\bf i}|\le \gamma-d} \frac{\partial^{\bf i}\hat f({\bf 0})}{{\bf i}!} \xi^{\bf i}\Omega(\xi)
+\sum_{|{\bf i}|\le N}
\frac{\partial^{\bf i}\hat f({\bf 0})}{{\bf i}!} g_{\bf i}(\xi)\Big).
\end{eqnarray*}
As ${\bf x}_0\in {\mathbb{R}}^d$ in \eqref{iomega4.tm.pf.eq1} is chosen arbitrarily, we conclude that
\begin{equation*}\label{iomega4.tm.pf.eq2}
-\sum_{|{\bf i}|\le \gamma-d} \frac{\partial^{\bf i}\hat f({\bf 0})}{{\bf i}!} \xi^{\bf i}\Omega(\xi)
+\sum_{|{\bf i}|\le N}
\frac{\partial^{\bf i}\hat f({\bf 0})}{{\bf i}!} g_{\bf i}(\xi)=0\quad {\rm for \ all} \ f\in {\mathcal S}.\end{equation*}
Substituting the above equation into \eqref{iomega4.tm.pf.eq0}, we then obtain
$\widehat{If}(\xi)= \hat f(\xi) \Omega(\xi)
$
for all $f \in {\mathcal S}$. This, together with
the observation that
$\hat f\Omega\in K_1$ for all $f\in {\mathcal S}$ if and only if $\gamma<d$, leads to the desired conclusion that
$I=J_\Omega$ and $\gamma\in (0, d)$.
\end{proof}
\subsection{Non-integrability in the spatial domain}
Let $\gamma>0$ with $\gamma-d\not\in {\mathbb{Z}}_+$ and
$\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be a nonzero
homogeneous function of degree $-\gamma$. For any Schwartz function $f$, there exists a positive constant $C$ by
Theorem \ref{generalizedrieszomega1.tm} such that $|J_\Omega f({\bf x})|\le C (1+\|{\bf x}\|)^{\gamma-d}$
for all ${\bf x}\in {\mathbb{R}}^d$. Hence $J_\Omega f\in L^p, 1\le p\le \infty$, when $\gamma<d(1-1/p)$.
In this subsection, we show that the above $p$-integrability property for the generalized Riesz potential $J_\Omega$
is no longer true when $\gamma\ge d(1-1/p)$.
\begin{Tm}\label{time1.tm}
Let $1\le p\le \infty, 0<\gamma\in [d(1-1/p), \infty)\backslash {\mathbb{Z}}$ and
$\Omega\in C^\infty ({\mathbb{R}}^d\backslash \{\bf 0\})$ be a nonzero homogeneous function of degree $-\gamma$.
Then there exists a Schwartz function $f$ such that
$J_\Omega f\not\in L^p$.
\end{Tm}
Letting $\Omega(\xi)=\|{\xi}\|^{-\gamma}$ in Theorem \ref{time1.tm} leads to the conclusion mentioned in the abstract:
\begin{Cr}\label{nonintegrable.cr}
Let $1\le p\le \infty$ and $d(1-1/p)\le \gamma\not\in {\mathbb{Z}}_+$.
Then
$I_\gamma f$ is {\bf not} $p$-integrable for some function $f\in {\mathcal S}$.
\end{Cr}
\begin{proof}[Proof of Theorem \ref{time1.tm}]
Let the Schwartz functions $\phi$ and $\psi_{\bf i}, {\bf i}\in {\mathbb{Z}}_+^d$, be as in the proof of Lemma \ref{homogeneous2.lm}.
We examine three cases to prove the theorem.
{\em Case I:\quad $d(1-1/p)\le\gamma< \min(d, d(1-1/p)+1)$}.\quad
In this case, $1\le p<\infty$ and
\begin{equation}\label{time1.tm.pf.eq1}
J_\Omega \psi_{\bf 0}({\bf x})=\int_{{\mathbb{R}}^d} K({\bf x}-{\bf y}) \psi_{\bf 0}({\bf y}) d{\bf y},
\end{equation}
by \eqref{fractionalderivative.neweq2}, where $K$ is the inverse Fourier transform of $\Omega$.
By \cite[Theorems 7.1.16 and 7.1.18]{hormanderbook},
$K\in C^\infty({\mathbb{R}}^d\backslash\{0\})$
is a homogeneous function
of order $\gamma-d\in (-d,0)$, which implies that
\begin{equation}\label{time1.tm.pf.eq2}
|\partial^{\bf i} K({\bf x})|\le C \|{\bf x}\|^{\gamma-d-|{\bf i}|} \quad {\rm for \ all}\ {\bf i}\in {\mathbb{Z}}_+^d \ {\rm with} \ |{\bf i}|\le 1.
\end{equation}
Using \eqref{time1.tm.pf.eq1} and \eqref{time1.tm.pf.eq2}, and
noting that $\psi_{\bf 0}\in {\mathcal S}$ satisfies
$\int_{{\mathbb{R}}^d} \psi_{\bf 0}({\bf y})d{\bf y}=1$, we obtain
that for all ${\bf x}\in {\mathbb{R}}^d$ with $\|{\bf x}\|\ge 1$,
\begin{eqnarray}\label{time1.tm.pf.eq3}
|J_\Omega \psi_{\bf 0} ({\bf x})-K({\bf x})|
\!\! & \le &\!\!
\int_{\|{\bf y}\|\le \|{\bf x}\|/2} |K({\bf x}-{\bf y})-K({\bf x})| |\psi_{\bf 0}({\bf y})| d{\bf y} \nonumber\\
& &\!\! +
\Big(\int_{\|{\bf x}\|/2\le \|{\bf y}\|\le 2 \|{\bf x}\|}+\int_{2\|{\bf x}\|\le \|{\bf y}\|}\Big) |K({\bf x}-{\bf y})||\psi_{\bf 0}({\bf y})| d{\bf y}
\nonumber\\
& &\!\! + |K({\bf x})| \int_{\|{\bf y}\|\ge \|{\bf x}\|/2} |\psi_{\bf 0}({\bf y})| d{\bf y}
\nonumber\\
\!\! & \le &\!\! C (1+\|{\bf x}\|)^{\gamma-d-1}.
\end{eqnarray}
We notice that $\int_{\|{\bf x}\|\ge 1} (1+\|{\bf x}\|)^{(\gamma-d-1)p}d {\bf x}<\infty$
and
$\int_{\|{\bf x}\|\ge 1} |K({\bf x})|^p d{\bf x}=\infty$ because
$K$ is a nonzero homogenous function
of degree $\gamma-d$ and $d-p<(d-\gamma)p\le d$.
The above two observations together with the estimate in \eqref{time1.tm.pf.eq3}
prove that $J_\Omega \psi_{\bf 0} \not\in L^p$, the desired conclusion with $f=\psi_{\bf 0}$.
{\em Case II: $d<\gamma<d(1-1/p)+1$}.\quad In this case, $d<p\le \infty$ and
\begin{eqnarray}\label{time1.tm.pf.eq4}
J_\Omega \psi_{\bf 0}({\bf x}) & = &\frac{1}{d-\gamma}
\sum_{|{\bf j}|=1} J_{\Omega_{\bf j}}(\varphi_{\bf j}) ({\bf x})
+ \frac{1}{d-\gamma}\sum_{|{\bf i}|=1} (-{\bf x})^{\bf i} J_{\Omega_{\bf i}}\psi_{\bf 0} ({\bf x})
\end{eqnarray}
by taking $k_0=1$ in \eqref{generalizedrieszomega1.tm.pf.eq1}, where $\Omega_{\bf i}(\xi)=(i\xi)^{\bf i} \Omega(\xi)$ and
$\varphi_{\bf i}({\bf x})={\bf x}^{\bf i} \psi_{\bf 0}({\bf x})$. Let $K_{\bf i}$ be the inverse
Fourier transform
of the function $\Omega_{\bf i}, |{\bf i}|=1$. Noticing that $\Omega_{\bf i}$ is homogeneous of degree $-\gamma+1$ and that $\int_{{\mathbb{R}}^d} \varphi_{\bf i}({\bf x}) d{\bf x}=0$, we then
apply similar argument to the one used in establishing
\eqref{time1.tm.pf.eq3} and obtain
\begin{eqnarray*}
|J_{\Omega_{\bf i}}(\varphi_{\bf i}) ({\bf x})|+
|J_{\Omega_{\bf i}}\psi_{\bf 0} ({\bf x})-K_{\bf i}({\bf x})|
\le C \|{\bf x}\|^{\gamma-d-2}\quad {\rm if } \ \|{\bf x}\|\ge 1.
\end{eqnarray*}
Hence
\begin{equation}
\label{time1.tm.pf.eq3b}
\int_{\|{\bf x}\|\ge 1} \big|J_\Omega \psi_{\bf 0}({\bf x})-\frac{1}{d-\gamma}\sum_{|{\bf i}|=1} (-{\bf x})^{\bf i} K_{\bf i}({\bf x})\big|^p d{\bf x}\le
C \int_{\|{\bf x}\|\ge 1} \|{\bf x}\|^{(\gamma-d-1)p} d{\bf x}<\infty
\end{equation}
if $d<p<\infty$ and
\begin{equation}\label{time1.tm.pf.eq4}
\sup_{\|{\bf x}\|\ge 1} \big|J_\Omega \psi_{\bf 0}({\bf x})-\frac{1}{d-\gamma}\sum_{|{\bf i}|=1} (-i{\bf x})^{\bf i} K_{\bf i}({\bf x})\big|\le
C \sup_{\|{\bf x}\|\ge 1} \|{\bf x}\|^{\gamma-d-1} <\infty
\end{equation}
if $p=\infty$.
Set $K({\bf x}):= \sum_{|{\bf i}|=1} (-{\bf x})^{\bf i} K_{\bf i}({\bf x})$.
Then $K$ is
homogeneous of degree $\gamma-d$ by the assumption on $\Omega$, and is not identically zero because
\begin{eqnarray*}
\langle K, g\rangle & = & \int_{{\mathbb{R}}^d}
\Omega(\xi) \Big(\sum_{|{\bf i}|=1} \xi^{\bf i} \partial^{\bf i} \hat g(\xi)\Big) d\xi
= -\int_{{\mathbb{R}}^d} \Big(\sum_{|{\bf i}|=1}\partial^{\bf i}( \xi^{\bf i} \Omega(\xi))\Big) \hat g(\xi) d\xi \\
& = & \int_{S^{d-1}} \int_0^\infty \big(d\Omega(r\xi')+ r \frac{d}{dr} \Omega(r\xi')\big) \hat g(r\xi') r^{d-1} dr d\sigma(\xi')\\
&
=& (d-\gamma) \int_{{\mathbb{R}}^d} \Omega(\xi) \hat g (\xi) d\xi
\not\equiv 0
\end{eqnarray*} where $g\in {\mathcal S}_\infty$.
Thus
$\int_{\|{\bf x}\|\ge 1} |K({\bf x})|^p d{\bf x}=+\infty$ when $d<p<\infty$, and
$K({\bf x})$ is unbounded on ${\mathbb{R}}^d\backslash B({\bf 0},1)$ when $p=\infty$.
This together with \eqref{time1.tm.pf.eq3b} and \eqref{time1.tm.pf.eq4}
proves that $J_\Omega \psi_{\bf 0}\not\in L^p$ and hence the desired conclusion with $f=\psi_{\bf 0}$.
{\em Case III: $\gamma\ge d(1-1/p)+1$.}
Let $k_0$ be the integer such that $d(1-1/p)\le \gamma-k_0<d(1-1/p)+1$, and set
$\Omega_{\bf j}(\xi)=(i\xi)^{\bf j} \Omega(\xi), |{\bf j}|=k_0$.
Noting that
$J_\Omega \psi_{\bf j}({\bf x})=
J_{\Omega_{\bf j}} \psi_{\bf 0} ({\bf x})/{{\bf j}!}$
and $\Omega_{\bf j}$ is homogeneous of degree $-\gamma+k_0$,
we have obtained from the conclusions in the first two cases that $J_\Omega \psi_{\bf j} \not\in L^p$.
Hence the desired conclusion follows by letting $f=\psi_{\bf j}$ with $|{\bf j}|=k_0$. \end{proof}
\subsection{Non-integrability in the Fourier domain}
If $\gamma<d$, it follows from \eqref{fractionalderivative.neweq2}
that for Schwartz functions $f$ and $g$,
$\langle J_\Omega f, g\rangle$ can be expressed as
a weighted integral of $\hat g$:
\begin{equation}\label{frequency.eq1}
\langle J_\Omega f, g\rangle=\int_{{\mathbb{R}}^d} h(\xi) \hat g(\xi) d\xi,
\end{equation}
where $h(\xi)=(2\pi)^{-d}\Omega(-\xi) \hat f(-\xi)\in K_1$.
In this subsection, we show that the above reformulation \eqref{frequency.eq1}
to define $\langle J_\Omega f, g\rangle$ via a weighted integral of $\hat g$ {\bf cannot} be extended to $\gamma>d$.
\begin{Tm}\label{frequency.tm1}
Let $\gamma\in (d, \infty)\backslash {\mathbb{Z}}$,
$\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be a nonzero homogeneous function of degree $-\gamma$,
and let $J_\Omega$ be defined by \eqref{fractionalderivative.def}.
Then there exists a Schwartz function $f$ such that the Fourier transform of $J_\Omega f$ does not belong to $K_1$.
\end{Tm}
\begin{proof}
Let $\phi$ and $\psi_{\bf 0}$ be the Schwartz functions in the proof of Lemma \ref{homogeneous2.lm}, and
let $g\in {\mathcal S}_\infty$ be so chosen that
its Fourier transform
$\hat g$ is supported in $B({\bf 0}, 1)$
and satisfies $\int_{{\mathbb{R}}^d} \Omega(\xi){ \hat g(-\xi)}d\xi=1$. Now we prove that
$\widehat{J_\Omega \psi_{\bf 0}}\not\in K_1$.
Suppose on the contrary that $\widehat{J_\Omega \psi_{\bf 0}}\in K_1$.
Then
\begin{eqnarray}\label{frequency.tm1.pf.eq1} \langle J_\Omega \psi_{\bf 0}, n^{-d} g(\cdot/n)\rangle
& = &\frac{ (2\pi)^{-d}\Gamma(d-\gamma)} {\Gamma(d+k_0-\gamma)}
\int_{S^{d-1}}\int_\epsilon^\infty
r^{k_0+d-\gamma-1} \Omega(\xi')\nonumber\\
& & \Big(-\frac{d}{dr}\Big)^{k_0}\Big(\widehat \psi_{\bf 0}(r\xi') \hat g(-rn\xi')\Big) dr d\sigma(\xi') \nonumber\\
& = & (2\pi)^{-d} \int_{{\mathbb{R}}^d}
{\hat g(-n\xi)} \Omega(\xi)d\xi
= (2\pi)^{-d} n^{\gamma-d}\int_{{\mathbb{R}}^d} \Omega(\xi) {\hat g(-\xi)} d\xi \nonumber\\
&\to& +\infty \quad {\rm as} \ n\to \infty
\end{eqnarray}
by \eqref{fractionalderivative.def} and \eqref{extension.eq}.
On the other hand,
\begin{eqnarray}\label{frequency.tm1.pf.eq2}
& & |\langle J_\Omega \psi_{\bf 0}, n^{-d} g(\cdot/n)\rangle|
= (2\pi)^{-d} \Big|\int_{{\mathbb{R}}^d} \widehat{J_\Omega \psi_{\bf 0}}(\xi) \hat g(-n\xi) d\xi\Big|\nonumber\\
& \le & (2\pi)^{-d} \|\hat g\|_\infty \int_{|\xi|\le 1/n} |\widehat{J_\Omega \psi_0}(\xi)| d\xi
\to 0 \ {\rm as} \ n\to \infty,
\end{eqnarray}
where we have used the hypothesis that $\widehat{J_\Omega \psi_{\bf 0}}\in K_1$ to obtain the limit.
The limits in \eqref{frequency.tm1.pf.eq1} and \eqref{frequency.tm1.pf.eq2} contradict each other, and hence
the Fourier transform $J_\Omega \psi_{\bf 0}$ does not belong to $K_1$.
\end{proof}
\subsection{Proof of Theorem \ref{generalizedriesz.tm}}
Observe that $J_\Omega=I_\gamma$ when $\Omega(\xi)=\|\xi\|^{-\gamma}$ and $\gamma>0$, and that
\begin{equation}
\label{generalized.tm.pf.eq1} J_\Omega=(-\triangle)^{-\gamma/2}\quad {\rm if}\ \Omega(\xi)=\|\xi\|^{-\gamma}\quad {\rm and} \ \gamma<0.
\end{equation} Then
the necessity holds by Theorem \ref{iomega2.tm}, while the sufficiency follows from Corollary \ref{generalizedrieszomega1.cr}, Theorem \ref{maintheorem.iomega1}, and Corollary \ref{composition.cr}.
\section{Integrable Riesz Potentials}\label{irp.section}
In Section \ref{grp.section}, we have shown that the various attempts for defining a proper (integrable) Riesz potential that is translation-invariant
are doomed to failure for $\gamma>d$. We now proceed by providing a fix which is possible if we drop the translation-invariance requirement.
Let $1\le p\le \infty, \gamma\in {\mathbb{R}}$, and $\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$
be a homogeneous function
of degree $-\gamma$. We define the linear operator $U_{\Omega,p} $ from ${\mathcal S}$ to ${\mathcal S}'$
with the help of the Fourier transform by
\begin{equation}\label{newfractionalderivative.def}
{\mathcal F}({U_{\Omega,p}f})(\xi)= \Big(\hat f (\xi)-\sum_{|{\bf i}|\le \gamma-d(1-1/p)} \frac{\partial^{\bf i}\hat f({\bf 0})}{ {\bf i}!} \xi^{\bf i}\Big) \Omega(\xi), \quad f\in {\mathcal S}.\end{equation}
We call the linear operator $U_{\Omega, p}$ a {\em
$p$-integrable Riesz potential associated with the homogenous function $\Omega$}, or {\em
integrable Riesz potential} for brevity, as
\begin{equation} \label{fractionalderivativeomegap.def}U_{\Omega, p}=I_{\gamma, p} \quad {\rm if } \quad \Omega(\xi)=\|\xi\|^{-\gamma}.\end{equation}
Define
\begin{equation}\label{fractionalderivative.tm1.pf.eq3}
U_{\Omega, p}^*f({\bf x}) = (2\pi)^{-d}
\int_{{\mathbb{R}}^d}\Big(e^{i\langle {\bf x}, \xi\rangle}-\sum_{|{\bf i}|\le \gamma-d+d/p}
\frac{(i{\bf x})^{\bf i}\xi^{\bf i}}{ {\bf i}!} \Big)
{\Omega(-\xi)}\hat f(\xi) d\xi, \quad f\in {\mathcal S}.
\end{equation}
Then $U_{\Omega, p}^*$ is the adjoint operator of the integrable Riesz potenrial $U_{\Omega, p}$:
\begin{equation}\label{fractionalderivative.tm1.pf.eq4}
\langle U_{\Omega, p}f, g\rangle=\langle f, U_{\Omega, p}^*g\rangle \quad {\rm for\ all} \ f, g\in {\mathcal S}.
\end{equation}
If $\gamma$ satisfies $0<\gamma< d(1-1/p)$, then
\begin{equation} U_{\Omega, p}f= J_\Omega f \quad {\rm for \ all} \ f\in {\mathcal S}.\end{equation}
Hence in this case, it follows from Theorem \ref{maintheorem.iomega1} that
$U_{\Omega, p}$ is dilation-invariant and translation-invariant, and a continuous
extension of the linear operator $i_\Omega$ on the closed subspace ${\mathcal S}_\infty$ to the whole space ${\mathcal S}$.
Moreover
$U_{\Omega, p} f\in L^p$ and ${\mathcal F}( {U_{\Omega, p}f})\in L^q, 1\le q\le p/(p-1)$, for any Schwartz function $f$
by Theorem \ref{generalizedrieszomega1.tm} and the following estimate:
$$
|{\mathcal F}({U_{\Omega, p}f})(\xi)|\le C \|\xi\|^{-\gamma} (1+\|\xi\|)^{\gamma-d-1}\ {\rm for \ all} \ \xi\in {\mathbb{R}}^d.$$
So from now on, we implicitly assume that $\gamma\ge d(1-1/p)$,
except when mentioned otherwise.
In the sequel,
we investigate with the properties of the $p$-integrable Riesz potential $U_{\Omega, p}$
associated with a homogenous function $\Omega$, such as
dilation-invariance and translation-variance (Theorem \ref{fractionalderivative.tm1}),
$L^{p/(p-1)}$-integrability in the Fourier domain (Corollary \ref{fractionalderivative.cr1}), $L^{p}$-integrability in the spatial domain (Theorem \ref{iomegap.tm1} and Corollary \ref{iomegap.cor1}), composition and left-inverse property (Theorem \ref{compositionp.tm} and Corollary \ref{leftinversefractionalderivative.cr}),
the uniqueness of dilation-invariant extension of the linear operator $i_\Omega$ from the closed subspace ${\mathcal S}_\infty$ to the whole space ${\mathcal S}$ with additional integrability in the spatial domain and in the Fourier domain (Theorems \ref{time2.tm} and \ref{iomega5.tm}).
The above properties of the $p$-integrable Riesz potential
associated with a homogenous function will be used to prove Theorem \ref{integrablefractionalderivative.tm} in the last subsection.
\subsection{Dilation-invariance, translation-variance and integrability in the Fourier domain}
\begin{Tm}\label{fractionalderivative.tm1} Let $1\le p\le \infty, \gamma\ge d(1-1/p)$, $k_1$ be the integral part of
$\gamma-d(1-1/p)$, $\Omega\in C^\infty({\mathbb{R}}^d\backslash \{{\bf 0}\})$ be a nonzero homogeneous function
of degree $-\gamma$, and let $U_{\Omega, p}$ be defined as in \eqref{newfractionalderivative.def}.
Then the following statements hold.
\begin{itemize}
\item[{(i)}] $U_{\Omega,p}$ is dilation-invariant.
\item[{(ii)}] $U_{\Omega, p}$ is not translation-invariant.
\item[{(iii)}] If $\sup_{{\bf x}\in {\mathbb{R}}^d} |f({\bf x})| (1+\|{\bf x}\|)^{k_1+d+1+\epsilon}<\infty$ for some $\epsilon>0$, then there exists a positive constant $C$ independent on $f$ such that
\begin{equation}\label{fractionalderivative.tm1.eq1}
|{\mathcal F}({U_{\Omega, p} f})(\xi)|\le C \Big(\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+d+1+\epsilon} \Big) \|\xi\|^{k_1-\gamma+1} (1+\|\xi\|)^{-1}\end{equation}
for all $\xi\in {\mathbb{R}}^d$.
\item[{(iv)}] $U_{\Omega,p}$ is a continuous linear operator from ${\mathcal S}$ to ${\mathcal S}'$, and an extension of the operator $i_\Omega$ on the subspace ${\mathcal S}_\infty$ to the whole space
${\mathcal S}$.
\end{itemize}
\end{Tm}
As a consequence of Theorem \ref{fractionalderivative.tm1}, we have the following result about the $L^{p/(p-1)}$-integrability of the Fourier transform
of $U_{\Omega, p} f$ for $f\in {\mathcal S}$.
\begin{Cr}\label{fractionalderivative.cr1}
Let $1\le p\le \infty$ and $\gamma\ge d(1-1/p)$ satisfy either $p=1$ or $\gamma-d(1-1/p)\not\in {\mathbb{Z}}_+$ and $1<p\le \infty$, $k_1$ be the integral part of
$\gamma-d(1-1/p)$, $\Omega\in C^\infty({\mathbb{R}}^d\backslash \{{\bf 0}\})$ be a homogeneous function
of degree $-\gamma$, and let $U_{\Omega, p}$ be defined as in \eqref{newfractionalderivative.def}.
Then
the Fourier transform of $U_{\Omega, p} f$ belongs to $L^{p/(p-1)}$ for any $f\in {\mathcal S}$.
\end{Cr}
\begin{proof} [Proof of Theorem \ref{fractionalderivative.tm1}]
{\em (i)}\quad Given any $t>0$ and $f\in {\mathcal S}$,
\begin{equation*}\label{fractionalderivative.tm1.pf.eq3}
{\mathcal F}(U_{\Omega, p} (\delta_t f))(\xi) = t^{-d}
\Big(\hat f\big(\frac{\xi}{t}\big)-\sum_{|{\bf i}|\le \gamma-d+d/p} \frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} \big(\frac{\xi}{t}\big)^{\bf i}\Big) \Omega(\xi) =t^{-d-\gamma}
{\mathcal F}( {U_{\Omega, p} f})\big(\frac{\xi}{t}\big).
\end{equation*}
This proves the dilation-invariance of the linear operator $U_{\Omega, p}$.
{\em (ii)}\quad Suppose, on the contrary, that $U_{\Omega,p}$ is translation-invariant. Then
\begin{equation} \label{fractionalderivative.tm1.pf.eq5} \Omega(\xi)
\sum_{|{\bf i}|\le \gamma-d+d/p}
\frac{\partial^{\bf i} \widehat {\tau_{{\bf x}_0}f}({\bf 0})}{{\bf i}!} \xi^{\bf i}=
\Omega(\xi) e^{-i\langle {\bf x}_0, \xi\rangle} \sum_{|{\bf i}|\le \gamma-d+d/p}
\frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} \xi^{\bf i},\quad \xi\in {\mathbb{R}}^d
\end{equation}
for all ${\bf x}_0\in {\mathbb{R}}^d$ and $f\in {\mathcal S}$.
Note that the left-hand side of equation \eqref{fractionalderivative.tm1.pf.eq5} is a polynomial in ${\bf x}_0$ by
\eqref{homogeneous2.lm.pf.eq11} while its right hand side is a trigonometric function of ${\bf x}_0$. Hence
both sides must be identically zero, which implies that
\begin{equation}\Omega(\xi)
\sum_{|{\bf i}|\le \gamma-d+d/p}
\frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} \xi^{\bf i}=0, \quad \xi\in {\mathbb{R}}^d
\end{equation}
for all $f\in {\mathcal S}$. Replacing $f$ in the above equation by the function $\psi_{\bf 0}$ in \eqref{homogeneous2.lm.pf.eq7} and using
\eqref{homogeneous2.lm.pf.eq8} and the assumption $\gamma\ge d(1-1/p)$ leads to a contradiction.
{\em (iii)}\quad
By the assumption on the homogeneous function $\Omega$,
$|\Omega(\xi)|\le C \|\xi\|^{-\gamma}$. Then
for $\xi\in {\mathbb{R}}^d$ with $\|\xi\|\ge 1$,
\begin{eqnarray*}
|{\mathcal F}({U_{\Omega,p} f})(\xi)| & \le &
C \Big(\|\hat f\|_\infty+\sum_{|{\bf i}|\le k_1}
\|\partial^{\bf i}\hat f\|_\infty \|\xi\|^{|\bf i|}\Big)
\|\xi\|^{-\gamma}\nonumber\\
& \le & C \Big(\sum_{|{\bf i}|\le k_1+1} \|\partial^{\bf i} \hat f\|_\infty\Big)
\|\xi\|^{k_1-\gamma}
\end{eqnarray*}
by \eqref{newfractionalderivative.def},
and for $\xi\in {\mathbb{R}}^d$ with $\|\xi\|\le 1$,
\begin{eqnarray*}
|{\mathcal F}({U_{\Omega,p} f})(\xi)| & \le &
C \Big(\sum_{|{\bf i}|\le k_1+1} \|\partial^{\bf i} \hat f\|_\infty\Big)
\|\xi\|^{k_1-\gamma+1}
\end{eqnarray*}
by the Taylor's expansion to the function $\hat f(\xi)$ at the origin.
Combining the above two estimates gives
\begin{equation}\label{fractionalderivative.tm1.pf.eq1}
|{\mathcal F}({U_{\Omega,p} f})(\xi)|\le C
\Big(\sum_{|{\bf i}|\le k_1+1} \|\partial^{\bf i} \hat f\|_\infty\Big) \|\xi\|^{k_1-\gamma+1} (1+\|\xi\|)^{-1}, \quad \xi\in {\mathbb{R}}^d.
\end{equation}
Note that
\begin{equation}\label{fractionalderivative.tm1.pf.eq2}
\|\partial^{\bf i} \hat f\|_\infty\le
C \int_{{\mathbb{R}}^d} |f({\bf x})| |{\bf x}|^{|{\bf i}|} d{\bf x}\le C
\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+|{\bf z}|)^{k_1+d+1+\epsilon}
\end{equation}
for all ${\bf i}\in {\mathbb{Z}}_+^d$ with $|{\bf i}|\le k_1+1$.
Then the desired estimate \eqref{fractionalderivative.tm1.eq1} follows from
\eqref{fractionalderivative.tm1.pf.eq1} and \eqref{fractionalderivative.tm1.pf.eq2}.
{\em (iv)}\quad By \eqref{newfractionalderivative.def} and the first conclusion of this theorem,
the Fourier transform of $U_{\Omega, p} f$ is continuous on ${\mathbb{R}}^d\backslash \{{\bf 0}\}$, and satisfies
$$\int_{{\mathbb{R}}^d} |{\mathcal F}({U_{\Omega,p} f})(\xi)| (1+\|\xi\|)^{\gamma-k_1-d-1}
d\xi\le C \sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf x})| (1+\|{\bf x}\|)^{k_1+d+2}.$$
Hence $U_{\Omega, p}$ is a continuous linear operator from ${\mathcal S}$ to ${\mathcal S}'$.
For any $f\in {\mathcal S}_\infty$, $\partial^{\bf i}\hat f({\bf 0})=0$ for all ${\bf i}\in {\mathbb{Z}}_+^d$. Then
${\mathcal F}({U_{\Omega,p} f})={\mathcal F}({i_\Omega f})$ for all $f\in {\mathcal S}_\infty$.
This shows that $U_{\Omega, p}, 1\le p\le \infty,$ is a
continuous extension of the linear operator $i_\Omega$
from the subspace ${\mathcal S}_\infty\subset {\mathcal S}$ to the whole space ${\mathcal S}$.
\end{proof}
\subsection{Composition and left-inverse of the fractional Laplacian}
Direct calculation leads to
$$\sum_{|{\bf i}|\le \gamma-d(1-1/p)}\frac{\partial^{\bf i} (\xi^{\bf k}\hat f(\xi))|_{\xi={\bf 0}}}{{\bf i}!}\xi^{\bf i}
=
\sum_{|{\bf j}|\le \gamma-|{\bf k}|-d(1-1/p)}
\frac{\partial^{\bf j} \hat f({\bf 0})}{{\bf j}!}\xi^{{\bf j}+{\bf k}}, \quad {\bf k}\in {\mathbb{Z}}_+^d$$
for any $\gamma\in {\mathbb{R}}, 1\le p\le \infty$ and $f\in {\mathcal S}$.
This together with \eqref{newfractionalderivative.def} implies that
\begin{equation}
U_{\Omega, p} (\partial^{\bf k} f)= U_{\Omega_{\bf k}, p} f, \quad {\rm for \ all} \ f\in {\mathcal S}\ {\rm and} \ {\bf k}\in {\mathbb{Z}}_+^d,
\end{equation}
where $\Omega_{\bf k}(\xi)= (i\xi)^{\bf k} \Omega(\xi)$ for ${\bf k}\in {\mathbb{Z}}_+^d$. In general, we have the following result about composition of integrable Riesz potentials.
\begin{Tm}\label{compositionp.tm}
Let $1\le p\le \infty$, real numbers $\gamma_1, \gamma_2$ satisfy $\gamma_1\ge d(1-1/p)$
and $-\gamma_2$ is larger than the integral part of $\gamma_1-d(1-1/p)$,
and let $\Omega_1, \Omega_2\in C^\infty({\mathbb{R}}^d\backslash\{0\})$ be homogenous of degree $-\gamma_1$ and $-\gamma_2$ respectively.
Then
\begin{equation}\label{compositionp.tm.eq1}
U_{\Omega_1, p} (J_{\Omega_2} f)=J_{\Omega_1\Omega_2} f\quad {\rm for \ all} \ f\in {\mathcal S}.
\end{equation}
\end{Tm}
As a consequence of Theorems \ref{composition.tm} and \ref{compositionp.tm}, we have the following result about the left-inverse of the fractional Laplacian $(-\triangle)^{\gamma/2}$.
\begin{Cr} \label{leftinversefractionalderivative.cr}
Let $1\le p\le \infty$ and $\gamma>0$ satisfy either $1<p\le \infty$ or $p=1$ and $\gamma\not\in {\mathbb{Z}}_+$, and
the linear operator $I_{\gamma, p}$ be defined as in \eqref{fractionalderivative.veryolddef}. Then $I_{\gamma,p}$ is a left-inverse of the fractional Laplacian $(-\triangle)^{\gamma/2}$, i.e., $I_{\gamma, p} (-\triangle)^{\gamma/2} f=f$ for all $f\in {\mathcal S}$.
\end{Cr}
\begin{proof}
[\bf Proof of Theorem \ref{compositionp.tm}]
Let $k_1$ be the integral part of $\gamma_1-d(1-1/p)$. Then $-\gamma_2>k_1$ by the assumption.
Then ${\mathcal F}(J_{\Omega_2} f)(\xi)=\Omega_2(\xi) \hat f(\xi)$ and
$\partial^{\bf i} ({\mathcal F}(J_{\Omega_2} f)(\xi))|_{\xi={\bf 0}}=0$
for any ${\bf i}\in {\mathbb{Z}}_+$ with $|{\bf i}|\le k_1$ and any Schwartz function $f$. This implies that
${\mathcal F}(U_{\Omega_1, p}(J_{\Omega_2} f))(\xi)$ is equal to
$$\Big(\widehat{J_{\Omega_2} f}(\xi)-\sum_{|{\bf i}|\le \gamma_1-d(1-1/p)}
\frac{\partial^{\bf i} ({\mathcal F}(J_{\Omega_2} f)(\xi))|_{\xi={\bf 0}}}{{\bf i}!} \xi^{\bf i}\Big)\Omega_1(\xi),$$
which is the same as ${\mathcal F}(J_{\Omega_1\Omega_2}f)(\xi)$. Hence the equation
\eqref{compositionp.tm.eq1} is established.
\end{proof}
\subsection{$L^p$-integrability in the spatial domain}
If $\gamma\in (0, d(1-1/p))$, then it follows from \eqref{newfractionalderivative.def} and Theorem \ref{generalizedrieszomega1.tm} that
$|U_{\Omega,p} f({\bf x})|\le C (1+\|{\bf x}\|)^{\gamma-d}, \ {\bf x}\in {\mathbb{R}}^d$ (hence $U_{\Omega, p}f\in L^p$)
for any Schwartz function $f$.
In this subsection, we provide a similar estimate for $U_{\Omega, p} f$
when $\gamma\ge d(1-1/p)$.
\begin{Tm}
\label{iomegap.tm1}
Let $0<\epsilon<1, 1\le p\le \infty, \gamma\in [d(1-1/p), \infty)\backslash {\mathbb{Z}}$,
$k_1$ be the integral part of $\gamma-d(1-1/p)$,
and $\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be
a homogeneous function of degree $-\gamma$.
If
\begin{equation} \label{iomegap.tm1.eq1}
|f({\bf x})| \le C (1+\|{\bf x}\|)^{-(k_1+1+d+\epsilon)}, \quad {\bf x}\in {\mathbb{R}}^d\end{equation}
then
\begin{eqnarray}\label{iomegap.tm1.eq2}
|U_{\Omega,p}f({\bf x})| & \le & C \Big(\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+1+d+\epsilon}\Big)\nonumber\\
& & \times
\|{\bf x}\|^{\min(\gamma-k_1-d,0)} (1+\|{\bf x}\|)^{\max(\gamma-k_1-d,0)-1}
\end{eqnarray}
for all ${\bf x}\in {\mathbb R}^d$, and
\begin{eqnarray}\label{iomegap.tm1.eq3}
|U_{\Omega,p}f({\bf x})-U_{\Omega,p}f({\bf x}')| & \le & C \Big(\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+1+d+\epsilon}\Big)\|{\bf x}-{\bf x}'\|^\delta \nonumber\\
& & \times
\|{\bf x}\|^{\min(\gamma-k_1-d-\delta,0)} (1+\|{\bf x}\|)^{\max(\gamma-k_1-d-\delta,0)-1}
\end{eqnarray}
for all ${\bf x}, {\bf x}'\in {\mathbb R}^d$ with $\|{\bf x}-{\bf x}'\|\le \|{\bf x}\|/4$, where $\delta<\min (|\gamma-k_1-d|, \epsilon)$.
\end{Tm}
As an easy consequence of Theorem \ref{iomegap.tm1}, we have
\begin{Cr}\label{iomegap.cor1}
Let $1\le p\le \infty, \gamma\ge d(1-1/p)$,
and $\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be
a homogeneous function of degree $\gamma$.
If both $\gamma$ and $\gamma-d(1-1/p)$ are not nonnegative integers, then
$U_{\Omega,p} f$ is H\"older continuous on ${\mathbb{R}}^d\backslash \{\bf 0\}$ and belong to $L^p$ for any Schwartz function $f$.
\end{Cr}
\begin{proof}[Proof of Theorem \ref{iomegap.tm1}] We investigate three cases to establish the estimates in \eqref{iomegap.tm1.eq2} and \eqref{iomegap.tm1.eq3}.
{\em Case I: $k_1+1-\gamma<0$}.\quad
Set $h_\xi(t)=\hat f(t\xi)$. Applying Taylor's expansion to the function $h_{\xi}$ gives
\begin{eqnarray}\label{iomegap.tm1.pf.eq1}
\hat f(\xi) & = & h_\xi(1)=\sum_{s=0}^{k_1} \frac{h^{(s)}(0)}{s!}+\frac{1}{k_1!}\int_0^1 h_\xi^{(k_1+1)}(t) (1-t)^{k_1} dt\nonumber\\
&= & \sum_{|{\bf i}|\le k_1} \frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} \xi^{\bf i}+ (k_1+1)
\sum_{|{\bf j}|=k_1+1} \frac{\xi^{\bf j}}{{\bf j}!} \int_0^1 \partial^{\bf j} \hat f(t\xi) (1-t)^{k_1} dt.
\end{eqnarray}
Hence
\begin{equation}\label{iomegap.tm1.pf.eq2}
\Big(\hat f(\xi)-\sum_{|{\bf i}|\le k_1} \frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} \xi^{\bf i}\Big) \Omega(\xi)=
\sum_{|{\bf j}|=k_1+1} \frac{1}{{\bf j}!}\Omega_{\bf j}(\xi) \widehat g_{\bf j}(\xi),
\end{equation}
where $\Omega_{\bf j}(\xi)=(i\xi)^{\bf j} \Omega(\xi)$ and
\begin{equation}\label{iomegap.tm1.pf.eq3}
g_{\bf j}({\bf x})=(k_1+1) \int_0^1 (1-t)^{k_1} (- {\bf x}/t)^{\bf j} f({\bf x}/t) t^{-d} dt\in L^1, \quad |{\bf j}|=k_1+1.
\end{equation}
Taking inverse Fourier transform at both sides of the equation \eqref{iomegap.tm1.pf.eq2} yields
\begin{equation}\label{iomegap.tm1.pf.eq4}
U_{\Omega, p} f({\bf x})=\sum_{|{\bf j}|=k_1+1}\frac{1}{{\bf j}!}
\int_{{\mathbb{R}}^d} K_{\bf j}({\bf x}-{\bf y}) g_{\bf j}({\bf y}) d{\bf y}.
\end{equation}
where $K_{\bf j}, |{\bf j}|=k_1+1$, is the inverse Fourier transform of $\Omega_{\bf j}$.
Therefore
\begin{eqnarray}\label{iomegap.tm1.pf.eq5}
|U_{\Omega, p} f({\bf x})| &\le & C \int_0^1\int_{{\mathbb{R}}^d} \|{\bf x}-{\bf y}\|^{\gamma-d-k_1-1} \|{\bf y}/t\|^{k_1+1} |f({\bf y}/t)| t^{-d} d{\bf y} dt\nonumber\\
& = & C \int_0^1\int_{{\mathbb{R}}^d} \|{\bf x}-t {\bf y}\|^{\gamma-d-k_1-1} \|{\bf y}\|^{k_1+1} |f({\bf y})| d{\bf y} dt\nonumber\\
&\le & C \Big (\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+1+d+\epsilon}\Big) \int_0^1 (t+\|{\bf x}\|)^{\gamma-d-k_1-1} dt\nonumber\\
&\le & C \Big (\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+1+d+\epsilon}\Big)
\nonumber\\
& & \times \|{\bf x}\|^{\min(\gamma-d-k_1,0)}
(1+\|{\bf x}\|)^{\max(\gamma-d-k_1,0)-1},
\end{eqnarray}
where
the first inequality holds because
$K_{\bf j}\in C^\infty({\mathbb{R}}^d\backslash \{{\bf 0}\})$ is homogeneous of degree $\gamma-d-k_1-1\in (-d, 0)$ \cite[Theorems 7.1.16 and 7.1.18]{hormanderbook}, and the second inequality follows from \eqref{generalizedrieszomega1.tm.pf.eq3}.
Similarly,
\begin{eqnarray}\label{iomegap.tm1.pf.eq5+}
& & |U_{\Omega, p} f({\bf x})-U_{\Omega, p} f({\bf x}')|\nonumber\\
&\le & C \sum_{|{\bf j}|=k_1+1}
\int_{\|{\bf x}-{\bf y}\|\ge 2\|{\bf x}-{\bf x}'\|} \|{\bf x}-{\bf x}'\|^\delta
\|{\bf x}-{\bf y}\|^{\gamma-d-k_1-1-\delta} |g_{\bf j}({\bf y})| d{\bf y}\nonumber\\
& & + C \sum_{|{\bf j}|=k_1+1}
\int_{\|{\bf x}-{\bf y}\|\le 2\|{\bf x}-{\bf x}'\|} \|{\bf x}-{\bf y}\|^{\gamma-d-k_1-1} |g_{\bf j}({\bf y})| d{\bf y}\nonumber\\
& & + C \sum_{|{\bf j}|=k_1+1}
\int_{\|{\bf x}-{\bf y}\|\le 2\|{\bf x}-{\bf x}'\|} \|{\bf x}'-{\bf y}\|^{\gamma-d-k_1-1} |g_{\bf j}({\bf y})| d{\bf y}\nonumber\\
&\le & C \Big (\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+1+d+\epsilon}\Big)\|{\bf x}-{\bf x}'\|^\delta\nonumber\\
& & \times \|{\bf x}\|^{\min(\gamma-d-k_1-\delta,0)}
(1+\|{\bf x}\|)^{\max(\gamma-d-k_1-\delta,0)-1}
\end{eqnarray}
for all ${\bf x}, {\bf x}'\in {\mathbb{R}}^d$ with $\|{\bf x}-{\bf x}'\|\le \|{\bf x}\|/4$, where $\delta<\min(\epsilon, |\gamma-k_1-d|)$.
Then the desired estimate \eqref{iomegap.tm1.eq2} and \eqref{iomegap.tm1.eq3} follow from
\eqref{iomegap.tm1.pf.eq5} and \eqref{iomegap.tm1.pf.eq5+}
for the case $k_1+1-\gamma<0$.
{\em Case II: $k_1+1-\gamma>0$ and $k_1\ge 1$. }\quad
Applying Taylor's expansion to the function $h_{\xi}(t)=\hat f(t\xi)$, we have
\begin{equation*}
\label{iomegap.tm1.pf.eq7} \hat f(\xi) -\sum_{|{\bf i}|\le k_1} \frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} \xi^{\bf i}
= k_1
\sum_{|{\bf j}|=k_1} \frac{\xi^{\bf j}}{{\bf j}!} \int_0^1 \big(\partial^{\bf j} \hat f(t\xi)-\partial^{{\bf j}}\hat f({\bf 0})\big) (1-t)^{k_1-1} dt.
\end{equation*}
Multiplying by $\Omega(\xi)$ both sides of the above equation and then taking the inverse Fourier transform, we obtain
\begin{equation}\label{iomegap.tm1.pf.eq8}
U_{\Omega, p} f({\bf x})= \sum_{|{\bf j}|=k_1}\frac{1}{{\bf j}!}
\Big(\int_{{\mathbb{R}}^d} K_{\bf j}({\bf x}-{\bf y}) g_{\bf j}({\bf y}) d{\bf y}-K_{\bf j}({\bf x})\int_{{\mathbb{R}}^d} g_{\bf j}({\bf y}) d{\bf y}\Big),
\end{equation}
where
\begin{equation}\label{iomegap.tm1.pf.eq8b}
g_{\bf j}({\bf x})=k_1 \int_0^1 (1-t)^{k_1-1} (- {\bf x}/t)^{\bf j} f({\bf x}/t) t^{-d} dt\in L^1, \quad |{\bf j}|=k_1.
\end{equation}
Recalling that $K_{\bf j}\in C^\infty({\mathbb{R}}^d\backslash \{{\bf 0}\}), |{\bf j}|=k_1$ are homogeneous of degree $\gamma-d-k_1\in (-d, 0)$,
\begin{equation}\label{iomegap.tm1.pf.eq9}
|\partial^{\bf i} K_{\bf j}({\bf x})|\le C \|{\bf x}\|^{\gamma-d-k_1-|{\bf j}|}, \quad |{\bf i}|\le 1.
\end{equation}
Combining \eqref{generalizedrieszomega1.tm.pf.eq3}, \eqref{iomegap.tm1.pf.eq8}, \eqref{iomegap.tm1.pf.eq8b} and \eqref{iomegap.tm1.pf.eq9}, we get
\begin{eqnarray} \label{iomegap.tm1.pf.eq10}
|U_{\Omega, p} f({\bf x})|
\!\!& \le &\!\! C \sum_{|{\bf j}|=k_1} \int_0^1 \int_{{\mathbb{R}}^d} |K_{\bf j}({\bf x}-t{\bf y})-K_{\bf j}({\bf x})| \|{\bf y}\|^{k_1} |f({\bf y})| d{\bf y}\nonumber\\
\!\!& \le &\!\! C \Big(\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+d+1+\epsilon}\Big)\nonumber\\
\!\! & & \!\!\times \Big\{\int_{0}^1 \int_{\|{\bf y}\|\le \|{\bf x}\|/2} t\|{\bf y}\| \|{\bf x}\|^{\gamma-d-k_1-1} (1+\|{\bf y}\|)^{-d-1-\epsilon} d{\bf y} dt\nonumber\\
\!\! & &\!\! + (1+\|{\bf x}\|)^{-1}
\int_0^1 \int_{\|{\bf y}\|\ge \|{\bf x}\|/2} \|{\bf x}-t{\bf y}\|^{\gamma-d-k_1} (1+\|{\bf y}\|)^{-d-\epsilon} d{\bf y} dt\nonumber\\
\!\! & &\!\! + \|{\bf x}\|^{\gamma-d-k_1}\int_0^1
\int_{\|{\bf y}\|\ge \|{\bf x}\|/2} (1+\|{\bf y}\|)^{-d-1-\epsilon} d{\bf y} dt\Big\}\nonumber\\
\!\! & \le & \!\! C\Big (\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+d+1+\epsilon}\Big)\nonumber\\
\!\!& & \!\! \times
\|{\bf x}\|^{\min(\gamma-k_1-d, 0)} (1+\|{\bf x}\|)^{\max(\gamma-k_1-d, 0)-1},
\end{eqnarray}
and
\begin{eqnarray} \label{iomegap.tm1.pf.eq10+}
& & |U_{\Omega, p} f({\bf x})-U_{\Omega, p} f({\bf x}') |\nonumber\\
\!\!& \le &\!\! C \sum_{|{\bf j}|=k_1} \int_0^1 \Big(\int_{\|t{\bf y}\|\le \|{\bf x}\|/4}+\int_{\|t{\bf y}\|\ge 4\|{\bf x}\|}
+\int_{\|{\bf x}\|/4\le \|t{\bf y}\|\le 4\|{\bf x}\|}
\Big) \nonumber\\
& & \quad |K_{\bf j}({\bf x}-t{\bf y})-K_{\bf j}({\bf x})-
K_{\bf j}({\bf x}'-t{\bf y})+K_{\bf j}({\bf x}')| \|{\bf y}\|^{k_1} |f({\bf y})| d{\bf y}\nonumber\\
\!\!& \le &\!\! C \Big(\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+d+1+\epsilon}\Big)\sum_{|{\bf j}|=k_1}
\Big\{ \|{\bf x}-{\bf x}'\|^\delta\nonumber\\
\!\! & & \!\!\times
\int_{0}^1 \int_{\|t{\bf y}\|\le \|{\bf x}\|/4} t\|{\bf y}\| \|{\bf x}\|^{\gamma-d-k_1-1-\delta} (1+\|{\bf y}\|)^{-d-1-\epsilon} d{\bf y} dt + \|{\bf x}-{\bf x}'\|^\delta \nonumber\\
\!\! & &\!\! \times
\int_0^1 \int_{t\|{\bf y}\|\ge 4\|{\bf x}\|}\big(\|{\bf x}\|^{\gamma-k_1-d-\delta} +\|{\bf y}\|^{\gamma-k_1-d-\delta}\big)
(1+\|{\bf y}\|)^{-d-1-\epsilon} d{\bf y} dt\nonumber\\
\!\! & &\!\! +
\int_0^1 \int_{\|{\bf x}\|/4\le \|t{\bf y}\|\le 4 \|{\bf x}\|}
\Big( | K_{\bf j}({\bf x}-t{\bf y})- K_{\bf j}({\bf x}'-t{\bf y})|+|K_{\bf j}({\bf x})-K_{\bf j}({\bf x})|\Big)\nonumber\\
& & (1+\|{\bf x}\|/t)^{-d-1-\epsilon} d{\bf y} dt\Big\}\nonumber\\
\qquad \!\! & \le & \!\! C\Big (\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+d+1+\epsilon}\Big)\|{\bf x}-{\bf x}'\|^\delta
\|{\bf x}\|^{\gamma-k_1-d-\delta} (1+\|{\bf x}\|)^{-1}.
\end{eqnarray}
Then the desired estimates \eqref{iomegap.tm1.eq2} and \eqref{iomegap.tm1.eq3} are proved in the case that $k_1+1-\gamma>0$ and $k_1\ge 1$.
{\em Case III: $k_1+1-\gamma>0$ and $k_1=0$.}\quad In this case, $\gamma\in (0, 1)$ and
\begin{equation}
U_{\Omega,p} f({\bf x})=\int_{{\mathbb{R}}^d}\big( K({\bf x}-{\bf y})-K({\bf x})\big) f({\bf y}) d{\bf y}
\end{equation}
where $K$ is the inverse Fourier transform of $\Omega(\xi)$. Then, by applying the argument used in establishing \eqref{iomegap.tm1.pf.eq10}, we have
\begin{eqnarray}
|U_{\Omega, p} f({\bf x})|\!\! & \le & \!\! C \Big(\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{d+1+\epsilon}\Big)\nonumber\\
\!\! & & \!\!\times \Big\{ \int_{\|{\bf y}\|\le \|{\bf x}\|/2} t\|{\bf y}\| \|{\bf x}\|^{\gamma-d-1} (1+\|{\bf y}\|)^{-d-1-\epsilon} d{\bf y} \nonumber\\
\!\! & &\!\! + (1+\|{\bf x}\|)^{-1}
\int_{\|{\bf y}\|\ge \|{\bf x}\|/2} \|{\bf x}-{\bf y}\|^{\gamma-d} (1+\|{\bf y}\|)^{-d-\epsilon} d{\bf y} \nonumber\\
\!\! & &\!\! + \|{\bf x}\|^{\gamma-d}
\int_{\|{\bf y}\|\ge \|{\bf x}\|/2} (1+\|{\bf y}\|)^{-d-1-\epsilon} d{\bf y} \Big\}\nonumber\\
\!\! &\le & \!\! C\Big (\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{d+1+\epsilon}\Big)
\|{\bf x}\|^{\gamma-d} (1+\|{\bf x}\|)^{-1},
\end{eqnarray}
and
\begin{eqnarray}
& & |U_{\Omega, p} f({\bf x})-U_{\Omega, p} f({\bf x}')|\nonumber\\
& \le &
\Big(\int_{\|{\bf y}\|\le \|{\bf x}\|/4}+\int_{\|{\bf y}\|\ge 4\|{\bf x}\|}
+\int_{\|{\bf x}\|/4\le \|{\bf y}\|\le 4\|{\bf x}\|}
\Big) \nonumber\\
& & \quad |K({\bf x}-{\bf y})-K({\bf x})-K({\bf x'}-{\bf y})+K({\bf x}')| |f({\bf y}) | d{\bf y}\nonumber\\
& \le &
C\Big (\sup_{{\bf z}\in {\mathbb{R}}^d} |f({\bf z})| (1+\|{\bf z}\|)^{k_1+d+1+\epsilon}\Big) \|{\bf x}-{\bf x}'\|^\delta \|{\bf x}\|^{\gamma-d-\delta} (1+\|{\bf x}\|)^{-1},
\end{eqnarray}
which yields the desired estimates \eqref{iomegap.tm1.eq2} and \eqref{iomegap.tm1.eq3} for $k_1+1-\gamma>0$ and $k_1=0$.
\end{proof}
\subsection{Unique dilation-invariant extension of the linear operator $i_\Omega$ with additional integrability in the spatial domain}
We now show that $U_{\Omega, p}$ is the only dilation-invariant extension of the linear operator $i_\Omega$ from the subspace ${\mathcal S}_\infty$
to the whole space ${\mathcal S}$ such that its image is contained in $L^p$.
\begin{Tm}\label{time2.tm}
Let $1\le p\le \infty$, $\gamma>0$ have the property that both $\gamma$ and $\gamma-d(1-1/p)$ are not nonnegative integers,
$\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be
a nonzero homogeneous function of degree $-\gamma$, and
the linear map $I$ from ${\mathcal S}$ to ${\mathcal S}'$
be a homogeneous extension of the linear operator $i_\Omega$ on ${\mathcal S}_\infty$.
Then
$If$ belongs to $L^p$ for any Schwartz function $f$ if and only if
$I=U_{\Omega, p}$.
\end{Tm}
\begin{proof}
The sufficiency follows from
\eqref{fractionalderivative.tm1.pf.eq3} and
Theorems \ref{generalizedriesz.tm} and \ref{generalizedrieszomega1.tm} for $\gamma<d(1-1/p)$, and
from
\eqref{fractionalderivative.tm1.pf.eq3}, Theorem \ref{fractionalderivative.tm1} and Corollary \ref{iomegap.cor1}
for $\gamma\ge d(1-1/p)$.
Now the necessity. By the assumption on the linear operator $I$ from ${\mathcal S}$ to ${\mathcal S}'$, similar to the argument used in Lemma \ref{homogeneous1.lm}, we can find an integer $N$ and tempered distributions $H_{\bf i}, |{\bf i}|\le N$, such that
\begin{equation}\label{time2.tm.pf.eq3}
If=U_{\Omega, p} f+\sum_{|{\bf i}|\le N} \frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} H_{\bf i} \quad {\rm for\ all} \ f\in {\mathcal S}.
\end{equation}
Replacing $f$ in \eqref{time2.tm.pf.eq3} by $\psi_{\bf j}$ in \eqref{homogeneous2.lm.pf.eq7} and using \eqref{homogeneous2.lm.pf.eq8}
gives that
$H_{\bf j}/{\bf j}!=I\psi_{\bf j}- U_{\Omega, p} \psi_{\bf j}$. Hence
\begin{equation}\label{time2.tm.pf.eq4} H_{\bf j}\in L^p\end{equation}
by Corollary \ref{iomegap.cor1} and the assumption on the linear map $I$.
By \eqref{time2.tm.pf.eq3}, Theorem \ref{fractionalderivative.tm1} and the assumption on the linear operator $I$,
$(I-U_{\Omega,p})(\delta_t f)=t^{-\gamma} \delta_t ((I-U_{\Omega,p})f)$ for all $f\in {\mathcal S}$.
Hence
$H_{\bf j}$ is homogeneous of order $\gamma-d-|{\bf j}|$ by Lemma \ref{homogeneous2.lm}.
This together with \eqref{time2.tm.pf.eq4} implies that $H_{\bf j}=0$ for all ${\bf j}\in {\mathbb{Z}}_+^d$ with $|{\bf j}|\le N$. The desired conclusion $I=U_{\Omega, p}$ then follows.
\end{proof}
\subsection{Unique dilation-invariant extension of the linear operator $i_\Omega$ with additional integrability in the Fourier domain}
In this subsection, we characterize all those dilation-invariant extensions
$I$ of the linear operator $i_\Omega$ on the subspace ${\mathcal S}_\infty$ to the whole space ${\mathcal S}$
such that $\widehat{If}$ is $q$-integrable for any Schwartz function $f$.
\begin{Tm}\label{iomega5.tm}
Let $1\le q\le \infty, \gamma\in [d/q, \infty)\backslash {\mathbb{Z}}$ and $\Omega\in C^\infty({\mathbb{R}}^d\backslash \{\bf 0\})$ be
a nonzero homogeneous function of degree $-\gamma$, and
the linear map $I$ from ${\mathcal S}$ to ${\mathcal S}'$
be a dilation-invariant extension of the linear operator $i_\Omega$ on ${\mathcal S}_\infty$.
Then the following statements hold.
\begin{itemize}
\item[{(i)}] If $1\le q<\infty$, then the Fourier transform
of $If$ belongs to $L^q$ for any Schwartz function $f$ if and only if
$\gamma-d/q\not\in{\mathbb{Z}}_+$ and $I=U_{\Omega, q/(q-1)}$.
\item[{(ii)}] If $q=\infty$ and $\gamma\not\in {\mathbb{Z}}_+$, then
the Fourier transform
of $If$ belongs to $L^\infty$ for any Schwartz function $f$ if and only if
$I=U_{\Omega, 1}$.
\item[{(iii)}] If $q=\infty$ and $\gamma\in {\mathbb{Z}}_+$, then
the Fourier transform
of $If$ belongs to $L^\infty$ for any Schwartz function $f$ if and only if
\begin{equation}\label{iomega5.tm.eq1}
\widehat{If}(\xi) = \widehat{U_{\Omega, 1}f}(\xi) +\sum_{|{\bf i}|=-\gamma}
\frac{\partial^{\bf i}\hat f({\bf 0})}{ {\bf i}!} g_{\bf i}(\xi)
\end{equation}
for some bounded homogeneous functions $g_{\bf i}, |{\bf i}|=-\gamma$, of degree $0$.
\end{itemize}
\end{Tm}
\begin{proof}
{\em (i)} \quad
The sufficiency follows from Theorem \ref{fractionalderivative.tm1} and Corollary \ref{fractionalderivative.cr1}.
Now we prove the necessity.
As every $q$-integrable function belong to $K_1$, similar to the argument used in the proof of Lemma \ref{homogeneous1.lm},
we can find functions $g_{\bf i}\in K_1, |{\bf i}|\le N$,
such that
\begin{eqnarray}\label{iomega5.tm.pf.eq1}
\widehat {If}(\xi) & = & {\mathcal F}(U_{\Omega, q/(q-1)}f)(\xi)
+ \sum_{|{\bf i}|\le N} \frac{\partial^{\bf i} \hat f({\bf 0})}{{\bf i}!} g_{\bf i}(\xi).
\end{eqnarray}
Let $\psi_{\bf j}, j\in {\mathbb{Z}}_+^d$ be defined as in \eqref{homogeneous2.lm.pf.eq7}.
Replacing $f$ by $\psi_{\bf j}$ with $|{\bf j}|\le N$ and using \eqref{homogeneous2.lm.pf.eq8} gives
\begin{eqnarray}\label{iomega5.tm.pf.eq2}
\widehat {I\psi_{\bf j}}(\xi) & = & \Big(\widehat{\psi_{\bf j}}(\xi) -\sum_{|{\bf i}|\le -\gamma-d/q} \frac{\partial^{\bf i} \hat \psi_{\bf j} ({\bf 0})}{{\bf i}!} \xi^{\bf i}\Big)\Omega(\xi)+ g_{\bf j}(\xi)\nonumber\\
& = & \left\{\begin{array}{ll}
\frac{\xi^{\bf j}}{{\bf j}!} (\phi(\xi)-1) \Omega(\xi)+ g_{\bf j}(\xi) &\quad {\rm if} \ |{\bf j}|\le \gamma-d/q,\\
\frac{\xi^{\bf j}}{{\bf j}!} \phi(\xi) \Omega(\xi)+g_{\bf j}(\xi) & \quad {\rm if}\ |{\bf j}|> \gamma-d/q.
\end{array}\right.
\end{eqnarray}
Note that $\frac{\xi^{\bf j}}{{\bf j}!} (\phi(\xi)-1) \Omega(\xi)\in L^q$
when $|{\bf j}|< \gamma-d/q$, and $\frac{\xi^{\bf j}}{{\bf j}!} \phi(\xi) \Omega(\xi)\in L^p$
when $|{\bf j}|>\gamma-d/q$.
This, together with \eqref{iomega5.tm.pf.eq2} and the assumption that
$\widehat{I\psi_{\bf j}}\in L^q$, proves that
\begin{equation} \label{iomega5.tm.pf.eq3} g_{\bf j}\in L^q\quad
{\rm for\ all} \ {\bf j}\in {\mathbb{Z}}_+^d\quad {\rm with} \
\gamma-d/q\ne |{\bf j}|\le N.
\end{equation}
By the homogeneous property of
the linear map $I$, the functions $g_{\bf i}, |{\bf i}|\le N$, are homogeneous of degree $-\gamma+|{\bf i}|$, i.e.,
\begin{equation}\label{iomega5.tm.pf.eq4}
g_{\bf i}(t\xi)= t^{-\gamma+|{\bf i}|} g_{\bf i}(\xi) , \quad \ {\rm for \ all} \ t>0.
\end{equation}
Combining \eqref{iomega5.tm.pf.eq3} and \eqref{iomega5.tm.pf.eq4}
proves that $g_{\bf j}=0$ for all ${\bf j}\in {\mathbb{Z}}_+^d$ with $\gamma-d/q\ne |{\bf j}|\le N$, and
the desired conclusion $\widehat {If}(\xi) = {\mathcal F}({U_{\Omega, q/(q-1)} f})(\xi)$
for all $f\in {\mathcal S}$
when $\gamma-d/q\not\in {\mathbb{Z}}_+$.
Now it suffices to prove that $\gamma-d/q\not\in {\mathbb{Z}}_+$. Suppose on the contrary that
$\gamma-d/q\in {\mathbb{Z}}_+$. Then $1<q<\infty$ as $\gamma\not\in {\mathbb{Z}}$.
By \eqref{iomega5.tm.pf.eq2} and the assumption on the linear map $I$, we have
$$\int_{\xi\not\in {\rm supp} \phi}
|g_{\bf j}(\xi)-\xi^{\bf j} \Omega(\xi)/{\bf j}!|^q d\xi=
\int_{\xi\not\in {\rm supp} \phi} |\widehat {I\psi_{\bf j}}(\xi)|^q d\xi <\infty$$
for all ${\bf j}\in {\mathbb{Z}}_+^d$ with $|{\bf j}|=\gamma-d/q$.
This, together with \eqref{iomega5.tm.pf.eq4} and the fact that the support ${\rm supp} \phi$ of the function $\phi$ is
a bounded set, implies that $g_{\bf j}(\xi)-\xi^{\bf j} \Omega(\xi)/{\bf j}!=0$ for all ${\bf j}\in {\mathbb{Z}}_+^d$ with $|{\bf j}|=\gamma-d/q$.
By substituting the above equality for $g_{\bf j}$ into \eqref{iomega5.tm.pf.eq2} we obtain
\begin{equation}\label{iomega5.tm.pf.eq5}
\widehat{I\psi_{\bf j}}(\xi)= \phi(\xi) \xi^{\bf j} \Omega(\xi)/{\bf j}!\end{equation}
for all ${\bf j}\in {\mathbb{Z}}_+^d$ with $|{\bf j}|=\gamma-d/q$.
This leads to a contradiction, as $\widehat{I\psi_{\bf j}}(\xi)\in L^q$
by the assumption on the linear map $I$, and
$\phi(\xi) \xi^{\bf j} \Omega(\xi)/{\bf j}!\not\in L^q$ by direction computation.
\bigskip{\em (ii) } and {\em (iii)}\quad
The necessity is true by \eqref{iomega5.tm.eq1} and Theorem \ref{fractionalderivative.tm1}, while
the sufficiency follows from \eqref{iomega5.tm.pf.eq1} -- \eqref{iomega5.tm.pf.eq4}.
\end{proof}
\subsection{Proof of Theorem \ref{integrablefractionalderivative.tm}}
The conclusions in Theorem \ref{integrablefractionalderivative.tm} follow easily from \eqref{generalized.tm.pf.eq1}, \eqref{fractionalderivativeomegap.def}, Theorem \ref{time2.tm}
and Corollary \ref{leftinversefractionalderivative.cr}.
\section{Sparse Stochastic Processes}\label{poisson.section}
In this section, we will prove Theorem \ref{generalizedpoisson.tm} and fully characterize
the generalized random process $P_\gamma w$, which is
a solution of the stochastic partial differential equation \eqref{randompde.def}. In particular, we provide its characteristic functional and its pointwise evaluation.
\subsection{Proof of Theorem \ref{generalizedpoisson.tm}}
To prove Theorem \ref{generalizedpoisson.tm}, we recall the Levy continuity theorem, and a fundamental theorem
about the characteristic functional of a generalized random process.
\begin{Lm}\label{levy.lm}{\rm (\cite{probabilitybook})}\
Let $\xi_k, k\ge 1$, be a sequence of random variables whose characteristic functions are denoted by $\mu_k(t)$. If
$\lim_{k\to \infty} \mu_k(t)=\mu_{\infty}(t)$ for some continuous function $\mu_\infty(t)$ on the real line, then
$\xi_k$ converges to a random variable $\xi_\infty$ in distribution whose characteristic function ${\bf E}(e^{-it \xi_\infty})$
is $\mu_\infty(t)$.
\end{Lm}
In the study of generalized random processes, the characteristic functional plays a similar role
to the characteristic function of a random variable \cite{gelfandbook}. The idea is to formally specify a generalized random process $\Phi$ by its
{\em characteristic functional} ${\mathcal Z}_\Phi$ given by
\begin{equation}
{\mathcal Z}_\Phi(f):={\bf E}(e^{-i\Phi(f)})=\int_{{\mathbb{R}}} e^{-ix} dP({ x}), \quad f\in {\mathcal D},
\end{equation}
where $P(x)$ denotes the probability that $\Phi(f)<x$.
For instance, we can show (\cite{Unser2009})
that the characteristic functional ${\mathcal Z}_w$ of the white Poisson noise \eqref{whitepoisson.def} is given by
\begin{equation}
{\mathcal Z}_w(f)=\exp\Big(\lambda \int_{{\mathbb{R}}^d}\int_{{\mathbb{R}}} \big(e^{-iaf({\bf x})}-1\big) dP(a) d{\bf x} \Big) , \quad f\in {\mathcal D}.
\end{equation}
The characteristic functional ${\mathcal Z}_\Phi$ of a generalized random process $\Phi$ is
a functional from ${\mathcal D}$ to ${\mathbb C}$ that is continuous and positive-definite, and satisfies
${\mathcal Z}_\Phi(0)=1$.
Here the {\em continuity} of a functional $L$ from ${\mathcal D}$ to ${\mathbb C}$
means that
$\lim_{k\to \infty} L(f_k)=L(f)$ if $f_k\in {\mathcal D}$ tends to $f\in {\mathcal D}$ in the topology of the space ${\mathcal D}$, while
a functional $L$ from ${\mathcal D}$ to ${\mathbb C}$ is said to be {\em positive-definite}
if
\begin{equation}
\sum_{j,k=1}^n L(f_j-f_k) c_j \bar c_k\ge 0
\end{equation}
for any $f_1, \ldots, f_n\in {\mathcal D}$ and any complex numbers $c_1, \ldots, c_n$. The remarkable aspect of the theory of generalized random processes is that specification of ${\mathcal Z}_\Phi$ is sufficient to define a process in a consistent and unambiguous
way. This is stated in the
fundamental Minlos-Bochner theorem.
\begin{Tm}\label{gelfandbook.tm} {\rm (\cite{gelfandbook})}\
Let $L$ be a positive-definite continuous functional on ${\mathcal D}$ such that $L(0)=1$.
Then there exists a generalized random process $\Phi$ whose characteristic functional is $L$.
Moreover for any $f_1, \ldots, f_n\in {\mathcal D}$, we may take the positive measure
$P({ x}_1, \ldots, { x}_n)$ as the distribution function of the random variable $\Phi(f_1), \ldots, \Phi(f_n)$,
where the Fourier transform of the positive measure $P({x}_1, \ldots, {x}_n)$ is $L(y_1 f_1+\cdots+y_nf_n)$, i.e.,
$$L(y_1f_1+\ldots+y_nf_n)=\int_{{\mathbb{R}}^n} \exp(-i (x_1y_1+\ldots+x_ny_n)) dP(x_1, \ldots, x_n).$$
\end{Tm}
We are now ready to prove Theorem \ref{generalizedpoisson.tm}.
\begin{proof}[Proof of Theorem \ref{generalizedpoisson.tm}] Let $N\ge 1$ and $\varphi$ be a $C^\infty$ function supported in $B({\bf 0},2)$ and
taking the value one in $B({\bf 0}, 1)$.
For any $f\in {\mathcal D}$, define a sequence of random variables $\Phi_{\gamma, N}(f)$ associated with $f$ by
\begin{equation}\label{generalizedpoisson.tm.pf.eq1}
\Phi_{\gamma, N}(f):=\sum_{k} a_k \varphi({\bf x}_k/N) I_{\gamma, 1} f({\bf x}_k),
\end{equation}
where the $a_k$'s are i.i.d. random variables with probability distribution $P(a)$, and where the ${\bf x}_k$'s
are random point locations in ${\mathbb R}^n$ which are mutually independent and follow a spatial Poisson distribution
with Poisson parameter $\lambda>0$.
We will show that $\Phi_{\gamma, N}, N\ge 1$, define a sequence of generalized random processes,
whose limit $P_\gamma w(f):=\sum_{k} a_k I_{\gamma, 1}(f)({\bf x}_k)$ is a solution of the stochastic partial differential equation
\eqref{randompde.def}.
As $\varphi$ is a continuous function supported on $B({\bf 0}, 2)$,
\begin{equation}\label{generalizedpoisson.tm.pf.eq2}
\Phi_{\gamma, N}(f)=
\sum_{{\bf x}_k\in B({\bf 0}, 2N)} a_k \varphi({\bf x}_k/N) I_{\gamma, 1} f({\bf x}_k).
\end{equation}
Recall that $I_{\gamma, 1} f$ is continuous on ${\mathbb{R}}^d\backslash \{\bf 0\}$ by Corollary \ref{iomegap.cor1}.
Then the summation of the right-hand side of \eqref{generalizedpoisson.tm.pf.eq2}
is well-defined whenever there are finitely many ${\bf x}_k$ in $B({\bf 0}, 2N)$ with none of them belonging to
$B({\bf 0}, \epsilon), \epsilon>0$. Note that
the probability that at least one of ${\bf x}_k$ lies in the small neighbor $B({\bf 0}, \epsilon)$
is equal to $$\sum_{n=1}^\infty
e^{-\lambda |B({\bf 0}, \epsilon)|} \frac{(\lambda |B({\bf 0}, \epsilon)|)^n}{ n!}
=1-e^{-\lambda |B({\bf 0}, \epsilon)|}\to 0 \quad {\rm as} \ \epsilon\to 0.$$
We then conclude that $\Phi_{\gamma, N}(f)$ is well-defined and $\Phi_{\gamma, N}(f)<\infty$ with probability one.
Denote the characteristic function of the random variable $\Phi_{\gamma, N}(f)$ by $E_{\gamma, N, f}(t)$:
$$E_{\gamma, N, f}(t)= {\bf E}(e^{-it\Phi_{\gamma,N}(f)})={\bf E}(e^{-i\Phi_{\gamma, N}(tf)}).$$
Applying the same technique as in \cite[Appendix B]{tafti2009}, we can show that
\begin{equation}\label{generalizedpoisson.tm.pf.eq3}
E_{\gamma, N, f}(t)=\exp\Big(\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}} \big(e^{-i a t \varphi({\bf x}/N) I_{\gamma, 1}f({\bf x})}-1\big) dP(a) d{\bf x}\Big).
\end{equation}
Moreover, the functional $E_{\gamma, N, f}(t)$ is continuous about $t$ by the dominated convergence theorem, because
$$\Big|e^{-i a t \varphi({\bf x}/N) I_{\gamma, 1}f({\bf x})}-1\Big|\le |a| |t| |I_{\gamma, 1}f({\bf x})|$$ and
$$\int_{{\mathbb{R}}^d}\int_{{\mathbb{R}}} |a| |I_{\gamma, 1}f({\bf x})| dP(a) d{\bf x}=
\Big(\int_{{\mathbb{R}}} |a| dP(a)\Big)\times \Big(\int_{{\mathbb{R}}^d} |I_{\gamma, 1}f({\bf x})| d{\bf x}\Big)<\infty$$
by Corollary \ref{iomegap.cor1} and the assumption on the distribution $P$.
Clearly the random variable
$\Phi_{\gamma, N}(f)$ is linear about $f\in {\mathcal D}$;
i.e.,
\begin{equation}\label{generalizedpoisson.tm.pf.eq4}
\Phi_{\gamma,N}(\alpha f+\beta g)=\alpha \Phi_{\gamma,N}(f)+\beta\Phi_{\gamma,N}(g) \quad\ {\rm for \ all}\ f, g\in {\mathcal D} \ {\rm and} \ \alpha, \beta\in {\mathbb{R}}.
\end{equation}
For any sequence of functions $f_k$ in ${\mathcal D}$ that converges to $f_\infty$ in the topology of ${\mathcal D}$,
it follows from Theorem \ref{iomegap.tm1} and Corollary \ref{iomegap.cor1} that
$\lim_{k\to \infty} \|I_{\gamma, 1} f_k-I_{\gamma, 1} f_\infty\|_1=0$.
Therefore
\begin{eqnarray}\label{generalizedpoisson.tm.pf.eq5}
& & \Big|\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}} \big(e^{-i a t\varphi({\bf x}/N) I_{\gamma, 1}f_k({\bf x})}-1\big) dP(a) d{\bf x}\nonumber\\
& & \quad -
\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}} \big(e^{-i a t \varphi({\bf x}/N) I_{\gamma, 1}f_\infty({\bf x})}-1\big) dP(a) d{\bf x}\Big|\nonumber\\
& \le & |t|\Big(\int_{{\mathbb{R}}} |a| dP(a)\Big)\Big( \int_{{\mathbb{R}}^d} \varphi({\bf x}/N) |I_{\gamma, 1}f_k({\bf x})-I_{\gamma, 1}f_\infty({\bf x})| d{\bf x}\Big)\nonumber\\
& \to & 0 \quad {\rm as} \ k\to \infty,
\end{eqnarray}
which implies that the characteristic function of $\Phi_{\gamma,N}(f_k)$ converges to the continuous characteristic function of $\Phi_{\gamma,N}(f_\infty)$. Hence
the random variable $\Phi_{\gamma, N}(f_k)$ converges to $\Phi_{\gamma, N}(f_\infty)$ by Lemma \ref{levy.lm}, which in turn implies that
$\Phi_{\gamma, N}$ is continuous on ${\mathcal D}$.
Set
\begin{equation}L_{\gamma, N}(f)=E_{\gamma, N, f}(1).\end{equation}
For any sequence $c_l, 1\le l\le n$, of complex numbers and $f_l, 1\le l\le n$, of functions in ${\mathcal D}$,
\begin{eqnarray} \label{generalizedpoisson.tm.pf.eq6}
\sum_{1\le l, l'\le n} L_{\gamma, N}(f_l-f_{l'})c_l \overline{c_{l'}} & = &
{\bf E}\Big(\sum_{l, l'=1}^n e^{-i \Phi_{\gamma,N}(f_l-f_{l'})} c_l\overline{c_{l'}}\Big)\nonumber\\
& =& {\bf E}\Big(\Big|\sum_{l=1}^n c_l
e^{-i \Phi_{\gamma, N}(f_l)}\Big|^2\Big) \ge 0,
\end{eqnarray}
which implies that $L_{\gamma, N}$ is positive-definite.
By Theorem \ref{gelfandbook.tm}, we conclude that $\Phi_{\gamma, N}$ defines a
generalized random process with characteristic functional $L_{\gamma, N}$.
Now we consider the limit of the above family of generalized random processes $\Phi_{\gamma, N}, N\ge 1$.
By Corollary \ref{iomegap.cor1}, $I_{\gamma, 1} f$ is integrable for all $f\in {\mathcal D}$. Then
\begin{equation} \label{generalizedpoisson.tm.pf.eq7}
\lim_{N\to +\infty} E_{\gamma, N, f}(t)=\exp\Big(\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}} (e^{-i a t I_{\gamma, 1}f({\bf x})}-1) dP(a) d{\bf x}\Big)=:
E_{\gamma, f}(t).
\end{equation}
Clearly $E_{\gamma, f}(0)=1$ and $E_{\gamma, f}(t)$ is continuous as $I_{\gamma,1}(f)$ is integrable.
Therefore by Lemma \ref{levy.lm}, $\Phi_{\gamma, N}(f)$ converges to a random variable, which is denoted by
$P_\gamma(f):=\sum_{k} a_k I_{\gamma, 1} f({\bf x}_k)$, in distribution.
As $I_{\gamma, 1} f$ is a continuous map from ${\mathcal D}$ to $L^1$, then
$\lim_{k\to \infty} \|I_{\gamma,1} f_k-I_{\gamma,1} f_\infty\|_1=0$ whenever $f_k$ converges to $f$ in ${\mathcal D}$.
Hence
\begin{eqnarray}\label{generalizedpoisson.tm.pf.eq8}
& & \Big|\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}} \big(e^{-i a t I_{\gamma, 1}f_k({\bf x})}-1\big) dP(a) d{\bf x}\nonumber\\
& & \quad -
\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}} \big(e^{-i a t I_{\gamma, 1}f_\infty({\bf x})}-1\big) dP(a) d{\bf x}\Big|\nonumber\\
& \le & |t|\Big(\int_{{\mathbb{R}}} |a| dP(a)\Big)\Big( \int_{{\mathbb{R}}^d} |I_{\gamma, 1}f_k({\bf x})-I_{\gamma, 1}f_\infty({\bf x})| d{\bf x}\Big)\nonumber\\
& \to & 0 \quad {\rm as} \ k\to \infty,
\end{eqnarray}
which implies that
the characteristic function of $P_\gamma(f_k)$ converges to
the characteristic function of $P_\gamma(f_\infty)$ (which is also continuous), and hence $P_\gamma(f_k)$
converges to $P_\gamma(f_\infty)$ in distribution by Lemma \ref{levy.lm}.
From the above argument, we see that $P_\gamma(f)$ is continuous about $f\in {\mathcal D}$.
Define
$L_{\gamma}(f)=E_{\gamma, f}(1)$.
From \eqref{generalizedpoisson.tm.pf.eq6} and \eqref{generalizedpoisson.tm.pf.eq7}, we see that
\begin{equation}
\sum_{1\le l, l'\le n} L_{\gamma}(f_l-f_{l'}) c_i\overline{c_{i'}}=
\lim_{N\to \infty}
\sum_{1\le l, l'\le n} L_{\gamma, N}(f_l-f_{l'}) c_i\overline{c_{l'}}\ge 0
\end{equation}
for any sequence $c_l, 1\le l\le n$, of complex numbers and $f_l, 1\le l\le n$, of functions in ${\mathcal D}$.
Therefore by Theorem \ref{gelfandbook.tm}, $P_\gamma w$ defines a generalized random process with its characteristic functional given by
\begin{equation}
{\mathcal Z}_{P_\gamma w}(f)=
\exp\Big(\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}} (e^{-i a I_{\gamma, 1}f({\bf x})}-1) dP(a) d{\bf x}\Big).\end{equation}
\end{proof}
\subsection{Pointwise evaluation}
In this section, we consider the pointwise characterization of the generalized random process $P_\gamma w$.
\begin{Tm}\label{pointpoisson.tm}
Let $\gamma, \lambda, P(a), P_\gamma w$ be as in Theorem \ref{generalizedpoisson.tm},
and $I_{\gamma, 1}$ be defined as in \eqref{fractionalderivative.veryolddef}.
Then
\begin{equation}
\label{pointpoisson.tm.eq3}
P_{\gamma} w({\bf y}_0):=\lim_{N\to \infty} P_{\gamma} w (g_{N, {\bf y}_0})
\end{equation}
is a random variable for every ${\bf y}_0\in {\mathbb{R}}^d$ whose characteristic function
is given by
\begin{equation} \label{pointpoisson.tm.eq4}
{\bf E}(e^{-i t P_\gamma w({\bf y}_0)})=
\exp\Big(\lambda \int_{{\mathbb{R}}}\int_{{\mathbb{R}}} \big(e^{-ia t H_{{\bf y}_0}({\bf x})}-1\big) d{\bf x} dP(a)\Big), t\in {\mathbb{R}},
\end{equation}
where $g\in {\mathcal D}$ satisfies $\int_{{\mathbb{R}}^d} g({\bf x}) d{\bf x}=1$, $g_{N, {\bf y}_0}({\bf x})=N^d g(N({\bf x}-{\bf y}_0))$, and
\begin{equation}\label{pointpoisson.tm.eq5}
\widehat{H_{{\bf y}_0}}(\xi)=\Big (e^{i\langle {\bf y}_0, \xi\rangle}-\sum_{|{\bf i}|\le \gamma} \frac{(i{\bf y}_0)^{\bf i} \xi^{\bf i}}{{\bf i}!}\Big) \|\xi\|^{-\gamma}.
\end{equation}
\end{Tm}
An interpretation is that the random variable $P_{\gamma} w({\bf y}_0)$ in \eqref{pointpoisson.tm.eq3}
and its characteristic function ${\bf E}(e^{-i t P_\gamma w({\bf y}_0)})$ in \eqref{pointpoisson.tm.eq4}
correspond formally to setting $f=\delta(\cdot-{\bf y}_0)$ (the delta distribution) in \eqref{generalizedpoisson.tm.eq1}
and \eqref{generalizedpoisson.tm.eq2}, respectively.
To prove Theorem \ref{pointpoisson.tm}, we need a technical lemma.
\begin{Lm}\label{generalizedpoisson.lm}
Let $\gamma$ be a positive non-integer number, $g\in {\mathcal D}$ satisfy $\int_{{\mathbb{R}}^d} g({\bf x}) d{\bf x}=1$, and $H_{{\bf y}_0}$ be defined in \eqref{pointpoisson.tm.eq5}.
Then
\begin{equation}\label{generalizedpoisson.lm.eq1}
\lim_{N\to \infty} \|I_{\gamma, 1} g_{N, {\bf y}_0}-H_{{\bf y}_0}\|_1=0
\end{equation}
for all ${\bf y}_0\in {\mathbb{R}}^d$, where $g_{N,{\bf y}_0}({\bf x})= N^d g(N ({\bf x}-{\bf y}_0))$.
\end{Lm}
\begin{proof} Let $K_{\bf j}$ be the inverse Fourier transform of $(i\xi)^{\bf j} \|\xi\|^{-\gamma}$ and $k_1$ be the integral part of the positive non-integer number $\gamma$. Then
from the argument in the proof of Theorem \ref{iomegap.tm1},
\begin{equation}\label{generalizedpoisson.lm.pf.eq1}
H_{\bf y}({\bf x})=\left\{\begin{array}{ll}
\sum_{|{\bf j}|=k_1} \frac{k_1}{{\bf j}!} \int_0^1 (K_{\bf j}({\bf x}-t{\bf y})-K_{\bf j}({\bf x})) (-{\bf y})^{\bf j} (1-t)^{k_1-1}
dt & {\rm if} \ k_1\ge 1\\
K_{\bf 0}({\bf x}-{\bf y})-K_{\bf 0}({\bf x}) & {\rm if} \ k_1=0.
\end{array}\right.
\end{equation}
Therefore for ${\bf y}_0\ne 0$,
\begin{eqnarray*}
& & \|I_{\gamma, 1} g_{N, {\bf y}_0}-H_{{\bf y}_0}\|_1 \nonumber\\
& \le & C \sum_{|{\bf j}|=k_1}
\int_{{\mathbb{R}}^d} \int_0^1 \int_{{\mathbb{R}}^d}
| (K_{\bf j}({\bf x}-t{\bf y})-K_{\bf j}({\bf x})) {\bf y}^{\bf j} \nonumber\\
& &\quad -
(K_{\bf j}({\bf x}-t{\bf y}_0)-K_{\bf j}({\bf x})) {\bf y}_0^{\bf j} | |g_{N, {\bf y}_0}({\bf y})| d{\bf y} dt d{\bf x}\nonumber\\
& \le & C \sum_{|{\bf j}|=k_1}
\int_{{\mathbb{R}}^d} \int_0^1 \int_{{\mathbb{R}}^d}
| K_{\bf j}({\bf x}-t{\bf y})-K_{\bf j}({\bf x}-t{\bf y}_0)| \| {\bf y}\|^{k_1}
|g_{N, {\bf y}_0}({\bf y})| d{\bf y} dt d{\bf x}\nonumber\\
& & +C\sum_{|{\bf j}|=k_1}
\int_{{\mathbb{R}}^d} \int_0^1 \int_{{\mathbb{R}}^d}
|K_{\bf j}({\bf x}-t{\bf y}_0)-K_{\bf j}({\bf x})| |{\bf y}^{\bf j}- {\bf y}_0^{\bf j} |
|g_{N, {\bf y}_0}({\bf y})| d{\bf y} dt d{\bf x}\nonumber\\
&\le & C
\int_0^1 \int_{{\mathbb{R}}^d} (t\|{\bf y}-{\bf y}_0\|)^{\gamma-k_1}
( \| {\bf y}_0\|^{k_1} +\|{\bf y}-{\bf y}_0\|^{k_1})
|g_{N, {\bf y}_0}({\bf y})| d{\bf y} dt \nonumber\\
& & + C
\int_0^1 \int_{{\mathbb{R}}^d} (t\|{\bf y}_0\|)^{\gamma-k_1}
( \| {\bf y}_0\|^{k_1-1}\|{\bf y}-{\bf y}_0\| +\|{\bf y}-{\bf y}_0\|^{k_1})
|g_{N, {\bf y}_0}({\bf y})| d{\bf y} dt \nonumber\\
&\to & 0 \quad {\rm as} \ N\to \infty
\end{eqnarray*}
if $k_1\ge 1$, and
\begin{eqnarray*}
& & \|I_{\gamma, 1} g_{N, {\bf y}_0}-H_{{\bf y}_0}\|_1 \nonumber\\
& \le &
\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}^d}
| K_{\bf 0}({\bf x}-{\bf y})-K_{\bf 0}({\bf x}-{\bf y}_0)| |g_{N, {\bf y}_0}({\bf y}) d{\bf y} d{\bf x}\nonumber\\
& \le &
\int_{{\mathbb{R}}^d} \Big(\int_{\|{\bf x}-{\bf y}\|\ge 2 \|{\bf y}-{\bf y}_0\|}| K_{\bf 0}({\bf x}-{\bf y})-K_{\bf 0}({\bf x}-{\bf y}_0)|
d{\bf x}\nonumber\\
& &
+\int_{\|{\bf x}-{\bf y}\|\le 2 \|{\bf y}-{\bf y}_0\|}
| K_{\bf 0}({\bf x}-{\bf y})| +
| K_{\bf 0}({\bf x}-{\bf y}_0)| d{\bf x} \Big) |g_{N, {\bf y}_0}({\bf y}) | d{\bf y} \nonumber\\
& \le & C N^d \int_{{\mathbb{R}}^d} \|{\bf y}-{\bf y}_0\|^\gamma |g(N({\bf y}-{\bf y}_0))| d{\bf y}\nonumber\\
& = & C N^{-\gamma} \int_{{\mathbb{R}}^d} \|{\bf z}\|^\gamma |g({\bf z})| d{\bf z}\to 0 \quad {\rm as} \ N\to 0,
\end{eqnarray*}
if $k_1=0$. This shows that \eqref{generalizedpoisson.lm.eq1} for ${\bf y}_0\ne {\bf 0}$.
The limit in \eqref{generalizedpoisson.lm.eq1} for ${\bf y}_0={\bf 0}$ can be proved by using a similar argument, the detail of which are omitted
here.
\end{proof}
\begin{proof} [Proof of Theorem \ref{pointpoisson.tm}]
By Lemma \ref{generalizedpoisson.lm} and the dominated convergence theorem,
\begin{equation}
\lim_{N\to \infty}
\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}} (e^{-i at I_{\gamma, 1} g_{N, {\bf y}_0}({\bf x})}-1) dP(a) d{\bf x}=
\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}} (e^{-i at H_{{\bf y}_0}({\bf x})}-1) dP(a) d{\bf x}
\end{equation}
for all $t\in {\mathbb{R}}$. Moreover as $H_{{\bf y}_0}$ is integrable from Corollary \ref{iomegap.cor1} and
Lemma \ref{generalizedpoisson.lm},
the function
$\int_{{\mathbb{R}}^d} \int_{{\mathbb{R}}} (e^{-i at I_{\gamma, 1} H_{{\bf y}_0}({\bf x})}-1) dP(a) d{\bf x}$ is continuous about $t$. Therefore
\eqref{pointpoisson.tm.eq3} and \eqref{pointpoisson.tm.eq4} follows from Lemma \ref{levy.lm}.
\end{proof}
\noindent{\bf Acknowledgement.} {\rm This work was done when the first named author was visiting
Ecole Polytechnique Federale de Lausanne on his sabbatical leave.
He would like to thank Professors Michael Unser and Martin Vetterli for the hospitality and fruitful discussions. }
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,128 |
{"url":"https:\/\/www.plumed.org\/doc-v2.7\/user-doc\/html\/tools.html","text":"Command Line Tools\n\nPLUMED contains a number of simple command line tools. To use one of these tools you issue a command something like:\n\nplumed <toolname> <list of input flags for that tool>\n\n\nThe following is a list of the various standalone tools that PLUMED contains.\n\n completion Dumps the body of a bash function to be used for auto completion. config inquire plumed about how it was configure driver driver is a tool that allows one to to use plumed to post-process an existing trajectory. driver-float Equivalent to driver, but using single precision reals. gen_example gen_example is a tool that you can use to construct an example for the manual that users can interact with to understand gentemplate gentemplate is a tool that you can use to construct template inputs for the various actions info This tool allows you to obtain information about your plumed version kt Print out the value of $$k_BT$$ at a particular temperature manual manual is a tool that you can use to construct the manual page fora particular action mklib compile a .cpp file into a shared library newcv create a new collective variable from a template partial_tempering scale parameters in a gromacs topology to implement solute or partial tempering patch patch an MD engine pathtools pathtools can be used to construct paths from pdb data pdbrenumber Modify atom numbers in a PDB, possibly using hybrid-36 coding. pesmd Pesmd allows one to do (biased) Langevin dynamics on a two-dimensional potential energy surface. selector create lists of serial atom numbers simplemd simplemd allows one to do molecular dynamics on systems of Lennard-Jones atoms. sum_hills sum_hills is a tool that allows one to to use plumed to post-process an existing hills\/colvar file vim2html convert plumed input file to colored html using vim syntax\n\nIn addition to the keywords above, by enabling optional modules you can access to the following keywords:\n\n drr_tool (from Extended-System Adaptive Biasing Force module) - Extract .grad and .count files from the binary output .drrstate - Merge windows ves_md_linearexpansion (from Variationally Enhanced Sampling (VES code) module) Simple MD code for dynamics on a potential energy surface given by a linear basis set expansion.\n\nFor all these tools and to use PLUMED as a plugin in an MD calculation you will need an input file.","date":"2021-05-13 00:26:49","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\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.23121705651283264, \"perplexity\": 3761.220340110318}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-21\/segments\/1620243991413.30\/warc\/CC-MAIN-20210512224016-20210513014016-00383.warc.gz\"}"} | null | null |
Q: Add via jQuery I have a problem and I have no idea how to solve it:
I have a table:
| A | B |
| D | C |
<table>
<tr>
<td>
A
</td>
<td>
B
</td>
</tr>
<tr>
<td>
C
</td>
<td>
D
</td>
</tr>
</table>
And now I need to add </tr><tr> after each odd td. Result should be one column table:
| A |
| B |
| C |
| D |
I was already trying to make this work with jQuery $("#table tr > td:nth-child(odd)").after("</tr><tr>");, but it doesn't work.
Can anyone advise?
A: Try
$('table td:odd').each(function(i, v){
var $this = $(this);
var parent = $this.parent();
$this.detach().wrap('<tr></tr>').insertAfter(parent)
})
Demo: fiddle
A: Try this: (http://jsfiddle.net/b5S3U/4/)
var cols = 1;
$('tr').each(function () {
var after = $(this);
while ($(this).children().length > cols) {
after = $('<tr>').insertAfter(after).append($('>:gt(' + (cols - 1) + '):lt(' + (cols) + ')', this));
}
})
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,288 |
Keith Robertson is back at the office following a jaunt in Ontario to present at the Canada Green Building Council's National Conference: Building Lasting Change 2014, followed by the Scotia Bank Ecoliving Awards.
While away, Keith's desk was quickly usurped by his son Clay who took the job-shadowing opportunity to hold a brainstorming session on a world class sports facility. Jordan Willet moderated while Clay and his schoolmate developed ideas.
After a brief appearance Keith was off again, this time to Fredericton, New Brunswick to serve as one of three jurors for the Architects' Association of New Brunswick Lieutenant Governor Awards. | {
"redpajama_set_name": "RedPajamaC4"
} | 96 |
Theganopteryx dimorpha es una especie de cucaracha del género Theganopteryx, familia Ectobiidae.
Distribución
Esta especie se encuentra en Costa de Marfil.
Referencias
dimorpha
Insectos de Costa de Marfil
Insectos descritos en 1971 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,953 |
layout: post
title: 코틀린으로 작성한 안드로이드 recycler view 중첩해서 사용하기
---
오늘은 recycler view 안에 recycler view가 들어있는, 즉 recycler view를 중첩해서 사용하는 방식을 알아보려합니다.
보통 recycler view는 xml과 activity가 adapter로 연결되어 있어서 쉽게 구현할 수 있습니다.
하지만 중첩된 recycler view는 잠깐 생각해보면 recycler view 안에 layout이 하나 더 있는 것입니다.
분명 activity에서는 중첩된 recycler view를 찾기 힘들지 않나라는 생각이 들겁니다.
하지만, 결론부터 말씀드리자면 Holder에서 adapter로 연결해주면 됩니다.
## 상위 xml
```xml
<?xml version="1.0" encoding="utf-8"?>
<layout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools">
<data>
</data>
<LinearLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:background="@drawable/border"
android:orientation="vertical">
<TextView
android:id="@+id/list_text"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_weight="1"
android:textAppearance="@style/TextAppearance.AppCompat.Large"
android:hint="@string/text"/>
<android.support.v7.widget.RecyclerView
android:id="@+id/list_recycler_view"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_weight="1" />
</LinearLayout>
</layout>
```
우선 recycler view에 들어갈 아이템을 구성하는 레이아웃을 만듭니다.
list_recycler_view 라는 id를 가진 RecyclerView 위젯이 아래에 구현될 중첩 recycler view입니다.
## 하위 xml
```xml
<layout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools">
<data>
</data>
<LinearLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:orientation="horizontal"
android:background="@drawable/border"
>
<TextView
android:id="@+id/product_name"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_weight="1"
android:gravity="center"
android:hint="@string/product"/>
</LinearLayout>
</layout>
```
중첩되어 들어갈 recycler view의 레이아웃입니다.
이 역시 위 레이아웃 코드와 마찬가지로 데이터 바인딩을 하기 위한 레이아웃 태그로 감싸져 있지만, 일반적인 레이아웃으로 해도 무관합니다.
하나의 레이아웃 형식으로만 유지하면 됩니다.
## 하위 recycler view adapter
```kotlin
class ListSubAdapter(private val context: Context, private val List: ArrayList<Count>) :
RecyclerView.Adapter<ListSubAdapter.Holder>() {
override fun onCreateViewHolder(p0: ViewGroup, p1: Int): Holder {
val view = LayoutInflater.from(context).inflate(R.layout.sub_listview, p0, false)
return Holder(view)
}
override fun getItemCount(): Int {
return List.size
}
override fun onBindViewHolder(p0: Holder, p1: Int) {
p0.bind(List[p1])
}
inner class Holder(itemView: View?) : RecyclerView.ViewHolder(itemView!!) {
private val p = itemView?.findViewById<TextView>(R.id.product_name)
fun bind(count: Count) {
p?.text = count.productName
}
}
}
```
중첩이 되어있는 recycler view의 xml 파일과 상위 recycler view의 holder를 연결할 adapter를 만들어 줍니다.
inner class로 holder 클래스를 만들어서 활용합니다.
이 클래스는 단순히 레이아웃을 맵핑해주는 수준에 그칩니다.
## 상위 recycler view adapter
```kotlin
class ListAdapter(private val context: Context, private val List: ArrayList<List>) :
RecyclerView.Adapter<ListAdapter.Holder>() {
override fun onBindViewHolder(p0: Holder, p1: Int) {
p0.bind(List[p1])
}
override fun onCreateViewHolder(p0: ViewGroup, p1: Int): Holder {
val view = LayoutInflater.from(context).inflate(R.layout.listview, p0, false)
return Holder(view)
}
override fun getItemCount(): Int {
return List.size
}
inner class Holder(itemView: View?) : RecyclerView.ViewHolder(itemView!!) {
private val s = itemView?.findViewById<TextView>(R.id.list_text)
fun bind(list: List) {
s?.text = list.name
val s = itemView.findViewById<RecyclerView>(R.id.list_recycler_view)
val mAdapter = ListSubAdapter(context,list.list_count)
s.adapter = mAdapter
val layoutmanager = LinearLayoutManager(context)
s.layoutManager = layoutmanager
s.setHasFixedSize(true)
}
}
}
```
이제는 하위 recycler view를 감싸고 있는 recycler view의 adapter를 만들어 보겠습니다.
아까 감싸진 recycler view의 adapter를 만드는 것과 크게 다를 것은 없지만, bind 함수가 조금 긴 것을 확인 할 수 있습니다.
그 이유는 감싸진 recycler view의 adapter를 가져와서 이 Holder 클래스에서 연결해주기 때문입니다.
일반적인 adapter 사용법과 별반 다를 것이 없지만, 차이점이 있다면 context를 가져오는 방식이 조금 다릅니다.
기존에서는 엑티비티를 가져왔다면, 이번에는 인자에 받아 온 context를 쓰기만 하면 됩니다.
## fragment xml
```xml
<?xml version="1.0" encoding="utf-8"?>
<layout
xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools">
<data>
</data>
<android.support.constraint.ConstraintLayout
android:layout_width="match_parent"
android:layout_height="match_parent"
tools:layout_editor_absoluteY="81dp">
<android.support.v7.widget.RecyclerView
android:id="@+id/recyclerView"
android:layout_width="0dp"
android:layout_height="0dp"
android:layout_marginBottom="8dp"
android:layout_marginEnd="8dp"
android:layout_marginStart="8dp"
android:layout_marginTop="8dp"
app:layout_constraintBottom_toBottomOf="parent"
app:layout_constraintEnd_toEndOf="parent"
app:layout_constraintStart_toStartOf="parent"
app:layout_constraintTop_toTopOf="parent" />
</android.support.constraint.ConstraintLayout>
</layout>
```
fragment 레이아웃 xml 파일에서는 상위에 존재하는 하나의 RecyclerView 위젯만 배치하면 끝납니다.
## fragment
```kotlin
override fun onActivityCreated(savedInstanceState: Bundle?) {
super.onActivityCreated(savedInstanceState)
updateData() // 데이터를 생성해주는 메소드로서 해당 포스트에서는 설명이 생략된 메소드입니다.
ListRecyclerView()
}
private fun ListRecyclerView() {
val mAdapter = ListAdapter(activity!!, list)
bind.recyclerView.adapter = mAdapter
val layoutmanager = LinearLayoutManager(activity!!)
bind.recyclerView.layoutManager = layoutmanager
bind.recyclerView.setHasFixedSize(true)
}
```
fragment 클래스에서 중요한 메소드는 두개가 있습니다.
엑티비티가 만들어진 뒤에 실행되는 메소드인 onActivityCreated를 오버라이드하여 이 곳에서 adapter를 연결해줍니다.
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,207 |
Krste Crvenkovski - Stevo, makedonski komunist, filozof, prvoborec, partizan, politik in narodni heroj, * 1921, † 2001.
Glej tudi
seznam narodnih herojev Jugoslavije
Rojeni leta 1921
Umrli leta 2001
Makedonski filozofi
Makedonski komunisti
Makedonski partizani
Makedonski politiki
Narodni heroji
Prvoborci
Veterani druge svetovne vojne | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,036 |
{"url":"https:\/\/support.bioconductor.org\/p\/9135935\/","text":"is the P value reliable if the counts are Low across the sample ?\n2\n0\nEntering edit mode\n@simplyphage-22396\nLast seen 29 days ago\nItaly\n\nI have these normalized counts for a gene under different conditions:\n\nMyc 8.703798652 17.15727528 12.74184922 20.88031384 19.31939574 19.51436733 15.22619271 11.25208598 13.03293781 16.08920907 16.8038009 7.560006805 ...........................!!!\n\nand the basemean is 12 and 8 in two conditions, the P value is also significant\n\nNow my question is ... 1) given this low number of counts, should I trust this data? 2) is it right to just remove these genes with low counts? if yes is there any cutoff value for it?\n\nDESeq2 sequencing \u2022 126 views\n1\nEntering edit mode\n@mikelove\nLast seen 14 hours ago\nUnited States\n\nI have no idea which counts are in which group.\n\nDESeq2 uses the distribution of dispersion across all genes, plus a model of the information content of the dispersion estimates, to determine if the difference across groups is more than would be seen under the null. It is more than just looking at the normalized counts.\n\nYou can remove low count genes ahead of analysis if you chose but it is not necessary. Additionally, see the DESeq2 paper on the use of an LFC threshold. If you want to prioritize genes with larger effect sizes, I highly recommend setting lfcThreshold.\n\n1\nEntering edit mode\nswbarnes2 \u25b4 710\n@swbarnes2-14086\nLast seen 9 hours ago\nSan Diego\n\nIf you didn't lie to the software, then trust the padj. Otherwise, why bother with the software at all?","date":"2021-05-07 01:10:54","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\": 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\": 0.30437153577804565, \"perplexity\": 1897.8757173608574}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-21\/segments\/1620243988774.18\/warc\/CC-MAIN-20210506235514-20210507025514-00184.warc.gz\"}"} | null | null |
Artists create life in ways others are unable to imagine it. Creativity matched with talent and knowledge becomes transforming. Rain Hannah, your lead instructor, is one of Hollywood's most sought after makeup artists. A consummate professional, Rain Hannah has hands on expertise in the beauty and entertainment industry ranging from weddings, pageants and photo shoots, to high-octane concerts and red carpet events. She has had a lifelong passion for makeup beginning with a fascination with her mother's makeup drawer at a very young age and even today classifies herself as a continual student of the art of makeup.
Rain Hannah got her start as a last minute stand in for an absent makeup artist and has never looked back. She learned from every formal and informal opportunity she could find, seeking out any new tips, tricks or mistakes to perfect her art. Her genuine love of people, and talent with a makeup brush, pushed her quickly into the spotlight. Her brushes have touched the faces of several of Hollywood A-Lister's such as Kirsten Dunst, Paris Hilton, Mandy Moore, and Britney Spears to name a few. It wasn't long before Rain realized the need for more options in both quality products and continuing education for aspiring makeup artists.
Additionally, Rain Hannah co-founded a company of unsurpassed quality cosmetics. Recently, in the beginning of 2014 Rain launched Serendipity Beauty www.serendipitybeauty.com with her dear friend and mentor Brian Fox. Hannah literally made headlines across the country as a entrepreneur always reinventing herself.
Rain's mission is to have the constantly reach people all over the world and inspiring their passion for the artists. Rain believes beauty is in the eye of the beholder and you are in control of your beauty shining bright.
As a graduate of the University of Nevada, Las Vegas with a bachelor's degree in Communications, Rain's ability to relate to others is unmatched. She decided to share her inside secrets with those who share her passion by using advanced virtual technology that creates a classroom environment that can be accessed from anywhere in the world. Rain's Academy's allow aspiring makeup artists to effectively learn at their own pace. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,125 |
Match Group to pay Tinder founders $441 million to settle lawsuit
Match Group to pay Tinder founders $441 million to settle lawsuit - Copyright Thomson Reuters 2021
– Match Group Inc said on Wednesday it would pay Tinder founders $441 million to settle a case in which the dating app's executives claimed the parent company lowballed the app's value to avoid paying billions of dollars.
The lawsuit filed in 2018 had stated that IAC/InterActiveCorp and subsidiary Match deliberately prevented Tinder founders Sean Rad, Justin Mateen and Jonathan Badeen from cashing in stock options they could exercise and sell to IAC.
The plaintiffs were given stock options in Tinder as part of their compensation in 2014, but because Tinder is a private company they were not able to exercise their options and then sell stock on the open market.
Instead, they were allowed to exercise their options and sell only to IAC and Match on specific dates, on which the stock options would be independently valued.
However, IAC and Match then merged Tinder into Match, which Tinder's board of directors was not aware of and did not consent, while canceling the future dates for exercising options, according to the lawsuit filed by the plaintiffs in 2018.
Tinder is one of Match Group's biggest and fastest-growing brands that has amassed millions of users worldwide and has benefited during the pandemic with many consumers using the app while locked in at home.
Match, which also owns online dating service Hinge, was spun off as a separate public company in 2015.
The company said it intends to pay the settlement from cash on hand. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,794 |
Q: How to change order of bar chart categories? I have a bar chart where the categories (on the x-axis) are numbers:
\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{filecontents}
\begin{filecontents}{foo.csv}
x,y
1,4
2,7
3,2
\end{filecontents}
\begin{document}
\begin{tikzpicture}
\begin{axis}[ybar, xtick={1,2,3}]
\addplot[x=x, y=y, fill] table[col sep=comma] {foo.csv};
\end{axis}
\end{tikzpicture}
\end{document}
I would like the columns to be plotted in the order [2,3,1] rather than [1,2,3]. Unfortunately, if I just use xtick={2,3,1} instead of xtick={1,2,3}, nothing changes. Presumably, pgfplots thinks that 1, 2, and 3 are numbers, but I want them to be understood as categories in my context. How can I reorder my columns?
A: Use symbolic x coords.
\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{filecontents}
\begin{filecontents}{foo.csv}
x,y
1,4
2,7
3,2
\end{filecontents}
\begin{document}
\begin{tikzpicture}
\begin{axis}[ybar, symbolic x coords={2,3,1},xtick=data]
\addplot[x=x, y=y, fill] table[col sep=comma] {foo.csv};
\end{axis}
\end{tikzpicture}
\end{document}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,536 |
{"url":"http:\/\/mathoverflow.net\/revisions\/31709\/list","text":"p. 78: Let $K_0=1$ and $K_{n+1}=1+\\min(2 K_{\\lfloor n\/2 \\rfloor}, 3 K_{\\lfloor n\/3 \\rfloor})$ for $n\\ge 0$. (\"One of the authors of this book has modestly decided to call these the Knuth numbers.\")\np. 97, exercise 3.25: Prove or disprove that the Knuth numbers satisfy $K_n \\ge n$ for $n\\ge 0$.\nInduction fails when trying to prove $K_n \\ge n$ directly (as explained in the text on p. 79), but works easily for the stronger statement $K_n > n$.","date":"2013-05-24 21:57:22","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.833472490310669, \"perplexity\": 343.6980657210461}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-20\/segments\/1368705097259\/warc\/CC-MAIN-20130516115137-00079-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction}
Supersymmetry (SUSY) is a mathematical framework showing how a symmetry exists relating bosonic and fermionic degrees of freedom. In order for it to hold in any theoretical formulation, known observed particles should have a partner with the same mass. This is not seen and so one expects that, if it is realized in nature, some mechanism should break this symmetry making superpartners very high in mass.
Some mechanism for supersymmetry breaking have been proposed so far. Spontaneous symmetry breaking has been proposed by Fayet and Iliopolous and by O'Raifeartaigh \cite{Fayet:1974jb,O'Raifeartaigh:1975pr}. In this case, auxiliary fields, $F$ or $D$, have a non-null vacuum expectation value. But these approaches do not apply to the minimal supersymmetric standard model (MSSM) and possible extensions. MSSM was firstly proposed by Georgi and Dimopolous \cite{Dimopoulos:1981zb}. In order to overcome the difficulties with breaking of supersymmetry and obtain low-energy phenomenology, they adopted ``softly'' broken SUSY. The idea is to use explicitly breaking terms in the Lagrangian of the model but granting renormalizability and invariance under electroweak symmetry group. A fundamental result due to Witten shows how an index can be computed for a given supersymmetric theory that immediately shows if symmetry breaking can occur \cite{Witten:1982df}.
Our aim in this letter is to provide a way to solve the classical equations of motion of a supersymmetric model in a regime where the value of the coupling can be varied arbitrarily. We choose the Wess-Zumino model as this is the simplest paradigm of supersymmetry \cite{Weinberg:2000cr}. The approach we use is a series in powers of currents as already devised in \cite{Cahill:1985mh} for quantum chromodynamics but we will keep our computations in a completely classical realm.
The reason why this analysis is relevant is that these classical solutions show an interesting behavior: In a small coupling limit supersymmetry is seen to be preserved why all the fields acquire an identical mass. On the other limit, taking the coupling running to infinity, a Nambu-Jona-Lasinio-like equation is seen to emerge for the fermion field and no conclusion can be drawn about supersymmetry being preserved or not.
\section{Massless Wess-Zumino model}
Massless Wess-Zumino model has the Lagrangian \cite{Weinberg:2000cr}
\begin{eqnarray}
L &=& \frac{1}{2}(\partial A)^2+\frac{1}{2}(\partial B)^2+\frac{1}{2}\bar\psi i\slashed\partial\psi \nonumber \\
&&-\frac{1}{2}g^2(A^2+B^2)^2-g(\bar\psi\psi A-\bar\psi\gamma^5\psi B)
\end{eqnarray}
being $\psi$ a Majorana field, $A=A^\dagger$ a scalar field and $B=B^\dagger$ a pseudo-scalar field. This Lagrangian is invariant under supersymmetric variations that can be stated in the form
\begin{eqnarray}
\delta A(x)&=&\bar\epsilon\psi(x) \nonumber \\
\delta B(x)&=&\bar\epsilon\gamma^5\psi(x) \nonumber \\
\delta\psi(x) &=& \partial_\mu(A-\gamma^5B)\gamma^\mu\epsilon.
\end{eqnarray}
These hold on-shell because we have already removed the auxiliary fields using the equations of motion. From Witten index we know that for this model spontaneous symmetry breaking does not occur \cite{Witten:1982df}. Equations of motion are
\begin{eqnarray}
\label{eq:susy}
\partial^2A+2g^2A(A^2+B^2)&=&-g\bar\psi\psi \nonumber \\
\partial^2B+2g^2B(A^2+B^2)&=&g\bar\psi\gamma^5\psi \nonumber \\
i\slashed\partial\psi&=&2g(A-\gamma^5B)\psi.
\end{eqnarray}
Now, let us consider the following two equations
\begin{eqnarray}
\label{eq:susy2}
\partial^2A+2g^2A(A^2+B^2)&=&j \nonumber \\
\partial^2B+2g^2B(A^2+B^2)&=&j_5
\end{eqnarray}
being $j=-g\bar\psi\psi$ and $j_5=g\bar\psi\gamma^5\psi$ These imply that $A=A[x;j,j_5]$ and $B=B[x;j,j_5]$ and so we take the functional Taylor series
\begin{eqnarray}
A &=& A_0(x)+\int dx'\left.\frac{\delta A}{\delta j(x')}\right|_{j,j_5=0}j(x')
+\int dx'\left.\frac{\delta A}{\delta j_5(x')}\right|_{j,j_5=0}j_5(x')
\nonumber \\
&&+\frac{1}{2}\int dx'dx''\left.\frac{\delta^2 A}{\delta j(x')\delta j(x'')}\right|_{j,j_5=0}j(x')j(x'')
+\int dx'dx''\left.\frac{\delta^2 A}{\delta j_5(x')\delta j(x'')}\right|_{j,j_5=0}j_5(x')j(x'') \nonumber \\
&&+\frac{1}{2}\int dx'dx''\left.\frac{\delta^2 A}{\delta j_5(x')\delta j_5(x'')}\right|_{j,j_5=0}j_5(x')j_5(x'')+\ldots \nonumber \\
B &=& B_0(x)+\int dx'\left.\frac{\delta B}{\delta j(x')}\right|_{j,j_5=0}j(x')
+\int dx'\left.\frac{\delta B}{\delta j_5(x')}\right|_{j,j_5=0}j_5(x')
\nonumber \\
&&+\frac{1}{2}\int dx'dx''\left.\frac{\delta^2 B}{\delta j(x')\delta j(x'')}\right|_{j,j_5=0}j(x')j(x'')
+\int dx'dx''\left.\frac{\delta^2 B}{\delta j_5(x')\delta j(x'')}\right|_{j,j_5=0}j_5(x')j(x'') \nonumber \\
&&+\frac{1}{2}\int dx'dx''\left.\frac{\delta^2 B}{\delta j_5(x')\delta j_5(x'')}\right|_{j,j_5=0}j_5(x')j_5(x'')+\ldots
\end{eqnarray}
having set $A_0(x)=A[x;0,0]$ and $B_0(x)=B[x;0,0]$. Then we insert this series into eqs.(\ref{eq:susy2}) and we get the leading order equations
\begin{eqnarray}
\partial^2A_0+2g^2(A_0^2+B_0^2)A_0 &=& 0 \nonumber \\
\partial^2B_0+2g^2(A_0^2+B_0^2)B_0 &=& 0
\end{eqnarray}
that can be solved exactly \cite{Frasca:2009bc}. This is easy to see as we set $B_0=\eta_pA_0$ with $\eta_p^2=1$ the parity factor. Then, setting $A_0=\phi$, we have to solve the equation $\partial^2\phi+4g^2\phi^3=0$ that has the solution $\phi(x)=\mu(1/2^\frac{1}{4}g^\frac{1}{2}){\rm sn}(p\cdot x+\theta,i)$ being $\mu$ and $\theta$ integration constants and sn a Jacobi elliptic function. This holds provided $p^2=\sqrt{2}\mu^2g$ that can be interpreted as a dispersion relation for a massive particle. At this order both boson fields get a mass but supersymmetry is preserved as we will also see for the Fermion field at small coupling. Next-to-leading order equations give
\begin{eqnarray}
\partial^2A_1+8g^2\phi^2A_1+4g^2\phi^2\eta_p\bar B_1&=&\delta^4(x) \nonumber \\
\partial^2\bar A_1+8g^2\phi^2\bar A_1+4g^2\phi^2\eta_pB_1&=& 0 \nonumber \\
\partial^2B_1+8g^2\phi^2B_1+4g^2\phi^2\eta_p\bar A_1&=& \delta^4(x) \nonumber \\
\partial^2\bar B_1+8g^2\phi^2\bar B_1+4g^2\phi^2\eta_p A_1&=& 0
\end{eqnarray}
where we have set $A_1=\left.\delta A/\delta j(x)\right|_{j,j_5=0}$, $\bar A_1=\left.\delta A/\delta j_5(x)\right|_{j,j_5=0}$, $B_1=\left.\delta B/\delta j_5(x)\right|_{j,j_5=0}$, $\bar B_1=\left.\delta B/\delta j(x)\right|_{j,j_5=0}$. Now, introducing the Green function $\partial^2\Delta+8g^2\phi^2\Delta=\delta^4(x)$, this set of equations can be turned into a single integral equation by noting that $B_1=A_1=\phi_1$ and so, we get
\begin{equation}
\label{eq:phi1}
\phi_1(x)=\Delta(x)+16g^4\int d^4x'\Delta(x-x')\phi^2(x')\int d^4x''\Delta(x'-x'')\phi^2(x'')\phi_1(x'').
\end{equation}
Use has been made of the equations
\begin{eqnarray}
\bar A_1 &=& -4g^2\int d^4x'\Delta(x-x')\phi^2(x')\eta_pB_1 \nonumber \\
\bar B_1 &=& -4g^2\int d^4x'\Delta(x-x')\phi^2(x')\eta_pA_1
\end{eqnarray}
that can be given by $\phi_1$. Now we turn to the computation of the Green function $\Delta(x)$. This can be obtained immediately \cite{Frasca:2009nt} as
\begin{equation}
\label{eq:prop}
\Delta(p^2)=\sum_{n=0}^\infty\frac{B_n}{p^2-m_n^2+i\epsilon}
\end{equation}
being
\begin{equation}
B_n=(2n+1)^2\frac{\pi^3}{4K^3(i)}\frac{e^{-(n+\frac{1}{2})\pi}}{1+e^{-(2n+1)\pi}}.
\end{equation}
and $m_n=(2n+1)(\pi/2K(i))(4/3)^\frac{1}{4}g^\frac{1}{2}\mu$ a possible mass spectrum when this propagator enters in quantum field theory and $K(i)$ an elliptic integral $\int_0^\frac{\pi}{2}1/\sqrt{1+\sin^2\theta}d\theta$ and the phase of $\phi$ is chosen to be $K(i)$. Eq.(\ref{eq:phi1}) admits a simple solution in the limit of very low momenta. In this case we get the simple expression
\begin{equation}
\Delta_0(x-x')=-\frac{\sqrt{3}}{4\mu^2g}\delta^4(x-x')
\end{equation}
proper to a contact interaction. So, putting this into eq.(\ref{eq:prop}) one gets
\begin{equation}
\phi_1(x)=\frac{\sqrt{3}}{2\mu^2g}\delta^4(x)
\end{equation}
and so,
\begin{equation}
\bar A_1 = \bar B_1 = \eta_p\frac{3}{2\sqrt{2}}\frac{1}{\mu^2g}\delta^4(x)
\end{equation}
Finally, the low-energy series for our solution is given by
\begin{eqnarray}
A &=& A_0(x)+\frac{\sqrt{3}}{2}\frac{1}{\mu^2g}\left(j(x)
+\sqrt{\frac{3}{2}}\eta_pj_5(x)\right)+O(j^2)+O(j^2_5)+O(jj_5) \nonumber \\
B &=& B_0(x)+\frac{\sqrt{3}}{2}\frac{1}{\mu^2g}\left(j_5(x)+\sqrt{\frac{3}{2}}\eta_pj(x)\right)+O(j^2)+O(j^2_5)+O(jj_5)
\end{eqnarray}
Now, turning our attention to the fermion field, we get
\begin{equation}
i\slashed\partial\psi-2g\phi(1-\eta_p\gamma^5)\psi=
-\sqrt{3}\frac{g}{\mu^2}\left(1-\sqrt{\frac{3}{2}}\eta_p\gamma^5\right)(\bar\psi\psi+\gamma^5\bar\psi\gamma^5\psi)\psi.
\end{equation}
Looking at the limit $g\rightarrow 0$, we observe that Fermion field has the same mass of the bosonic degrees of freedom. In this case one gets the equation of motion
\begin{equation}
i\slashed\partial\psi_c-2g\phi(1-\eta_p\gamma^5)\psi_c=0.
\end{equation}
This equation can be solved by putting $\psi_c=e^{-ikS(x)}u_{ps}$, being $k$ a real constant, and we get $k\gamma\cdot\partial Su_{ps}-2g\phi(1-\eta_p\gamma^5)u_{ps}=0$. But we notice that $\phi$ depends just on the product $\xi=p\cdot x$ and we choose $\partial_\xi S(\xi)=2g\phi(\xi)$. So, we are left with the algebraic equation $[\slashed p-k^{-1}(1-\eta_p\gamma^5)]u_{ps}=0$. We solve this equation by remembering that $p^2=\sqrt{2}\mu^2g$ and we get our proof: In the small coupling limit supersymmetry is preserved at classical level as also happens in quantum field theory in agreement with Witten index for this theory.
This equation appears interesting instead when the limit $g\rightarrow\infty$ is taken. Then, at the leading order, the contribution coming from the external field $\phi$ drops out with respect to the non-linear one as one has $\phi\sim 1/\sqrt{g}$ and an overall $\sqrt{g}$ with respect the latter going like $g$. So, one gets
\begin{equation}
i\slashed\partial\psi_0=
-\sqrt{3}\frac{g}{\mu^2}\left(1-\sqrt{\frac{3}{2}}\eta_p\gamma^5\right)(\bar\psi_0\psi_0+\gamma^5\bar\psi_0\gamma^5\psi_0)\psi_0
\end{equation}
that is a Nambu-Jona-Lasinio-like equation of motion. Working in quantum field theory, this could give rise to a symmetry breaking but already at classical level we observe a fermion with a different mass from the boson fields. Supersymmetry appears to be broken in classical equations of motion but we cannot exclude that quantum corrections can change the situation in agreement with Witten index.
\section{Conclusions}
We have provided an approach to solve the classical equations of motion for the Wess-Zumino model. This is a series in powers of currents. The solutions we obtained can be analyzed both at small and large coupling showing different behavior for the fermion field. In the former case, supersymmetry appears to be preserved as both bosonic and fermionic degrees of freedom acquire the same mass. This does not happen in the limit of the coupling running to infinity. In this case a Nambu-Jona-Lasinio-like equation is obtained and no conclusion about the mass of the fermion field can be drawn unless we turn to a quantum field theory.
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"redpajama_set_name": "RedPajamaArXiv"
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Q: C# ASP.Net : How to call a web service in .NET 4.0 C# without using the WSDL or proxy classes I have to send some XML DATA to web service via POST Command , I have no information about the webserice or anything at all , i only know that i need to send a XMLstream to it , i know the server IP adress and the port , the XML tree of the parameters. and that all , I am a bet lost on how to consumme this web service and get the response . I've never worked with Web services so please understand if my code have some major errors and kindly guide me :
public void Execute()
{
HttpWebRequest request = CreateWebRequest();
XmlDocument soapEnvelopeXml = new XmlDocument();
soapEnvelopeXml.LoadXml(@"<?xml version=""1.0"" encoding=""utf-8""?>
<soap:Envelope xmlns:soap=""http://schemas.xmlsoap.org/soap/envelope/"" xmlns:xsi=""http://www.w3.org/2001/XMLSchema-instance"" xmlns:xsd=""http://www.w3.org/2001/XMLSchema"">
<soap:Body>
<mergeprofiles xmlns=""http://127.0.0.1:90"">
<Profile>
<Member>278615</Member>
<ExtRef>003D000001StY68IAF</ExtRef>zs
<Name>LESCA</Name>
<ChangedBy>user</ChangedBy>
<FirstName>Paolo</FirstName>
<Street1>via magnanina 3947</Street1>
<Street2></Street2>
<Street3></Street3>
<City>VIGEVANO</City>
<ZIP>27029</ZIP>
<EMail>test@test.it</EMail>
<Phone></Phone>
<MobilePhone>+39331231233</MobilePhone>
<Fax></Fax>
<ISOLanguage>en</ISOLanguage>
<Salut1>Mr</Salut1>
<Homepage></Homepage>
<VATNo1>0</VATNo1>
</Profile>
<EndOfMessage>@@@</EndOfMessage>
</mergeprofiles>
</soap:Body>
</soap:Envelope>");
using (Stream stream = request.GetRequestStream())
{
soapEnvelopeXml.Save(stream);
}
using (WebResponse response = request.GetResponse())
{
using (StreamReader rd = new StreamReader(response.GetResponseStream()))
{
string soapResult = rd.ReadToEnd();
Console.WriteLine(soapResult);
}
}
}
/// <summary>
/// Create a soap webrequest to [Url]
/// </summary>
/// <returns></returns>
public HttpWebRequest CreateWebRequest()
{
HttpWebRequest webRequest = (HttpWebRequest)WebRequest.Create(@"http://127.0.0.1:90/");
webRequest.Headers.Add(@"SOAP:Action");
webRequest.ContentType = "text/xml;charset=\"utf-8\"";
webRequest.Accept = "text/xml";
webRequest.Method = "POST";
return webRequest;
}
The problem is when ever I call the method Execute in page_load, it runs and runs and never stops. The web service is working when I call using other methods, I don't know how or why is that happening, can you please help ?
A: Try following some of the steps from this article:
http://www.asp.net/web-api/overview/advanced/calling-a-web-api-from-a-net-client
WebAPI is the latest round of .NET's service frameworks, and it differs quite a lot from the code-generated SOAP classes. Of particular use to you will probably be the following method:
response = await client.PostAsync("your url", new StreamContent(yourStream));
If you are using < .NET 4.5, you may not be able to use this syntax. In that case, try using this answer instead:
.NET: Simplest way to send POST with data and read response
| {
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{"url":"http:\/\/kpb.pl\/assassin-s-szvdaqe\/b79c65-homogeneous-production-function","text":"Homogeneous and homothetic functions are of interest due to the simple ways that their isoquants vary as the level of output varies. Such a production function is called linear homogeneous production function. A function is said to be homogeneous of degree n if the multiplication of all of the independent variables by the same constant, say \u03bb, results in the multiplication of the independent variable by \u03bbn. It is important to. Such as, the output gets doubled with the doubling of input factors and gets tripled on the tripling of \u2026 Keywords: Homogeneity, Concavity, Non-Increasing Returns to Scale and Production Function. 4. The significance of this is that the marginal products of the inputs do not change with proportionate increases in both inputs. The theoretical part of the book critically examines both homogeneous and non-homogeneous production function literature. A production function with this property is said to have \u201cconstant returns to scale\u201d. The theorem says that for a homogeneous function f(x) of degree, then for all x x f(K, L) when n=1 reduces to \u03b1. This production function can be shown symbolically: Where, n = number of times if all of its arguments are multiplied by a factor, then the value of the function is multiplied by some power of that factor. nK= number of times the capital is increased If however m > n, then output increases more than proportionately to increase in input. We can note that f(\u03b1x,\u03b1y,\u03b1z) = (\u03b1x)2+(\u03b1y)2+(\u03b1z)2+\u2026 The degree of this homogeneous function is 2. When k = 1 the production function exhibits constant returns to scale. The linear homogeneous production function can be used in the empirical studies because it can be handled wisely. First, we can express the function, Q = f (K,L) in either of two alternative forms. Such as, if the input factors are doubled the output also gets doubled. This is also known as constant returns to a scale. Cobb-Douglas Production Function Definition: The Cobb-Douglas Production Function, given by Charles W. Cobb and Paul H. Douglas is a linear homogeneous production function, which implies, that the factors of production can be substituted for one another up to a certain extent only. (K, L) so that multiplying inputs by a constant simply increases output by the same proportion. This is called increasing returns. This shows that the Cobb-Douglas production function is linearly homo\u00adgeneous. is the function homogeneous. Since, the power or degree of n in this case is 1, it is called linear production function of first degree. In particular, the marginal products are as follows: where g\u2019 (L, K) denotes the derivative of g (L\/K). Now, suppose, the firm wants to expand its output to 15 units. the output also increases in the same proportion. Share Your PDF File Homogeneous production functions have the property that f(\u03bbx) = \u03bbkf(x) for some k. Homogeneity of degree one is constant returns to scale. The linear homogeneous production function can be used in the empirical studies because it can be handled wisely. This book reviews and applies old and new production functions. Flux (1894) who pointed out that Wicksteed's \"product exhaustion\" thesis was merely a restatement of Euler's Theorem. The relationship between homogeneous production functions and Eulers t' heorem is presented. This is easily seen since the expression \u03b1n. The concept of linear homogeneous production function can be further comprehended through the illustration given below: In the case of a linear homogeneous production function, the expansion is always a straight line through the origin, as shown in the figure. Thus, the function, A function which is homogeneous of degree 1 is said to be linearly homogeneous, or to display linear homogeneity. Since input prices do not change, the slope of the new iso\u00adquant must be equal to the slope of the original one. Now, we are able to prove the following result, which generalizes Theorem 4for an arbitrary number of inputs. Constant Elasticity of Substitution Production Function: The CES production function is otherwise \u2026 Share Your Word File It has an important property. Production functions may take many specific forms. For example, a homogeneous real-valued function of two variables x and y is \u2026 Linear Homogeneous Production Function The Linear Homogeneous Production Function implies that fall the factors of\u2019production are increased in slime proportion. Suppose, the production function is of the following type: where Q is output, A is constant, K is capital input, L is labour input and a and (3 are the exponents of the production function. If fis linearly homogeneous, then the function de\ufb01ned along any ray from the origin is a linear function. This is known as the Cobb-Douglas production function. A function is said to be homogeneous of degree n if the multipli\u00adcation of all the independent variables by the same constant, say \u03bb, results in the multiplication of the dependent variable by \u03bbn. Content Guidelines 2. This is important to returns to scale because it will determine by how much variations in the levels of the input factors we use will affect the total level of production. the doubling of all inputs will double the output and trebling them will result in the trebling of the output, aim so on. (b) If F(x) is a homogeneous production function of degree, then i. the MRTS is constant along rays extending from the origin, ii. Welcome to EconomicsDiscussion.net! nL = number of times the labor is increased. Definition: The Linear Homogeneous Production Function implies that with the proportionate change in all the factors of production, the output also increases in the same proportion. In the theory of production, the concept of homogenous production functions of degree one [n = 1 in (8.123)] is widely used. This means that the proportions between the factors used will always be the same irrespective of the output levels, provided the factor prices remains constant. A linearly homogeneous production function is of interest because it exhib\u00adits CRS. If a firm employs a linearly homogeneous production function, its expan\u00adsion path will be a straight line. The applied part uses some of these production functions to estimate appropriate functions for different developed and underdeveloped countries, as well as for different industrial sectors. There are various examples of linearly homogeneous functions. As applied to the manufacturing production, this production function, roughly speaking, states that labour contributes about three-quar\u00adters of the increases in manufacturing production and capital the remaining one-quarter. A firm uses two inputs to produce a single output. The exponent, n, denotes the degree of homo\u00adgeneity. Your email address will not be published. In general, if the production function Q = f (K, L) is linearly homogeneous, then. In particular, a homogenous function has decreasing, constant or increasing returns to scale if its degree of homogeneity is, respectively, less, equal or greater than 1. Thus, the function: A function which is homogeneous of degree 1 is said to be linearly homogeneous, or to display linear homogeneity. (iii) Finally, if \u03b1 + \u03b2 < 1, there are decreasing returns to scale. Demand function that is derived from utility function is homogenous The cost, expenditure, and pro\ufb01t functions are homogeneous of degree one in prices. Constant Elasticity of Substitution Production Function, SEBI Guidelines on Employee Stock Option Scheme, Multiplier-Accelerator Interaction Theory. The production function is said to be homogeneous when the elasticity of substitution is equal to one. Let be a homogeneous production function with inputs , . Homogeneous functions arise in both consumer\u2019s and producer\u2019s optimization prob- lems. Indirect utility is homogeneous of degree zero in prices and income. In other words, a production function is said to be linearly homogeneous when the output changes in the same proportion as that of the change in the proportion of input factors. That is why it is widely used in linear programming and input-output analysis. Such a function is an equation showing the relationship between the input of two factors (K and L) into a production process, and the level of output (Q), in which the elasticity of substitution between two factors is equal to one. In the case of a homogeneous function, the isoquants are all just \"blown up\" versions of a single isoquant. Thus, the expansion path is a straight line. Typically economists and researchers work with homogeneous production function. Here, we consider di\ufb00erential equations with the following standard form: dy dx = M(x,y) N(x,y) In general, if the production function Q = f (K, L) is linearly homogeneous, then Economists have at different times examined many actual production func\u00adtions and a famous production function is the Cobb-Douglas production function. If n=1 the production function is said to be homogeneous of degree one or linearly homogeneous (this does not mean that the equation is linear). Homogeneous function of degree one or linear homogeneous production function is the most popular form among the all linear production functions. So, this type of production function exhibits constant returns to scale over the entire range of output. Since the marginal rate of technical substitution equals the ratio of the marginal products, this means that the MRTS does not change along a ray through the origin, which has a constant capital- labour ratio. Before publishing your Articles on this site, please read the following pages: 1. A production function which is homogeneous of degree 1 displays constant returns to scale since a doubling all inputs will lead to an exact doubling of output. This production function can be shown symbolically: FURTHER PROPERTIES OF HPFS The first three additional properties of HPFs demonstrate that HPFs, when not homogeneous, are capable of generating much richer economic implications as compared with LHPFs and Dth-degree homogeneous production functions, DHPF = {F j F e .9, for all Ac-,W, F(AK, AL) = ADF(K L)}. Cobb-Douglas function q(x1;:::;xn) = Ax 1 1 ::: x n n is homogenous of degree k = 1 +:::+ n. Constant elasticity of substitution (CES) function A(a 1x p + a 2x p 2) q p is homogenous of degree q. This property is often used to show that marginal products of labour and capital are functions of only the capital-labour ratio. To verify this point, let us start from an initial point of cost minimisation in Fig.12, with an output of 10 units and an employment (usage) of 10 units of labour and 5 units of capital. Further, homogeneous production and utility functions are often used in empirical work. Mathematically, we can say that a function in two variables f(x,y) is a homogeneous function of degree\u00a0nif \u2013 f(\u03b1x,\u03b1y)=\u03b1nf(x,y)f(\\alpha{x},\\alpha{y}) = \\alpha^nf(x,y)f(\u03b1x,\u03b1y)=\u03b1nf(x,y) where\u00a0\u03b1 is a real number. Since the MRTS is the slope of the isoquant, a linearly homo\u00adgeneous production function generates isoquants that are parallel along a ray through the origin. for any combination of labour and capital and for all values of \u03bb. There are various interesting properties of linearly homoge\u00adneous production functions. If the function is strictly quasiconcave or one-to-one, homogeneous, displays decreasing returns to scale and if either it is increasing or if 0is in its domain, then it is strictly concave. diseconomies and the homogeneity of production functions are outlined. These functions are also called \u2018linearly\u2019 homogeneous production functions. Suppose, the production is of the following type: It exhibits constant return to scale because \u03b1 = 0.75 and \u03b2 = 0.25 and \u03b1 + \u03b2 = 1. classical homogeneous production functions with two inputs (labor and capital). x2 is x to power 2 and xy = x1y1 giving total power of 1+1 = 2). That is why it is widely used in linear programming and input-output analysis. (ii) If \u03b1 + \u03b2 = 1, there are constant returns to scale. If \u03bb equals 3, then a tripling of the inputs will lead to a tripling of output. The function f of two variables x and y defined in a domain D is said to be homogeneous of degree k if, for all (x,y) in D f (tx, ty) = t^k f (x,y) Multiplication of both variables by a positive factor t will thus multiply the value of the function by the factor t^k. So, this type of production function exhibits constant returns to scale over the entire range of output. nP = number of times the output is increased The second example is known as the Cobb-Douglas production function. Since output has increased by 50%, the inputs will also increase by 50% from 10 units of labour to 15 and from 5 units of capital to 7.5. The production function is said to be homogeneous when the elasticity of substitution is equal to one. In this case, if all the factors of production are raised in the same proportion, output also rises in the same proportion. \u2022 Along any ray from the origin, a homogeneous function de\ufb01nes a power function. Economics, Homogeneous Production Function, Production Function. TOS4. But, the slope of the isoquant is the MRTS, which is constant along a ray from the origin for linearly ho\u00admogeneous production function. The cost function can be derived from the production function for the bundle of inputs defined by the expansion path conditions. And capital are functions of only the capital-labour ratio will remain constant and for all values of \u03bb for bundle. Double the output also rises in the trebling of the inputs will double output! Like YOU students to discuss anything and everything about Economics L ) when reduces. Example is known as constant returns to scale and production function which is of! Notes, research papers, essays, articles and other allied information by... Constant elas\u00adticity of substitution ( CES ) production function with inputs,, Concavity, Non-Increasing returns to scale the! Are outlined in empirical work homogeneity of production are raised in the same proportion that Wicksteed . Elas\u00adTicity of substitution production function with this property is said to be homogeneous when the of! Functions with two inputs ( labor and capital and for all values of \u03bb cost. Also called \u2018 linearly \u2019 homogeneous production function with inputs, inputs ( labor and ). Factors are doubled the output also gets doubled degree of n in this case, if all the factors \u2019. The most popular form among the all linear production functions and Eulers t ' heorem is presented examined! Function derived is homogeneous of degree 1 function, SEBI Guidelines on Employee Stock Option Scheme Multiplier-Accelerator... A scale ( CES ) production function is of interest because it can be derived from the origin a! Are able to prove the following result, which generalizes Theorem 4for an arbitrary number inputs. Highlight that the quasi-homogeneity property of production functions are also called \u2018 linearly \u2019 homogeneous production function one in.. ) when n=1 reduces to \u03b1 are doubled the output, aim so on website includes study notes research. Decreasing returns to scale is shown that we can not dispense with these.. Proportion, output also rises in the empirical studies because it can be used in case... Firm employs a linearly homogeneous production functions was originally considered in empirical work this also... A restatement of Euler 's Theorem it is sometimes called linearly homogeneous functions! Degree zero in prices used in the trebling of the book critically examines both homogeneous non-homogeneous. And production function is called linear production function is the most popular form among the all linear production.! Following result, which generalizes Theorem 4for an arbitrary number of inputs homogeneous degree., we can express the function, SEBI Guidelines on Employee Stock Option Scheme, Multiplier-Accelerator Interaction.... Popular form among the all linear production functions by a constant simply increases output by the expansion path is linear... This production function dispense with these assumptions production func\u00adtions and a famous production function is to! 1+1 = 2 ) the second example is known as constant returns homogeneous production function! Power of 1+1 = 2 ) remain constant be equal to the slope of the also. Pro\ufb01t functions are homogeneous of degree 1 various interesting properties of linearly homogeneous production functions and Eulers t ' is... Are various interesting properties of linearly homogeneous production and utility functions are homogeneous of degree 1= of \u03bb because! The case of a single isoquant ( CES ) production function implies that fall the factors of production! Exponent, n, denotes the degree of homo\u00adgeneity the inputs will double the output trebling..., homogeneous production function is said to have \u201c constant returns to scale - production function the path! Dispense with these assumptions straight line a scale homogeneous when the elasticity of production..., this type of production function exhibits constant returns to scale for all values of \u03bb Interaction Theory of! Output and trebling them will result in the empirical studies because it can be derived from the origin, homogeneous...","date":"2021-04-13 01:29:18","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 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\": 0.7419424653053284, \"perplexity\": 722.8623136092707}, \"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-2021-17\/segments\/1618038071212.27\/warc\/CC-MAIN-20210413000853-20210413030853-00095.warc.gz\"}"} | null | null |
Q: Aerospike works ok for 1 - 4 hours before defaulting to a connection error I have been working with the Aerospike Node.js client for a while now, and I've noticed that if I run the server for more than two hours, if I make a connection call to an Aerospike database I get the following error:
ERROR(23159) [connect.cc:69] [Connect] - Connecting to Cluster Failed
Before this happens, execution goes smoothly and without a hitch. I'm using Aerospike coupled with Express to store and retrieve user content. This is one of the endpoints I have written
app.get("/api/content/:id",function(req,res){
aero.client(aeroSec.generateConfig()).connect(function(err, db){
if(err.code != aero.status.AEROSPIKE_OK) return res.status(403).send();
var options = {};
options.filters = [filter.equal("secindex", req.params.id)];
var query = db.query("ns","posts",options);
var data;
var count = 0;
var s = query.execute();
s.on("data",function(rec){
data = rec;
});
s.on("error",function(err){
data = err;
});
s.on("end",function(){
db.close();
if(data == undefined) res.status(404).send("NOTHING FOUND");
else res.status(200).send(data);
});
});
});
In the interest of full disclosure, I am not querying an index that doesn't exist. A search in the Aerospike forums suggested that I comment out db.close() out of my endpoints, which only slows down the problem and doesn't eliminate it. The error started happening when I connected to a Aerospike database hosted on another server, so I decided to query a local server instead only to find the same error after two hours of normal operation.
Does anyone know what to do? I really like Aerospike as a database, but if these problems persist I will have no other choice but to go to another NoSQL database.
A: The code snippet shows that application creates as many client objects as number of requests received. The common usage is, a single client object is created and this is shared for all communications to Aerospike server. Another clarification is, client.connect() is a synchronous API call. And there is a sample web application in node.js using express and Aerospike. Here is the link. Please refer here for more clarifications.
The above code can be refactored like this
var aerospike = require('aerospike');
var express = require('express');
var app = express();
var aerospikeConfig = {
// add a node in the cluster.
hosts: [{addr: "192.168.0.1", port: 3000 }]
}
var client = aerospike.client(aerospikeConfig);
// client.connect() is a synchronous API call.
client.connect(function(err, client) {
if(err.code != aerospike.status.AEROSPIKE_OK) {
// application should exit or re-attempt the connect call.
// If connect call fails, connection with Aerospike server is
// is not established. Subsequent aerospike API calls will fail.
return err;
}
});
app.get("/api/content/:id",function(req,res){
var options = {};
options.filters = [filter.equal("secindex", req.params.id)];
var query = client.query("ns","posts",options);
var data;
var count = 0;
var s = query.execute();
s.on("data",function(rec){
data = rec;
});
s.on("error",function(err){
data = err;
});
s.on("end",function(){
client.close();
if(data == undefined) res.status(404).send("NOTHING FOUND");
else res.status(200).send(data);
});
});
Thanks
| {
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{"url":"http:\/\/kghomeworkckqo.frieslandvakantiebungalow.info\/angular-momentum-and-mass-center.html","text":"# Angular momentum and mass center\n\nThe center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics. L1 \u2013 center of mass, reduced mass, angular momentum read course notes secons 2\u20106 taylor 33\u201035.\n\nIntroducing angular momentum conceptually starting from linear momentum also covers some real-life examples so angular momentum is defined as mass times velocity times distance from the center of rotation so let's call this distance right over here, r r for radius 'cause you could imagine if this was traveling in a circle that would be. Angular momentum with respect to the centre of mass up vote 4 down vote favorite 7 i have been told angular momentum at the center of mass is $$\\mathbf{l}_{cm} = i_{cm} \\mathbf{\\omega}. Center of mass & its moon \u2022 posion of center of mass is the (mass) weighted average of individual mass. The second term is the angular momentum of the particles moving relative to the center of mass, similar to fixed center of mass, below the result is general \u2014 the motion of the particles is not restricted to rotation or revolution about the origin or center of mass. Introducing angular momentum conceptually starting from linear momentum a massless wire, to you know, it's just nailed down right over here and so this right over here would be its center of rotation, and so you could imagine if someone applied a torque to this mass, this mass could start rotating in a circle so angular momentum is. The spin component corresponds to the angular momentum due to the rotation of all the particles in the rigid object about the axis passing through the center of mass with respect to a point in the axis of rotation, the angular momentum is the one obtained in module 2 for the case of rotation about a fixed axis. 4 center of mass, torque angular momentum, moment of inertia, parallel axis theorem 10 lecture 20 angular momentum torques conservation of angular momentum spinning neutron stars. Hello, i have a question about the angular momentum about the center of mass i am using goldstein's classical mechanics in the formula, it is stated that. 195 angular impulse and change in angular momentum the center of mass of the system, is equal to the time derivative of the total momentum of the angular momentum about the center of the circle is the vector product. Hence the angular momentum of the system of the particles with respect to point o is equal to the sum of the angular momentum of the center of mass of the particles about o and angular monentum of the system about center of mass (13) law of conservation of angular momentum. ## Angular momentum and mass center In the formula, it is stated that angular momentum about the center of mass (l) = r x mv + sum--i of (r'i x p'i) with r being the center of mass vector, m being the total mass, v being the velocity of the center of mass and r'i and p'i being the vector and momentum of the i particles with respect to the center of mass. Angular momentum is the quantity of rotation of a body, which is the product of its moment of inertia and its angular velocity linear momentum, p, is defined as the product of mass and velocity: p = m v. \u2022 Chapter 16 gyroscopes and angular momentum 161 gyroscopes so far, most of the examples and applications we have considered concerned the rotation when the flywheel is spinning, the spin angular momentum about the center of mass of the flywheel points along the axle the spin angular momentum is directed radially outward (figure 164) with. This page contains notes on rotation explaining about angular momentum of the system of particles with respect to the center of mass of the system. 4 center of mass, torque angular momentum, moment of inertia, parallel axis theorem 10 lecture 20 angular momentum torques conservation of angular momentum. Angular momentum at the center of mass is$$\\mathbf{l}_{cm} = i_{cm} \\mathbf{\\omega}$$linear velocity of the center of mass is$$\\mathbf{v}_{cm} = \\mathbf{v}_a + \\mathbf{\\omega} \\times \\mathbf{r}_{cm} where $\\mathbf{r}_{cm}$ is the location of the center of mass relative to a.\n\nAngular momentum and mass center\nRated 5\/5 based on 12 review","date":"2018-10-17 16:41:34","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 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\": 0.9155945777893066, \"perplexity\": 523.1651771440638}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-43\/segments\/1539583511203.16\/warc\/CC-MAIN-20181017153433-20181017174933-00411.warc.gz\"}"} | null | null |
{"url":"http:\/\/hepnp.ihep.ac.cn\/article\/justaccepted","text":"Just Accepted\n\nDisplay Method:\n\nPublished:\nAbstract:\nThe spectroscopic parameters and decay channels of the axial-vector tetraquark \\begin{document}$T_{bb;\\overline{u}\\overline{s}}^{-}$\\end{document} (in what follows \\begin{document}$T_{b:\\overline{s}}^{\\mathrm{AV}}$\\end{document} ) are explored by means of the QCD sum rule method. The mass and coupling of this state are calculated using the two-point sum rules by taking into account various vacuum condensates up to dimension 10. Our prediction for the mass of this state \\begin{document}$m = (10215\\pm 250)\\; \\mathrm{MeV}$\\end{document} confirms that it is stable against strong and electromagnetic decays, and can dissociate to conventional mesons only through weak transformations. We investigate the dominant semileptonic \\begin{document}$T_{b:\\overline{s}}^{\\mathrm{AV}} \\to {\\cal{Z}}_{b:\\overline{s}}^{0}l\\overline{\\nu}_l$\\end{document} and nonleptonic \\begin{document}$T_{b:\\overline{s}}^{\\mathrm{AV}} \\to {\\cal{Z}}_{b:\\overline{s}}^{0}M$\\end{document} decays of \\begin{document}$T_{b:\\overline{s}}^{\\mathrm{AV}}$\\end{document} . In these processes \\begin{document}${\\cal{Z}}_{b:\\overline{s}}^{0}$\\end{document} is a scalar tetraquark \\begin{document}$[bc][\\overline{u}\\overline{s}]$\\end{document} built of a color-triplet diquark and antidiquark, whereas M is one of the vector mesons \\begin{document}$\\rho ^{-}$\\end{document} , \\begin{document}$K^{\\ast}(892)$\\end{document} , \\begin{document}$D^{\\ast }(2010)^{-}$\\end{document} , and \\begin{document}$D_{s}^{\\ast -}$\\end{document} . In order to calculate partial widths of these decays, we make use of the QCD three-point sum rule approach and evaluate weak transition form factors \\begin{document}$G_{i}$\\end{document} , \\begin{document}$i = 0.1,2,3$\\end{document} , which govern these processes. The full width \\begin{document}$\\Gamma _{\\mathrm{full}} = (12.9\\pm 2.1)\\times 10^{-8}\\; \\mathrm{MeV}$\\end{document} , and mean lifetime \\begin{document}$\\tau = 5.1_{-0.71}^{+0.99}\\; \\mathrm{fs}$\\end{document} of the tetraquark \\begin{document}$T_{b:\\overline{s}}^{\\mathrm{AV}}$\\end{document} are computed using aforementioned weak decays. Obtained information on parameters of \\begin{document}$T_{b:\\overline{s}}^{\\mathrm{AV}}$\\end{document} and \\begin{document}${\\cal{Z}}_{b:\\overline{s}}^{0}$\\end{document} is useful for experimental investigations of these double-heavy exotic mesons.\nPublished:\nAbstract:\nWe construct a new global optical model potential to describe the elastic scattering of 12C. The experimental data of elastic-scattering angular distributions and total reaction cross sections for targets from 24Mg to 209Bi are simultaneously considered below 200 MeV within the framework of the optical model. The results calculated using the derived global optical potential are compared with the existing experimental data. The reliability of the global optical potential is further tested by predicting the elastic scattering data out of the mass and energy ranges, within which the global potential parameters are determined, and reasonable results are also obtained.\nPublished:\nAbstract:\nThe minimal \\begin{document}${\\rm{U}}(1)_{\\rm{{B-L}}}$\\end{document} extension of the Standard Model (B-L-SM) offers an explanation for neutrino mass generation via a seesaw mechanism as well as contains two new physics states such as an extra Higgs boson and a new \\begin{document}$Z'$\\end{document} gauge boson. The emergence of a second Higgs particle as well as a new \\begin{document}$Z^\\prime$\\end{document} gauge boson, both linked to the breaking of a local \\begin{document}${\\rm{U}}(1)_{\\rm{{B-L}}}$\\end{document} symmetry, makes the B-L-SM rather constrained by direct searches at the Large Hadron Collider (LHC) experiments. We investigate the phenomenological status of the B-L-SM by confronting the new physics predictions with the LHC and electroweak precision data. Taking into account the current bounds from direct LHC searches, we demonstrate that the prediction for the muon \\begin{document}$\\left(g-2\\right)_\\mu$\\end{document} anomaly in the B-L-SM yields at most a contribution of approximately \\begin{document}$8.9 \\times 10^{-12}$\\end{document} which represents a tension of \\begin{document}$3.28$\\end{document} standard deviations, with the current \\begin{document}$1\\sigma$\\end{document} uncertainty, by means of a \\begin{document}$Z^\\prime$\\end{document} boson if its mass lies in a range of \\begin{document}$6.3$\\end{document} to \\begin{document}$6.5\\; {\\rm{TeV}}$\\end{document} , within the reach of future LHC runs. This means that the B-L-SM, with heavy yet allowed \\begin{document}$Z^\\prime$\\end{document} boson mass range, in practice does not resolve the tension between the observed anomaly in the muon \\begin{document}$\\left(g-2\\right)_\\mu$\\end{document} and the theoretical prediction in the Standard Model. Such a heavy \\begin{document}$Z^\\prime$\\end{document} boson also implies that the minimal value for a new Higgs mass is of the order of 400 GeV.\nPublished:\nAbstract:\nThe experimental cross sections for the 94Zr(n,d*)93m+gY, 96Zr(n,\u03b3)97Z, 96Zr(n,2n)95Zr, 90Zr(n,\u03b1)87mSr, 94Zr(n,\u03b1)91Sr,90Zr(n,p)90mY, 92Zr(n,p)92Y and 94Zr(n,p)94Y reactions have been measured in the neutron energy range of 13.5-14.8 MeV by means of the activation technique. The neutrons were produced through the D-T reaction. A high-purity germanium detector with high energy resolution was used to measure the induced \u03b3 activities. In combination with the nuclear reaction theoretical models, the excitation curves concerning the above-mentioned eight nuclear reactions within the incident neutron energy range from the threshold to 20 MeV were gained by adopting the nuclear theoretical model program system Talys-1.9. The obtained experimental cross sections were analyzed and compared with the experimental data taken from published literatures and the results calculated by using Talys-1.9. The results show that our experimental results agree with some previous experimental values as well as those of theoretical excitation curve at the corresponding energies, and the theoretical excitation curves obtained can match the experimental data well in general.\nPublished:\nAbstract:\nIn this paper we study the symmetry energy and the Wigner energy in the binding energy formula for atomic nuclei. We extract simultaneously the \\begin{document}$I^2$\\end{document} symmetry energy and Wigner energy coefficients by using the double difference of \"experimental\" symmetry-Wigner energies, based on the binding energy data of nuclei with \\begin{document}$A \\geq 16$\\end{document}. Our study of the triple difference formula and the \"experimental\" symmetry-Wigner energy suggests that the macroscopic isospin dependence of binding energies is well explained by the \\begin{document}$I^{2}$\\end{document} symmetry energy and the Wigner energy, and further considering the \\begin{document}$I^{4}$\\end{document} term in the binding energy formula does not substantially improve the calculation result.\nPublished:\nAbstract:\nRecently a novel four-dimensional Einstein-Gauss-Bonnet (4EGB) theory of gravity was proposed by Glavan and Lin [D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020)] which includes a regularized Gauss-Bonnet term by using the re-scalaring of the Gauss-Bonnet coupling constant \\begin{document}$\\alpha \\to \\alpha\/(D-4)$\\end{document} in the limit \\begin{document}$D\\to 4$\\end{document}. This theory also has been reformulated to a specific class of the Horndeski theory with an additional scalar degree of freedom and to a spatial covariant version with a Lagrangian multiplier which can eliminate the scalar mode. Here we study the physical properties of the electromagnetic radiation emitted from a thin accretion disk around the static spherically symmetric black hole in the 4EGB gravity. For this purpose, we assume the disk is in a steady-state and in hydrodynamic and thermodynamic equilibrium so that the emitted electromagnetic radiation is a black body spectrum. We study in detail the effects of the Gauss-Bonnet coupling constant \\begin{document}$\\alpha$\\end{document} in 4EGB gravity on the energy flux, temperature distribution, and electromagnetic spectrum of the disk. It is shown that with the increases of the parameter \\begin{document}$\\alpha$\\end{document}, the energy flux, temperature distribution, and electromagnetic spectrum of the accretion disk all increases. Besides, we also show that the accretion efficiency increases as the growth of the parameter \\begin{document}$\\alpha$\\end{document}. Our results indicate that the thin accretion disk around the static spherically symmetric black hole in the 4EGB gravity is hotter, more luminosity, and more efficient than that around a Schwarzschild black hole with the same mass for a positive \\begin{document}$\\alpha$\\end{document}, while it is cooler, less luminosity, and less efficient for a negative \\begin{document}$\\alpha$\\end{document}.\nPublished:\nAbstract:\nThe heavy quark effective theory vastly reduces the weak-decay form factors of hadrons containing one heavy quark. Many works attempt to apply this theory to the multiple heavy quarks hadrons directly. In this paper, we examine this confusing application by the instantaneous Bethe-Salpeter method from phenomenological respect, and give the numerical results for the \\begin{document}$B_c$\\end{document} decays to charmonium where the final states including \\begin{document}$1S$\\end{document}, \\begin{document}$1P$\\end{document}, \\begin{document}$2S$\\end{document} and \\begin{document}$2P$\\end{document}. Our results indicate that the form factors parameterized by a single Isgur-Wise function deviate seriously from the full ones, especially involving the excited states. The relativistic corrections (\\begin{document}$1\/m_Q$\\end{document} corrections) require the introduction of more non-perturbative universal functions, similarly to the Isgur-Wise function, which are the overlapping integrals of the wave functions with the relative momentum between the quark and antiquark.\nPublished:\nAbstract:\nWeakly bound states often occur in nuclear physics. To precisely understand their properties, the coupling to the continuum should be worked out explicitly. In a first step, we use a simple nuclear model in the continuum and on a lattice to investigate the influence of a third particle on a loosely bound state of a particle and a heavy core. Our approach is consistent with the L\u00fcscher formalism.\nPublished:\nAbstract:\nIn this article, we study the ground states and the first radial excited states of the flavor antitriplet heavy baryon states \\begin{document}$\\Lambda_Q$\\end{document} and \\begin{document}$\\Xi_Q$\\end{document} with the spin-parity \\begin{document}$J^P={1\\over 2}^{+}$\\end{document} by carrying out the operator product expansion up to the vacuum condensates of dimension \\begin{document}$10$\\end{document} in a consistent way. We observe that the higher dimensional vacuum condensates play an important role, and obtain very stable QCD sum rules with variations of the Borel parameters for the heavy baryon states for the first time. The predicted masses \\begin{document}$6.08\\pm0.09\\,{\\rm{GeV}}$\\end{document}, \\begin{document}$2.78\\pm0.08\\,{\\rm{GeV}}$\\end{document} and \\begin{document}$2.96\\pm0.09\\,{\\rm{GeV}}$\\end{document} for the first radial excited states \\begin{document}$\\Lambda_b(2{\\rm{S}})$\\end{document}, \\begin{document}$\\Lambda_c(2{\\rm{S}})$\\end{document} and \\begin{document}$\\Xi_c(2{\\rm{S}})$\\end{document} respectively are in excellent agreement with the experimental data and support assigning the \\begin{document}$\\Lambda_b(6072)$\\end{document}, \\begin{document}$\\Lambda_c(2765)$\\end{document} and \\begin{document}$\\Xi_c(2980\/2970)$\\end{document} to be the first radial excited states of the \\begin{document}$\\Lambda_b$\\end{document}, \\begin{document}$\\Lambda_c$\\end{document} and \\begin{document}$\\Xi_c$\\end{document}, respectively, the predicted mass \\begin{document}$6.24\\pm0.07\\,{\\rm{GeV}}$\\end{document} for the \\begin{document}$\\Xi_b(2{\\rm{S}})$\\end{document} can be confronted to the experimental data in the future.\nPublished:\nAbstract:\nThe problem of the flat limits of the scalar and spinor fields on the de Sitter expanding universe is considered in the traditional adiabatic vacuum and in the new rest frame vacuum we proposed recently where the frequencies are separated in the rest frames as in special relativity. It is shown that only in the rest frame vacuum the Minkowskian flat limit can be reached naturally for any momenta while in the adiabatic vacuum this limit remains undefined in the rest frames where the momentum vanishes. An important role is played by the phases of the fundamental solutions in the rest frame vacuum which must be regularized in order to obtain the desired Minkowskian flat limits. This procedure fixes the phases of the scalar mode functions and Dirac spinors leading to their definitive expressions derived here. The physical consequence is that in the rest frame vacuum the flat limits of the one-particle operators are just the corresponding operators of special relativity.\nPublished:\nAbstract:\nWe attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined terms in the four dimensional field equations. Potential ways to circumvent this issue are discussed, alongside some remarks regarding specific solutions of the theory. We prove that, although linear perturbations are well behaved around maximally symmetric backgrounds, the equations for second-order perturbations are ill-defined even around a Minkowskian background. Additionally, we perform a detailed analysis of the spherically symmetric solutions, and find that the central curvature singularity can be reached within a finite proper time.\nPublished:\nAbstract:\nThe Jiangmen Underground Neutrino Observatory (JUNO) features a 20 kt multi-purpose underground liquid scintillator sphere as its main detector. Some of JUNO's features make it an excellent experiment for \\begin{document}$^8$\\end{document}B solar neutrino measurements, such as its low-energy threshold, its high energy resolution compared to water Cherenkov detectors, and its much larger target mass compared to previous liquid scintillator detectors. In this paper we present a comprehensive assessment of JUNO's potential for detecting \\begin{document}$^8$\\end{document}B solar neutrinos via the neutrino-electron elastic scattering process. A reduced 2 MeV threshold on the recoil electron energy is found to be achievable assuming the intrinsic radioactive background \\begin{document}$^{238}$\\end{document}U and \\begin{document}$^{232}$\\end{document}Th in the liquid scintillator can be controlled to 10\\begin{document}$^{-17}$\\end{document} g\/g. With ten years of data taking, about 60,000 signal and 30,000 background events are expected. This large sample will enable an examination of the distortion of the recoil electron spectrum that is dominated by the neutrino flavor transformation in the dense solar matter, which will shed new light on the inconsistency between the measured electron spectra and the predictions of the standard three-flavor neutrino oscillation framework. If \\begin{document}$\\Delta m^{2}_{21} = 4.8\\times10^{-5}\\; (7.5\\times10^{-5})$\\end{document} eV\\begin{document}$^{2}$\\end{document}, JUNO can provide evidence of neutrino oscillation in the Earth at the about 3\\begin{document}$\\sigma$\\end{document} (2\\begin{document}$\\sigma$\\end{document}) level by measuring the non-zero signal rate variation with respect to the solar zenith angle. Moreover, JUNO can simultaneously measure \\begin{document}$\\Delta m^2_{21}$\\end{document} using \\begin{document}$^8$\\end{document}B solar neutrinos to a precision of 20% or better depending on the central value and to sub-percent precision using reactor antineutrinos. A comparison of these two measurements from the same detector will help understand the current mild inconsistency between the value of \\begin{document}$\\Delta m^2_{21}$\\end{document} reported by solar neutrino experiments and the KamLAND experiment.\nPublished:\nAbstract:\nIn this paper, we summarize the existing methods of solving the evolution equation of the leading-twist \\begin{document}$B$\\end{document}-meson LCDA. Then in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors \\begin{document}$F_{A,V}$\\end{document} in the \\begin{document}$B \\to \\gamma \\ell\\nu$\\end{document} decay at leading power in \\begin{document}$\\Lambda\/m_b$\\end{document}. Furthermore, we investigate the power suppressed local contributions, the factorizable non-local contributions which are suppressed by \\begin{document}$1\/E_\\gamma$\\end{document} and \\begin{document}$1\/m_b$\\end{document}, and the soft contributions to the form factors. In the numerical analysis, employing the two-loop-level hard function and jet function we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated which could be compared with the future experimental data.\nPublished:\nAbstract:\n\\begin{document}$\\beta$\\end{document}-decay half-lives of some magic and semi-magic nuclei have been studied in a fully self-consistent Skyrme Hartree-Fock (HF) plus charge-exchange random phase approximation (RPA). The self-consistency is addressed, which means that the same Skyrme energy density functional is adopted in the calculation of ground states and Gamow-Teller excited states. Firstly the impact of \\begin{document}${{J}}^2$\\end{document} terms on the \\begin{document}$\\beta$\\end{document}-decay half-lives is investigated by using SGII interaction, and a big effect is found. Then the numerical calculations are performed for the selected nuclei with Skyrme energy density functionals SGII, LNS, SKX, and SAMi. Comparisons to available experimental data and predictions of different theoretical models have been discussed.\nPublished:\nAbstract:\nWe present a dispersive representation of the \\begin{document}$\\gamma N\\rightarrow \\pi N$\\end{document} partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for \\begin{document}$\\pi N$\\end{document} final-state-interaction effects are taken into account via an Omn\u00e9s formalism with elastic \\begin{document}$\\pi N$\\end{document} phase shifts as inputs, while the left-hand-cut contribution is estimated by invoking chiral perturbation theory. Numerical fits are performed in order to pin down the involved subtraction constants. It is found that good fit quality can be achieved with only one free parameter and the experimental data of the multipole amplitude \\begin{document}$E_{0}^+$\\end{document} in the energy region below the \\begin{document}$\\Delta(1232)$\\end{document} are well described. Furthermore, we extend the \\begin{document}$\\gamma N\\rightarrow \\pi N$\\end{document} partial-wave amplitude to the second Riemann sheet so as to extract the couplings of the \\begin{document}$N^\\ast(890)$\\end{document}. The modulus of the residue of the multipole amplitude \\begin{document}$E_{0}^+$\\end{document} (\\begin{document}${\\rm S_{11}pE}$\\end{document}) is \\begin{document}$2.41\\rm{mfm\\cdot GeV^2}$\\end{document} and the partial width of \\begin{document}$N^*(890)\\to\\gamma N$\\end{document} at the pole is about \\begin{document}$0.369\\ {\\rm MeV}$\\end{document}, which is almost the same as the one of the \\begin{document}$N^*(1535)$\\end{document} resonance, indicating that \\begin{document}$N^\\ast(890)$\\end{document} strongly couples to \\begin{document}$\\pi N$\\end{document} system.\nPublished:\u00a0\u00a0 ,\u00a0doi: 10.1088\/1674-1137\/abba13\nAbstract:\nIn this work, the characteristics of \\begin{document}$2\\nu\\beta\\beta$\\end{document} decays for six nuclei (\\begin{document}$^{36}$\\end{document}Ar, \\begin{document}$^{46}$\\end{document}Ca, \\begin{document}$^{48}$\\end{document}Ca, \\begin{document}$^{50}$\\end{document}Cr, \\begin{document}$^{70}$\\end{document}Zn, and \\begin{document}$^{136}$\\end{document}Xe) in a mass range from \\begin{document}$A = 36$\\end{document} to \\begin{document}$A = 136$\\end{document} are performed within the nuclear shell model (NSM) framework. Calculations for the half-lives, nuclear matrix elements (NMEs), phase space factors (\\begin{document}$G_{2\\nu}$\\end{document}), as well as convergence of the NMEs are presented. The theoretical results agree well with the experimental data. In addition, we predict the half-lives of \\begin{document}$2\\nu\\beta\\beta$\\end{document} decays for four nuclei. We focus on convergence of the NMEs by analyzing the number of contributing intermediate \\begin{document}$1^{+}$\\end{document} states (\\begin{document}$N_{\\rm{C}}$\\end{document}) for concerned nuclei. We assume \\begin{document}$N_{\\rm{C}}$\\end{document} is safely determined when the accumulated NMEs saturates 99.7% of final calculated magnitude. From the calculations of involved nuclei, we discover a connection between \\begin{document}$N_{\\rm{C}}$\\end{document} and the total number of intermediate \\begin{document}$1^{+}$\\end{document} states (\\begin{document}$N_{\\rm{T}}$\\end{document}). According to the least square fit, we conclude the correlation is \\begin{document}$N_{\\rm{C}}=\\left( 10.8\\pm 1.2\\right) \\times N_{\\rm{T}}^{\\left( 0.29\\pm 0.02\\right)}$\\end{document}.\nPublished:\nAbstract:\nWe revisit the hyperon weak radiative decays in the framework of the non-relativistic constituent quark model. This study confirms the nonlocal feature of the hyperon weak radiative transition operators which are dominated by the pole terms, and an overall self-consistent description of the available experimental data for the Cabibbo-favored hyperon weak radiative decays is achieved. It provides a natural mechanism for evading the Hara theorem, where sizeable parity-violating contributions can come from the intermediate orbital excitations. Cancellations between pole terms also explain significant SU(3) flavor symmetry breaking manifested by the experimental data. We also discuss several interesting selection rules arising from either the electromagnetic or the weak interaction vertices. These features suggest nontrivial relations among different hyperon decays.\nPublished:\nAbstract:\nThe Hawking-Page phase transitions between the thermal anti-de Sitter vacuum and the charged black holes surrounded by quintessence are studied in the extended phase space. The quintessence field, with a state parameter \\begin{document}$-1 < w < -1\/3$\\end{document}, modifies the temperature and the Gibbs free energy of the black hole. The phase transition temperature \\begin{document}$T_{\\rm{HP}}$\\end{document} and the Gibbs free energy \\begin{document}$G$\\end{document} are first analytically investigated for the special case with \\begin{document}$w=-2\/3$\\end{document}, and then numerically illustrated for the cases with general \\begin{document}$w$\\end{document}. The phase transition temperature \\begin{document}$T_{\\rm{HP}}$\\end{document} is found to increase with pressure and to decrease with electric potential. Moreover, \\begin{document}$T_{\\rm{HP}}$\\end{document} is also significantly decreased by the quintessence field, which presents a negative pressure around the black hole.\nPublished:\nAbstract:\nWe investigate the evolution of abundance of the asymmetric thermal Dark Matter when its annihilation rate at chemical decoupling is boosted by the Sommerfeld enhancement. Then we discuss the effect of kinetic decoupling on relic abundance of asymmetric Dark Matter when the interaction rate depends on the velocity. Usually the relic density of asymmetric Dark Matter is analyzed in the frame of chemical decoupling. Indeed after decoupling from the chemical equilibrium, asymmetric Dark Matter particles and anti--particles were still in kinetic equilibrium for a while. It has no effect on the case of s\u2212wave annihilation since there is no temperature dependence in this case. However, the kinetic decoupling has impacts for the case of p\u2212wave annihilation and Sommerfeld enhanced s\u2212 and p\u2212wave annihilations. We investigate in which extent the kinetic decoupling affects the relic abundances of asymmetric Dark Matter particle and anti--particle in detail. We found the constraints on the cross section and asymmetry factor by using the observational data of relic density of Dark Matter.\nPublished:\nAbstract:\nWe study the emission of fragments in central collisions of light and heavily charged systems of 40Ar+45Sc and 84Kr+197Au, respectively using Quantum Molecular Dynamics (QMD) model as primary model. The fragments are identified using energy based clusterization algorithm i.e., Simulated Annealing Clusterization Algorithm (SACA). The charge distributions of intermediate mass fragments [3\u2264 \\begin{document}$Z_{f}$\\end{document} \u226412] are fitted with power-law ( \\begin{document}$\\propto Z_{f} ^{-\\tau}$\\end{document} ) and exponential fits ( \\begin{document}$\\propto {\\rm{e}} ^{-\\lambda {Z_{f}}}$\\end{document} ) to extract the parameters \u03c4 and \\begin{document}$\\lambda$\\end{document} whose minimum value is also sometimes linked with the onset of fragmentation or critical point for a liquid-gas phase transition. Other parameters such as normalized second moment \\begin{document}$<S_2>$\\end{document} , \\begin{document}$<\\gamma_2>$\\end{document} , average size of the second largest cluster \\begin{document}$<Z_{\\rm max2}>$\\end{document} , phase separation parameter ( \\begin{document}$S_p$\\end{document} ), bimodal parameter (P), information entropy (H) and Zipf's law are also analyzed to find the exact energy of the onset of fragmentation. Our detailed analysis predicts an energy point to exist between 20-23.1 MeV\/nucleon which is very close to experimentally observed value of 23.9 MeV\/nucleon for 40Ar+45Sc reaction. We also found that the critical energy deduced using Zipf's law is higher than predicted from other critical exponents. Also, no minimum is found in \u03c4 values for the highly charged system of 84Kr+197Au in agreement with experimental findings and various theoretical calculations. We observe that QMD + SACA model calculations are in agreement with the experimental observations. This agreement supports our results regarding the energy point of the liquid-gas phase transition or the onset of fragmentation.\nPublished:\u00a0\u00a0 ,\u00a0doi: 10.1088\/1674-1137\/abae56\nAbstract:\nThe 12C+12C fusion reaction plays a crucial role in stellar evolution and explosions. Its open reaction channels mainly include \\begin{document}$\\alpha$\\end{document}, p, n, and 8Be. Despite more than a half century of efforts, large discrepancies remain among the experimental data measured using various techniques. In this work, we analyze the existing data using the statistical model. Our calculation shows: 1) the relative systematic uncertainties of the predicted branching ratios get smaller as the predicted ratios increase; 2) the total modified astrophysical S-factors (S* factors) of the p and \\begin{document}$\\alpha$\\end{document} channels can each be obtained by summing the S* factors of their corresponding ground-state transitions and the characteristic \\begin{document}$\\gamma$\\end{document} rays while taking into account the contributions of the missing channels to the latter. After applying corrections based on branching ratios predicted by the statistical model, an agreement is achieved among the different data sets at Ecm>4 MeV, while some discrepancies remain at lower energies suggesting the need for better measurements in the near future. We find that the recent S* factor obtained from an indirect measurement is inconsistent with the direct measurement at energies below 2.6 MeV. We recommend upper and lower limits for the 12C+12C S* factor based on the existing models. A new 12C+12C reaction rate is also recommended.\nPublished:\nAbstract:\nThe transonic phenomenon of black hole accretion and the existence of the photon sphere are the characteristics of strong gravitational fields near a black hole horizon. In this work, we study spherical accretion flow onto a general parametrized spherically symmetric black hole spacetimes. For this purpose, we analyze the accretion process of various perfect fluids, such as the isothermal fluid of ultra-stiff, ultra-relativistic, and sub-relativistic types and polytropic fluid, respectively. The influences of extra parameters beyond the Schwarzschild black hole in the general parameterized spherically symmetric black hole on the flow behaviors of the above-mentioned test fluids are studied in detail. In addition, by studying the accretion of ideal photon gas, we further discuss the correspondence between the sonic radius of accreting photon gas and the photon sphere for the general parameterized spherically symmetric black hole. Some possible future extensions of our analysis are also discussed.\nPublished:\nAbstract:\nWe investigate the bulk viscosity of strange quark matter in the framework of equivparticle model, where analytical formulae are obtained for certain temperature ranges and can be readily applied to those with various quark mass scalings. In the case of adopting a quark mass scaling with both linear confinement and perturbative interactions, the obtained bulk viscosity increases by \\begin{document}$1 \\sim 2$\\end{document} orders of magnitude comparing with bag model scenarios. Such an enhancement is mainly due to the large quark equivalent masses adopted in the equivparticle model, which essentially attribute to the strong interquark interactions and are related to the dynamical chiral symmetry breaking. Due to the large bulk viscosity, the predicted damping time of oscillations for canonical 1.4 \\begin{document}${\\rm{M}}_\\odot$\\end{document} strange star is less than one millisecond, which is faster than previous findings. Consequently, the obtained \\begin{document}$r$\\end{document}-mode instability window for the canonical strange stars well accommodates the observational frequencies and temperatures for pulsars in the low-mass X-ray binaries (LMXBs).\nPublished:\nAbstract:\nScrupulous theoretical study of 8Be nucleus states, both clustered and non-clustered, is performed over a wide range of the excitation energies. The quantities which characterize the degree of the alpha-clustering of these states: spectroscopic factors, cluster form factors as well as the alpha-decay widths are computed in the framework of an accurate ab initio approach developed. Other basic properties of 8Be spectrum: the binding and excitation energies, mean values of the isospin are calculated simultaneously. In the majority of instances the results of the computations turn out to be in a good agreement with the spectroscopic data. A number of predictions are made and corresponding verification experiment is proposed. Prospects of the developed approach for nuclear spectroscopy are demonstrated.\nPublished:\nAbstract:\nMotivated by the problem of expanding single-trace tree-level amplitude of Einstein-YangMills theory to the BCJ basis of Yang-Mills amplitudes, we present an alternative expansion formula in the gauge invariant vector space. Starting from a generic vector space consisting of polynomials of momenta and polarization vectors, we define a new sub-space as gauge invariant vector space by imposing constraints of gauge invariant conditions. To characterize this sub-space, we compute its dimension and construct an explicit gauge invariant basis from it. We propose an expansion formula in the gauge invariant basis with expansion coefficients being linear combinations of Yang-Mills amplitude, manifesting the gauge invariance of both expansion basis and coefficients. With help of quivers, we compute the expansion coefficients via differential operators and demonstrate the general expansion algorithm by several examples.\nPublished:\nAbstract:\nThe Circular Electron Positron Collider (CEPC) proposed as a future Higgs boson factory will operate at a center-of-mass energy of 240 GeV and accumulate 5.6 ab-1 of integrated luminosity in 7 years. In this paper, we estimate the upper limit of BR(\\begin{document}$H \\rightarrow$\\end{document} inv) for three independent channels including two leptonic channels and one hadronic channel at the CEPC. Based on the full simulation analysis, the upper limit of BR(\\begin{document}$H \\rightarrow$\\end{document} inv) could reach 0.26% at the 95% confidence level. In the Stand Model (SM), the Higgs boson can only decay invisibly via \\begin{document}$H\\rightarrow ZZ^\\ast\\rightarrow\\nu\\overline{\\nu}\\nu\\overline{\\nu}$\\end{document}, so any evidence of invisible Higgs decays that exceeds BR(\\begin{document}$H \\rightarrow$\\end{document} inv) of SM will indicate a phenomenon that is beyond the SM (BSM). The invariant mass resolution of visible hadronic decay system \\begin{document}$ZH(Z \\rightarrow qq$\\end{document}, \\begin{document}$H \\rightarrow$\\end{document} inv) is simulated and the physics requirement at the CEPC detector to reach this is given.\nPublished:\nAbstract:\nWe use a geometric model for hadron polarization in heavy ion collisions with an emphasis on the rapidity dependence. The model is based on the model of Brodsky, Gunion, and Kuhn and that of the Bjorken scaling. We make predictions for the rapidity dependence of global \\begin{document}$\\Lambda$\\end{document} polarization in the collision energy range 7.7-200 GeV by taking assumed rapidity dependence of two parameters \\begin{document}$\\kappa$\\end{document} and \\begin{document}$\\left\\langle p_{T}\\right\\rangle$\\end{document}. The predictions can be tested by the future beam-energy-scan experiments at Relativistic Heavy Ion Collider of Brookhaven National Lab.\nPublished:\u00a0\u00a0 ,\u00a0doi: 10.1088\/1674-1137\/44\/5\/055101\nAbstract:\nWe construct an alternative uniformly accelerated reference frame based on 3+1 formalism in adapted coordinate. It is distinguished with Rindler coordinate that there is time-dependent redshift drift between co-moving observers. The experimentally falsifiable distinguishment might promote our understanding of non-inertial frame in laboratory.","date":"2020-09-24 01:18:49","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\": 0.7633571624755859, \"perplexity\": 1190.3503688577366}, \"config\": {\"markdown_headings\": false, \"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-2020-40\/segments\/1600400213006.47\/warc\/CC-MAIN-20200924002749-20200924032749-00670.warc.gz\"}"} | null | null |
Your chance to adopt Harlow Town Railway Station
News / Mon 19th Mar 2018 am31 11:21am
Rail station adoption scheme blossoming as number of volunteers exceeds 200
Greater Anglia's station adopters are swinging into action with the arrival of Spring, as the number of volunteers across the region exceeds 200 for the first time.
With the increase in station adopters, the scheme is blossoming, just like the station gardens and community projects they have created.
There are still 46 stations available for adoption on the Greater Anglia network, with 94 already being cared for by teams and individuals who are making use of their local rail station to benefit their community or are improving them so that visitors get a better first impression of their area.
The most recent stations to be adopted are Braintree, Bury St Edmunds, Ely, Hertford East and Witham.
The adopters will get together to share ideas and learn about the train operator's plans for 2018 at four special coffee mornings being held in Norwich and Chelmsford this week, and at Cambridge and Ipswich later this month.
Alan Neville, Greater Anglia's Community and Customer Engagement Manager, said, "Our station adopters are doing great things for their communities and this year will be no exception, with more stations being adopted and some exciting plans for gardens and events.
"We are very grateful for their continued hard work which has brought real benefits by improving the links between Greater Anglia and the communities we serve.
"There are many more stations across the network waiting to be adopted and I would urge anyone who has an idea for a project to get in touch."
Greater Anglia is also offering empty spaces in stations to local communities across Norfolk, Suffolk, Essex, Cambridgeshire and Hertfordshire. Anyone who is interested should visit https://www.greateranglia.co.uk/about-us/community-space
1 Comment for Your chance to adopt Harlow Town Railway Station:
JerryFromQueens
The railway station is beautiful to me, the addition of flowers can only add to the effect. | {
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{"url":"https:\/\/www.nature.com\/articles\/nmat2409?error=cookies_not_supported&code=6542fc65-5e19-4434-9196-06b9d06aa98a","text":"Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.\n\n# Lessons in science education\n\nStrong science education is an important part of any modern education. To ensure scientific progress, however, students need to aspire to academic careers.\n\nEducation forms a substantial part of the $787 billion American Recovery and Reinvestment Act, signed by Barack Obama on 17 February this year. A total of about 100 billion US dollars is allocated for education-related programmes1,2. This includes significant portions of a$54 billion public sector fund to prevent teachers from being laid off3, as the entire US school system was in danger of collapse with the threat of over 500,000 job losses in schools4. Furthermore, large portions of these funds will be spent on modernizing schools and improving early childhood development, as well as providing tax credits and tax breaks to make college more affordable for students from poor backgrounds.\n\nEven though such measures are unlikely to yield short-term gains, they are invaluable for the long-term scientific and technological development that is the basis for innovation and economic wealth. It is these long-term aspects in which the scope of Obama's stimulus package is different from economic rescue programmes discussed and implemented in other countries, such as Germany or the UK, where money is mostly awarded to short-term measures aimed at kick-starting the economy.\n\nAlthough improvements to US school infrastructure and teachers' salaries are desperately needed, particularly in poorer regions, an area that remains in urgent need of improvement is school education. There needs to be stronger emphasis on a good science curriculum. According to data from the OECD's 2006 PISA assessment study, the science literacy of 15-year-old students in the US ranks only in 23rd place out of 41 nations studied5.\n\nThe problem is not confined to the US but is endemic in many other developed countries. Although the UK, for example, lies in a seemingly better 12th place in the same OECD study, a recent survey conducted by the UK Royal Society of Chemistry observed an erosion of standards in chemistry education6. Such a drop in standards may in part be a consequence of the continuing unfortunate situation that in many UK state schools science is only offered as a single subject, a far cry from the comprehensive and intensive curriculum standards in those countries coming out on top of this comparison \u2014 Finland, Japan, Hong Kong and Korea.\n\nThere are many ingredients to good science education: qualified teachers educated to the latest standard of scientific knowledge, a comprehensive curriculum that provides a broad scientific overview and supports creative thinking, well-equipped school laboratories where students can learn science in a practical way, and good textbooks that illustrate scientific concepts in a suitable and exciting fashion.\n\nThe importance of these criteria for good science education at schools is certainly well understood. Unfortunately the problem for many schools remains obtaining sufficient funds in support of such ideals. The near-disaster in the US of losing many school teachers is merely a point in case.\n\nThere is another crucial ingredient for successful scientific education: to get the students interested in the topic. Science, particularly in the physical sciences, is much less a part of everyday life than, for example, law or economics. Probably very few students have even a basic understanding of how many scientific breakthroughs are at the core of modern products such as smart mobile phones or high-density storage media.\n\n\u201cWhat better place than research labs to inspire teenagers in science?\u201d\n\nCredit: SPL\n\nTherefore, it is important to convey experience of scientific research, and the excitement of state-of-the art scientific research. Examples of public outreach are science fairs at US high schools, international science Olympiads and exhibitions such as Strange Matter, organized by the Materials Research Society7. Another notable scheme is PhysiScope, based at the University of Geneva in Switzerland. In his Commentary on page 245, Christoph Renner describes this initiative8, where teenagers experience practical experiments centred on advanced scientific concepts such as superconductivity. The experiments are conducted by PhD students and postdocs, and the venue is embedded within the physics department, so that students can also peek into the research labs. What better place to inspire students with the work of scientists?\n\nAlthough to sustain initiatives such as the PhysiScope a substantial long-term financial commitment is required, its impact should not be underestimated. Innovation and technological progress require an educated work force that has been given a firm understanding of scientific principles; and if we are to motivate gifted students to take up an academic career in the sciences, they need to be inspired and their curiosity awakened.\n\nA sound strategy for science education therefore needs more than a good financial basis. To stimulate interest in an academic career, students need to be encouraged and supported from an early age. Public outreach programmes are essential, and scientists' duties as teachers begin far sooner than with beginners' classes in college.\n\n## References\n\n1. 1\n2. 2\n3. 3\n4. 4\n5. 5\n6. 6\n7. 7\n8. 8\n\nRenner, C. Nature Mater. 8, 245\u2013247 (2009).\n\n## Rights and permissions\n\nReprints and Permissions\n\nLessons in science education. Nature Mater 8, 243 (2009). https:\/\/doi.org\/10.1038\/nmat2409\n\n\u2022 Issue Date:\n\n\u2022 ### Magnetic Proximity Effects in V\/Fe Superconductor\/Ferromagnet Single Bilayer Revealed by Waveguide-Enhanced Polarized Neutron Reflectometry\n\n\u2022 Yu. N. Khaydukov\n\u2022 , V. L. Aksenov\n\u2022 , Yu. V. Nikitenko\n\u2022 , K. N. Zhernenkov\n\u2022 , B. Nagy\n\u2022 , A. Teichert\n\u2022 , R. Steitz\n\u2022 , A. R\u00fchm\n\u2022 \u00a0&\u00a0L. Botty\u00e1n\n\nJournal of Superconductivity and Novel Magnetism (2011)","date":"2021-09-21 03:57:35","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.1861990988254547, \"perplexity\": 3296.1089341354955}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-39\/segments\/1631780057131.88\/warc\/CC-MAIN-20210921011047-20210921041047-00171.warc.gz\"}"} | null | null |
Onto my valentines day, it was my first year actually celebrating valentines day and it was really nice.
It started off with a late breakfast at my place and then we drove to a shopping centre as we had planned on playing bowling but all the lanes were full booked so instead we wandered around the shopping centre and then ate some lunch at a cafe before we drove back to A's place and then started getting ready to go out to dinner.
He had booked a table at this super fancy restaurant, infact i was almost a little shocked not to mention that it was extremely expensive!! -_-' i almost felt bad because it was so fancy and expensive, haha. But we ordered a 3 course meal and i began with smoked salmon with these different sauces, then for main i had cod with a creamy risotto followed by creme brulee for dessert!! It was all super delicious and tasted amazing!!!
Then we headed back to his place where we watched Big Hero 6 (super cute film, haha) before we went to bed!!! | {
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# **VÁCLAV HAVEL**
**_A POLITICAL TRAGEDY IN SIX ACTS_**
_JOHN KEANE_
For Kathy O'Neil
## **Contents**
_Prologue_
_The Young Prince (1936-1945)_
Beginnings
Folly
Republicans
Devil's Playground
Zoology
Resistance
Cold Peace
_Red Dawn (1945-1956)_
Red Stars
Coup de Prague
Flying Splinters
Trials
Thirty-Sixers
Ashes on Ice
_Stalin's Shadows (1956-1968)_
The public Poet
Stalin's Carcass
To Barracks
Socialist Realism
Garden Party
The Crises
The Memorandum
Summer Friendship
Mid-Summer's Night
A Politician of Retreat
_Late-Socialism (1969-1989)_
Normalization
Late-Socialism
Beggars' Opera
Charter 77
Violence
Courage
The Powerless
The Victim
Prison
Largo Desolato
Temptation
Cliff-Hanging
_Velvet Revolution (1989)_
Revolution
Velvet Power
Machiavelli
A Crowned Republic
Te Deum Laudamus
Fun and Games
The Manipulator
_Decline (1990-1999)_
Defections
Parliament
Lustration
Market Power
Velvet Divorce
Oh Europe!
Metamorphosis
The Gift of Death
_Acknowledgements_
_Illustrations_
_Guide to Czech Pronunciation_
_Footnotes_
_A Note on the Author_
_By the Same Author_
## **_Prologue_**
Time can be a cruel despot. Acting on a whim, it sometimes pounces on particular lives, pushing them into custody, dragging them to a destination of suffering and unhappy endings. Such has been the fate of Václav Havel. Resembling a classical political tragedy, his life has been clamped by moments of sensation and moral gravity, episodes of joy ruined by sadness, courage mixed with vacillation, honesty tainted by knavery, triumph spoiled by defeat — and deathly climaxes linked to the struggle for power.
Havel is of course currently much better known world-wide for his dazzling achievements as a talented playwright, courageous dissident, and as a moral leader of the democratic world. This reputation is justified, but incomplete. Many pertinent episodes of his life remain unknown, including the one that currently grips the early winter of his life. Abroad, in countries like the United States, Japan, Germany and Britain, the name of Václav Havel is a synonym for integrity, probity, freedom. At home, within the tiny landlocked European country he governs, impressions are different. The final act of a splendid political tragedy is now unfolding. Public grumbling and grave personal illness, like a crowd of blanketed beggars, are huddling at the gates of his hilltop Castle in Prague. It is true that its young soldiers, dressed in red, white and blue, still dutifully stand guard, beneath the fluttering national flag. And each day, tourists with clicking cameras arrive in their thousands to walk its courtyards, marvel at the Spanish Hall, and listen to the chiming bells of St Vitus's Cathedral. But the harsh fact is that most of the citizens of President Havel's republic think less of him than they did a year ago. Some say that he is hindering the process of consolidating good government, or that he is too ill to be a statesman. More than a few have been calling for his resignation.
Havel's political star at home is evidently waning. It may do so abroad as well. Perhaps nobody should be surprised, for final-term, 'lame duck' presidencies are commonplace in other democracies around the world. The reason was once explained to me by a wise old politician. Political careers, he told me, usually end in failure. Especially during second or third or fourth terms of office — as Havel has had — politicians often suffer from the hardening of their political arteries, he explained. Their charisma fades. They fall into a pit of narcissism, or become cloth-eared and haughty, or lose their guard. Meanwhile, their critics and enemies have time to group and regroup, which is why the terminal phases of a political career are often scarred by scandals, public grumbling, and sounds of sharpening knives.
Havel is currently in the grip of such trends, and it is therefore unsurprising that in recent times he has swung between dejection and anger, and that he has considered resignation. His opponents smile coldly as they clutch at their weapons, but before they make their next moves, or draw their conclusions, they should read this book. Within its pages, they may be surprised to discover many things hitherto unknown about Havel. They will taste the moments of joy, irony, farce and misfortune through which he has lived. They will see that his life displays great generosity and courage in the face of misery and defeat. They will understand better why he, the 'post-modern president', has admirers in the four corners of the earth. Above all, they will discover something that both his critics and supporters must never forget: that Václav Havel suffered the misfortune of being born into the twentieth century, that his fate was politics, that by any standards of reckoning he rose to become a flamboyant political animal who achieved fame by teaching the world more about the powerful and the powerless, power-grabbing and power-sharing, than virtually any other of his twentieth-century rivals.
My grandiloquent suggestion that Havel will be judged by posterity as among the most distinguished political figures of our century is bound to raise eyebrows. He naturally has many competitors. All kinds of famous twentieth-century heads of state — Masaryk, Hitler, Brezhnev, Reagan, Gorbachev, Mandela, Kohl, Clinton, to mention a few — have passed through the magnificent gates of his splendid Castle. Not only that, but to predict that he will be remembered as a great political figure of the century presumes some things about the course of the past hundred years. Our century has had many unique features, including the way in which it stimulated awareness of the difference between historical time and clock time and, for the first time, nurtured the widespread perception that the twentieth century was indeed a century, and that as a century it has meant various things to many different people. So the century was ripe with technical inventions — the radio, the telephone, the automobile, the refrigerator, the washing machine, the television, the computer — whose diffusion has radically altered the sense of time and spatial movements of millions of people. It was the century in which economic life finally went global, for instance in the fields of telecommunications and travel, thanks to which time and space barriers for some people were wiped out and the Grand Tour began to be democratized by becoming financially accessible to millions called tourists. The twentieth century saw the rise of modernist art — and 'post-modern' challenges to its penchant for self-edifying abstraction. And as Havel knows from bitter personal experience, the twentieth century will for ever be recorded as the century that perfected the arts of violently misusing power over others. Aerial bombardment became commonplace. There were planned attempts to exterminate whole peoples. Corpses were burned and recycled into gunpowder to make more skeletons from future enemies. There were bombs whose flash proved brighter than the sun. The domination of the world by European colonial empires, dating back to the eighteenth century, came to a bloody end. And just as comrade V. I. Lenin predicted, more people were pushed and bullied and killed in wars and revolutions than in all previous centuries combined.
Comrade Lenin was not completely right, however. His fascination with bossy power, revolution, war and state-building blinded him to the fact, clearer now than in his times, that the twentieth century saw a growth spurt in what can be called the modern democratic revolution. This quiet revolution began long ago, with such events as the Dutch resistance against the government of Philip II in the Low Countries, the bashed-up English revolution of the 1640s, the surprise defeat of the British Empire by the American colonists, and the disturbances that swept through Europe in 1848 — the year that marked the birth of the Czechs' long struggle for civil freedoms. The twentieth-century quest for democracy started out badly, but it subsequently yielded surprising results. Totalitarian regimes were defeated, not only by military action but also by the peaceful revolution of citizens. In the four corners of the earth, the power-constraining pinch of international humanitarian law, covering such matters as torture, rape and genocide, began to be felt for the first time. Heavily armed, nasty dictatorships were effectively resisted, or simply collapsed, on a breathtaking scale. Within the actually existing democracies, meanwhile, the century saw various experiments in rejuvenating the principle of non-violent power-sharing — think of the suffragettes dressed in purple and green, or the black and white protesters at Little Rock. And the century witnessed as well organized efforts to transport that slippery ideal into concrete institutions — from the workplace to the bedroom — that were previously untouched by the idea of publicly monitored and shared power, the principle for which democracies are justly famous.
Havel has always been sensitive to these trends — not only because from an early age his political instincts were opposed to power-grabbing, but also because his greatest political achievement is that he personally helped to make the growth spurt of democracy happen. As a sandy-haired young boy, he had a healthy disdain for troops in uniform, armoured cars, and the terror of air raids. During Stalin's times, as a young teenager, he daringly organized a remarkable literary circle called the Thirty-Sixers — so named because he and its other members were all born in the fateful year 1936. Havel soon mounted comical assaults on the socialist theatre establishment. His earliest — still unappreciated — plays like _You've Got Your Whole Life Ahead of You_ and _Hitchhiking_ matured into award-winning, side-splitting plays like _The Memorandum,_ which granted him the gift of global fame for defending the view that theatre should raise more questions than it answers, that it should make people laugh at unaccountable power, and that theatre should democratically unnerve, not soothe or patronize its audiences.
Havel offered other gifts to the modern democratic revolution. His first important confrontations with the Communist authorities took place in the early 1960s, when he fancied himself as a bluejeaned poet and essay-writer, and served on the editorial board of a revamped monthly journal called _The Face (Tvá ř)._ That period blessed him with the reputation of 'clean hands' and it helped launch him into prominence as a playwright, radio announcer and street activist during the 1968 Prague Spring — the time when he first met Dubček and began to play something of a public-political role. Havel was soon forced to endure the miseries of the Cold War and Brezhnev-style 'real socialism'. Struggling to keep his sanity amidst terrible personal suffering, he staged a dramatic undercover version of John Gay's _The Beggar's Opera_ and played a key role in convening the human-rights initiative called Charter 77. Praise for his efforts came from the lips of statesmen like Henry Kissinger and Zbigniew Brzezinski — alongside bitter Communist attacks on him as the spoiled son of _'nouveau riche_ millionaires', or (as an American congressman once said) as a dropout wearing 'ten dollars' worth of clothes and badly needing a haircut'. Then came the revolutionary upheavals during the magical autumn of 1989 — the 'velvet' events which transformed him into a leather-jacketed hero, then into a besuited politician politicking on all fronts as his state and its citizens tread the dangerous path of consolidating a new configuration of institutions that are conventionally called democratic: precious institutions like the rule of law, free elections, parliamentary government, a civil society, and independent media and public life.
Havel's life has been so blown about by the winds of twentieth-century history that it is impossible to understand him without understanding the events that shaped and reshaped, racked and ruined not only the Czechs but the whole of Europe. In this book, I try to retell his life against the backdrop of the collapse of the Habsburg monarchy, the rise of Hitler, the Stalin trials, and the horror of the concentration camps. I show how his life and writings were later shadowed by the Berlin Wall and encouraged by the events of May 1968. I emphasize as well the 1989 revolutions against Communism, the collapse of the Soviet empire — the last modern empire in Europe — and all the key events that have since followed: the painful transitions to parliamentary democracy in central Europe, war in the Balkans, the global resurgence of free-market economics, and the accelerated growth of the world's most advanced experiment in regional integration, the European Union.
My treatment of Havel's life naturally tries to be sensitive to the Czech context into which he was born. There is admittedly little here about the collage of Romanesque, Gothic, Renaissance, baroque, art-nouveau and post-modern architecture that in comparison to Prague makes most other modern cities look like urban eyesores. The spas of Karlovy Vary, known for their beneficial effects on arthritis and constipation, hardly rate a mention. Tripe soup, dumplings, sauerkraut and roast pork are absent fare. So too are the fiery brandies tasting of cloves and plums. There are no stories of Bohemian bears and wolves — or Czech tennis and hockey players. The allure of the Škoda, the 'foreign' car that advertisers tell us is less likely than most other cars to be stolen in towns like Edinburgh, Hamburg, and Denver, goes unmentioned. Some readers, unfamiliar with Prague — and having never visited his splendid Castle — nevertheless will happily encounter the influences of Franz Kafka, Karel Čapek and Milan Kundera. They will read as well about Havel's predilection for Moravian white wine, free-and-easy bohemian nights, good dinners and endless cigarettes. And they will learn about the Czech women in his life, his taste for Anglo-American politics and post-Heideggerian philosophy, and his love of the music of the contemporary Prague scene, from the scores of Smetana and Dvořák to punk bands like Plastic People of the Universe, and elderly pop musicians who are still loved in Prague, like Tina Turner, Lou Reed and the Rolling Stones.
There is more in this book than the minutiae of a remarkable life lived in a hapless country during an extraordinary century. In keeping with the style of Havel's plays, poems, essays, and speeches, my biography pays attention to its own form. Gone are the days when it could be presumed that biography was about recording the facts, and literature was about experimental fiction. My account of Havel's life is unavoidably 'factional'. By that I mean two things. Although I try hard to 'fill gaps' and to pay meticulous attention to all of the important details, the story that I tell is based on principles of selection and interpretation that unavoidably highlight certain aspects of his life, rather than others. Where there are 'facts' there are 'theories', and where there are 'theories' there are value-laden 'interpretations'.
The way a biography is written counts as one of these shaping conditions, which is to say that every 'factual' biography is a work of fiction. If that is so, then questioning and overturning the pseudo factual form of old-fashioned biographies becomes important. This I have tried to do, and it is the second sense in which my account of Havel's life is 'factional'. I have set out to tell an unusual story about his life by means of _tableaux vivants_ that not merely pay homage to his love of theatre, but also resonate with the fragmentation of his life by historical events beyond his control. More than that, these _tableaux vivants_ are designed to heighten readers' sense that his actions in the world are understandable as a tragedy; and to have the 'cubist' effect of producing deliberately broken narratives that warn readers from the outset that the stories told here are 'fabricated' by certain — but challengeable — points of view.
Havel's closest aides at the Castle — bearded, bow-tied Vladimír Hanzel, for instance — urged me to capture his many faces. The advice reminded me of Nietzsche's remark that 'one's own self is well hidden from one's own self; of all mines of treasure one's own is the last to be dug up'. Whether or not Mr Hanzel intended this, his advice in effect urged me not to mythologize Havel, to see that he is not always himself, that his own self-assessments should be believed and disbelieved. Hanzel was implying, probably against his will, that Havel is not fully comprehensible, that he will continually be out of reach, and, thus, that readers should accept that neither he nor anybody else is entitled to exercise ultimate power over defining exactly who Havel is. That being so, it follows that Havel himself — presuming that he has the time and energy to read the book — will not necessarily accept all or most of the viewpoints that I use to structure my account of his tragic life.
My probe into his life and writings also presents a philosophical reflection upon a subject that is of perennial importance, because it is inextricably bound up with the human condition: the subject of power. Philosophers and political thinkers tell us that power (originally from the Latin _posse,_ to be able) is the ability of actors — individuals, groups, organizations, whole states or international bodies — to make a difference upon the people and things within their environment. It is said that the term power refers to humans' ability to make their marks on the world; that power is the production of desired or valuable effects; and that power is the capacity to achieve whatever effects are desired by drawing upon certain resources, such as money, guns, or images, even in the face of stiff controversy and opposition. It follows from such definitions that to study power in any context is to consider who gets what, when and how, and whether they ought to have done so.
Havel's life, deeply ensnared as it is with the political crossroads of Prague and the Bohemian lands, provides rich material indeed for taking a new look at the old subject of power. Havel has of course written many essays and plays on the subject. His speeches as head of state sometimes dwell on the same theme. He has also been unluckily privileged to live through virtually all of the major changes of power in twentieth-century Europe. Five-sixths of Havel's life has been lived under anti-democratic regimes of one kind or another. The hands of a breathtaking variety of power regimes — I count eight altogether — have in fact touched him. He was born into a republican bourgeois family shaped by the Habsburg empire, whose collapse was hastened by the First World War and the birth of the Czechoslovak parliamentary republic led by the philosopher-president Masaryk, who was personally known to Havel's family. That First Republic was Havel's Athens: understandably so, since it was the most successful parliamentary republic in middle Europe, until British and French politicians knifed it in the back with the Munich agreement. Havel went on to live his early years under Nazi occupation and the threat of total war. He tasted a brief period of multi-party social democracy that was forcibly terminated by the cunning and violence of the 1948 _coup de Prague._ As a teenager and then as young man, he and his family suffered under Stalinism, but he contributed actively to Czech efforts, culminating in the 1968 Prague Spring, to liberalize that Soviet model of totalitarian power. For the next two decades, Havel was tormented by various forms of persecution at the hands of what I call 'late-socialism' — a post-totalitarian regime that felt like one big grey prison ruled by a single party. Then came the magical 'velvet revolution' of the autumn of 1989 — a dramatic upheaval that radically altered the patterns of who got what, when and how and catapulted Havel into the office of President of the Czechoslovak Republic. The wildest of his wild dreams came true. And now, for the past ten years of your life, he has headed a state that has trodden the unknown path of post-Communism.
Since this is a study of these different — mainly despotic — régimes of power that have criss-crossed, moulded and complicated Havel's life, readers should not be surprised to find that I have chosen to write the book as a political tragedy. As with all tragedies, there are some memorable moments of triumph and _jouissance,_ certainly. Like the assassination of Heydrich. Or Havel's first public address during the Hungarian Revolution. Or his release after four years in prison. Or the day of his election as unchallenged charismatic ruler of a landlocked country called Czechoslovakia. But these are exceptions, for within the stories that I tell Havel appears more often as a tragedian — as an actor in a prose drama riddled with calamities, injustices, and unhappy endings. Many readers outside the Czech Republic will be surprised to find that the past decade, when supposedly the world has been his oyster, has been no exception to this set pattern. If anything — some will recoil from this claim, even though Havel himself knows that it's true — this period has been the most crisis-ridden of his life. It is now taking its toll. Death and public grumbling are camped outside his Castle gates. It is as if he is being punished for living most of his life in unfreedom. One of his oldest friends told me recently that Havel still might be rescuable from this sad fate, but that that would require the political kidnapping of the century, followed by strenuous efforts to rehabilitate his best qualities. That friend's joke was revealing. It suggested that Havel's greatest misfortune in life is to have found that his final big dream — to become a president — came true. It seems that the words of his favourite relative, Uncle Milos Havel, written after being bullied into exile in Germany by Czechoslovak Communists, applies well to Havel himself: 'In the free world, I continue to suffer from lack of freedom.'
Aristotle recommended (in his _Poetics)_ that a tragedy should be structured in such a way that those who encounter it 'thrill with horror and melt to pity at what takes place'. The sad stories told about Havel here may well leave readers with feelings of sorrow aroused by his suffering. They are not likely to be left with the impression that his life deserves heroization. Typically for someone of my generation, I have never believed in heroes, and I certainly never became interested in Havel and his work because I thought of him as a hero — a substitute for Mahatma Gandhi, or Martin Luther King, or Jack Kennedy, or Che Guevara, or Chairman Mao, or God. I remember well the first time we met. It was 1984. We were supposed to discuss the English version of his _The Power of the Powerless,_ which I was then editing. Havel had just come from a long spell in prison, and his circumstances were difficult, to say the least. But he didn't look like much of a hero to me. If anything, I felt sorry and upset for him. He seemed like a hapless victim of the absurdity of so-called reality. He was exhausted, overweight, depressed, his restless fingers shook. He grated the gears and several times got lost when he drove me and a friend around Prague in his old Mercedes. He seemed baffled by the streets of his birthplace. Whisky and cigarettes and words seemed to be his anchor in life.
When, some years ago, we corresponded about my decision to embark on this book, I stressed to Havel that I did not believe in the genre of 'authorized biography'. I explained that I did not need his permission to tell his life as I thought fit. Nothing subsequently changed. Since Havel too believes in 'living in the truth', since this is a new approach to the understanding of power, and since my vocation is that of a political thinker and writer intent on stretching the concept of power into the most private domains — to uncover the naked bodies in the bedroom, or to peek through the keyhole into the top-secret meeting taking place behind closed doors — my book publicly scrutinizes his life in great detail, without apologies, without illusions. I have tried my best to research things meticulously, to write accurately, to draw conclusions and to make judgements without malice — in the same spirit of honesty and openness that Havel himself has championed at various points in his life. There may be comments recorded and tales told in this book that he finds unsettling. Some incidents may cause him discomfort, either because he does not remember them, or because he disagrees with the interpretations proffered, or even because he considers them potentially ruinous of his political reputation. I cannot apologize for these possible reactions. For it is the duty of political writing to call things by their proper name, to refuse nonsense and to scale down the pompous — to say things that shake the world and stop it from falling asleep.
My ultimate aim in writing this study of power in biographical form is to invite comparison with the 'classic' attempts to treat questions about who gets what, when and how, and whether they ought to. In early modern times, say from the early sixteenth century onwards, two different but related genres of the study of power began to crystallize, and then to dominate the field. One type is the so-called 'realist' account of power. An early version is on display in Niccolò Machiavelli's research into the contemporary politics of the emergent states around Firenze, which led him to write tracts like _Il principe_ (1513), which aimed to serve as a guide or handbook for rulers like the Medici, to enable them better to rule their subjects. This approach to power concentrates on the political manoeuvring for the levers and resources of government. It emphasizes, for instance, the necessity of foresight and flexible planning for the future; the importance of winning friends and allies; the vital political role of trickery, which depends upon deception, secrecy and surprise; and the need to avoid halfway measures. The aim of political struggle, it is said, is state power over its subjects, the people, just as the military commander's aim is power over the defeated enemy.
Then there is the inverse approach, let us call it the obedience view of power, an early example of which can be seen in the writings of the seventeenth-century political analyst, Thomas Hobbes. His reflections on the revolutionary upheavals in England during the 1640s resulted in works like _De Cive_ (1642) and _Leviathan_ (1651), which are less manuals of statecraft than grammars for obedient subjects. This second approach shares with the first a belief in the need for institutions of top-down government, and in the unavoidability of cunning and knavery in human affairs. But in contrast to the first view, it concentrates less on the power dynamics in the alpine regions of state institutions and more on the importance of laying down the ground rules of obedience for subjects living in the valleys and on the plains below. Observing that men and women are proud and passionate and prone to disorder and violent conflict, this approach specifies the morally binding laws that must be observed by everybody in order for a stable political community to survive through time. 'I put for a general inclination of all mankind,' wrote Hobbes, 'a perpetual and restless desire of power after power, that ceaseth only in death.' That being so, individual subjects are required to enter into a peace contract. It specifies that everybody must obey the civil laws laid down by the individual or council whom they recognize as their sovereign ruler. In return for their obedience, all individuals receive the assurance that each will honour their agreement. They have the assurance, backed by the sovereign's threat of force, that each will abide by the rule: Do not do unto others what you would not have them do unto you. If anybody steps out of line — if at the outset they refuse to enter the contract of obedience, or if they subsequently express infidelity to the contract by breaking the law — then woe betide them. Following the Book of Job, Hobbes with good reason compared the necessary sovereign ruler to Leviathan, whom God called 'King of the Proud'. The job of the Leviathan is to rule by making subjects permanently afraid — that if they break the laws then they will be punished severely, certainly with death.
Burdened by these two different but complementary approaches, the study of power in modern times has been skewed in favour of the powerful. The capacity for action and entitlements of the governed — the dark side of the moon of modern accounts of power — have been badly neglected. A third approach, one that explores power from the standpoint of the governed, is required. This is what I have attempted here. The new probe into power stands firmly within the modern democratic revolution. It certainly recognizes that state institutions are important for the maintenance of the lives and livelihoods of people, wherever they live; and it recognizes as well that subjects' consensual obedience to state institutions is critical for the survival of good government. I do not suppose that power contests, hubris and fear can be made to disappear from human affairs. But that is exactly why the inbuilt prejudice of the two orthodoxies against the entitlements of the governed needs to be counterbalanced with a radically different perspective.
So this study of Havel's life and times might be described as a manual for democrats. It supposes that the lust for power is polymorphously perverse, that power, wherever it is exercised, is therefore always in need of public monitoring and control. It further supposes that such monitoring is best done within a democratic order marked by non-violent power-sharing arrangements, including limits on the scope and potential arrogance of governmental institutions. A democracy, ideally conceived, is a fractured and self-monitoring system of power in which there are daily reminders to governors and governed alike that those who exercise power over others — whether in the bedroom or on the battlefield — cannot do just anything they want, and that (as the Dutch Jewish political philosopher Spinoza put it) even sovereigns are forced in practice to recognize their own limitations, to admit that they cannot make a table eat grass.
The spirit of democracy in this sense is evident throughout this book, for instance in its accounts of the causes and — sometimes grotesque — effects of various power-thirsty anti-democratic regimes that straitjacketed Havel's life for fifty years. The concern for democracy can be seen as well in the _tableaux vivants_ structure, which aims to discourage readers from 'understanding' the text as indisputably True, and instead to encourage them to 'overstand' the text, that is, to read the accounts with frowns on their faces in order better to make up their own minds about the subject of power — and about Havel himself. And this is a manual for democrats in a third sense: in its attempt to explore dimensions of power that for too long have been neglected. The _tableaux vivants_ sketched here try to inject life into conventionally stale, power-related topics such as parliaments, freedom of expression, and civil society. But I have tried to do more than resuscitate dead subjects. Topics such as courage, fear, and temptation are also shown to be integral to the subject of power. So too are matters like theatre and literature, prison and sex, folly and cunning, friends and enemies, birth and death.
Such themes conspire to produce a political tragedy, albeit with a difference. Tragedy is of course a form of writing, not of living. The stories I tell display many of the ingredients of classical tragedy, defined as it was by figures like Aristotle and Seneca, Shakespeare and Lessing. In this book, the private anguish of a single individual — an innocent and courageous mortal with marked imperfections — is re-enacted on a public stage that is cluttered with great evil and suffering caused by violent struggles for power over others. Like the classical tragic form as well, my book offers insights into how the tough-skinned victim is exposed and broken by forces that are, in the circumstances, neither fully understandable nor controllable by prudent calculation. This political tragedy, like those written before it, also aims to arouse concern and pity, and so to uplift its reading audience. Tragedy most certainly does not aim to make us love our misery. It is potentially a source of _catharsis_ and _pleasure_ and _political wisdom._ By confronting readers with some terrible episodes of human history, tragedy can arouse and discharge compassion for the undeserved misfortune of the victims, partly because readers can recognize _themselves_ in the misfortune. Tragedy thereby demonstrates (as Shakespeare observed) that great griefs are powerful medicine, that excessive human suffering can incite human claims to dignity and freedom.
To these familiar ingredients of classical tragedy I add certain 'modern' elements, like the absence of Absolutes. Traditional forms of tragedy supposed the omnipresence of the gods, or of a God who although not on stage is always there as a spectator, watching and judging the action, capable even of maddening or destroying the central characters. In this book, the suffering of the main character is not traced to irresistible forces that are divinely destined, cosmic forces that hunger for retribution against those who have bared their behinds to the divine order of things. The cautionary tales about power told here see Havel's suffering as contingent rather than necessary, as an effect of certain historically specific regimes of power, especially those in which some men — like the Titans who set off to scale Mount Olympus — acted as if they were God. My democratic form of tragedy turns its back on talk of unchanging 'human nature'. It also rejects the bias of classical tragedy towards fixed hierarchies of worldly power, whose victims were the playthings of aristocracies, armies and monarchs. The political tragedy that follows is simply the sad but inspiring story of an individual whose astonishing life was pushed and pulled, twisted and torn by all of the tumultuous political forces of a century — thankfully — which is now past.
London and Prague
May 1999
## **_The Young Prince_**
## **_(1936-1945)_**
### **Beginnings**
Those who gathered around tiny 'Venoušek' from his first day in the world — Monday, 5 October 1936 — had no doubt that he was special. His family luckily believed in the power of recorded images so that, unusually for this period, his first few months are well preserved as black-and-white home movies. Although inexpertly shot by his father, the granular frames leave behind a striking impression of a child swaddled in high expectations — a child whose early months were not only coddled but _crowned._ At two weeks of age, freshly home from his birthplace at Dr Záhorský's private hospital on Prague's Londýnská Street, he appears as a wispy cherub robed in white, crying, showered in words by his proudly smiling, brown-haired mother. A few months later, sitting but not yet able to walk, he appears in various poses: enveloped by admiring, kissing, stroking relatives eager to attract his attention at a summer garden party; propped up on a sofa, cornered by a toy dog that he regards with deep suspicion; seated in a stroller entertained by a moustached man, dressed up in the suave style of Adolf Hitler, clasping young Venoušek's rattle; and, most strikingly, watched by the Mayor of Prague, sitting in a wooden high chair, enthroned ceremoniously by his father with a crown made of summer flowers, confidently looking straight at the camera, backgrounded by an ivy-clad wall and a bronze plaque of his famous grandfather, himself a friend of T. G. Masaryk, founding President of the fledgling Czechoslovak Republic.
Like all past relics that defy the ruthlessness of time, these photographic images can be interpreted in a dizzying variety of conflicting ways. Havel himself emphasized their absurdity. 'In those films,' he once mused, 'I am a small baby who is constantly the subject of everyone's attention, a pampered bourgeois child attended by governesses, relatives, friends, even the Mayor of Prague himself Pestering admirers, he continued, made him feel a deep sense of loneliness amidst love. 'This love is so overpowering and burdensome that the child seems constantly to be petrified and astonished. This I think developed in me at an early age a strengthened sense of the absurdity of the world, a certain distance from it, even a kind of fear of the world.'
Probably Havel here inflated his earliest powers of perception, as well as understated the ways in which he, like all newcomers on earth, yearned for comforting breasts and chests, exactly because the world is an unintelligible, potentially frightening place. Havel nevertheless correctly put his finger on the unusual cluttering of his early months with admirers. Not many new arrivals on earth were so showered with privileged well-wishers, with adult faces exuding the magic of birth, the excitement and joy evoked by beginners in the world. Many of the curled and scratched photographs in the Havel family albums are additional testimony to this power of beginning — to the human ability to create a being which did not exist before, and so to ensure that the world does not remain at a standstill.
Some beginnings, such as revolutionary upheavals, are of course unplanned spectacular events that take humans completely by surprise. Birth, by contrast, is both a regular and ineradicable — but no less special — feature of the human condition. The human species is naturally bound and gagged in its absolute dependence upon birth for its survival and reproduction. Yet birth is not just a natural event — as if birth is merely a shield against death, or merely the prelude to death. Birth is more interesting than that, and it is little wonder that it is marked with rites of passage — gifts, visits, celebrations, the giving of names — and proverbial turns of phrase about its importance. The beginning is half the whole, some say. Others add: things are always best in their beginning; from small beginnings grow mighty things; and all glory comes from daring to begin. The first yelps and whimpers of blue-eyed Venoušek confirmed all this. They proved yet again that birth is a vital moment of beginning. Here was a single individual — like all other individuals — endowed with unique and unpredictable qualities making his appearance in the world. He weighed only 3.27 kilograms and stretched a mere 50 centimetres, but the world was never again to be the same. His birth, like the birth of all other human beings, was a beginning pregnant with unforeseeable consequences. Venoušek's arrival might even be said to have been beginning's revenge upon those who wanted to resist novelty and to keep the world predictably on course. Like all newborns — his first admirers wrote — he had within him the potential power of the newcomer to begin something anew, that is, to act not only within but upon the world. 'Your Honour, Esteemed Sir', began the very first correspondence he received. It was a postcard signed by the tenants and servants at the family's country house called Havlov. 'We dare to send you our greetings full of respect,' they continued. The tone resembled that of royal petitioners humbly waiting upon their new king. The conclusion squeezed into the corner of the card was equally deferential. 'We trust that you are in the best condition of health,' they wrote, 'and we hope when we see you that you will show favour on us.'
### **Folly**
The learned ability of the newborn to flourish in the world's fields of power is always fragile and risky. There are times when the cries of innocents are extinguished by stupidity, squalor, hunger, violence. Even when they survive the perils of birth, the newborn find their lives complicated by the power dynamics of families, communities, business firms, whole economies, parties, governments, and states. Such organizations are menacing. They tower over them like colossi. Organizations make the innocent look and feel small. The newborn are turned into the playthings of power relations — of which they know little, let alone can understand, or tame or control.
Young Venoušek's early years were exactly like this. It has often been said — by card-carrying Communists, sceptical conservatives, guilted liberals — that he enjoyed a comfortable 'bourgeois' upbringing. The sad truth is that his life as 'a well-fed piglet' began badly within a family whose ideals were smashed up by folly, military occupation, surveillance, air raids, war, and totalitarianism. Venoušek took his first steps in the early autumn of 1937 — at precisely the moment that Czechoslovakia was pushed to its knees by the power-posturing of neighbouring states and alliances. Not everybody saw what was happening. Or they foolishly turned a blind eye, as did the most popular contemporary guide for foreign travellers to Prague. First published in the month of Venoušek's birth, the guide conjured his home town into an exotic haven. The guide marvelled over Prague's green spaces and wooded surroundings; the breathtaking views of the city from the heights of Petříin, Hradčany, and Letná; and the wealth of architectural beauty — Romanesque, Gothic, Renaissance, rococo, and especially baroque buildings resonating its varied history from the time of the seventh century. Praise was heaped upon the Prague diet of freshwater trout and carp; goose, duck and venison; pilsner, dark beer from Smíchov, fiery plum brandy and agreeable Moravian wine; only a small frown was reserved for the 'unexpected' local sandwiches, consisting of _topless_ slices of buttered bread covered in salami, egg, pickled cucumber, fish or ham. The guide noted that central heating of residences was common; that road traffic moved on the left; and that a system of red letter-boxes for the quick delivery of letters franked with 90-heller stamps functioned well. Although sugar was rationed, commodities like soap and matches were plentiful, while the commercial hub in St Wenceslas Square was often thronged with shoppers, said the guide.
The guide admired Prague's modernist feel. It pointed to the example of 'a new suburb' called Barrandov, built on a rock cliff overlooking the River Vltava and offering magnificent views of the city. The text left unmentioned that it was owned by the Havel family; it simply noted that Barrandov had 'a magnificent restaurant which has become a popular afternoon and evening rendezvous for those wishing to escape from the city for an hour or two. It has a well-equipped bathing pool and numerous tennis courts.' The guide went on to report the popularity of bookable cinema performances, theatres, music halls, cabarets, low-price symphonies, the opera performances of Smetana's _Libuše,_ Dvořák's _Rusalka_ and Janáček's _Jen ůfa,_ and the amusing comedies of Voskovec and Werich. The guide noted the enthusiasm in Prague for public performances by Sokol gymnasts, at which thousands of young women in loose Romanesque dresses and young men dressed in red shirts and feathered caps together performed exercises in lines and patterns designed to highlight the values of self-control, cool courage, and the synchronism of body and mind. The guide reported that in matters of recreation young people were keen on tennis, volleyball, _házená_ (a handball game played by women), football, ice-hockey, skating, skiing, athletics, and (thanks to the local Barrandov studios) the new medium of cinema. The professional classes, the guide reported, seemed unusually knowledgeable about world and current affairs, no doubt because for two or three hours per week on average they frequented cafés well stocked with a wide range of domestic and foreign newspapers and periodicals, both illustrated and literary. The guide reserved a short epilogue for politics and international affairs. It noted that the citizens of Prague had every right to be proud of their country's achievements. There had been a steady consolidation of its various territorial units. The Czechs and Slovaks were setting an example to other nations by practising tolerance and respect towards the claims of the minority populations of Germans, Hungarians, Poles and others. Czechoslovakia enjoyed warm relations with its neighbours. The country was an ardent supporter of the League of Nations. The recent resignation (on 14 December 1935) for health reasons of the great statesman, eighty-five-year-old President T. G. Masaryk, had changed nothing. 'At the election held in the Vladislav Hall of the Prague Castle,' the guide concluded, 'Dr Edward Beneš was elected to succeed him. Thus, after having been its Foreign Secretary ever since the republic was founded, Dr Beneš became Czechoslovakia's second President and a continuity of the country's internal and external policies, with Dr Milan Hodža as Prime Minister, was assured.'
The words harboured foolish thinking, proving yet again that fools enjoy serenity in the company of knaves. The unpleasant fact was that Havel's country of birth was about to be strangled alive by a Nazi Germany on the loose in central Europe. Ever since late 1933, when Hitler had pulled Germany out of the League of Nations, the tiny middle-European state of Czechoslovakia had begun to look and feel ever smaller. During the summer of 1934, in clear defiance of the Versailles settlement, the Nazis had managed'a coup in Austria by murdering its Chancellor, Dr Engelbert Dolfuss, who favoured a one-party dictatorship but anti-Nazi state. In 1935, by means of a plebiscite envisaged in the Versailles Treaty, the Saarland had been incorporated within the Reich. Hitler promptly compounded the victory by reconstituting the Luftwaffe, reintroducing conscription, and renouncing any commitment to disarmament. In the spring of 1936, in open defiance of the Treaty, the Nazis marched into the demilitarized zone in the Rhineland, and during the course of the next year they signed the Anti-Comintern Pact with Mussolini's Italy and withdrew from the British-backed Non-Intervention Committee that was aiming to shield Spain from foreign armies. Then in March 1938 — Havel was eighteen months old, still in nappies but mincing his first words — the Nazis tasted their greatest triumph yet: the engineered _Anschluss_ or 'annexation' of Austria, the proclamation of a Greater German Reich, and the welcoming of Hitler's splendid cavalcade in Vienna by flag-waving, cheering crowds kept orderly by Austrian police proudly wearing Nazi insignia.
The Western powers reacted to expansionism with foolish fumblings. Especially given that Hitler had no prepared timetable for his forays, and that his so-called policy of 'peaceful aggression' relied at this stage mainly on huffing and puffing, big-mouthed bluffing and local cuffing — he judged that he could get his way mainly by localized conflict that fell short of war — the reactions of states like Britain appear in retrospect to be nothing short of political lunacy. It seemed obvious to the British in particular that the best antidote to Hitler was on the one hand to recruit France and the Soviet Union as counterweights to Nazism, thereby re-creating the security triangle of the Great War, meanwhile hoping that Germany could be lured into playing the role of anchor state in a new European security zone. This episode of balance-of-power politics produced perverse results.
For many contemporary observers, the specifically modern principle of the balance of power among territorial states — a power-sharing arrangement that ensures that 'a tiny republic is no less a sovereign state than the most powerful kingdom' — was the dominant principle, the fundamental law of interstate relations in the European region. It had indeed been so since the emergence, during the Renaissance, of a system of armed territorial states. British foreign policy supposed that the principle was still operative, but the commitment produced evil contradictions. Quite apart from the problem of complicity with the most horrendous programme of organized murder that Europe had ever seen — Stalin was in the middle of liquidating more Communists than any despot of the twentieth century — the British vision required giving the Nazis precisely what they wanted: more room in middle Europe to secure and expand the _Volksmasse,_ the racial community of Germans not yet united under one state. For various reasons, the requirement came easily to the British. Influential conservatives in that country considered that Germany had suffered unjustly at the hands of the victors at Versailles while British policy-makers, too ignorant about German politics to grasp the novelty of totalitarianism, took Hitler at his word in presuming that Nazi ambitions were strictly limited to areas inhabited by Germans. Prime Minister Neville Chamberlain even hoped that Hitler would turn out to be another Bismarck. If Germany were satisfied by concessions, he supposed, it would prove to be a safeguard of European security — thereby overcoming the instability caused by France's little ally Czechoslovakia, and all the other weakling states of central-eastern Europe created by the controversial Versailles settlement.
It followed from this view of Germany as a steadying force that Prague would need to be pressed into concessions to Berlin. Czechoslovakia, the most resilient parliamentary republic of central Europe, was to be turned into a devil's playground. It did not follow automatically that Czechoslovakia had to be sacrificed without any tangible security guarantees from the Nazis, but that was to be the tragic outcome. During the second half of September 1938, Chamberlain met thrice with Hitler. 'In spite of the hardness and ruthlessness of his face,' the Prime Minister mused of the ex-Austrian ex-corporal, 'I got the impression that here was a man who could be relied upon.' At their meeting at Berchtesgaden on 15 September, Hitler insisted on the right of 'Sudetenland' to secede from Czechoslovakia. He added positively that this was 'the Führer's last demand'.
Like a dog returning to its vomit, the fool Chamberlain returned to his folly. The fools listened. Chamberlain agreed to give Hitler's demand careful consideration, but he did not expect Hitler to move so swiftly, as he did on 23 September at Godesberg by demanding the evacuation and annexation of the Sudetenland within five days. While the British cabinet initially rejected the ultimatum, France and Germany began to mobilize their armies, and at Munich on 29—30 September, in the presence of the Führer, Mussolini and the socialist Edouard Daladier, the spineless and clueless Chamberlain willingly caved in. The British in effect did the work of the Nazis. Chamberlain, who said he was _pleasantly_ tired after nine long hours with Hitler, was certain that there would now be no war. He immediately issued an ultimatum to the Czechoslovak delegation, huddled in an adjoining room, that they should accept the amputation of their state or else suffer more dramatic consequences, like the death of their body politic. Between yawns, Chamberlain spoke fine words about how the big powers would protect the rump Czechoslovak state. The Czechoslovak delegates were told that their response was not required, and that they should leave. In the same spirit as the Nazi-saluting English football team playing against Germany earlier that year in Berlin, Chamberlain then proceeded to put his hopes in a draft declaration on Anglo—German friendship, some version of which was waved in the air as he stepped from his plane in London, announcing with a triumphant smile the outbreak of 'Peace in our time'.
These foolish words of a man who thought himself wise but made his folly sovereign turned out to be the elixir of Hitlerite power. In this fools' paradise called Europe, foul-tempered Hitler — nicknamed the _Teppichfresser_ (carpet-eater) by some diplomats — drank delight. Folly nourished his worst qualities. He shouted, threatened violence, grudgingly promised to keep the dogs of war leashed for a while, then shouted and threatened violence again. _'Es hat keinen Sinn weiter zu verhandeln_ [There's no sense at all in negotiating further],' he bellowed to Chamberlain's emissary. 'Germans are being treated like niggers,' he screamed. 'No one would dare to treat even the Turks like that.' Like a rapist, he then lowered his voice, and growled, 'On 1 October [1938] I shall have Czechoslovakia where I want her. If France and England decide to strike, let them strike.'
This kind of behaviour, succoured by Chamberlain's foolishness, disgraced the art of negotiation, undermined Western support for further talks with Hitler, and convinced him, and probably Stalin and Mussolini as well, that further 'peaceful aggression' elsewhere in Europe would reap easy dividends. The policy of appeasement spelled immediate disaster for the rump Czechoslovak polity, which under the initial leadership of President Beneš was forced to suffer textbook lessons in the art of destroying a state by stages. Verbal threats followed by confusion; the confiscation of land; the spreading fever of fear; growing military pressures from without: all this served within the republic to create power vacuums within which politicians and other actors seemed to float helplessly.
The immediate effect of the Munich appeasement was to intensify the powerlessness of the state authorities. In matters of foreign policy, Czechoslovakia slipped to the status of a mere satellite state. At home, its parliamentary republican institutions suffered paralysis. Indistinct leadership, directionless policy-making, the open flouting of laws began to pave the way for a peaceful transition from democracy to dictatorship. As if hypnotized by their Nazi neighbours, the Czechoslovak political class tried desperately to forestall German interference in their affairs and to promote political recovery by emulating certain key features, but not the excesses, of Nazi rule. Within a few months of the Munich fiasco — young Venoušek was now just over two years old — pre-publication press censorship was introduced. Political exiles from Germany were extradited into the hands of the Gestapo without any vocal opposition. The National Assembly authorized the executive to legislate by decree in cases of emergency. The Communist Party was abolished and trade unions were merged into a single organization dominated by the right-wing social-democratic National Labour Party. Jews were encouraged to emigrate and many of them encountered growing discrimination by the authorities in both the private professions and state-sector employment. The election, on 30 November 1938 by the National Assembly, of Emil Hácha as third President of the country (which was soon to be renamed 'The Protectorate of Bohemia and Moravia') symbolized all these developments. So did his foolish cabinet address shortly after his election. Formulated in the rear-view mirror of time, it perfectly reflected the new-fangled policy of appeasement. 'Czechoslovak statesmen should take the national saint, Prince Wenceslas, as their model,' he told his ministers. 'Prince Wenceslas fought for German-Czech understanding, although initially he did not find understanding with his own people.'
### **Republicans**
Hácha's advice was insulting to young Venoušek's family. The historical analogy he drew was not merely unfortunate — Prince Wenceslas was murdered in A.D. 935 by his younger brother Boleslav, whose sibling jealousy was combined with strong disapproval of Wenceslas's political concessions to the German Empire. Pressured by Great Britain, abandoned by France and the Soviet Union, the Czechoslovak government's capitulation to the Munich agreement and to the growing military power of Nazism was understandable. But it flung the whole Havel family into turmoil. Václav M. Havel, Venoušek's father, was a strong-minded entrepreneur-citizen with definite anti-fascist views. 'We reject the prophets who want to solve the Depression by a return to lower levels of culture and economy,' he wrote shortly after Hitler had come to power. Wavy-haired, grey-blue-eyed, tiny Mr Havel was known to be a kind and generous man of calm moderation. He held firm political views. 'We do not want to go backwards in civilization', he wrote. He found repugnant 'nationalism', 'irredentism' and 'racialist messianism'. These evils needed to be wiped out — principally by embracing the power-sharing, social-liberal principles of 'openness and truthfulness, purity of political ends and political means, intelligent and honest politics'.
Venoušek's father thought that these high principles required a new system of welfare-state-regulated capitalism and parliamentary democracy guided by a 'cultural elite'. A modern-mannered republic was his ideal. 'To avoid any misunderstanding,' he once said in a speech, 'by "elite" we do not mean a closed caste, but rather an unorganized, unorganizable partnership of creative spirits, who thanks to their strong cultural values form a cultural authority in society, a spiritual government which — free of all means of power — is a durable and continuous guardian of successful social improvement.' The task of the cultural elite, of which he clearly considered himself a member, was to work for a polity defined by the non-violent sharing of power. Mr Havel was not a man of the Left. He usually voted for the National Democrats — a party founded by Karel Kramář, who in 1919 became Prime Minister of the new Czechoslovak state. Mr Havel stood for open government, full employment, socially responsible investment, the cultivation of individual conscience and creative responsibility through education, and nurturing 'mutual assistance and co-operation' through civilized corporatist bargaining among unions, businesses and professions. 'Democratically onwards!' he liked to say to his friends. He usually added, in the next breath, that the world of international politics now needed to cultivate genuine patriotism among citizens, support for peace through the League of Nations, and the protection of sovereign autonomy of nation states. His conclusion was utterly old-fashioned. 'The unity and independence of the Czechoslovak state,' he said, 'are not subjects open for discussion.'
These patriotic social-liberal views were redolent of an old and respectable family whose known roots stretched back into the late eighteenth century. Young Venoušek was soon to hear tales, told by his father and mother, of the family's fair share of misfits and tragic figures: a great-great-grandmother who died in childbirth; a distant cousin who was taken by tuberculosis; a great uncle Rajmund who probably drank himself to death; another uncle, a butcher by trade, who died young of blood-poisoning. The family otherwise consisted of stolidly bourgeois stock. A rare photograph of Venoušek, a smiling four year old, dressed in a heavy coat and beret and clutching an umbrella, shows him standing in Prague's Košíře cemetery, beside the soon-to-be-destroyed family tomb that contained family members dating back 200 years. His great-great-grandfather, Vácslav Julius Havel was the first-born son of a well-known Prague miller and citizen; his wife, Terezie (1816—1882), who died suddenly from an attack of pneumonia, came from a family of moderately prosperous farmers. Venoušek's great-grandparents were prominent merchants and restaurateurs, while his grandfather, a successful Prague building contractor who married a much sought-after wealthy beauty, lived and worked, surrounded by servants, within a 'bourgeois milieu'.
Venoušek's grandparents were also members of the 'cultural elite' that favoured independence from the Austro-Hungarian empire. They grew up as Czech patriots within a territory whose ruling group remained instinctively 'Austrian'. Unlike Lieutenant Lukáš — a character in Jaroslav Hašek's _The Good Soldier Švejk —_ the Havels were not Czechs who equated being a Czech with membership of some kind of secret organization, who spoke German in society, wrote German, and who read Czech books and said to others in confidence: 'Let's be Czechs, but no one need know about it.' The Havels refused to educate their children in German-speaking schools. Young Venoušek's industrious grandfather, Vácslav Havel, 'employed only Czechs wherever he could'. He built the first indoor ice rink in Prague; sited on Primátorský Island, it was called Harmonia, and quickly proved to be a popular meeting point for Prague's cultural elite. His greatest project was the design and construction, from 1905 onwards, of Lucerna, the first and largest modern entertainment complex in Prague. It was inspired by his travels to such cities as Paris, Copenhagen, Milan and Berlin and by his patriotic faith that one day Prague would become a European metropolis.
In political terms, Venoušek's grandfather openly described himself as a 'Young Czech'. That meant that he had a poor opinion of the Habsburg dynasty that ruled over the Bohemian lands for 300 years. It was bad rule, he thought. The dynasty had destroyed religious freedom and suppressed the Czech language. It had driven the elite of the nation's nobility and church into exile, distributed estates and offices to alien caretakers, and turned the Czechs into an impotent minority within an ill-administered province. Venoušek's grandfather was proud of the 1918 declaration of Czechoslovak independence. He considered it a brave revolution, in which not a drop of blood was spilled, no windows were broken, and in which the first law passed by the revolutionary committee declared: 'All existing laws remain in force.'
These opinions counted. Venoušek's grandfather was well connected within the worlds of Prague business, medicine, arts, education, and politics. He was good friends, for example, with Karel Kramář, a well-known founder of the Czechoslovak state and political rival of Tomáš G. Masaryk. He kept company with the Deputy Mayor of Prague, Dr Stech, and was well acquainted with Professor Jan Jesenský, the father of Milena Jesenská, and Alois Rašín, who later became Minister of Finance in the First Republic of Czechoslovakia. Venoušek's grandfather was also active in theatre circles. He was treasurer of the National Theatre Association (among whose members his nickname was 'The Finance Minister'). He and his wife, who was a renowned cook, were regular hosts of lavish dinner parties, whose invited guests included many well-known artistic personalities, among them the lyric poet and dramatist Jaroslav Kvapil, and the most famous Prague poet of the day, Jaroslav Vrchlický, revered for his weaning of Czech literature away from German domination and (as his blurred images in the Havel family archives reveal) notorious for refusing to sit or stand still before the magnesium lamp camera, to which he had a principled aversion.
Venoušek's father — according to the rather dry account he gave of his own early years — thought of himself as a faithful carrier of this family tradition of republican Czech bourgeois respectability. By European standards, the family was 'apparently wealthy'.Although considerable debts were incurred from building the Lucerna complex, its assets enabled the family to lead a life of cosmopolitan luxury. As a young boy, before the First World War, Venoušek's father was taken on family trips to Italy, France, Belgium, and to Holland, where in Oostende (according to family folklore) he heard a performance of the great Italian opera singer, Caruso. The family often took holidays abroad. During the First Republic, they travelled on summer holidays to seaside resorts in Germany and Italy, and to the breathtaking lakeside setting at Bled, located in today's Slovenia; in wintertime, they liked to stay closer to home, at favourite ski slopes in Mnichovice and in the Giant Mountains (Krkonoše). After Venoušek was born, the Havel family liked to stay in their spacious summer residence at Havlov, a few hours by car from Prague. Accompanied by servants, the family also loved to venture out of Prague on fine-weather Sunday outings, especially by car, and then steamboat down the Vltava River to Braník, where they were ferried across the river to picnic and climb the cliffs of Barrandov in search of trilobites. Venoušek's father and mother also hosted visits to Havlov from Prague notables. Painters, lawyers, politicians, writers — what they called 'educated Prague society' — were regular guests at the family table. Among them was the most influential Czech writer of the First Republic, the witty and wise Karel Čapek, whose novel _War with the Newts_ (published in the year of Venoušek's birth) satirized fascism, colonialism and greedy capitalism, all in the spirit of what Czechs like to call _lidskost:_ down-to-earth sympathy and kindness for others.
True to the family's Young Czech instincts, Venoušek's father was sent to his father's old school, the Czech reálke, located in Ječná Street, near Charles Square, in central Prague. He later went on to study construction engineering at the Czech Polytechnic in Prague, where amidst the fears and hopes, disruption and destruction generated by the Great War, he became active in student politics. Shortly after the end of hostilities, at the moment of the birth of Czechoslovakia in 1918, he was elected as the first Chairman of the Union of Czechoslovak Students. The political experience made him 'a life-long democrat, an admirer of Masaryk'. He was attracted to Masaryk's ideal of a 'perpetually self-reforming democracy' and he became convinced, for the rest of his life, that politics was important and that thinking and acting as an informed citizen was a duty, not a luxury. 'Political activity or inactivity is a question of conscience,' he later wrote. 'We are the state — and each of us is therefore responsible for its condition and future. If we tolerate a defective system, it is because we have not yet created anything better; bad people will make decisions only until such time as better people have acquired the courage, strength and ability to replace them. A new political programme requires creativity, activity and radicalism, both intellectual and moral.'
The spirit of republicanism pervaded his visionary advice to an audience of young people, given in the month of Hitler's accession to power, to work for a 'quality democracy' in the new Czechoslovakia. Contemporary democracies like Czechoslovakia, he argued, suffered from a variety of ailments, most of them traceable to the tyranny of 'the mechanical spirit'. Venoušek's father here drew upon the authority of a family friend, the Brno philosopher J. L. Fischer, to condemn the hegemony of mechanical reason. Mr Havel disliked the bad habit of supposing that both nature and society can and should be observed, numbered, recorded, planned, and ordered about at will. The mechanical spirit, he told his young audience, had colonized the dominant ideologies of the times. Liberal individualism, which presumes like an accountant that each and every individual is 'an absolutely free unit' guided by the criteria of'size and number, minimum expense and maximum benefit', was a case in point. Bossy forms of collectivism pushed in the same direction. Fascism perversely worships the Nation and state-building, while Communism, guided by the doctrine of the dictatorship of the proletariat, ends up doing the same by greedily monopolizing power over its subjects in the name of class struggle.
Despite the rise of German fascism, Mr Havel predicted that these ideologies of impersonal mechanization would eventually lose their grip upon the world. His stated belief in human progress was often put so fulsomely that the faces of its nineteenth-century exponents would have flushed. 'Every thought and every organism goes through a certain development,' he wrote. 'The times call for new relations and contexts. Progress then assumes that the positive values and achievements bequeathed to us by the past and still unsurpassed will be preserved. Those, however, which have lost their significance cannot be permitted to be an obstacle to new development. That is the principle of evolution.'
Venoušek's father used this principle to predict the end of liberal democracy. 'The idea of the responsibility of the individual for the whole, and of the whole for each individual' was gaining ground. So too was the related insight that the individual, far from being an atom whose motion is calculable, is rather 'a person and personality variously capable of various tasks and continually changing'. All this was plainly evident in contemporary architectural designs that favoured simplicity, horizontality and function, rather than mere form. The trend was evident as well in industrial experiments, like the Bat'a employee autonomy-and-performance schemes in the field of shoe-manufacturing. And it could be seen in the magnificent Sokol rallies, held to the sound of loudspeaker music. 'Everyone who has watched the undulating masses during physical training notes with interest the individuals, the beauty of the function of man in relation to the tremendous whole. More striking, however, is the way that every individual is trained in his unit to develop his own unique characteristics and attitude, despite the tremendous and uniform appearance of the whole.' Such experiments, observed Mr Havel, signalled the demechanization of life and the birth of a _quality_ democracy that values power-sharing, choice, personal responsibility, equality of opportunity, patriotism, functionalism _[ú čelnost],_ voluntary discipline, beauty, openness, public accountability, and personal belief in a God. 'I am convinced that there is a more effective form of democratic government than today's,' he concluded. 'It is the task of all who acknowledge the high moral value of democratic ideals to strive, without delay and with every ounce of energy, for the reconstruction of our democracy in the spirit of the times.'
### **Devil's Playground**
The times were unripe for such dreaming. The fledgling parliamentary republic of Czechoslovakia was on the verge of becoming the unlucky testing ground for something new in the ways and means of power. A bizarre symbol of things to come was the kowtowing of one head of state to another. The old Chinese custom of touching the ground with one's forehead as a sign of worship or absolute submission to power _(k'o-t'ou,_ from _k'o,_ knock, _t'ou,_ head) — the Czechs call it crawling up someone's arse — was repeated on the evening of 14 March 1939, when the top-hatted, stooping President of the Czechoslovak Republic, Emil Hacha, hurried by train from Prague to Berlin to keep an appointment with Hitler. It is unclear just how well Hacha along the way had digested the ominous news that that same evening, at 17.30 hours, the crack SS Bodyguard 'Adolf Hitler' had begun to occupy the Ostrava region, in the north of the country. It is known that Hácha's appointment began badly. The moody film buff Führer — the man who seemed to regard total war as a big-budget film — made his counterpart wait two hours so that he could finish watching a movie. It was an escapist romance, recommended to him as usual by Goebbels, appropriately enough entitled _A Hopeless Case (Ein Hoffnungsloser Fall). 21_
Business got under way at a quarter-past one in the morning, by which time the old and frail Hacha had been mesmerized into playing the role of the mouse before the lion. Hacha was the first to open his mouth. He repeated what he had said publicly before leaving Prague: that the Czechoslovak state indeed belonged both geographically and historically to the sphere of German power. Apparently so surprised by Hácha's submissiveness, Hitler, sipping his favourite mineral water, quickly roared that within six hours the German armed forces would invade Czechoslovakia from three sides, crushing ruthlessly any resistance along the way. It was a lie. German airfields were at that moment enshrouded in fog. But the lie had instant effect. The faint-headed Hácha collapsed into the arms of the Führer's personal physician, Dr Morell, who injected him at once with dextrose and vitamins. The kowtowed Hácha with eyes barely open was then told by Göring that the Luftwaffe would smash any Czech resistance by reducing Prague to a pile of rubble. The bluffing worked. Hácha telephoned Prague to order that there be no resistance to the invading troops. He then reassured Hitler and his entourage of clever thugs that Czechoslovakia would do anything to avoid bloodshed. Sitting beside Hitler just before dawn, Hácha concluded the meeting by signing a statement prepared by the Nazis. 'The Czechoslovak President declared that ... he confidently placed the fate of the Czech people and country in the hands of the Führer of the German Reich,' the statement ran. It was a masterpiece of political deception. 'The Führer accepted this declaration and expressed his intention of taking the Czech people under the protection of the German Reich and of guaranteeing them an autonomous development of their ethnic life as suited their character.'
The words were to be written like foul-mouthed graffiti over the young Václav Havel's life during the next six years. Hácha's faint-headed behaviour before Hitler fitted perfectly the stereotype of Czechs as self-pitying, childlike subjects skilled at stepping away from responsibility — subjects who are then forced by others to pay heavily for their cowardice and to wallow in a 'martyr complex'.It was later said in Hácha's defence that he tried his best under difficult circumstances to protect his fellow citizens. And Hácha himself claimed that he had sacrificed the state to save the nation. But the bitter truth was that the Czechs were forced to pay heavily for their leader's kowtowing. The Czechoslovak state was rapidly dismembered. Ruthenia was forcibly annexed by Hungary. Slovakia was reorganized into an independent state with limited sovereign powers. And Bohemia and Moravia, once the heartlands of the republic, were pushed and shoved through several stages of Nazification.
_'Es kommt der Tag_ [The day will come],' Czech friends of the Nazis used to whisper, and here it was. Hours after Hácha's fateful meeting with Hitler, in blizzard conditions, German troops poured into Prague, red-faced by sleet and frost, and perhaps even a touch of shame. Hitler followed, checking in to Prague Castle at Hradčany on the evening of 15 March. Initially, the Nazis treated their prey with caution. Militant pragmatism dictated that the Czechs were to be exploited for the Nazi war effort with a minimum outlay of German resources. Talk of Czech-German co-operation abounded. The important independent powers of the provinces of Bohemia and Moravia — customs and monetary affairs, military authority and defence, foreign affairs, and postal and telecommunications facilities — were all wiped out by decree. All governmental institutions were placed under the immediate authority of the 'Reichsprotektor', an office filled by the former German foreign minister, Baron von Neurath, who from here on countermanded 'in the interest of the Reich' any measures of the government of the Protectorate. The Czechoslovak army was disbanded. Parliament was dissolved. All political parties were suspended. Privileges were extended to the ethnic German-speaking minority, such as the right of Reich citizenship, immunity from Czech courts of justice, and promotion within the administration of such cities as Prague, Brno, Olomouc, and České Budějovice. Meanwhile, 'sensible' measures against Jews were taken, which meant that a climate of fear and suspicion was nurtured, for instance by sacking Jewish civil servants and banning the Jewish population from purchasing or disposing of their property.
Following the declaration of war on Germany by Britain and France on 3 September 1939, but especially after the posting to Prague two years later of Reinhard Heydrich, former boss of the Reich Security Office _(Reichssicherheitshauptamt),_ the Nazis toughened their methods of governing. Stimulated by military victories against the Soviet Union, and confident in their own ability to deal with reported Czech resistance, and keen to win what Goebbels liked to call the 'chess match for power,' the Heydrich administration swiftly moved in for the kill. Martial law was declared. The Gestapo undertook large-scale arrests, turning first mainly to German political _émigrés._ Rounds of summary court judgements and executions followed. Material concessions to peasants and workers were combined with policies aimed at terrorizing and weeding out intellectuals. The Czechs were entitled to live a private existence so long as they didn't think or act publicly. Colleges and universities were closed and their buildings assigned either to the German University in Prague or used for different functions, as happened to the building of Prague's college of law, which was turned into a _Schutzstaffel_ (SS) barracks. Student dormitories were ransacked. Thousands of students and staff were arrested. The 'ring-leaders' among them were summarily shot. Many others were carted off as hostages to the Oranienburg concentration camp, from which they were set free by handfuls and permitted to return home, frightened by their brush with death.
Nazi government in this form bore the stamp of Heydrich, under whose leadership the Protectorate was changed by fits and starts into a well-functioning system of total power, the likes of which Czechs had never before experienced. This was no dictatorship or despotism. It was an entirely new configuration of power, whose contours defied all traditional categories of political thought. It was soon to be called 'totalitarian'. The word has subsequently lost much of its sting through familiarity and misuse, but for descriptive purposes it remains chillingly apt. Under conditions of totalitarianism, nobody — not even its commanders — was safe from persecution, or death. Totalitarian rule was specifically geared to organizing, breaking up and destroying everything that was living, dead, inert. Land, shared historical memories, men, women, and children: these were the objects of totalitarian rule, which more savagely rampaged through the world only _after_ its adversaries were defeated and destroyed.
The totalitarian power that the Nazis brought to Prague was unhinged power. Balzac (in _Cousine Bette)_ noted that 'arbitrary rule is power gone mad', but the madness of totalitarian power was beyond the bounds of his wildest imaginings. Transforming the world into a hell-hole, totalitarianism was uninhibited power enjoying a monopoly of the means of available violence. Totalitarian power was the unrestricted capacity to organize and push people and things down the path of complete annihilation. Totalitarian power produced total powerlessness. It even regarded suicide as an insult, and it did all it could to prevent it by emaciating and grinding down the bodies of its victims — in the last instance by means of torture, or by a bullet through the head of the one trying to reach the electrified fence. Totalitarian power naturally created an inferno of fear and uncertainty for everybody and everything. Nobody was safe from annihilation. Totalitarian power certainly relied upon formal organizations: specialized administrative staff; hierarchies of command; the scheduling of services; codes of conduct and discipline for personnel; systematic record-keeping. In this way, totalitarian power could function well by ensuring smooth administration, even if its staff were second-rate, or prone to rivalry, protection and corruption. Totalitarian rule also certainly put to good use individuals who were careerists, or who had a strong sense of duty and a knack for organizing things and getting jobs done. Yet totalitarian power was most definitely not a species of bureaucratic rule. For one thing, it cultivated and required its victims' willingness to take the initiative in performing the dirty business — for instance by informing on others, or supervising prison work-squads. For another thing, totalitarianism recognized no hindering rules or restrictions; it was self-propelling power that thrived on crashing through the world, demolishing all barriers along the way. Totalitarian power tended to undermine bureaucratic rule. It ignored considerations of economic utility or _Realpolitik._ And it did away with talk of moral or ethical restrictions. It treated such talk as rubbish left over from a corrupted past.
The totalitarianism of the Reichsprotektorat dispensed with ideological convictions. Although it operated under the canopy of a totalizing ideology — the ideology stressed the animal-like struggle of the new Reich against its enemies, and the imperative of building a new Europe modelled on the emerging _Volksgemeinschaft_ of the Third Reich — totalitarian power effectively broke free from all such ideological self-justifications. The old maxim that power is only effective when it is legitimate in the eyes of the ruled was disproven by totalitarian power, which was not at all a type of rule guided by principled aims and calculations of how to achieve certain ends. Or, rather, totalitarian power was guided by only one end: the annihilation of its designated enemies. Totalitarian power was impulsive, arbitrary, terroristic, murderous. Not even its unlimited power of culling and sewing a label on whole categories of the population — Jews, homosexuals, Romanies, Poles, Jehovah's Witnesses, the unfit — was free of arbitrariness, uncertainty and disorder. Everything became provisional. The essence of totalitarian power was terror — soul- and body-destroying fear driven by the expectation that death and destruction at the hands of the secret police, army or 'unidentified thugs' were just around the corner.
Thanks to the Reichsprotektorat, everybody, including the administrators and accomplices of the regime, was potentially superfluous. 'Force should be right,' said the totalitarian voice, 'or rather, right and wrong should lose their names, and so should justice.' The living were flung into a merciless struggle of each against all. The boundaries between life and death dissolved. Past and present and future collapsed into each other. Each minute was potentially the last minute. A second could feel like a lifetime. Or like nothing at all. Everyone was 'raw material'. Each individual was on terror's hit list. Anyone — in the Auschwitz jargon — could be turned into a walking dead _Muselmann_ ('Muslim') whose body and soul disintegrate before the eyes of others. Anyone could be disposed of without trace. Murder naturally succoured this form of power. It demonstrated its omnipotence. Gruel excess was constantly required. Talented and ingenious barbarism functioned as a form of self-assertion — as sadistic proof that there were no external barriers to power, that those who were acting on the world were capable of anything, that the unthinkable was real.It was therefore not surprising that bizarre forms of dastardly evil resulted. Totalitarianism was a killing field, which is why the mass grave and the concentration camp, in which subjects were stripped of the right to have rights and then exterminated, were its perfect manifestations — and not somehow embarrassing exceptions. Extermination of individuals and whole groups — one might even say all of humanity — was the logical and practical end point of totalitarian power.
### **Zoology**
The frightening novelty of the regime convinced the Havel family to remove young Václav and his little brother Ivan from the hell-hole of Prague to the relative tranquillity of their country house, near Tišnov in Moravia. Havlov served for a time as something like a rural retreat. The half-wooden, white-plastered villa with green window-frames and a swimming pool was tucked away within a forest, above a little stream called Bobrůvka, within hiking distance of old Pernštejn Castle. The house was also within walking distance of a school in the nearby village of Žd'árec, which Havel began attending during the first week of September 1942. The decision to move the children and send them to a country school was his mother's. Božena Havlová, like many other thinking Czechs, tried to act as if life were normal, all the while knowing that the world was now being divided, violently and irreversibly, between those who valued human omnipotence and those for whom utter powerlessness was a simple fact of life.
Reinhard Heydrich, who prior to his rule of Czechoslovakia had been among Himmler's closest collaborators, was emblematic of the trend. Here was a new type of ruler, unfamiliar to most Czechs, a man convinced of his own omnipotence and skilled in the art of repeatedly insulting his opponents to demonstrate to everybody that they were not merely flesh-and-blood opponents but 'objective enemies'. Those who knew him personally — the Havel family did not — confirmed his habit of regarding friends as potential foes, and rivals as enemies, 'not as individuals, but as carriers of tendencies endangering the State and therefore beyond the pale of the National Community'. His obsession with 'objective enemies' evidently led down the path of reducing them to nothing, or killing them in 'self-defence'. This meant the extermination of whole categories of flesh-and-blood mortals. Heydrich was of course temporarily interested in Jews and in Romanies — thousands of whom reportedly died from 'typhus', which meant beating, starvation, transportation to Auschwitz as slave labourers, gassing in nearby Birkenau, or being burned, tossed into latrines, or buried in mass graves in forests. But the list of future potential victims was infinitely expandable. It was well known to the Havel family, and to others in informed Prague circles, that as early as 1941 proposals had been circulating among the Nazis to treat the entire Polish population as Jews: making them the objects of compulsory changes of name if they were of German origin; forcing them to wear the P-sign, which would function like the yellow star worn by Jews; and making sexual intercourse between Germans and Poles punishable by death. Many Czechs, the Havel family included, naturally began to fear that they might be next in line.
Their fears were laced with rumours, deliberately planted by the German authorities, that they would deport or eliminate hundreds of thousands of Czechs. Driven by expectations of total victory in Western Europe, plans for the deportation of the Czechs — what later would be called 'ethnic cleansing' — were indeed drawn up. The Havel family knew that tens of thousands of Czech workers were being compulsorily drafted into work teams and sent to the Reich. They knew that Jews were receiving orders to hand over their typewriters and musical instruments, furs and microscopes, that they were now forbidden to enter certain streets and parks, that they were now prevented from disposing of their property, or making gifts. The family also knew that the once-small fortress town of Terezín (Theresienstadt) was being transformed into a 'self-administered' ghetto for Jews, even those who considered themselves Czechs and Christians. The Havels knew as well that Jews were cruelly saddled with the jobs of selecting candidates for 'resettlement lists', which meant transport to death camps elsewhere, and of apportioning the starvation rations of a few grams of bread and potatoes and teaspoonfuls of soup to inmates too old or exhausted to work.
The implication was clear: the punishment of non-Germans and 'unfit' Germans was a precondition of the triumphant will to total power over others. World conquest required breaking down the division between the conquering regime and the conquered territories. Even the distinction between 'at home' and 'abroad' had to be dissolved. A totalitarian conqueror like Heydrich had to act as if the territory he had conquered were his very own home — by eliminating strangers who did not belong. And so the Nazis' ultimate aim — as Heydrich clearly stated in his first speech after assuming office — was to undo the work of young Czechs like Havel's father, to 'Germanize' Bohemia and Moravia by incorporating them fully into the Reich. Hitler's 'table conversations' about the Czechs made it clear that while the Nazis aimed within their borders to build a suave totalitarianism, this involved no sympathy or respect for the Czechs. 'Germanizing' them meant expelling or exterminating elements of the population 'unsuited' for Germanization. It also meant acting like locusts within the country's rich fields of political culture and inherited republican parliamentary institutions. The final aim was to be linguicide. 'By firmly leading the Protectorate,' said Hitler during the third year of occupation — young Venoušek was now five and a half years old — 'it ought to be possible in about twenty years to push the Czech language back to the importance of a dialect.' All this required that the Nazis had to be cruel. But, in order not to trigger explosions, or simply to avoid strikes and sabotage, or even guerrilla warfare behind the lines of the German army, the Nazis had to be kind. They had merely to be cruel by stealth. The aim was to kill the Czechs with kindness. So although the Führer stressed just how useful threats of expulsion of the Czechs from their homeland were as a means of government, he also instructed his Prague henchmen that Czechs should not be involved directly in the war effort. If that happened, they would likely raise their demands. Better then to seduce the Czechs into obedience and hard work by 'good treatment' and 'double rations'.
The dilemma hiding within the Nazis' conquering power over the Czechs mirrored a dilemma lurking within the ranks of the conquered, young Václav included. From the side of all Czechs of (potential) anti-Nazi sentiment, threats of arrest, deportation, murder, imprisonment and extermination were self-evident from the moment of occupation. Like the man who worked in the crematorium in Prague at the time of the Nazi occupation — the 'hero' of Ladislav Fuks's novel, _The Cremator 32 — _ virtually every household was touched by the thought that individuals, groups, indeed the whole population would suffer interrogation, or arrest, or extinction. Various reactions were thinkable, including stashing weapons in sofas, cupboards and coffins, and martyrdom in the form of open resistance. Yet the nasty experience of the Poles when resisting Nazi occupation, combined with the fact that the Czechs themselves had already been the victims of appeasement at Munich, made many Czechs think twice about this option. It encouraged them to conform, to tiptoe across puddles of blood, to take the road of self-abasement in order to guard themselves against the dreaded outcome.
At Havlov, Havel's parents heard through radio reports of the huge rally of 200,000 Czechs packed into Wenceslas Square in the mid-summer of 1942, singing the national anthem whilst pledging allegiance to the Third Reich and giving the Hitler salute. It depressed them. The rally demonstrated to them, and to every thinking person, that collaboration in the exact sense of the word was widespread among Czechs. Sometimes the cooperation assumed crude forms, symbolized by the case of Colonel Emanuel Moravec, a former prominent nationalist member of the Czechoslovak Legion, who accepted from the Nazis the job of heading the Ministry of Education and the new Office for Public Enlightenment. Such arse-crawling by Czech stooges and quislings was abnormal. Quite a number of Czech governmental and political-party figures, for instance, saw instead that their interest lay in keeping calm, maintaining order, keeping the population politically alert, and, wherever possible, subtly 'throwing sand into the cogwheels'. The response of many civil servants ran in a parallel, but different direction. They certainly knew that if they caused trouble they would lose their jobs and suffer police action. So they stayed at their desks not out of simple opportunism but rather because they were titillated by the vague hope that the country would survive in the eye of the storm of totalitarianism if they zipped their lips and kept their heads down.
Then there was the disquieting response of those whose reaction to total power is best described as zoological: better to live well fed and quietly than not to live at all. As a type of collaboration, zoologism was a complex matter hedged in by dimly expressed motives. Zoologism supposed a tacit agreement between rulers and ruled that peace and quiet served the interests of both. Bearers of the 'contract' understood that it was renewable daily by possible annihilation and the impossibility of calm calculation; that fear ate the brain and soul; and that when the fear-stricken ruled thought about it at all, martyrdom in the face of total power seemed pointless, simply because their own superfluousness had been decided in advance. For these 'reasons' alone, plenty of Czechs adjusted their lives to the simple obligatory maxims of zoologism: Powerless of the Great German Reich! Quietly comply! Conform and be dull! Tell yourselves as you look in the mirror each day that it is better not to die. Forget about a most basic freedom, the freedom to tell others what they don't want to hear. Get on with existing. Do whatever you feel like doing! Shave, wash, work, shop, cook, eat, drink, chat, bathe, make love, fall asleep. Keep your chins up. Keep your noses clean. Clink glasses. Grumble quietly. Tell jokes, if you can. And no matter what happens, avoid thinking, let alone uttering the word collaboration. If you do, regard it as a meaningless slip. Then quickly change the subject. Define away questions about whether co-operation with the powerful is ever shameful, or treasonable. Above all, regard collaboration as a non-existent word.
### **Resistance**
Czech pusillanimity later became the butt of Czech humour. Among the favourites that circulated in the Havel household was the one about the Yugoslav and Czech tourists who meet on a pebbled summer's beach in Dalmatia. 'Whenever we came across Germans in uniform, we used to shoot them or, to save bullets, slit their throats,' said the reminiscing Yugoslav, matter-of-fact. Replied the Czech: 'Well, you know, we would have liked to do the same thing, but at the time in our country it was against the law.'
It was later easy to laugh. But in the dark times of the Reichsprotektorat the rampant conformism of many Czechs validated the fear, shared by the republican-minded Havel family, that the world was dividing into omnipotence and powerlessness. In the lugubrious circumstances, it seemed out of the question that Reinhard Heydrich, the superman of total power, could himself be harmed by powerless conformists. But it happened. On the morning of 27 May 1942, a great drama — one that young Venoušek Havel was old enough to remember for the rest of his life — was performed in the streets of Prague. Two of seven parachute agents sent by the Czechoslovak government-in-exile in London successfully launched a bomb attack on Heydrich's car as it rounded a sharp bend into the street V Holešovičkách in the grey factory district of Prague-Libeň. A lorry from a nearby factory jammed the road, forcing Heydrich's driver to brake suddenly. Tommy-gun shots rang out. Heydrich fired twice from his service revolver, but both shots missed their target. Two bombs then exploded in quick time, ripping out the car's undercarriage. Heydrich was rushed to the nearby Bulovka hospital, where he died nine days later from infected wounds.
Heydrich was the only leading Nazi to be assassinated during World War II. The whole Czech population was made to pay for the daring act. On the evening after Heydrich's death, the body was carried through the ghostly curfewed streets lined with SS men wielding flaming torches. The cortège passed through the hilltop Castle gates at exactly the moment the city clocks below chimed midnight. The precise timing was a wicked omen. Terror straightaway stalked the streets of Prague. Each morning and evening, firing squads in the Prague-Kobylisy execution grounds could be heard ruining lives. It was announced that anybody suspected of concealing knowledge of the assassins would be shot, along with their entire families. Suspicion was soon directed (mistakenly) at the village of Lidice, near Prague, whose men, women and children were ritualistically murdered, deported to Ravensbrück concentration camp, or (the fate of small children) physically separated and adopted out in preparation for 'Germanization'. Rumours were deliberately planted that every tenth Czech would meet the same fate unless the parachute assassins were apprehended. Then Himmler ordered the SS to arrest and murder 30,000 politically active Czechs — a final solution that proved unnecessary after Heydrich's assassins were finally cornered, two weeks after his death, in the Church of St Cyril and St Methodius on Resslova Street, several blocks from the Havels' house in central Prague. Following a shoot-out with the _Waffen-SS,_ the men took their own lives in dignity, rather than surrender in humiliation to the Nazis.
The Nazis' revenge against the Czechs undoubtedly complicated lives, including the Havels'. It felt as if the whole nation now lived in a house suffering a great misfortune. Silent lips quivered. Daily life trudged heavily uphill. Resistance to totalitarianism in any form became more difficult, not to say dangerous, but the miracle was that it did not disappear entirely. Quiet methods were mostly employed, ranging from private bellyaching and jokes — various forms of underhanded, petty, anti-authoritarian guile that the Czechs call _švejkovina_ — to random acts of sabotage, and a special kind of resistance, one that harnessed the power of beginning. Women's efforts _not_ to conceive by practising contraception are most often a form of resistance to power that governs them. But in the Reichsprotektorat the willingness to risk conception, although it bordered on nonchalance and added to the daily pressures on women, had a politically important effect: a substantial increase in the birth-rate from 15 per thousand in 1938 to, 16.7 in 1940 and to 20.7 in 1943. Despite everything — during the five-year Reichsprotektorat up to 135,000 Czechs died from political persecution and in concentration camps, including the murder of about two-thirds of the Jewish population — births markedly outstripped deaths and the overall population of Havel's homeland increased by some 236,000.
This was not the route Havel's mother took — her last child and second son, Ivan, was born on 11 October 1938 — which raises the pertinent question of which other methods, if any, she and her family used consciously to resist the Nazis. The surviving past fragments are few, and indistinct. During the course of 1944, for instance, Havel's father, who had Jewish friends and a history of acquaintances stretching back to his own father's business dealings with a Prague Jew named Kohn, was visited by the Gestapo and threatened with reprisals for allegedly sheltering a Jewish family in the Lucerna building. Fearing for their collective lives, the Jewish family had in fact already fled to Canada, perhaps with the secret assistance of the Havels, and no further action was taken, luckily so since it was a capital offence to shelter unregistered persons.
More definite — and most instructive — are the surviving details of the fraught involvements with the Nazi-dominated Czech film industry of young Venoušek's Uncle Miloš. Good-looking, intelligent, youthful, always stylishly dressed, Miloš (1899-1968) was from an early age his nephew's favourite relative. Miloš was the sort of character who was bound to clash with the local Reichsprotektorat quislings. Since his teenage years, Miloš had had a keen eye for social justice and lived by the motto of 'the self-determination of the individual'. His friends, most of them in the smart set of Prague, found him 'charming, generous, elegant, gifted... a man of great style who was capable of brilliant ideas'. Miloš was a 'generous, gregarious' figure who liked to drink wine and (as he put it) inhale 'the odd cigarette' in the company of theatre and film directors, actors and actresses, musicians, dancers and painters. He was a lifelong close friend of the famous writer-performer, Jan Werich, and his professional and personal contacts ran deep and wide. Women found him attractive. 'Many a proud mother would have found him a suitable husband for her daughter,' remarked his stolid brother, young Václav's father, but mothers and daughters alike were consistently disappointed. For convenience's sake, Miloš was briefly married in 1934 to an old friend, the daughter of a wealthy Prague architect, Maria ('Mánička') Weyrová. At the beginning of the Reichsprotektorat, their platonic relationship was dissolved by mutual consent. Thereafter — the anachronism is descriptively appropriate — Miloš led a life that was openly gay.
That fact alone made Miloš a potential victim of Nazi terror. So too did his interest in the film business. He had been trained at the commercial academy in Prague, and had genuine entrepreneurial flair. 'Miloš was a natural-born boss,' noted his brother. 'He didn't shout or use insults or vulgar language, but he knew how to get his wishes and orders across; rarely was he opposed.' The born boss had a soft heart — numerous times he intervened to prevent the sacking of his own staff accused of wrongdoing by their supervisors. He was most definitely not a bourgeois philistine: not a businessman who was an _épicier_ (the word used by Gustave Flaubert to condemn the uncultured bourgeoisie), a colourless materialistic creature from head to toe, an unadventurous figure bereft of all sense of the extraordinary and the exotic. Miloš was averse to the seductions of the easy and as a member of the cultivated upper middle class he tried to combine business with strongly modernist sympathies for the unconventional. He liked motor cars and car-racing — he was among the first to drive a Mercedes in Prague — and he was excited by the new medium of radio. At a very young age, he founded Radio Lucerna, a company which successfully imported from England all the latest radios, including cheap crystal sets, which sold like hot cakes in Prague. During World War I, he became interested as well in film, and set up a cinema company called Lucernafilm and a cinema called Bio Lucerna. It released silent films (like American Westerns) never before seen in Prague; and in 1929, using Western Electric equipment, it was the first moviehouse in the country to introduce talkies like _Ship of Fools_ and _Six Wives of Henry VIII,_ starring Charles Laughton, both of which caused a sensation among audiences who found themselves returning again and again to see the same film.
Well before the Nazi invasion of Czechoslovakia, Miloš naturally explored the possibility of commercially producing Czech films. He did so by setting up the Barrandov Studios — the Czech Hollywood — and a film-production company called AB, both of which instantly became the targets of fascist intrigue. The Nazis had an interest in retaining the services of Miloš, and in preserving and expanding the film industry as a whole. For the majority of the Czech population, cinema was the preferred entertainment amidst misery and, from the Nazis' point of view, it was an important added consideration that the Prague Barrandov studios were technically advanced and initially beyond the range of allied bombers. Soon after invading the country, the Nazis seized a 51 per cent stake in Barrandov and set up a new German front company, Prag-Film. It managed all aspects of film production, linked it to its German counterpart, and worked hard to improve the already excellent technical facilities by expanding the studio complex and building the largest sound stage in Europe. So long as the Czechs avoided 'stupid nationalism', explained Joseph Goebbels, they could play a key role in the cinema of the New Europe. European cinema, he predicted, would eventually eclipse Hollywood in its power of seducing audiences.
The reaction of employees at Barrandov varied. Some had to get out, like the Jews of the film world, who left in search of the kind of success that blessed Miloš's friend, the actor Hugo Haas, who went all the way to Hollywood. Others at Barrandov reacted like scared quislings. The famous director Leni Riefenstahl, who worked periodically at Barrandov, and who shot the final scenes of _Tiefland_ there in the autumn of 1944, later recalled that her rapport with the Czech stagehands was 'amazingly good. Not a word was uttered about war or politics.' Fearing the worst or directed by envy, some locals even spoke out positively in favour of Nazification. 'We shall continue our work,' commented an article in the magazine _Filmový kurýr_ , 'for we share the Führer's belief that Prague will flourish and will enjoy long-lasting peace. We also share our President's sincere hope that even within the new form of statehood our nation can realize a peaceful and successful existence and can accomplish great prosperity in the future.' Then there were the locals who tried to ignore the whole dirty business by living a life of champagne jollity and good sex. The Prague colony of pin-up stars, many of whom fantasized they were already living in Hollywood, and who bathed in luxury villas with swimming pools, fanzines and fashionable parties, certainly fell into this category. A few of them — sitting on the lap of Lída Baarová, the Czech film star who had an affair with Goebbels even before the Nazis conquered Prague — even found fascism fascinating.
Then there were many others, among them Uncle Miloš, who were disgusted by fascism. He was dead against emigration — which probably would have meant internment in Switzerland. He instead worked hard, often diplomatically behind the scenes, to ensure the survival of Czech cinema — without soiling either his own or its reputation by manufacturing propaganda. The choice required him to tread a dangerous high wire. Miloš reasoned that not only his, but hundreds of workers' jobs, and the survival of their families, were at stake. So too, he told his friends privately, was the 'national spirit' and language of the Czechs, whose slow death by strangulation would otherwise be the probable effect of 'the great concentration camp of the German Protektorat'. And when the war and Nazi occupation ended, as surely they would, post-war reconstruction would require a vibrant Czech film industry, which could not easily be built from images alone.
His reasoning yielded fruits of questionable sweetness. Miloš's stubbornness meant that several dozen of the best Czech film talents — including the writer (and later the first Czech to win the Nobel Prize for Literature) Jaroslav Seifert, actor Karel Höger, the writer Vítězslav Nezval, the director František Čáp, the actress Nataša Tánská — were spared from having to work directly for the Nazis. The Havel studios at Barrandov were also spared, even though during the occupation the output of Czech feature films steadily declined, from thirty-two films in 1939 to nine in 1944. Over three dozen films altogether appeared during the Reichsprotektorat. Easily the most popular was _The Grandmother (Babi čka),_ based on Božena Němcová's classic nineteenth-century novel about a wise and powerful heroine who brings up her grandchildren as good, devout Czechs — a film which pictured Czech identity as threatened constantly by foreigners, for instance by an invading Hungarian soldier, who rapes a young Czech girl, who becomes pregnant and goes mad.
It was also an achievement that no openly pro-Nazi film was ever produced by AB Studios, although some scenes from the anti-Semitic epic _Jud Süss,_ whose final scenes of vengeance against the victim proved rousing for German audiences in Prague, were shot there. Miloš knew of course that there were official restrictions on what could be made at the studios. Escapist entertainment was acceptable, but the Reichsprotektor's office was clear about the fascist _noblesse oblige:_ Barrandov was allowed to survive and thrive so long as it accepted the indisputable guidelines laid down by the Führer. Historical dramas were forbidden from scorning the Habsburg Empire. Jews were not to be represented favourably. Student life had to be ignored. Any visual representation of groups or individuals suspected of 'anti-German' behaviour was strictly forbidden.
The task of saving what could be saved forced Miloš personally to swim in ice-cold waters. Trouble began immediately after the Nazis poured across the Czechoslovak border. The day after Hitler checked into the Prague Castle, AB Studios was visited twice by a Reichsprotektorat agent guarded by a squad of patriotic Czech fascists _(gajdovci —_ supporters of an errant Czechoslovak officer, Radola Gajda). They bore the news that the Barrandov facilities now belonged to the 'National Fascist Community'. Miloš threw them off the premises. The Gestapo responded by searching his flat, confiscating documents, including his passport, and taking him away for interrogation. Miloš was then summoned before Herr Glesgen, the Reichsprotektorat Commissioner of Film, who told him that AB Studios was 'a Jewish enterprise'. Miloš had anticipated the charge. He quickly won the consent of his friend Osvald Kosek, the only Jew on the board of AB Studios, to step down from 16 March 1939 — the day he was first honoured with a visit by Nazi agents. When Miloš coolly explained his actions to Commissioner Glesgen, he grew angry. 'We're therefore going to have to change the Jewish law because of you, so that it will have been in effect from 15 March 1939,' Glesgen snapped. He added, red-faced, with a cold laugh: 'We shall call it _lex Havel.' 43_
So the law was backdated. Rough treatment of Miloš followed. He was offered 'peace and quiet' and a handsome pay-off in Reichsmarks if he sold his shares in the studios. When he carried on acting like a figure of granite he was threatened with homelessness and consignment to a concentration camp. The Reichsprotektor, dispatching a trustee _(Treuhänder)_ , Herr K. Schulz, to run the business, soon acquired a majority share in AB Studios by fiddling the value of its share capital through the courts. Miloš then had no option but to lease back AB Studios from the Reichsprotektorat, and to dig deep into his own pockets to pay his employees. The Nazis meanwhile employed a favourite tactic: publicizing the false information that Miloš had joined the cultural section of the National Czech Council, a front organization of the League Against Bolshevism. He threw the letter officially informing him of his Council membership into the wastepaper bin; instructed his secretary, Eva Svobodová, not to reveal his whereabouts to strangers; and, using a secret radio transmitter, sent a message for help to the exiled Beneš government in London.
From there on, his world at Barrandov, like the rest of society, was prey to terror. Miloš became frightened, especially after Heydrich's assassination. On the day after, he recalled being at home in his Barrandov villa, sitting with Venoušek's father, glued with fear to the wireless as it warmed up, listening to news of the revenge executions. 'Many of our friends met with this fate, among them Dr Veleslav Wahl and his brother. It was a beautiful day, but for us the atmosphere was stifling. On the River Vltava, we saw a large punt sailing towards Prague, carrying something like gallows on its stern... We didn't know how they executed people.'Shortly afterwards, his trusted lawyer, Dr Jan Hochmann, was carted off to a concentration camp. Paul Thümmel, otherwise known as Dr Holm, an agent of the London-based Czech intelligence service who had earlier protected Miloš from the Gestapo, was arrested and sent to Theresienstadt. Miloš was enveloped as well in the stench of suicides — of Lucerna administrators like Mr Sedláček, who found the terror of total power too much. And there were executions. Among the murdered was František Stejskal, the same good friend who had appeared beside young Venoušek's stroller, rattle in hand, dressed in the suave style of Adolf Hitler. Also murdered was Miloš's architect friend Vladimír Grégr, who designed his Barrandov villa, in whose elegant wooded garden (surviving photographs show) his nephew Venoušek and his young brother Ivan liked to play hide-and-seek.
Miloš feared he would be next, that only time stood between him and his crushing under what he called 'the wheel of the German inquisition'. From one day to the next, he never knew whether an informer or an imprudent remark would earn him a final visit from the SS. He continued to believe in the eventual defeat of the Nazis. But the fact was that the secret police now had him in their sights. Death chalked crosses on his doors and ravens flew overhead. All exits were blocked. Only the defeat of Nazism and the advent of peace in Europe — whatever that meant — seemed capable of saving him from paying the supreme price for failing quietly to rescue what could not be rescued.
### **Cold Peace**
9 May 1945: the day after the beast War has been pronounced officially dead in Europe. Angels with trumpets play tunes of peace to heaven and earth. The politicians, flanked by journalists, formally declare the wings of violence to have been clipped. Men of religion remind the faithful that peacemakers are blessed, and that where there is peace there is God. Moralists agree that peace is the elevating and healing face of the world. Philosophers add: peace is liberty with tranquillity. But seated at his desk at his parents' country house at Havlov, near the Moravian village of Žd'árec, a little boy trembled.
The boy gripped his pen. In his neatest handwriting, eight-year-old Václav Havel recorded on paper that the day of general jubilation was for him filled with scenes of panic, slaughter, destruction. 'On the 9th of May in the morning,' he began, 'Žd'árec was bombed because German troops who had not surrendered were still there.' He continued: 'After the air raid many residents of Žd'árec came to our house to seek shelter. In the afternoon, we experienced a stampede of German troops near us and shooting at them. They left behind a lot of ammunition, wagons, cannon, horses. Russian shells almost landed on Havlov.' The young boy added: 'We children were afraid (and I think the grown-ups were as well). At that moment I wanted to be in Australia and little Ivan pooed himself.'
For the past year, the Havel family had shivered through the cold dawn of peace. They had been gripped by the feeling that peace would be war in masquerade — that the earth and skies of middle Europe would continue to be convulsed by men slaying each other like wild animals. Talk of peace had begun to seem like words in the wind, thanks to a miscalculation by the Americans. Early in the afternoon of St Valentine's Day, 1944, a squadron of American bombers lost its way in thick cloud and strong winds over Czech territory. Thinking Prague was Dresden, the pilots roared from the direction of Jinonice through the city centre, dumping a deadly cocktail of high-explosive, incendiary and phosphorous bombs as they passed over the Jirásek Bridge. More than 500 people were killed and many others wounded. Extensive damage was caused to several hospitals and to the bridge itself. Many residential buildings were wrecked, including a block on the Vltava embankment. In the middle of the afternoon, young Václav, together with his little brother and parents at Havlov, huddled around the wireless to listen to a special report from Prague about the bombing raid. An hour later, Uncle Miloš telephoned with bad news. The apartment next door to the Havels' flat had been hit directly. Fire had spread to their apartment, destroying its roof and top floor. 'Our house is now uninhabitable,' reported Miloš. 'Mr Hartvich and a few other employees from Lucerna rushed there to rescue whatever they could. You must stay at Havlov.'
The misdirected 'bloody February' assault on Prague was not unexpected, since the allied air forces had been in a position to bomb the Protectorate from bases in Italy from late 1943. From the summer of 1944, Prague could be reached as well from airfields in France. Partly for humanitarian reasons, the Czechs were spared destruction until the autumn of that year. Prague was first deliberately bombed in the late autumn of 1944. Damage was officially declared as light — the phrase 'light bombing' is insulting to its victims — for a total of five stray bombs hit a suburban electricity station, killing four and injuring thirty people. The following year's raids were considered 'heavier': for instance, during the miscalculated 'bloody February' attack, and again on Ash Wednesday, 25 March, when American bombers targeted the Böhmen und Mähren engine works, which manufactured self-propelled guns for the Nazis. The bombs killed another 500 Prague residents and left the city in a thick pall of black smoke.
By German and British and Russian standards, these attacks resembled nuisance encounters. But for many Prague citizens air raids meant weeks of screaming sirens, the wails and grunts of men, women, and children helter-skeltering into railway tunnels, coal cellars, and basement apartments, their faces and spines chilled with the fear of ending up underneath a mountain of choking, crushing rubble. As a young boy — a child born six months before the Franco-Hitler assault on the Basque town of Guernica — Havel twice tasted one of the twentieth century's foulest technical inventions. He never forgot them, and it is unsurprising that several of his earliest notebooks, completed around this time, contain crayon and black-and-white sketches of fighter planes, as menacing as those drawn by Otto Dix.
The air raid was especially terrifying for children. It was technical power at its most destructive. Once upon a time, technical methods of killing others in war were clumsy. Read, for example, how Carthaginian elephants were used in the concluding cruel moments of the first Punic War to trample mutinous mercenaries to death.Compare the twentieth-century masterpiece of finishing off the enemy with mechanical power. The air raid: a new and improved form of mechanized power over human beings. From great heights, its potential victims look faintly absurd. Reduced to ant-like figures in the far distance below, they scurry for shelter, if they can. The young are swaddled, dragged, cajoled. The old hobble, fall, and are collared and hauled to safety. There is great tumult and much confusion. Nobody wastes time. Everybody's ears ring with sirens, screams, shouts. It is as if each person is suspended in time and pinned down in space. It is almost as if they don't exist. Hearts thump. The hunted feel both weightless and leaden. Their existence now depends upon architecture. And technical error. Or survival is a matter of instinct, or pure luck.
The airborne masked raiders: looking down from their flying machines, armed like Jove with thunderbolts that can be hurled from the sky, the bombers' hearts beat equally fast, but for different reasons. The attack is the perfection of technical power in the face of danger. The attackers zoom and turn and zoom again, and yet again. Their mission involves cleverly dodging their opponents — if there are any — so as to hit their target. The prize is obliteration. Armed with the means of burning and levelling everything, and killing everyone below, the attackers buzz over their victims, delivering their sting with anonymity, and impunity. Then they roar away, at high speed. Clouds of smoke rise. The attackers vanish. Hidden from their eyes are wrecked and burning buildings, maimed and dying and dead victims. The raiders' ears are meanwhile deafened by the roar of steel machines. Below, the air bursts with groans and screams and pitiful whimpers. Roofs collapse. Metal carcasses burn. Human victims lie as still as stone. Dogs sniff and lick at their wounds. Crows peck and tear at their limbs.
## **_Red Dawn_**
## **_(1945-1956)_**
### **Red Stars**
The terror of the air raids for peace omened the end of the Nazi occupation. But terror also paved the way for the rapturous welcome given to the columns of Soviet tanks bearing red stars as they rumbled through the torn-up streets of Prague in May 1945. Out from under their turrets leapt weather-beaten, sandy-haired young men bearing machine guns. Young women in nylons posed before cameras, sitting on gun barrels laced with flowers. Crowds cheered, threw hats in the air, kissed the soldiers, invited them to their homes, offered them gifts, bore their children. The good-humoured Russians laughed and brought out their accordions. People chatted about a new and happy life in a free, democratic, truly people's Czechoslovakia. They danced, drank, and sang. Fragrance and joy filled the cobbled streets of Prague. From every lamp post and window the Soviet flag flew beside the red, white and blue colours of free Czechs.
The air raid and the rumbling tank: two key symbols of the killing power of the twentieth century. Though nobody yet knew, they were the midwives of a new system of government that would corrupt and deform the lives of Czechs for at least forty years. The basic elements of the new regime were detectable in the organized political attacks on Havel's Uncle Miloš at the start of the cold peace. On the last day of June 1945 — a day bathed in brilliant Prague sunshine — the new Minister of Culture, Václav Kopecký, freshly back from exile in Moscow, accepted an invitation to address a gathering of film-industry workers and others on the restaurant terraces at Barrandov. It was a charity event to raise money for families whose loved ones had died at the hands of the Reichsprotektorat. Kopecký seemed irritable. He used the occasion to hurl insults, threats and warnings at all those in the industry who had 'collaborated' with the Nazis. Later that day, when introduced to Miloš for the first time at a meeting of the National Committee for Prague District 16, Kopecký kept up the class-war offensive. 'I've heard some unpleasant things about you,' he said in a loud voice, not shaking hands. 'Since I am an outspoken person, I shall tell you these things to your face.'
It was a bad start for Miloš and the rest of the family. In front of other members of a Prague branch of the resistance organization of Communists and non-Communists, Kopecký went on to accuse 'that film-industry Havel' of associating with senior Nazis, like Karl Hermann Frank, the Higher SS and Police Leader in the Reichsprotektorat. Kopecký repeated the Nazi claim that Miloš had willingly joined the Cultural Section of the Czech National Council. And he insisted, pointing a finger at Miloš, that anybody who owned capital in either the First Republic or the Reichsprotektorat — and then made money off the Nazis — must be politically suspect. Miloš later denied each of these charges in a carefully worded letter to Kopecký. No reply was forthcoming. Kopecký's aim was to discredit Miloš as a 'class traitor' and to expel him from the soon-to-be nationalized film industry. He succeeded — using well-tried Bolshevik methods. Rumours, even bigoted remarks about his homosexuality, continued to circulate. A network of informers was set up around him. Attempts were made to recruit his chauffeur at Barrandov studios. Elaborate secret-police files on him were built up. Miloš was soon carted off for interrogation by the Commission for Internal National Security. During the month of October 1945, the Communist-dominated Senate of the Disciplinary Council of the Union of Czechoslovak Film Workers voted to expel him from the film industry.
Hemmed in by methods of harassment that sometimes resembled those of the Nazis, Miloš (reported his brother, Václav's father) began to suffer a 'great disillusionment'. Many of his former friends, now concerned about their careers, their children and their lives, abandoned him. There were even family friends — like the father of Václav Havel's good friend Radim Kopecký — who said privately that they considered Miloš to be a collaborator. And some former colleagues, like Otakar Vávra, atoned for their co-operation with the Nazis by becoming Communists and pitching in with their own denuciations of him. During the first week of March 1948, he and his brother were informed that the Lucernafilm company would be nationalized and renamed Czechoslovak State Film. Their appeals to have the decision reviewed were rejected, as was their own free-standing plan for nationalization. Miloš was then offered a job by the Israeli envoy in Prague to help set up film studios in the nascent state of Israel. His application to emigrate to that country was personally refused by Václav Kopecký, without any proffered explanation.
Shortly afterwards, on the last day of March 1949, the penniless and haggard Miloš was picked up by the secret police, charged under the Law for the Protection of the Republic, and put in Prague's Pankrác prison for three months. While awaiting trial, he tried to escape across the border to Austria. But a Russian patrol nabbed him, and handed him back to the secret police in Budějovice. He spent the next two years in the dreaded Bory prison and in a labour camp near Ústí nad Labem. Depressed and ill, his face covered in a 'glassy look, the look of a hunted man who had lost faith in human justice', Miloš finally returned home to stay with Václav's family for Christmas 1951. It was a mixed homecoming. His sister-in-law, Václav's mother Božena, concerned to protect her sons from political trouble; told him that he couldn't stay indefinitely. 'We've had enough troubles already because of you,' she reportedly said. Meanwhile, young Václav, now fifteen years old, sobbed over the state of his loved uncle. So too did his brother Ivan. They were last together with Miloš at Havlov, where one summer's afternoon, chatting while sitting on a log, he gave them each 500 crowns. Václav had the distinct impression that his favourite relative was saying goodbye. He was right. During the first week of September 1952, he and his parents heard over the wireless from Radio Free Europe, which broadcast from Frankfurt am Main, that an 'important refugee, Miloš Havel', travelling under the name of 'Karel Stránský', had been helped by American troops to escape through Vienna safely to the Federal Republic of Germany.
### **Coup de Prague**
The Communist savaging of Havel's uncle — and the subsequent harassment of the rest of the Havel family — foreshadowed the fate of many other Czechs. Following the military defeat of Nazism, they found themselves once again flung back into the laboratories of power. They experienced something new: a semi-constitutional seizure of state power, backed by street demonstrations, secret subversion and threats of armed force, the combined effect of which was to abolish the old constitutional and state structures to produce a one-party state that governed its subjects' lives for over forty years. It was later to be called the _coup de Prague —_ in honour both of its geographic locus and some similarities between this type of seizure of political power and that of its predecessors.
Talk of _coups d'état_ echoes from the depths of early modern European political history. The term was first used to baptize a reality that had hitherto been without a name. It first gained currency in works like Gabriel Naudé's _Considérations sur les coups d'état_ (1632). Here the term _coup d'état_ was used to describe an 'extraordinary' measure taken by the sovereign for the sake of the public good. The idea that an organized group — for 'reasons of state' — could legitimately plot to use the state to protect itself by wielding blows against its opponents survived well into the nineteenth century. The sixth edition of the _Dictionnaire de l'Académie Française_ (1823) tells us that a _coup_ is 'an extraordinary and always violent measure to which a government resorts when it deems the security of the state to be in jeopardy'. The definition is interesting because, under the impact of the terror of the French Revolution and the strengthening pressures for democratic power-sharing, the term _coup d'état_ begins to accentuate its violent character. It comes to signify intrigue, manipulation, illegality, illegitimacy, bloodshed. In so doing, the term casts doubt on the 'public-spirited' motives of those who seize power. The suspicion grows that their talk of the public good is _maquillage,_ that justifying power-grabbing with reference to _raison d'état_ is an alibi, that power games of this sort are undemocratic. The _coup de Prague_ undoubtedly helped to tarnish the reputation of calculated and violent seizures of state power. It did so for a reason that was understood by eleven-year-old Havel and helped dramatically to complicate his teenage years. Simply put, the _coup de Prague_ had totalitarian effects. This is how it happened:
According to the Košice programme proclaimed by the new Czechoslovak government on 22 March 1945, the restored republic was to be a state of Czechs and Slovaks based on the principles of the rule of law and power-sharing. It was supposed to be governed by a coalition of parties called the National Front, which, unlike its counterpart in Yugoslavia, was not supposed to function as a single monolithic organization. Yet from the moment of its birth, the new republic contained a central contradiction. Its protection of formal liberties to share state power extended opportunities to foxes to hunt down chickens. The Communists, who were familiar with the theory of the 'contradictions' of'bourgeois democracy' and the need to 'smash' it, took full advantage of the opportunity provided them. Manipulating with great skill the Front structures, they craftily worked to transform it into a one-party system. Their struggle to control the Ministry of Agriculture, which controlled the distribution of land seized from 'collaborators', was a vital case in point. So too was their control of the Ministry of Interior, which allowed them to command the police and to penetrate, from the top downwards, the National Security Corps (SNB). The Party also manoeuvred a prominent Communist intellectual and biographer of T. G. Masaryk, Professor Zdeněk Nejedlý, into the post of Minister of Education. And the Communists gained control over the Ministry of Information, which was responsible for Prague Radio and the Union of Czechoslovak Youth (CSM).
So the Communist Party started out as a strong force in the fledgling republic. But at the first parliamentary elections, held in May 1946, its hand was massively strengthened within the governing coalition of independent parties. Uncontaminated by the betrayal at Munich, proudly claiming solidarity with the glorious Red Army that had liberated the country from Nazi rule, the Communist Party registered big electoral successes. The results were especially striking, not only because they were obtained without widespread rigging — both local and foreign observers confirmed that the elections were freely conducted by secret ballot — but also because of the size of the Communist vote.Support for the Communists was especially strong among Czech workers, and it also received hearty support from the peasantry, who were among the beneficiaries of land confiscated during the previous twelve months by the Communist-controlled Ministry of Agriculture from the German and (in Slovakia) Hungarian minorities and other 'collaborators' immediately after the defeat of the Nazis. The scale of the expropriation was considerable: in the space of just over a year, nearly _2¼_ million Germans alone were expelled from the Czech lands, enabling nearly the same number of Czechs to move in. Little wonder that they voted for the Communist Party in droves. Most were formerly peasants, landless labourers, and smallholders, and many of them, thanks to Communist Ministry patronage, acquired well-functioning German farms with excellent equipment and livestock.
The expulsions were officially declared ended by October 1946. Inevitably, they resulted in confusion, hardship and violence against the German-speaking Czechoslovak citizens. Official responsibility for some measure of the whole bloody process — and the political advantages it gave to the pro-Soviet Left — is traceable to the Communist-controlled Ministry of the Interior, which together with the Ministry of Agriculture began to function as a state within a state. The Communist Party naturally attracted, like rats to rubbish, fellow-travelling opportunists and hangers-on from all classes, who saw that the Communists could help them climb ladders of opportunity. That expectation translated into votes in the May 1946 parliamentary elections. It also fed the widespread presumption that the Communists, backed by the great Soviet Union, were the up-and-coming political party.
It would have been possible for the Communist Party to seize power in the spring of 1945, had it so wished. But in politics the cultivated art of waiting is often critically important, and in accordance with that rule the Party, under the leadership of the Moscow-trained Klement Gottwald, cunningly chose to wait. This had the immediate benefit of maximizing his reputation as a 'patriotic and moderate' leftist, thus ensuring that at some later point in time the Communists could seize everything, and claim to be doing so legitimately. So they waited for their moment, which came in the summer of 1947, just before Václav Havel's eleventh birthday. On 7 July, an invitation was accepted by the Czechoslovak government to attend a preliminary conference in Paris on the Marshall Plan. The next day, in Moscow, Stalin told a Czechoslovak government delegation led by Gottwald, the Foreign Minister Jan Masaryk, and Minister of Justice Prokop Drtina, a friend of Václav Havel's father, that they must decline the invitation. Stalin's ultimatum posed the question of whether the country 'considered the Pact of Friendship and Mutual Aid between our countries valid, or preferred to go to Paris'. Gottwald immediately telephoned Prague. The government reluctantly accepted Stalin's point. Soon after, on 10 July, it issued a declaration that sealed the geopolitical fate of the country for the next four decades: 'Czechoslovak participation would be accepted as a deed aimed against friendship with the Soviet Union and the other Slav allies.'
The rejection of the Marshall Plan signalled the beginning of a permanent political crisis within the People's Front government. The Communists tried all manner of political trickery, beginning with a sensational attempt, by Gustáv Husák and others in November 1947 in Slovakia, to implicate prominent members of the (majority) non-Communist Slovak Democrat Party in an alleged 'conspiracy' linking fascist elements and Slovak _émigrés,_ especially the former quisling Foreign Minister, Ďurčanský. The Prague Communist Premier Klement Gottwald backed the Slovak conspirators, and together they tried to take advantage of the ensuing rumpus about suspected fascist takeovers by calling an emergency meeting of the National Front, to which Gottwald invited representatives of the Communist-controlled trade unions and the Czech Farmers' Association. Several of the governing parties objected strongly to the proposed cynical favouring of their 'class friends'. And loud voices were raised against the unconstitutional attempt of the Communists to transform the governing National Front structures into an instrument of the Communist Party's will by inviting non-party-political organizations, who had no business being there.
The tactic of producing political confusion and deadlock through concocted conspiracies of imagined 'class enemies' was a sobering lesson to sections of the Czechoslovak political class. During the same month of November, at its congress held in Brno, the Social Democrats voted by a majority to replace their chairman, Zdeněk Fierlinger, who several months earlier had struck a secret co-operation deal with the Communists, with the more independently minded Bohumil Laušman, who still believed in the need to keep the National Front intact. Friction between the Communists and others worsened. The Communists played every trick in the handbook of those plotting a _coup d'état._ Irresponsible demagogy: the Communists publicly proposed a 'tax on millionaires', supposedly to pay compensation to peasants hard-hit by the preceding summer's severe drought, but whose key purpose in fact was to create a climate of fear among those loyal to the republic and arouse bullish resentment among the potentially disloyal. The Communists tried to shout down opponents of the proposed tax, who pointed out that the revenues to be generated would nowhere near compensate the peasants, and that the tax was a 'political' contrivance. Sabotage of markets: the Communist-controlled Ministry of Trade unfairly accused some leading Prague shops of hoarding textiles (when in fact it had earlier forbidden them to sell their stocks until the lists of new prices — subsequently never delivered — were issued). Amidst a storm of protest, the Minister then proceeded to accuse the owners of sabotage and to close their shops. Sowing seeds of incivility: within the cabinet, permanent aggravation surrounded the agitation for a new land reform led by the Communist Minister of Agriculture, Duriš. He was repeatedly accused of using his department unashamedly to favour Communist Party clients. He responded by calling a mass meeting of delegates of the Communist-controlled Farmers' Union, to be held in Prague on 29 February 1948. Agitation from the streets: a tactic used to frustrate the pay increase for all state-sector workers proposed by the Social Democratic Minister of Food, Majer. The Communist trade-union leader Antonín Zápotocký, who had plans to purge and award certain civil servants, summoned a congress in Prague of delegates of factory councils, to be held in Prague on 22 February. It was as if he knew by heart Machiavelli's stricture that whenever a party of men residing in a city call in outside support, something is wrong in its constitution.
The timing of the two mass meetings summoned revealed the Communists' planned desire to consign others to the dustbin of history. But the decisive crisis was unplanned. It was generated by a string of rows about the precious republican principle of public control and monitoring of police powers. With new elections due in the early summer of 1948, there were many calls publicly to ensure that the police did not tamper with basic civil liberties, such as freedom of public assembly and freedom of the press and radio. Nosek, the Communist Minister of the Interior, ignored such 'bourgeois' advice and merrily carried on stacking the police force with his own men. He even did battle with the Ministry of Justice, whose investigations showed that the Olomouc branch of the Communist Party was responsible for dispatching letter bombs to the Minister of Justice himself, Prokop Drtina, as well as to the National Socialist vice-Premier Zenkl, and to the Foreign Minister Jan Masaryk. The Communist press replied with heavy abuse. Nosek, backed by the Communist premier Gottwald, meanwhile instructed the police to delay or refuse action. Class justice had to be done, and seen to be done.
On 21 February 1948, after repeated warnings to Nosek, some part of the cabinet — comprising twelve ministers from the Slovak Democrat and Czechoslovak People's and National Socialist Parties — resigned in protest. Here was the moment that proved that miscalculation is ultimately the key player in the drama of a _coup d'état._ In moments of power struggle, miscalculation reveals weakness. Weakness slakes the thirst of those wanting power. It provides them with enough energy to make the last climb to the summits of power. So climb the summits the Communists did — vigorously, and without procrastination. Their opponents were ill-prepared and short-sighted. They committed the initial mistake of missing the chance of enforcing a constitutional solution to the crisis. By failing to ensure that the Social Democrats resigned along with them, the outgoing ministers made the fatal error of voting themselves into a minority. They also failed to win over ailing President Beneš to their side. Since liberation, Beneš had enjoyed immense popularity as a patriotic defender of the Czechs. Despite poor health — he had suffered a major stroke the previous summer, and was still physically tired and seriously ill — he tried to defuse the mounting crisis by acting even-handedly. The resigning ministers thought that they had had an understanding with him. They supposed that he would refuse to accept their resignations, and would then either enforce a more favourably balanced cabinet, or call for elections earlier than the scheduled May date. Beneš indeed warned against the 'split of the nation into two quarrelling halves'. He insisted that the new government must be based on the political parties of the National Front, and led by their recognised leaders. But the Communists bombastically refused discussions with the old leaders. At the same time, they insisted that the working class 'with absolute unanimity and indignation condemns the policy of these parties'. Beneš hesitated, especially because he was anxious to avoid a quarrel with the Soviet Union, which (like many across the political spectrum) he considered the principal defender of Czechoslovakia against the German phoenix. The Western powers stood by in silence.
The Communists knew well that on the eve of a putsch fine words butter no parsnips. They proceeded to arm squads of factory workers and to parade them under Communist leadership through the streets of Prague. The tactic went unchallenged, and indeed was helped along by General Svoboda, the pro-Communist Minister of Defence, who ordered his troops to remain strictly neutral. That was the signal for Communist gangs to enter the offices of the ministries and party headquarters of those ministers who had just resigned. In one extraordinary scene, the headquarters of the Social Democratic Party were occupied by Communist toughs so that the left-wing minority led by Zdeněk Fierlinger could seize control of the party machine. Throughout the country, like attractively red-coloured poisonous mushrooms, Communist-dominated 'action committees' sprang up to replace the all-party people's committees. Their job was to prepare for the final push to power, aided and abetted by the Communist Minister of the Interior Nosek, who warned public officials everywhere to co-operate with the action committees. Gottwald helped out, on 22 February, when he addressed the long-planned congress of factory councils. The mood of the congress quickly grew militant. Hell-bent on destroying the old political class, it passed resolutions condemning the ministers who had resigned; insisted that they should never again be allowed to hold office; and demanded a programme of nationalization that was far more sweeping than that of 1945.
Three days later, under immense pressure from all directions, Beneš caved in. The moment of the _coup d'état_ came on the morning of 25 February 1948, when Beneš agreed to the formation of a new government dominated by the Communists. The trade-union leader Zápotocký became vice-Premier, the pro-Communist Social Democrats were well represented, while for appearance's sake the other parties each had a 'representative' chosen for them by the Communists. Among them was the charming and good-natured democrat Jan Masaryk, who agreed to stay on as Foreign Minister. He knew that Beneš was a broken man, and that the President's attempt to act as a bridge between East and West had failed. Yet Masaryk accepted the post avowedly to attempt to blunt Communist ruthlessness, and especially to help citizens to escape the country into exile. Despite the political tragedy that had now befallen the country, he tried to keep his dignity. He also retained his razor-sharp sense of irony, manifested for instance in his private remarks about how he didn't mind working with Communists in the Foreign Ministry, simply because they expedited business considerably, and certainly saved on telephone calls to and from Moscow.
Masaryk was the last surviving male member of the family of the 'President-Liberator', and he had a considerable following within and without Czechoslovakia, especially in the Anglo-Saxon countries. None of this mattered. According to the once-standard story, a fortnight after accepting his post Masaryk fell deeply into depression, especially after visiting his father's grave and (after seeing Beneš for the last time on 9 March) realizing that the President had no plans and had already lost the fight to control the future. So Masaryk had committed suicide by jumping from a window of the Foreign Ministry building, the Černín Palais. According to others — the relevant documents, including the Masaryk archives, were carted off to Moscow, and are still incomplete — the official story doesn't add up. Masaryk after all left behind no last testament. Those who knew him well also suspected, as did the Soviets and some local Communists, that he was preparing to flee the country. This would have been so embarrassing to the new government that Masaryk's plans had to be thwarted and an alternative plan devised, at any cost. Thus — according to the alternative view — the new Communist authorities decided upon making it look as if the last icon of democracy was after all a coward who had finally conceded with his own suicide that the age of bourgeois democracy was over. So during a moment when he was unattended, they arranged for his arrest within his apartment in the top floor of the Foreign Ministry building. His murderers then suffocated him without leaving marks on his body, and then shoved the corpse out of a small bathroom window into the courtyard below. There he lay, sharing the fate of parliamentary democracy, a harbinger of the coming purges, the new Soviet-style constitution, and President Gottwald, standing proudly before the rising sun of Czechoslovak socialism.
### **Flying Splinters**
Strong mother, strong son: such was the formula by which Václav Havel survived the onset of Communist rule. Powerful his mother Božena certainly was. She was the daughter of Hugo Vavrečka, who had been co-editor of _Lidové noviny,_ a keen ceramics collector, Ambassador to Hungary and Austria during the First Republic, and (briefly in 1938) Czechoslovak Minister of Propaganda. Everyone who made the acquaintance of the journalist diplomat politician's daughter — even those who didn't warm to her snobbishness and supercilious kindness — noted her self-confidence, her tendency to impatience with low standards, her methodical approach to everything she took on.
These qualities were certainly applied to her first-born son's education, for which she took charge. Shortly after the assassination of Heydrich, and a month before his sixth birthday, she had arranged for young Venoušek to attend his first school near Havlov, where the family spent most of the wartime and early post-war periods. Throughout those years, not unusually for his class background, a good deal of his early education was carefully conducted at home. Božena closely supervised him, helped along by a succession of au pairs, whose names were Hana, Eva, and one whom Havel respectfully called 'Slečna' (Miss). Božena introduced her son to a wide variety of intellectual challenges. Before getting married, she had studied the applied arts, and had begun writing a thesis on footware styles of the medieval Czech nobility. She was a keen artist, and especially tried to get Václav interested in watercolours and drawing — with good success, as the surviving examples in his first scrapbooks show.
Božena also believed in books. The family library was small, but it contained a wide selection of titles, including for instance a six-volume, nicely bound history of the twentieth century in Czech. Václav had a natural curiosity, read much, and sometimes talked to his young brother Ivan about exciting discoveries, like the strange-sounding word 'metaphysics'. At Havlov, at the age of ten, he read with great excitement a biography of the famous Czech historian, František Palacký, who (Havel noted) read the whole Bible when he was only five years old. Like Palacký, Havel proved to be the family bookworm. While young brother Ivan loved to play outside, or stalk through the woods, or play with his parents or the governesses, Václav would sit in his room, reading literature and philosophy. He was also enthusiastic about poetry, especially (he told his father) after the day, aged ten, dressed in a navy-blue suit, he had recited before his class a little poem about seasons and politics:
If I were a little boy
I'd bring snowdrops and
the first violets
that bloomed in hiding
and I'd say:
'Take them, Mr President, I
bring you greetings of spring.'
He was encouraged to supplement his bookworming with conversations with friends of the family, like the philosopher Josef Šafařik. Václav's mother also tried to interest him in foreign literature and foreign languages — she spoke French and German from her childhood, and started on Russian and learned good English during the Reichsprotektorat period. She liked to use such skills in front of the children, and after 1945 she took out subscriptions to _Time_ magazine, _The National Geographic_ and _Illustrated London News._ She encouraged her children to look at the pictures, to learn to recognize foreign words like 'the', and told them of stories and news from afar, for instance descriptions of the first Univac I computer, which — young Václav was amazed to learn — could recognize its own errors and, like a proto-human robot, confess them automatically by means of a flashing red light.
A few months before the Communist putsch of February 1948, at the age of eleven, Havel was transferred by his mother to a small private boarding school located at Poděbrady, a spa town straddling the River Elbe thirty miles east of Prague. The King George School of Poděbrady was the brainchild of its Director, Dr Jahoda. When in Dachau concentration camp, he had made secret plans with several other prisoners to set up a new type of school aimed at educating a cosmopolitan elite of future leader-citizens who would strive to repair the damage done to a Europe ravaged by war, totalitarianism, and social injustice. Named after a fifteenth-century Bohemian king famous for having written a tract outlining the building of peace in Europe, and housed in his draughty old castle, King George School was a boys-only institution, mainly for boarders. It was sometimes likened to Eton. The eighty boys who had been admitted were by definition special. The school emphasized ruggedness, resilience, high intellectual standards, the ability to survive extremes of temperature, and discipline by severe whippings handed out on long benches in the boys' toilets. The pupils were pushed hard by their teachers, who included an English teacher, Miss Henry. Stress was placed upon academic excellence, including the learning of languages (Czech, English, Latin, Russian). Failure was frowned upon — poor performance was subject to expulsion — and rule-breaking was not tolerated. Havel never forgot the bellowing that came his way one morning for wanting to go to the toilet before early-morning exercises, which was strictly forbidden. Equally memorable was the moment when he exceeded his quota of detention points and ended up nursing a bruised and bleeding bottom. And there was also the day, following a minor misdemeanour, when a petty-minded master forced him to transport a large pile of heavy stones, one by one, across a fast-flowing stream, then to return them to their point of origin, one by one.
Havel the boarder had exeats once a fortnight, but (unlike his younger brother Ivan, who joined him later at the school for a brief, homesick six-month period) he seemed not to mind the separation from his parents. Although his grades were below average — several classmates remember him being near the bottom of his class — he adjusted to the limited free time and strict schedules. There was obligatory study time in the evenings, heavy loads of homework, and rigid lights-out rules supervised by dormitory monitors, who were boys (like Miloš Forman) several years older than those in their charge. Various extra-curricular activities were offered, including drama (at which Václav showed some early talent), typesetting, book-binding, cabinet-making, and metal-working. Sports like ping-pong, volleyball, canoeing, and bicycle-riding also featured. The chubby and bandy-legged Havel wasn't much good at any of them — his classmates never forgot the day the short-legged, panic-stricken Havel careered recklessly out of the school gates on to an open road on a bicycle whose pedals he was unable to reach — and indeed his nickname from this time was _chrobák,_ a type of cumbersome beetle. So Havel concentrated on other extra-curricular activities, like onanism. 'Mr Havel,' Dr Jahoda said stiffly to him one day, 'it's been brought to my attention that you've been immoral with yourself'. There were the boy scouts, which he joined and whose activities in the 'Arrow' group (trips to the mountains, first aid, camping, general-knowledge quizzes) he enjoyed. After the Communist coup, scouting was banned — one of his scout-leaders, Dagmar Skálová, was subsequently jailed for sixteen years — and the school troop was forced to operate secretly under the leadership of a master named Mr Hoffhans, nicknamed 'the long man' ( _Dlouhán)._ Havel admired him, and began, for the first time in his life, correspondence with him during the summer holidays. Unfortunately, the carefully composed letters he wrote to Hoffhans from the age of twelve appear to have been lost.
Before its closure by the Communists for 'class bias' — never mind that the school had a policy of funding itself by mixing the fee-paying well-to-do with wartime orphans and a few local village pupils who received free tuition — King George School turned out some prominent people. Among them were not only Havel's mathematician and philosopher younger brother, Ivan; the film-makers Miloš Forman, Ivan Passer, and Jerzy Skolimowski; the _Sesame Street_ animator Pavel Fierlinger; the politician and General Secretary of the Czechoslovak Socialist Party Jan Škoda; Ctirad Mašín, who took up arms against the local Communists, and then made a daring escape through East Germany to the United States; the chairman of the Czechoslovak Olympic Committee, Milan Jirásek; and Alois Strnad, a successful businessman whose father had been carted off by the Nazis and then the Communists to concentration camps. Havel was to join the list of future distinguished Poděbrady boys. But his academic or career prospects didn't seem at all bright in the spring of 1950, when he was expelled from the school after a mere two and a half years there. The reason was made clear by a secret-police agent who visited the school: the building of socialism necessitated the levelling and clearing of forests of privilege, and that meant that some were bound to suffer the punishment and pain of flying splinters.
Labelled officially for the first time as a member of the privileged 'bourgeoisie', condemned therefore as an enemy of socialism, Havel was forced to attend several state schools in Prague, in the neighbourhood of the family's rebuilt home on the Rašínovo (renamed Engelsovo) embankment. There was to be no respite in the Party's class struggle against his origins and attitudes — against his subjective and objective class treachery, as was said by the Stalinists of the time. His early teenage years began to feel like a merry-go-round of class defeats and expulsions. Alois Strnad, his classmate from Poděbrady who had been expelled from there and (also like Havel) subsequently from several Prague schools, explained that 'Václav simply couldn't settle down at school or take the classroom seriously. Formal education, the target of Stalinist reforms and expulsions, resembled a bad joke.' No doubt, this was why he never completed the first phase of secondary school, and why the two friends hung out in cafés and (prompted by Havel's mother) went along to dancing classes and balls, where Havel learned to quickstep, waltz, and foxtrot.
For a time, he worked as an apprentice carpenter. _Chrobák_ suffered from dizziness, so his mother, worried that he might slip from a ladder and that the job would reinforce his tendency to coast intellectually, took measures to educate her son in unofficial ways. In 1951-1952, through a friend of the family named Otto Wichterle, the inventor of contact lenses, his parents found him a job as an apprentice laboratory assistant at the Institute of Chemical Technology in Prague, which Wichterle had just founded. They reasoned that working in a tertiary-level institution might give him a taste for further study. They encouraged him as well to apply for night school at an institution in Štěpánská Street, just off Wenceslas Square, and for several years, four hours a night and five nights a week, he worked towards his final matriculation _[maturita]_ examinations. Not only did he come to consider himself a practising scientist with a serious interest in chemistry, on which he wrote an early paper that proposed an alteration of the Periodic Table. It was at night school that he also came to talk philosophy and politics, thanks to his friendship with a fellow student of equally bad class origins named Radim Kopecký, an apprentice blacksmith/ironmonger and son of a former politician and ambassador to Switzerland, who had been arrested by the Communists, and was at that time still behind bars.
After passing his matriculation exams at night school — his grades were good, but not as good as those of his younger brother Ivan — the eighteen-year-old Havel made two attempts to get into Charles University, but he was rejected, both by the Arts Faculty and the Film and Drama Faculty. He settled eventually for a place at the Technical University in the Economics Faculty to study urban transport. It was not what he wanted to do, but it allowed him to lead a double life.
From around the time he was seventeen, Havel was tutored privately in philosophy by J. L. Fischer, a friend of the family who had helped Václav's father found the Barrandov discussion group. Born in 1896, Fischer is not well remembered today, but his influence on young Václav was considerable. Fischer was an inspired teacher and story-teller. He told Havel that after studying with Masaryk at Charles University, his university teaching career had given him the freedom to play the role of a democrat with a social conscience. So, during the First Republic, he had publicly criticized the policies of Rašín (even after his assassination), which he considered socially divisive, and inimical to the interests of the little man and the middle and lower classes. For that outburst, Masaryk had him transferred to a regional university in Olomouc, where he won a reputation as a gifted teacher with high ('Oxford-style') standards. He published furiously, read widely and deeply in several languages, and was the joint editor of the cosmopolitan and most highly respected academic journal in the human sciences, the _Sociologická revue._ His best-known work (published just after he had pushed himself to the point of physical exhaustion and a nervous breakdown) was the two-volume _The Crisis of Democracy (Krize democracie_ [1933]). He was an honest and independent thinker who published brave attacks on the Stalin trials. He was also a constant target of Communist surveillance.
During the Reichsprotektorat, fearing for his life, he fled to Holland, helped materially by a generous going-away gift from Havel's father of a box containing gold, platinum and other precious metals. Fischer left behind a family and flat in Brno. It was repeatedly searched during his absence, although (he told Havel) he later learned that the Gestapo stopped visiting only after one of its officers, rummaging through his library in search of something on Schopenhauer, discovered with joy the very book he had been hunting. Fischer also told the young Havel — it was among his favourite stories — how the Nazis treated him less bookishly in Holland. Bearing down on the frail Czech intellectual wanted for questioning in the Reichsprotektorat, the Gestapo hunted him to the port from which he had planned to sail that day across the Channel to England. He hid for five hours in a barn, crouched and crammed into a barrel of hay. During the search, a Gestapo officer reported that there was nothing inside after poking with his bare hands the top of the barrel of hay in which he was hiding. Later that day, sheltered by a local Dutch family, in the middle of a massage to relieve the painful cramps caused by confinement in the barrel, Fischer heard the same Gestapo officers pounding down the door of the house where he had crawled to hide. They ransacked the house, and before leaving thrust bayonets into a curtained wall behind which he was hiding — stab, slash, stab — narrowly missing Fischer's body in three places.
Upon returning to Czechoslovakia in 1945, he told the young Havel, his social conscience had led him to join the Communist Party — he liked in conversation to distinguish between Lenin and Stalin — but immediately after the _coup de Prague_ he had handed in his Party card, which cost him the rest of his university career. As the sun of socialism brought dawn to the country, Fischer continued his quest for synthesizing his various thoughts, likening the process to the difficulty of constructing a Gothic cathedral. He also remained gregarious, and was often visited by former students, who sometimes brought him gifts of his favourite forest mushrooms. Yet Fischer's philosophical interests changed. He focused more on the natural sciences, and at one point worked hard to develop a fourth law of thermodynamics. He also became preoccupied with philosophical categories. He was particularly interested in the possibility of overcoming modernist preoccupations through a new emphasis on quality, for instance through the development of a 'quality democracy'. Fischer practised the quality he preached. He expected much from his pupils, even though during these Stalinist times he had compulsorily lost all but one of them. Whenever Havel visited him, sometimes in Brno for advice and tutoring, Fischer would present the teenage boy with a long list of books to read, including titles in German philosophy. 'But, Professor, I don't know how to read German,' confessed the young Havel during one session. 'Well, young Mr Havel,' replied Fischer, 'you will just have to apply yourself to learn that language.'
### **Trials**
Down below, in the penumbrae of state power: young people like Václav Havel imaginatively rescuing a philosophical heritage. Up above, at the grisly summits of totalitarianism: men in grey suits plotting to murder each other. The absolute contrast was not immediately evident, not even to those caught up in the business of murder. On 31 July 1951, in the form of a telegram, President Klement Gottwald sang a hymn of high praise to the General Secretary of the Czechoslovak Communist Party, Rudolf Slánský, on the occasion of his fiftieth birthday. 'Honoured comrade!' began Gottwald's greeting. 'You were always an effective fighter for the promulgation of the Bolshevik line against all opportunist saboteurs and traitors and for the forging of a Bolshevik party.' And so he steadfastly remained, Gottwald continued. 'Our whole party, our working people, salute you as their faithful son and warrior filled with love for the working classes and with loyalty to the Soviet Union and to the great Stalin.'
On exactly the same day that Gottwald sent his telegram, in the basement cellars of Ruzyně prison in Prague, Soviet teachers (as advisers from the motherland were called by their Czechoslovak colleagues) were hard at work torturing their victims into spluttering concocted evidence and spewing false confessions that would soon be used to bring Slánský's life to a gruesome ending. Such were the paradoxes of socialism that its faithful son and warrior certainly knew and approved of the Soviet and Czechoslovak torturers, who had been busy for at least two years nurturing a climate of terror in the ruling circles of Czechoslovakia. The dirty business of Communists liquidating Communists by means of Communism had begun in the Soviet Union itself, where, against the backdrop of the onset of the Cold War, Stalin's creeping paranoia, and the Soviet-Yugoslav split, show trials were already an integral feature of Stalinism by the time of Slánský's fiftieth birthday. The Soviet Union, conforming to the rule that big powers always strive to become even bigger powers, now controlled all of Europe east of a line drawn from Stettin on the Baltic Sea to Trieste on the Adriatic. Led by the United States, the Western powers, fearing further expansion of Communism westwards, pursued a geopolitics of 'containment'.
The Cold War intensified. American strategic support for the Royalists in the Greek Civil War in 1946 was widened the following year into the Truman Doctrine, which offered economic, political, and military assistance to any state threatened by Communism, and the announcement of the Marshall Plan to rebuild Western Europe so that it could resist Communism from within. Then during the month of June 1948 two significant Western moves were made to counter Stalinism. The Western powers decided to build up a strong, anti-Soviet West Germany, thus preparing the way for the transformation of the Brussels Union into NATO, so completing the job of ring-fencing the Soviet Union with a global network of strategic military bases. In the same month, President Truman announced that the brief of the newly established Central Intelligence Agency (CIA) would be broadened to include covert operations against the Soviet Union and its satellites in the fields of 'propaganda and economic warfare; preventive direct action including sabotage; subversion including assistance of underground resistance groups; and support for indigenous anti-Communist elements'.
Stalin ensured that all national roads to socialism were blocked. The western satellites of his empire were now subject unconditionally to the exclusive validity of the Soviet example. The onset of Cold War was interpreted in terms of the 'growing intensity of class struggle' in the transition from capitalism to socialism. According to this interpretation, vigilance against class enemies became of paramount importance, since it was to be expected that the enemy, beaten and cornered, would resort to desperate and devious measures to conspire against socialism and its people's democracies. Class enemies and agents of imperialism would certainly try to infiltrate the Party, which is why, in the spring of 1948, the paranoid suspicions of Stalin found a convenient validation in the Stalinist Tito's rebellion against Stalin's own attempts to turn Yugoslavia into a subservient client state. The purges would undoubtedly have taken place without Tito's antics, but the fact that they occurred confirmed the principle that the most dangerous class enemy was the one who held a Party card and occupied a high-ranking position in the apparatus.
The purges that followed in the Soviet Union were not a replay of the Great Terror of the 1930s. In those power struggles, the victims were first selected and the necessary script written afterwards. This time round, the script was first written and then the victims were selected. The point was to produce a 'theatrical masterpiece', broadcast live from the courtroom and given the widest possible publicity. The identity of the player-victims was also different. Arthur Koestler's tragic hero and victim, Rubashov, talked and acted like Bukharin and wore Trotsky's pince-nez and represented the entire Bolshevik old guard, Lenin's comrades-in-arms brutally destroyed by Stalin's thirst for absolute power. Now, fifteen years later, it was the turn of the young guard of the Communist leadership to be annihilated. These were men and women who were most definitely not opponents of Stalin. No less devoted to the policies of Moscow than their executioners, they simply had the misfortune of having been chosen by their master to serve him as victims, according to the rule: genuine Communists were required to distrust pseudo-Communists.
The ageing paranoiac Stalin applied this rule by accusing Molotov, Zhukov, Beria, Voroshilov, Mikoyan, and even his personal secretary Poskrebyshev of being English spies. Some of their relatives were arrested; even their wives and children were thrown into prison as traitors. Chief Party ideologist Andrei Zhdanov was forced into early retirement and died suddenly under mysterious circumstances. Stalin, who was probably responsible for his death, reacted by accusing the top Jewish physicians in the Kremlin of his murder by a 'doctors' plot'. Many thousands of prominent Soviet Jews were liquidated. Plans were drawn up to deport all remaining Jews to Birobidjan in Central Asia. In the so-called 'Leningrad affair', which was closely related to Zhdanov's death, virtually the entire staff of Leningrad's Party apparatus, the local Komsomol and Soviet executive committee, as well as teachers, professors, factory managers and scientific personnel, were arrested. Many thousands were executed. Even Stalin's chief weapon of terror, the security service headed by Lavrentii Beria, was torn apart by accusations of spying, arrests, and plans to liquidate Beria himself.
From the Soviet Union, the terror spread, first to Albania, with the secret proceedings against the fallen Albanian Minister of the Interior, Koci Xoxe; into Bulgaria, in the form of the Kostov trial; and then to Hungary, where the trial of Lászlo Rajk served as the prelude of the terror in Czechoslovakia. The spreading pattern of terror in Havel's own country was virtually formulaic. The executioners wasted no time with the victims. They certainly had their methods of humiliating class enemies in civilized ways. Diets were improved, espresso was offered in proper cups, calcium shots were administered, and waiters brought sandwiches and wine into prison cells. Concerned doctors healed tortured bodies. Kind interrogators handed out cigarettes, promised light sentences and helped their prey to rehearse their memorized confessions, which sometimes changed in accordance with the latest Party lines. The pampered victims suffered terribly. In a matter of weeks or sometimes only days, Communists who were physically and psychologically tortured were robbed of their clear-headed humanity, transformed into helpless clumps of inhuman flesh. Comrades beat comrades with rifle butts and rubber truncheons. The victims' nails were ripped out. They were then denied food and drinking water and forced to drink the piss and eat the shit of their captors. They were dragged unconscious into cages in which they could only crouch; submerged in electrified water baths; threatened with the arrest and disposal of their children and spouses. The world-historical point was to humiliate them, to teach them the meaning of class struggle. The methods were mostly failsafe... except when overzealous comrades, acting out the laws of history, tortured their comrades into insanity, or plunged them into the deep night of death.
During the long period of terror that raged for five and a half years in all, rotating the whole time on the narrow axis of the Slánský trial, the prisons of Pankrác, Koloděje, Leopoldov, and Ruzyně were stuffed full of class enemies. More than a hundred people were murdered. Tens of thousands were jailed or deported, and — the figures apply to a country with a population of only 14 million — more than 136,000 souls, Communists, fellow travellers and non-Communists alike, were victims of the terror in one way or another. Although, as Havel's private schooling at this moment illustrated, the terror did not penetrate every nook and cranny of Czechoslovak life, its scope was considerable. Since its epicentre was the Party — according to one interpretation — the large footprint of the terror should not be surprising.Prior to the outbreak of World War II, this view supposes, the highly industrialized parliamentary republic of Czechoslovakia had (after Germany and France) the third largest Communist Party in non-Soviet Europe. Its supporters had been prominent as volunteers in the International Brigade during the Spanish Civil War. Most of its cadres and leaders had fled from the Nazis to France and then England, where they worked with the Czechoslovak government-in-exile. From the point of view of the post-'48 terrorists, therefore, Czechoslovakia contained the largest nest, on the western margins of the Soviet empire, of Spaniards, Westerners, Trotskyists, Titoists, Jews, and other unreliable — and exterminable — elements.
Large numbers of potentially 'objective' enemies of socialism cannot alone explain the frenzied terror during Havel's teenage years. Nor can the terror be understood by means of explanations that refer symptomatically to 'personality cults' or the frenzied paranoia about 'bourgeois nationalism' or 'imperialism' or 'Trotskyism' or 'Titoism' or 'Zionism'. The depurators' detailing of 'class enemies' and their crimes in this way was obviously a key feature of the terror. But to say that it was caused by paranoiac labelling is merely to redescribe the metaphors mobilized by men and women who were dragged from their beds at night into a laboratory of power organized by the rule that politics could do anything. The belief in the necessity of conducting politics as a vicious, life-or-death struggle between friends and enemies no doubt stemmed partly from the deracination and consequent dehumanization of significant parts of the Czech and Slovak political classes by nearly two decades of international betrayal, Nazification, total war, zoologism, and a Communist _coup d'état._ During the Terror phase of the French Revolution, it was noted by Germaine de Staël that the prior breakdown of social bonds fed the irritability and mutual jealousy of actors who were consequently inclined to humiliate one another. During the Czechoslovak terror this same pattern of incivility was at work. But it was fed as well by the key actors' belief in the possibility of human regeneration through power politics.
Actors like Gottwald and Slánský thought of themselves as waging a struggle for universal human emancipation. The point was to change the world through revolution. This meant that it was imperative to recognize the gap between the facts of life as it was currently and the wished-for goal of a classless society without state power. That gap between facts and vision could not be denied or overlooked without abandoning the principles of the revolution itself. So the revolution dictated only one alternative: if Communist society was not yet a fact, then this was because there were enemies who stood in the way. Fashioning the human condition in unprecedented ways thus required everybody to realize that the revolution was endangered, that its enemies had precipitated an emergency situation which could only be resolved by cunning political action aimed at liquidating such enemies. The stage of revolution was thick with wilful actors divided between those with pure intentions and others with evil plans. No power was innocent, no will beyond suspicion. The only certain thing was that the impure should be purged from the body politic — by actors arrogating to themselves what had once been a divine monopoly, that of creating the human world by redesigning it. Insofar as perverse wills still stood like logs on the road to socialism, politics had to eliminate all opposition. This was the ultimate purpose of the terror: to frighten and then do away for ever with the adversaries of history. The show trial was its necessary propaganda arm: its immediate purpose was to personalize class enemies, to put them in the dock in flesh and blood, to put a face on abstract, 'objective' political crimes, to give the world one last look at the scoundrel enemies of history before their physical liquidation and political murder.
### **Thirty-Sixers**
While the Party was terrorizing itself, Havel, actively encouraged and organized by his mother, drew together during the autumn of 1952 a remarkable literary circle of friends and acquaintances who were all his age, and whom he soon began to call the Thirty-Sixers. The name was thought up by the son of the jailed former Ambassador to Switzerland, his good friend from evening gymnasium, Radim Kopecký. It seemed appropriate, not only because participation was restricted to people born in that year, but because 1936, Havel noted at the time, was 'the characteristic year of our accursed _[postižená]_ generation'. Aside from Kopecký, whose father was serving a life sentence for 'anti-socialist behaviour', the circle included schoolfriends like Miloš Dus, the imprisoned industrialist's son, Stanislav Macháček, his friend František Pecák, Libuše Ryglová, the enthusiastic young philosopher of pragmatism, Ivan Koreček, and an acquaintance from Poděbrady, Honza Škoda, who first nicknamed Havel _'chrobák'._ There was as well a chapter formed soon afterwards in Brno. The key link in the invisible chain stretching between Prague and Brno was the ill-at-ease, constantly fidgeting, highly talented poet Jiří Paukert (who later wrote under the name of Kuběna). Others active in the Brno circle included two woman writers, Marie-Luisa ('Pipka') Langrová and Alena Wagnerová; the tall and lanky essayist and prose fiction writer Pavel Švanda; the talented pianist Petr Wurm; and the young poet and daughter of the philosopher J. L. Fischer, Viola Fischerová.
The circle of the accursed came together in a variety of unplanned ways. After returning from Poděbrady, for instance, Havel got together with a childhood friend named Ivan Hartmann, who went to Prague's French gymnasium. The sixteen year olds liked to spend their Sunday afternoons going on long walks round the romantic old Prague district of Malá Strana, pondering philosophical problems. The peripatetics convinced the two boys of the need somehow to keep their conversation going; Havel took a step further by completing, in the quiet of his bedroom at the embankment, a draft of a short book on philosophy, which he called _A First Look at the World._ The evening gymnasium located in Štěpánská Street was another source of Thirty-Sixers. A largish group met regularly outside the school gates after classes ended at 9 p.m. The group of young women and men felt a common bond based on official disapproval of their 'bourgeois' origins. Academic achievement was important to them: they thought of knowledge as power, the power somehow to survive and perhaps even succeed in life, despite living in a one-party regime. The group called themselves 'the young ones', and they often walked together all the way from the gymnasium in the direction of Vinohrady, where most of them lived, towards Mírové náměstí (Peace Square), where individuals then began to split off in the direction of their homes. They debated on the move, and did so both light-heartedly and passionately, Havel recalled.
There were as well individuals who burst into the circle. An example was Milan Kalous, a friend of Ivan Hartmann's from the French gymnasium, a highly intelligent young man with sparkling eyes and a sharp tongue capable of debating for hours on end. Havel found his opinions remarkable, if repugnant — 'a fanatical worshipper and devotee of Nietzsche, an admirer of the cult of power and the individual, even a preacher of fascism' — but Kalous's provocations didn't last long. He soon quit the group, leaving them to feel a bit sorry for him, convinced that this passionate, highly-strung, almost hermit-like loner would one day become a great philosopher, or end as a suicide statistic.
Then there was Jiří Paukert, who at the time lived in Brno. Havel learned about him through Kopecký, and corresponded with him — each week 'in characteristic round hand, full of harmony, in green ink' — for nearly a year before meeting him for the first time in Prague at the end of the summer of 1953. It so happened that Kuběna had to change trains at the Woodrow Wilson Station _en route_ to a hop farm, where his gymnasium class, like so many others, was required by the authorities to help bring in the harvest in time to meet socialist beer-production targets. He had a few hours to spare and decided without warning to see if his 'unknown, old good friend' Havel was at home. At around eleven in the morning he rang the doorbell at the embankment flat. Božena came to the door. 'She was so unbelievably young and cheerful, as if she wasn't his mother, but his older sister,' recalled Paukert. Božena ushered him towards her son's back den. Paukert never forgot the moment he first set eyes upon Havel — lying in bed. 'I had imagined him as a dark-haired Eugene Onegin type,' said his new friend for life. Instead there lay 'a plaster-white-faced, reddish-tinged, blond-haired Ilya Ilyich Oblomov, fatally hesitating to decide whether or not it made any sense at all to get out of bed, just as noon approached.'
First appearances were deceptive. Jiří Paukert soon spoke in superlatives about 'Vašek', whom he described as 'an art-loving soul ... a free spirit open to everything ... beautifully broad-minded, even though in the corner of his soul there lurked a natural scientist who had respect for all aspects of reality, natural as well as social'. He remarked that Havel was endowed with 'a thirst for philosophy', a tendency to synthesize (rather than to analyse), and a good sense of seeing and judging things disinterestedly. Paukert also noted his new friend's 'intellectual agility, quick and sharp thinking, his spiritual clear-sightedness'. He didn't overlook Havel's 'great personal charm', as well as what he considered to be perhaps his strongest quality: that 'this apparently shy boy', someone who at first sight looked nearly like a 'simpleton', in fact resembled 'a young sovereign' ( _vlada ř)_ who had the remarkable capacity of using his good brain to 'gather around himself crowds of friends, as if he lived only to think about others and the general good'.
The strong feelings were mutual. Paukert turned out to be one of Havel's favourite friends. He was highly intelligent, had a deep love of poetry, and was deeply committed to the Thirty-Sixers. It was also significant that Havel's mother adored him. She was especially keen to put him at the centre of the meetings that she hosted and catered for at the spacious embankment flat. Her idea of forming a circle was first successfully floated during a gathering of Havel's friends at Havlov in August 1952, and the group first met formally at the embankment flat in early October that same year. It was followed by another twenty or so meetings at the embankment during the course of the next two years, culminating (during the second week of August 1954) in a memorable week's residence at Havlov. Hosted by Božena, the meeting (according to everybody who attended) was marked by mirth, earnest discussion, photography and poetry competitions, long breakfasts on the patio, sunrise and sunset dips in the swimming pool, and by Jiří Paukert's openly displayed crush on Václav's young brother, Ivan. Counselled by Božena, Paukert soon came out.
The Prague group was sometimes (at Havlov, for instance) joined by members of the Brno chapter, and sometimes they all met elsewhere: at Charles University, in cafés like Pasáž and Tatran, and especially in the smoke-filled, riverbank Café Slavia, where practically every Saturday at noon the group gathered at the 'headquarters' of the circle, as Havel described it. During the winter of 1952-1953, after their meetings, they often went walking as a little group through snow-covered Prague. Sometimes, out of curiosity, they attended the round-table discussions and literary matinees organized by the Writers' Union. The circle was preoccupied with literature, and it learned, as teenagers, the enjoyable if disorientating art of criticizing and being criticized in turn — to concede, as Havel put it at the time, that 'it was finally necessary to disclose, to reveal oneself, and to look at oneself as well through the eyes of others'.
The circle loved to discuss forbidden books such as Kafka's _Der Schloss,_ the works of Herman Hesse and Anna Akhmatova, and debated such questions as whether Karel Čapek or F. X. Salda was more important for the survival and growth of twentieth-century Czech literature. They read works by Masaryk and the memoirs of Beneš. An old family friend, the engineer and philosopher Josef Šafařik, author of _Sedm list ů Melinovi (Seven Letters to Melin),_ came to talk about his views on modern technological civilization. Havel himself ploughed through a Czech translation of Marx's _Das Kapital._ He and Paukert also liked to draw up tables of dozens of writers and poets for the purpose of evaluating their work on a scale of 1 to 5; they agreed at one point that the highest possible score ('1') should be awarded to two officially approved writers, Vítězslav Nezval and Konstantin Biebl, and three writers 'neglected by official culture': Jiří Kolář, Josef Palivec, and Vladimír Holan. The circle of Thirty-Sixers took an active interest in French and American literary trends, dug around in second-hand bookshops, and borrowed and circulated among themselves books from libraries. They also published two magazines: a poetry review called _St říbrnývítr. básnícká revue 36 (Silver Wind_); and _Rozhovory 36 (Discussions 36_ ), a few hand-made copies of which were lovingly prepared and typed by Havel, with the artistic assistance of his mother. Only one issue of _Silver Wind_ seems to have appeared. It contained two short poems by Havel: a page-long 'Gold Coins of Faith' ( _Zlat'áky víry)_ and a three-page piece entitled 'In the morning when' ( _Kdyžráno)._ The first issue of _Rozhovory_ appeared in October 1953. Five more numbers appeared before the next summer. Each had the feel of a _samizdat_ publication: unsanctioned essays, polemics, literary criticism, and (as Paukert put it) 'the main discipliner of youth: poems, poems, poems'.
Havel quickly established himself as the group's unrivalled convenor. The others found him enthusiastic, confident, outgoing and a good diplomat, who usually greeted people with a wide smile, shuffling feet, stooping shoulders and bobbing head movements that resembled those of a wooden duck. Havel was also good at offering advice and 'a born organizer'. Some group members were amused at his ability to 'stage-manage situations'. He was certainly quick to issue orders, for instance by providing detailed instructions to each member of the group to read this book, to go to see that film or play, or to organize a visit to meet this or that previously unknown person, like the poet and painter Jiří Kolář. Havel was often impatient, sometimes even bossy. He wanted results. 'Now! Now! Go on!' he told Viola Fischerová as she found Kolář's number after nervously searching the Prague telephone book. She got through straightaway, explained that she and some friends wanted to meet the poet, which they did two days later, only to find that Kolář was the very same man near whom they had often sat at the Café Slavia.
Just how much he was a born organizer — and not the shy, self-conscious diffident that he later tried to project publicly — is revealed in recently discovered correspondence from this period. Towards the end of the first year of the Thirty-Sixers — the circle had met twenty times — he wrote a twenty-eight-page assessment of its performance. The report, _After a Year of Sculptural Work,_ contains a striking contradiction. While it emphasized that the Thirty-Sixers were 'a circle of good friends, whose aim is no manifesto or commonly declared summary', a group based on 'voluntary discipline, concord, serious discussion', the report reads a bit like the carefully composed memorandum of a (potentially) domineering party-political whip urging his comrades to raise their consciousness, to work harder and more efficiently. So, with a sharp eye for power relations within the group, it systematically surveyed their range of individual concerns. 'Ivan Hartmann always makes his presence felt with a cogent reminder,' wrote the leader, in a typical passage, 'he follows the discussion with his illuminating sense of logic. He chips in mainly if art is being talked about, also when Ivan Koreček and Miloš Dus (if he's present) have the floor. Both the Ivans repeatedly give accounts of their abundant _oeuvre_ in the field of art; Ivan enthusiastically composes music. Perhaps the best results in poetry are achieved by our "corresponding member" from Brno, Jirka Paukert.'
Havel's report also mapped out the ways in which, during discussions of ethics, the group dynamics split into 'two main camps' — despite the fact that he had come to the group armed with a carefully prepared 'ethical system' that he called 'optimalism'. The ethical doctrine had been concocted in advance with the help of his friend Radim Kopecký, and it amounted to a simple species of rationalistic liberalism. 'Optimalism' supposed that individuals strive rationally to calculate and to fulfil their own personal needs. Havel described how it proved untenable when confronted with the unbridled criticism of good friends. Radim Kopecký was adamant that Havel was too sentimental about terms like morality and humanity, that Havel was unprepared to admit competition outside the intellectual field, and that especially in matters of economics he failed to grasp the importance of material competition. Sixteen-year-old Havel denied the charges. Man is not a beast but a 'thinking creature', he insisted. And that meant that man does not simply apply 'his reason as an animal for the sake of merely satisfying his needs'. He rejected the philosophical conviction that life is 'an eternal struggle, tough, even cynical, and merciless egoism'. Havel soon reasoned himself into the philosophical counter-conclusion that egoism in the human condition is muted by sympathy for others. He considered himself a 'soft humanist' (others in the group presumably thought this about him too). He confessed that he had become 'a devotee of Masaryk in ethics, combining it with some sort of conception of socialism and with Hegelian pantheism in metaphysics'.
Finally, and most revealing of all, is that Havel's end-of-year report recommended stern measures against some of the dozen-or-so participants who showed signs of 'passive resistance'. Havel mentioned no names, but he referred to 'boys' who 'sat and occasionally uttered their "I agree" or, less frequently, "I disagree", to keep up appearances'. These young men, who 'came, puffed away at their cigarettes, and then left', or who 'showed interest in another area' or 'looked down on the Thirty-Sixers', had to be excommunicated, 'in as decent and as tactful a form as possible', Havel insisted. The language sounded almost Bolshevik at certain points. What Havel called 'our congenital Czech Svejkian behaviour' had to be exorcized through a 'great intensification' of all individuals' active involvement with the Thirty-Sixers. 'To work actively is, after all, nothing to be ashamed of!' he wrote. No one should 'hide any more behind the curtain of collective discussion'. It needed to be made clear to everybody that the group needed 'quality people'. And why? Because each Thirty-Sixer should see that they had 'founded some sort of cell which could become the crystallized core of a future movement, the work of the young, a political and cultural movement!'.
Such proto-Bolshevism was perhaps expressive of the hormonal exuberance of youth, but it also revealed something of the ambitious and power-conscious character of this particular sixteen year old. What is also interesting about Havel's little-known memorandum is not that his puerile dreams of an emergent 'political and cultural movement' went unrealized, but that the document prefigures, in clear outlines, his later principle of empowering the powerless by living responsibly in the truth. On one reading of the memorandum, the Thirty-Sixers represented a remarkable example of what Masaryk called 'small-scale work' _(drobná práce)._ Better, it was an attempt to create what the French political thinker Alexis de Tocqueville long ago called a _corps intermédiaires._ Positioned between the individual and the state, civil associations of this kind were commonplace during the First Republic. They had been badly weakened in Czechoslovakia by fifteen years of appeasement and political demoralization, invasion, fascist occupation, total war, geopolitical uncertainty, social fragmentation, enforced exile, Communist takeover, and Stalinization. The Thirty-Sixers glimpsed the importance of renewing group solidarity. It was for them an effective means of making friends, having fun, tasting the joy of acting together, widening horizons, learning how to recognize and regulate differences at close range, and of putting down roots in the present and thinking about the future by reconnecting with the past.
The formation of the Thirty-Sixers was certainly an act of remembering — especially the remembering of literary traditions that were under threat of destruction by a decade and a half of fascism, total war, and socialism. Havel was among the most vigorous historians of the group. He and Paukert conducted what they called 'raids'( _výboje)_ on various cultural figures, in other words, purposeful visits to cultural figures linked directly with the First Republic, like Eduard Valenta and Karel Čapek's widow, Olga Scheinpflugová; painters old and new, such as Libor Fára, Karel Souček, and Jan Koblasa; and actors and film-makers like Eduard Kohout and Václav Krška. Havel, playing the role of the bourgeois rebel unhappy with his bourgeois origins, liked to carry out his raids well into the night, much to the annoyance of his disapproving mother. Undaunted by her chiding, the subject of occasional meal-table rows, he tried hard to relive the atmosphere of some of the famous bars of the First Republic — especially Olympie in the Smíchov quarter, and the Old Town's Sherry Club, where the legendary pianist Jiří Eliáš had once played. Accompanied sometimes by Paukert, he liked to stay out late before returning home to his den, slightly drunk, to plates of sandwiches lovingly prepared by his disappointed mother.
Through his father's contacts, and accompanied on one occasion by Miloš Forman, Havel also had several audiences with the man who would later be the first Czech to win the Nobel Prize for Literature, the man considered widely to be the greatest Czech poet of the twentieth century, Jaroslav Seifert. Havel showed the poet some of his own earliest poems, and the two spent time discussing Seifert's work: his earliest Proletarian Poetry, in which the poet, like a prophet, sings revolutionary songs on behalf of the downtrodden; his later use of jolly verbal and visual jokes, in which the poet rather resembles a clown who talks much of love; and the work he was soon to publish, the rather sentimental _Maminka (Mummy,_ 1954). Havel also found his way to Seifert's friend, the prolific poet, novelist, and dramatist Vítězslav Nezval, who had just been removed from his post as head of the Ministry of Information's Film Department. Old family photographs show young Venoušek sitting on Nezval's knee. Two decades later, Havel was struck by Nezval's capacity for free association, his mastery of rhyme and rhythm. He noted as well his unlimited _joie de vivre —_ Nezval still adored the modernized epicurism of brightly lit cafés, excursions, intoxicating drinks, spa promenades, teeming boulevards — and his sickly odes to peace, Stalin, and President Gottwald.
Then there were the visits to see Vladimír Holan, to whom Havel had been introduced by Seifert. 'I was terrified by the thought that somewhere in Prague, living and available to me, was the physical person of this great poetical sorcerer,' Havel later remarked. Too shy to go alone to Kampa, where Holan lived with his wife and daughter in an apartment tucked away next to the medieval Charles Bridge, in the heart of old Prague, Havel asked for the moral support of Miloš Forman. 'He hasn't stepped out of his apartment in years,' Havel explained to Forman on the way. 'He just won't set a foot out so long as other poets are sitting in jail in this country.' The two young men shook with fright. The unsmiling raven-faced poet, squinting at the bright spring day as he opened the door, ushered them into a room with closed shutters, lit by a single lamp that cast expressionist shadows. Wine was poured, Holan soon loosened up, even expressing interest in the young men's work. Havel plucked up courage to ask the poet to read from his works. For two hours Havel and Forman were treated to Holan's neologisms, cryptic metaphors, distorted syntax, and obsolete, recondite and twisted expressions. Havel visited Holan regularly thereafter, on average once a month, always armed with Moravian wine. He was fascinated by Holan's striving after a coldly cerebral and deliberately unorthodox poetic style. But Havel cared neither for his anti-Semitic talk nor Holan's most recent — fellow-travelling — poetic homages to the Red Army, his protests against imperialism, and his cheap cracks against the Naziphilia of Pope Pius XII. Still the two men got along well. Holan sometimes invited other poets to their gatherings — including Jan Zábrana, who was the first to tell Havel in detail of the existence of the banned poet and collagist Jiří Kolář and his Group 42.
Havel found the meetings on Kampa exciting. They provided him with a map and compass with which gradually to piece together the fragments of the alternative Prague literary scene, much of it by now buried under the rubble of socialist realism. The teenager grasped for the first time that an intellectual (as he later put it) is a person 'who perceives a broader interconnection of phenomena than others and feels a broader responsibility'. He also observed at close range older men who were no longer allowed to climb the road to Parnassus, but who were literary survivors nonetheless — men who quietly cursed political power, avoided theatricality and bombast, and who simply loved literature and spirited their poetic talk with free-flowing wine. 'I even celebrated his fiftieth birthday with him,' Havel later said, recalling his invitation as an intrigued nineteen year old to Holan's half-century celebration. 'We got drunk on wine that had been sent to him, clearly out of a guilty conscience, by the Writers' Union.'
There was certainly plenty of undisciplined carousing within the circle of Thirty-Sixers, and what is striking in retrospect (even to those who remember their involvement well) is just how little the members considered their activities dangerous. Certain precautions, like not writing up circulated minutes or reports of their meetings, were deliberately taken, but generally they didn't worry their heads about official punishments. 'When I think back on it,' Havel reflected, 'my hair stands on end: if we'd been five years older, we'd have almost certainly ended up in Mírov labour camp; in those days, you could easily get twenty years for that kind of thing.' Havel and his poet friends certainly lived a paradox. In the 'damned birdcage of Bohemia' (as Seifert later described the scene), they survived daily under a canopy of Stalinist repression and cruelty. And yet they enjoyed considerable civil freedom, right under the noses of vicious apparatchiks, to write and discuss their poems and essays, then to fling them to the wind, as if they were launching gifts from the living to the not yet born. Given the generally repressive atmosphere in Prague, the group naturally had a touch of daring about it, symbolized by Paukert's openly flouted homosexuality after coming out in front of Václav's brother, Ivan. There were also jibes at the authorities, for instance the favourite joke about one of their high-school teachers, a disagreeable Bolshevik character, who one Friday afternoon, at the end of a week of intense speculation about possible reform of the Czechoslovak currency, had insisted before his pupils that since the Party had said that there would be no currency reform then there would be no currency reform. The teacher mockingly told his pupils of a friend who, sceptical of the Party's assurances, had searched Prague's shops for a suit of armour, which would serve as a valuable collector's item that symbolized the need for protection against monetary devaluation. The whole class laughed. Next day a major currency reform was announced. On Monday morning, the teacher, looking sheepish, asked the class whether they would rather discuss chemistry or current events. 'Comrade teacher,' barked a spindly boy with a deep voice, 'I think we ought to discuss current events.' The teacher asked the same boy to begin. 'Well,' he said, 'you know that friend of yours with armour? At least he's got armour and we've now got fuck all.'
The Thirty-Sixers thrived on ribaldry and individual members saw each other socially. There were no affairs, although dark-eyed Viola Fischerová, who complained often to the boys about their bad habit of seeing her as body and not as mind, was close to Václav, whom she trusted and whose intellect she respected. She didn't fancy him. None of the women in the group did. They liked his brain, but felt that he 'had about as much sex appeal and sex awareness as a bear cub'. Rumours nevertheless circulated that Božena feared that her son would get involved with Viola, and that she disapproved, perhaps (the evidence is unclear) because of maternal jealousy, or because she thought Fischerová was not good enough for him.
Vàclav nevertheless persisted in seeing her, as if he were practising the art of rebellion against his strong mother. One scorching summer's day, Viola went swimming with Vàclav in a public pool on Prague's Zofín island, accompanied by kid brother Ivan. There was nothing to slake their thirst with except beer, so the three began to drink their fill, during which time a bronzed stranger came and sat down in their midst. As the curious Václav began politely to ask him about his profession — under socialism, lazing about in the sun was politically incorrect and therefore discouraged, except for some privileged holidaymakers — the stranger interrupted. 'You are Václav Havel. I know, because I knew well your Uncle Miloš, who would have had no time for all this riff-raff here.' The stranger embarrassed the three friends. They had been raised by their parents in the democratic spirit of the First Republic, so they blushed when the stranger continued to rant in old bourgeois language for some minutes about the noisy chaos of the swimming pool. After the bronzed stranger had said goodbye, Havel couldn't resist a squiffy, sarcastic remark. 'Now there's a man who understands the meaning of the Great October Revolution!' The three revellers laughed loudly, drank more beer, and staggered back home. There a chiding mother helped dizzy young Ivan to the toilet, with a calm father standing in the background, exclaiming in a quiet drawling voice, 'Václav, Václav... You have got your brother Ivan drunk again.'
### **Ashes on Ice**
On 20 November 1952 — at the moment when the strongly mothered sixteen-year-old Havel was beginning to fancy himself an intellectual — there began the week-long 'Trial of the Leadership of the Anti-State Conspiratorial Centre led by Rudolf Slánský'. Comrade Slánský and his thirteen co-defendants were led handcuffed into the courtroom of Prague's Pankrác prison and seated before the chief prosecutor, Josef Urválek, the hand-picked members of the court, and the counsels for the defence. Pre-printed copies of the trial script, complete with questions and answers, were on hand. Everything was pre-planned. Nobody was allowed to forget their lines, which was unlikely since Security Minister Karol Bacílek had arranged beforehand the taped filming of a dress rehearsal of the trial, with the interrogators acting the role of the judges, just to ensure that on the day no defendant retracted his confession. And so that everybody of note could relax in the certainty of the trial's outcome, the tape of the dress rehearsal had been screened privately a few days beforehand to an audience consisting of Gottwald and chosen members of the inner Party leadership.
This was no ordinary kangaroo court, but instead a bizarre exercise of totalitarian power. The particulars of the alleged crimes were incidental to the proceedings. The individual defendants themselves were of no significance as individuals. It is true that here stood men with rich biographies. For a moment or two longer they would remain high-ranking Communists. Once, some had risked their lives on the battlefields of Spain. Others had served in the French Resistance. There were those who had fought with the partisans in the forests and mountains of Slovakia. Still others had endured the hell of Nazi prisons and concentration camps. None of this mattered, for now their time had come to be reduced to nothingness — to be transformed into inert molecules in a crazed experiment in the arts of legalized terror.
According to the surviving trial transcripts and press reports, Slánský and his comrades were police informers, imperialist spies, Trotskyite traitors, ultimately agents of a bourgeois-nationalist-Titoist plot to murder Klement Gottwald and overthrow the government of Czechoslovakia. Slánský was accused of conspiring with the arch-criminal Konni Zilliacus, a left-wing British Labour Member of Parliament, 'with the aim of detaching Czechoslovakia from the Soviet Union and from the camp of the people's democracies'. Slánský was implicated as well in what the indictment called the work of the 'Fascist-Tito clique'. He in fact confessed in his deposition to a meeting with Moša Pijade, who gave him Tito's order to step up the counter-revolutionary struggle in Czechoslovakia. Slánský admitted that 'the anti-state conspiracy centre followed a line similar to that of Tito'. Then came the anti-Semitic abuse. The Jewish ancestry and habits of Slánský and the other defendants were repeatedly emphasized. One of the witnesses reported that Slánský had developed contacts with the spies of 'international Zionism'. Another described him as 'the son of a wealthy Jewish family, the great hope of all of the Jews within the Communist Party'. Yet another prattled on about Slánský as an agent of Zionism, and Zionism as an agent of American imperialism in its fight against the Soviet Union and the people's democracies. 'Under the pretext of helping the Jewish emigration to Israel,' he added, 'Slánský assisted the illegal flight of a great number of capitalist elements who fraudulently smuggled out of the country large quantities of gold, silver, and jewellery.'
Trials peppered with words like these were commonplace throughout the courts of the country. The show trials even gathered momentum _after_ news of the death of Stalin reached Prague during the first week of March 1953. Stalin may have expired; his body could no longer breathe or move, but in Czechoslovakia his nails continued to lengthen. Within the Soviet Union, the death of the butcher led almost immediately to the issuing of some closure notices on the whole bloody business of slaughter. The Jewish physicians arrested in connection with the alleged 'doctors' plot' were released from their Moscow prison cells. The first groups of intrepid survivors of the Gulag archipelago were released. Khrushchev ordered the arrest and execution of Beria and other administrators of the apparatus of terror. The stage-managers of the show trials in central-eastern Europe, former State Security Minister Abakumov and General Byelkin, were shot. So too were the two main Ministry of Internal Affairs (MVD) advisers in the Czechoslovak purges, Generals Likhachev and Makarov.
But in Czechoslovakia the incarceration and killing by show trial gathered pace. Even the death of Gottwald, one week after returning from the funeral of his master in Moscow, failed to bring the terror to a halt. The committee led by Gottwald's successor, Antonín Zápotocký, who was assisted by such people as Václav Kopecký, the personal enemy of Miloš Havel, actually worked hard to step up the terror. The political reason was clear: since they were the ones whose political careers were deeply entangled in the terror, and certainly responsible for the torture and trial and disposal of their comrades, any reprieve would most probably have resulted in their own arrest, torture, and killing. So _tu quoque_ terror claimed its victims. A number of high-ranking diplomats and officials of the Ministry of Foreign Affairs — Pavel Kavan from the embassy in London; Eduard Goldstücker, former envoy to Israel; Karel Dufek, chargé d'affaires in Turkey — were given long-term sentences and packed off to prison. There were six secret trials of key officials in the Ministry of the Interior. Among them were the head of its security department, Osvald Závodský, a former International Brigade commander in the Spanish Civil War; and the Deputy Minister of the Interior, Josef Pavel, who was sentenced to twenty-five years in a concentration camp. Shortly afterwards, there were another six secret trials of senior army officers. There was also the trial of the 'Trotskyist Grand Council', which comprised seven second-rank Communist apparatchiks who were sentenced to a total of 103 years in prison. This was followed by the major show trial of Slovak Communist leaders, including the 'Slovak bourgeois-nationalist' Gustáv Husák, who retracted his confession in court and was sentenced to life imprisonment.
The whole project of terror during this period was a considerable technical achievement. Hundreds of high-ranking Communists of Party and state had to be rounded up, interrogated, tortured, imprisoned, executed, disposed of. Thousands of trial witnesses had to be primed, only later to be arrested and brought into the dock in connection with things they had or had not said. There were in addition tens of thousands of lesser Communists who had to be sentenced summarily to long spells in prison or shipped off to concentration camps on elaborately prepared fictitious crimes of sabotage, espionage, Zionism and bourgeois-nationalism. Many of them had to be kept under surveillance in prison for two or three years before their cases were heard. During that time, Party security agents had to organize their signing of revised versions of their confessions, in accordance with the latest changes in government policy.
The terrorists huddled around Antonín Zápotocký had their hands full in supervising the sorting of victims into the proper groups, dictating their statements, preparing their show trials, and administering their punishment. Yet at no point did they ever overlook their important task of finishing off the high-ranking apparatchiks who (for reasons of time and showcasing) had not featured in the earlier trial of Slánský. So they set upon heads of the regional organizations; members of the Central Committee, most of them Jews; and a key defendant, the Secretary of the Central Committee of the Czechoslovak Communist Party, Marie Švermová, for whom the prosecutor had asked the death penalty, but who was sentenced merely to life imprisonment. She was lucky, if a reprieve from death by terror can be called luck. On 27 November 1952, the hapless Slánský and ten of his co-defendants, tranquillized into indifference with pills and staring fixedly straight ahead, were handed the prearranged verdict of the Pankrác prison court: death. Six days later, on a chilly but.bright 3 December, each was hanged. The bodies were immediately cremated, the ashes shovelled into sacks and scattered on an icy side road in the outskirts of Prague.
## **_Stalin's Shadows_**
## **_(1956-1968)_**
### **The public Poet**
Those who heard him speak publicly for the first time swore they saw him shake while shuffling towards the podium. Tense-faced, clean-shaven, dressed in a brown check suit and matching tie, blond hair neatly parted and combed, looking the part of a public-transport student, or perhaps more like a chubby sportsman about to receive an award, the twenty-year-old Havel laid down his notes on the carved oak lectern, quivered, glanced up at the smoke-filled conference hall of Dobříš Castle, and began, looking down and slow-drawling the compulsory salutation, 'Distinguished Comrades!'
The young rebel who fancied himself a poet had risen early that morning. Wanting to calm his nerves before breakfast, he had walked briskly through the thickly timbered castle grounds, alone, wrapped in a heavy coat and scarf, early winter mist biting his ears. The setting of the 'writers' home' — a confiscated eighteenth-century château sitting atop a hill in a little town a few kilometres south of Prague — felt intimidating; it was as if he were the peasant guest of a prince. It was 9 November 1956, the second day of a three-day meeting of young Czech and Slovak writers, gathered together by the Party journal for young writers, _Kv ěten,_ to discuss the past, present and future of art. The first day had been dominated by dry discussions about art and everyday life. Havel had sat silently in the smoke, listening carefully, paralysed by the feeling of being encircled by famous people. 'The place was literally swarming with them,' he later recalled. They came in various shapes and sizes — short and tall, round and slim, garrulous and reserved, drunkards and teetotallers, bookworms and womanizers — but all of them nomenklatura men and women. Over there was Pavel Kohout, best known for his recent collection of verse mourning the death of the Stalinist President Gottwald, _A Time of Love and Struggle (Cas lásky a boje),_ and for his socialist-realist drama, _The Good Song (Dobrá píse ň),_ which justified the show trials by suggesting that anyone who betrays their beloved is prone to betraying their country. Next to him stood the Central Committee member and novelist Jan Drda, the well-known author of a collection of sentimental stories about Czechs resisting Nazification and a novel, _The Wanderings of Peter the Liar (Putování Petra Sedmilhá ře)_, which carefully mixed realism, whim, optimism and fairy-tales to tell the story of a boy who concocts fantastic stories about himself and his unknown father. Standing behind Kohout and Drda were distinguished guests like Jiří Hájek, the editor-in-chief of _Mladá fronta publishers_ , and Marie Pujmanová, a founder of Czech socialist realism and well-known Stalinist. Next to them were the editors of _Kv ěten,_ chatting to the elderly novelist Marie Majerová, whose earliest writings, touched by feminism and anarchism, underwent heavy self-revision just before the Communist take-over, leaving her reputation hanging on socialist-realist novels like _Ballad of a Miner (Haví řskà balada)_ and a Communist Utopian novel about overthrowing the capitalist state by sabotaging a reservoir, _The Dam (P řehrada)._ Havel wasn't much impressed. There was something odd about such company, he later said. People like this divined out of him a strange respect for the famous and, at the same time, the feeling that they were unworthy of admiration, that they were Party hacks and time-servers, and that he was on his own, an utter outsider.
The first day's proceedings had begun with short addresses by Antonín Jelínek and Vítězslav Kocourek on the subjects of poetry and prose. Dull skirmishes ensued. The atmosphere was stiff and theoretical. Some participants sided with the view that art is or ought to be a testimonial to life, a midwife to the facts of everyday life. They thought of art as a recording angel. Others took issue with this view, insisting that art is a hanging judge. Artists are not spectators, but co-creators of reality, and therefore the best art is thoughtful, enthusiastic, self-sacrificing — and well equipped to pass definitive judgements on everyday life.
The call for _art engagé_ had quickly produced a second, much livelier discussion about 'progressive art'. Should art be 'progressive' and, if so, does that mean that it is indistinguishable from modernism? Some participants proposed definitions of modernity and modern art, with others insisting that 'progressive' art, which for them was synonymous with the struggle for socialism, was quite different. This discussion spilled over into the second morning, and was sharpened unintentionally by a short speech by _Kv ěten'_s editor-in-chief, Bohuslav Březovský. A good Communist who was nearly twice the age of most participants, Březovský rambled through remarks about the role of the journal, the young artists listening in silent half-concentration. After Březovský sat down, a string of comrades stood up to emphasize the danger of art losing touch with young workers and young farmers. Along similar lines, others warned against the pitfalls of 'intellectual exclusivity' and pointed to the limits of 'the passionate need to theorize about art'. A political twist was given to the discussion by Milan Schulz, who shortly afterwards published an account of the meeting. 'Something important and new has appeared in our midst', he reportedly said to a sea of silent faces. 'There are clearly now great differences among people who are thirty, those who are twenty-five and those who are twenty.' Havel, in the latter category and one of the youngest artists present, froze. Schulz continued: 'One should not play up general differences, of course. But the representatives of these different generations who are here look at the world around them in completely different ways. They do the same with the past, which for some of them was a time of maturing and for others a time of childhood. One cannot overestimate the influence of even five years — nor ignore the warning signals produced by the literary efforts of the youngest, who are inclined to be apolitical.'
The words chilled the spines of the audience, who understood well the wider webs of power in which their own narrow discussions were operating. Schulz's remark served as a chilling reminder, especially to those who harboured political illusions, or who had drunk too much or slept badly the night before, that in matters of culture things were not going well. The unveiling of a giant granite statue of Stalin on the banks of the Vltava River on May Day, 1955 signalled the intention of the Czechoslovak Party to resist any local attempts to loosen the ties of Stalinist Communism now that Stalin was dead. The Party closed ranks. It refused to find a senior sacrificial figure like Malenkov, who had been pushed from power in the USSR. Slánský was not rehabilitated, although the slanderous charges of Zionism and Titoism against him were muffled. Following the strong criticisms of Stalin at the CPSU's Twentieth Party Congress in February 1956, the Czechoslovak Party made mere noises about the cult of personality. Gottwald, dead for three years, was spared. Especially after a series of meetings and demonstrations of students and young writers in Brno and Prague in April and May — six months before the Dobříš meeting — the Party authorities and their newspapers adopted a hard line against cultural dissent. The attack on the cultural policies of the Party by the distinguished poet Jaroslav Seifert at the Second Congress of Czechoslovak Writers at the end of April — Seifert called on writers to act as 'the conscience of the people' — was denounced in tough terms. And at a Party conference in June, amidst mouthed slogans about the importance of the 20th Party Congress, the leaders Novotný and Zápotocký sideswiped abstract 'bourgeois' concepts of freedom in the name of waging the class struggle. The charges made by writers, students and others were viciously attacked. The Party would keep its grip on national life. It would move ahead with a new Five-Year Plan (1956-1960) that emphasized heavy industry and the completion of collectivization. Liberalization was not to be permitted. It was not even a word to be used.
Then there were the current events in neighbouring Hungary. At the very moment that Havel and his young fellow artists were listening to talk of 'progressive art' and warnings about 'exclusivity' and 'apolitical' attitudes, Hungarian youths with only their bare hands were fighting the Soviet tanks crashing through the rubble-strewn streets of Budapest. A fortnight earlier, in the same city, the cornered Hungarian Communist Party's Stalinist Secretary and head of the secret police, Ernö Gerö, had called for Soviet military intervention to save his skin. The Red Army had bashed its way into Budapest and then retreated, and it seemed for a few days as though a peaceful compromise had been struck. The Soviet Ambassador and later First Secretary of the CPSU, Yuri Andropov, dumped Gerö and approved his replacement by János Kádár, a loyal Communist and former victim of Stalinist persecution. The forces of reform, gathered around the Prime Minister, Imre Nagy, were heartened by the appointment of several non-Communist ministers into his government, and by the release from prison of Cardinal Mindszenty. Joyous demonstrations followed. The short-lived Communist monopoly on power seemed to be crumbling. Revolution was on the cards. In quick succession, the hated security-police building was attacked, Budapest came to be run by popular councils, and the Nagy government announced Hungary's withdrawal from the Warsaw Pact, at the same time calling on the United Nations for help. Unluckily for the revolutionaries, the Western powers were preoccupied with the presidential election in the United States and with resolving their serious differences over the Suez crisis. Four days before the beginning of the Dobříš conference, Moscow removed its velvet gloves. Supposing that political power springs from the barrels of guns, Soviet tanks smashed their way back into Budapest against their street-fighting opponents. There were hundreds of casualties. The job of replanting the tree of Communism in a puddle of blood had begun.
The young outsider paused. He began, first with a nervous cough, then by praising in stiff words the journal _Kv ěten_ for having grouped together like-minded writers: 'It is an important phenomenon in our literary life,' he said, 'because here for the first time in a long time writers are finally recognizing that a shared basic attitude towards the creative efforts of today does not necessarily require it to be the complete ideological unifier of the artistic front. The bearers of this shared attitude can be people of very different artistic means and ends, and it is not at all unhealthy for our culture if people who are artistically close come together, either around journals or directly within groups.' It was a plea for pluralism, admittedly in convoluted words. But then Havel bit back at the hand currently feeding him. Pluralism necessarily implied the recognition of differences of opinion, he argued. Consider _Kv ěten_ itself. 'No matter how healthy the central idea of _Kv ěten'_s programme, that does not mean that its current theoretical formulation and concretely poetic form in _Kv ěten_ has reached maturity, or that it is the only possible way of helping our literature to perform its social and human role.'
The young Havel was only minutes into his headstrong speech. The nomenklatura began to twitch. Havel didn't let them relax. He criticized _Kv ěten_ for pursuing theoretical ideas that were generally 'unclear and inconsistent'. Its concern with artistic practice rated no better. It contained 'many mistakes and much confusion'. Havel also pointed out that _Kv ěten'_s programme resembled the work of the explorer who persisted in discovering lands that had already been mapped. Why had the editors so far been silent about earlier Czech aesthetic trends, like the once-respected modern realist movement in poetry originating in the circle around Skupina 42 (Group 42), including modernist poets like Josef Kainar, Jiří Kolář, and Jiřina Hauková? Why had they so far said nothing about the important notion of the heroism of everyday life crystallized in the pre-World War II publications of the anti-romantic Czech dramatist, prose writer and columnist Karel Čapek? What were their opinions about his argument that individuals comprised many potential selves, that prudence was to be preferred over the potential 'inhumanity' that resulted from self-sacrifice, daring, dogmatism, and flaunted sexuality, and who, on the basis of doubting all absolutes, championed the virtues of down-to-earth 'ordinariness'? And finally, why had the editors so far dodged basic questions about the essence of 'socialist art' and its relationship to modern art? Why the continuing ambiguity about 'the basic driving motives, the means, ends and significance of art'?
Havel's cloudburst of questions was daring, but even his sympathizers must at this point have hoped, for the sake of prudence under difficult circumstances, that he would thank the comrades, pick up his notes, step down from the podium and let others run with the argument. He didn't. Sweating but now relaxed, he began to hammer away at the presumption that art and truth are a happily married couple. Alluding to the earlier discussion about whether art is a recording angel or a hanging judge, Havel pointed out that both sides were secretly agreed that art lives in the Temple of Truth. This amounted to saying nothing, he continued, for the brutal fact is that virtually every artist can in principle say that their work is an expression of the truth. Why would they ever want to do otherwise? Surely it would be ludicrous for them to insist that their art is an expression of falsity? The key philosophical point, argued Havel, is that 'knowledge of the truth is the fruit of discussion', from which it followed that the editors of _Kv ěten_ should not presume that they somehow had a monopoly on the process of defining truth. On the contrary, the editors needed to be more humble. They should realise that there are 'positive forces that are appearing increasingly in the literature of young people on a variety of fronts', and that _Kv ěten_ could be a 'journal richer in ideas and artistic successes'. The final criticism was tough. 'Because there is still no forum or journal other than _Kv ěten_ for expressing young writers' different currents of thinking about art, it is clear that it should become such a forum for diversity, which means that it cannot rigidly limit itself to the opinions and established taste of a handful of its collaborators.' _Kv ěten_ was full of people who had been 'spoiled and pampered by power from the very first lines they wrote'. These were people who had had 'audiences with the President at twenty', who were 'used to the limelight', and who had been 'decorated with state prizes for literature'. Things had to change. The implication was diamond clear. Poets shouldn't be Party sutlers. 'After the Twentieth Congress of the CPSU and the Second Writers' Congress, it is obvious that all restrictions on the freedom to develop different opinions and to express reality can only burden our cultural and national life with the repetition of past mistakes and negative results, in every sense.'
The odd thing about Havel's dare-devil speech is that its published version contains an ill-fitting paragraph about socialism. After defending the principle of the indivisibility of art and freedom of expression, Havel went on clumsily to acknowledge the need for placing limits upon that freedom. 'At the same time, however,' he wrote, 'the unifying condition of the most diverse efforts consists, of course, in a positive attitude towards the basis of our socialist system.' He added: 'And it is mainly young authors who can never be allowed to be satisfied with themselves and left to assume that they have attained the ultimate and absolutely irrefutable truth of some matter — anyway, that is clearly contradicted by the dialectical conception of things.'
Did Havel actually utter these words about socialism and dialectics at the Dobříš gathering? Were they merely added by him in the subsequently published report? Voluntarily, or under pressure from the editors of _Literární noviny?_ We do not know. Years later, Havel recalled that, after his speech, over drinks and into the wee hours of next morning, he had debated the nature of art and truth with comrades who, 'as they got drunker, would alternately heap ashes on their own heads and accuse me of betraying socialism'. Perhaps. But what is clear is that Havel's first public performance as a young man of letters produced explosions. Marie Pujmanová, herself a tough-minded Stalinist from rich bourgeois stock, in effect called Havel a traitor. She expressed astonishment that a young upstart could arrogantly witter on about long-forgotten Czech poets when at that very moment socialism was fighting for its life and bleeding in the streets of Budapest. From the floor, Havel replied by saying that he simply couldn't understand how such an elaborate and costly conference on poetry could be held without discussing Czech poets like Čapek and Skupina 42. This won him some sympathy from the audience, some of it in the form of coded encouragement to throw more stones. 'Do you realize,' said the satirist Jiří Robert Pick, 'that those who sit here represent at least two generations — the over-politicized generation that is now around thirty years of age, and the apolitical generation that is already twenty years of age? Well, on behalf of the thirty-year-old grandfathers I'd like to tell our "youngsters": we've already "experienced" a thing or two of what you've discovered here, but we don't say it.'
This roused others (reported Havel) into open praise for his 'daringly critical' and 'courageous' speech. Still others launched aggressive rebuffs, of which Miroslav Červenka's was the most sophisticated. Červenka had already jousted with the young Havel in the pages of _Kv ěten._ Some time before the Dobříš conference, in the second issue of the journal, Havel had responded to the editors' call for comments on the journal's promotion of a type of poetry — 'a poetry of everyday life' — that aimed to express daily human experience. He was astonished when the editors invited him to Dobříš and then published his poorly written, one-page piece — his first-ever publication. In it he rebuked _Kv ěten'_s 'theoretical inconsistency and lack of systemization'. Although he had sympathized with the launch of the journal after the Second Congress of Czechoslovak Writers, it struck him as a bundle of dimly expressed contradictions. He accused it of silencing alternative views about the nature of poetry, and warned that, whenever there is ideological and institutional favouritism, damage is necessarily done to the whole of art, including alternative views, which are 'automatically pushed aside to the fringes of the current generation and its literature'. Havel again cited the wartime group Skupina 42. Why was their work being passed over in silence, he had asked? Was this because the editors were secretly attached to the view that modern art was 'bourgeois'? Were they supporters of the socialist-realist view that Josef Škvorecký had already shown to be absurd when applied to the work of great writers like Walt Whitman? Then Havel cheekily asked the editors the embarrassing key question: were the editors remaining silent about socialist realism because they presumed its tenets to be true, or rather because they were 'simply afraid to say that today they can no longer agree with all its postulates'?
In his written reply to 'Comrade Havel' in the second issue of _Kv ěten_, Červenka had dodged the question and issued a denial as smooth as a pebble: 'It is pointless assuming that my friends or I have wilfully avoided any question whatsoever, perhaps even because we were calculating or afraid.' The key criterion of artistic truth, he had added vaguely, was art's 'noetic stance' — its relationship to reality, including its basic emotional and intellectual attitude towards life. At Dobříš, Červenka now had a chance to elaborate his disagreements face-to-face with Havel. Poetry indeed needs facts, he argued from the floor of the conference hall, quoting the Czech immunologist, poet and essayist, Miroslav Holub. But Comrade Havel was utterly mistaken in thinking that the poet is just an 'ordinary civilian' distinguished from other people only by an unusual capacity to write on the basis of 'a stronger sensation of existence'. Poetry is not merely the recorder of everyday facts. It 'grows out of indignation and desire: out of indignation at everything which weakens life, and out of desire for a united harmonious humanity'. What is metaphor, Červenka asked, if not a basic instrument for shaping objects and situations through the mental images and judgements of the poet? And what else is the subtext of a poem than a certain mood produced by the juxtaposition and jostling of words? 'The meaning that results from the connection of two words is different from the sum of their individual meanings,' he added, quickly acknowledging to the other comrades that of course the criteria of 'socialist humanism' serve ultimately as the 'court of final appeal' in matters of artistic truth.
In the ensuing discussion, this kind of argument proved vulnerable to two strong, if conflicting objections. First, within the socialist system, understood merely as a 'court of final appeal', did it not license poetry with a bit too much 'civil' freedom to define its own metaphors and subtexts? And, secondly, didn't Červenka's argument rather arbitrarily, or at least offhandedly, specify the criteria of 'socialist humanism'? What was so special about these criteria? Were they really true? Hadn't Červenka at one point in the discussion described himself as a romantic? Wasn't he obsessed with the inner life of the poet and the ideal of the poet as a harbinger of human harmony sensitive to the sweet fragrances of the world? What did any of that have to do with socialism? And didn't the young Havel secretly agree with the anti-socialist thrust of this view?
The debate on the conference-hall floor gradually turned nasty. In the end, Havel later recalled, power-broking Jiří Hájek stood up and played the role of peacemaker. Delivering a long-winded sermon in the delicate art of dialectics, he faintly praised Havel for having triggered a lively debate of fundamental importance. He then turned on Havel by stressing that Czech literature could never allow itself to be robbed of its partisan socialist qualities. 'Dear comrades,' he concluded, 'although we all still have much to learn, the most important thing to remember is: the task of art is to create.'
### **Stalin's Carcass**
The unlucky sculptor named Otakar Švec discovered in grief that the times were more lunatic than these fine comradely words implied. His work of creative art — the World's Biggest Statue of Josef Vissarionovich Stalin, flanked by eight Soviet and Czechoslovak peasants, intellectuals and workers wielding flags and guns — had just been unveiled. Whether or not it was artistically 'creative', the statue certainly made him larger than life. Residents of Prague swore that he 'could be seen from everywhere', recalled Otakar Svec's co-worker. The monument was to dominate the Prague skyline for seven years. Rumour had it that Švec had halfheartedly entered the compulsory competition for the monument design, and only then after one afternoon's work of modelling, washed down with two bottles of vodka. He had presumed that the competition would be rigged, and that from the ranks of the fifty-four entrants a Party-approved leading architect like Karel Pokorný would get the job. It is probable as well that he privately doubted the motives of the Party, which likely wanted something imposing, since they understood well the time-honoured law that all political rulers struggle to define and to control space in their honour; that is, to inspire devotion among their subjects by making the exercise of power seem unblemished — and unchallengeable — by carving out places and stamping them with the symbols of their own power.
Perhaps indeed Švec had been worried about prostituting his talents. Although the gifted pupil of the famous Czech sculptors Josef Václav Myslbek (the creator of the Wenceslas monument in Wenceslas Square) and Jan Štursa, Otakar Švec had tried his hand at imprinting power on public places several times before: a proud T. G. Masaryk for a town square; a bulky statue of the fourteenth-century religious dissenter Jan Hus for another square; and on yet another site a blustering sculpture of Franklin Delano Roosevelt. The Nazis saw to it that the first two were demolished, while the homage to the American New Deal was scrapped following the _coup de Prague._ So checkered by previous paymasters was Švec's career that, understandably, he felt reticent about serving yet a new set. 'švec was a pessimist from the beginning,' remarked one of his assistants. Little wonder, considering that, when the surprise announcement came that he was the winner of the statue competition, the judges ordered him to make the figure of Stalin bigger, and considering as well that as soon as construction got under way bags of anonymous hate mail began to arrive. The commonplace accusation that he was unoriginal, even a plagiarist, was tolerable. So was the popular joke that the statue resembled a queue for scarce meat. More worrying were the insinuations of declared Stalinists who criticized him for demeaning their master by placing him on the same plinth as ordinary proles — and even committing the crime of lining them up behind him in such a way that the whole structure looked like a catafalque. Others said the same thing by accusing him openly of 'Trotskyism'. Still others — scribbling from a variety of standpoints — berated him for legitimating and actively promoting the 'murder' of the Czech nation.
Švec began to be shadowed by the secret police. President Antonín Zápotocký, a former stonemason, personally urged him to stand firm for socialism, but the sad fact was that the razzmatazz caused by the statue broke its creator's heart. He started womanizing and drinking heavily; his wife was so depressed that she locked herself in her kitchen and turned on the gas; a year later, and only three weeks before the unveiling of the statue, Otakar Švec did the same thing. The suicide pact spared him the ordeal of having to come to terms emotionally with his most imposing creation. Mounted on a huge concrete plinth high above the Vltava River, on the clifftops of the Letná Plain, the 12 metres-wide and 22 metres-long granite statue stood 15 metres high, dominated by a faintly smiling Stalin, dressed in a greatcoat, right hand on heart, left hand clutching a book, presumably a volume of the collected works of Marx and Engels. The sheer scale of the 6,240-ton monument, which took five years to build, using 8-cubic-metre blocks of granite quarried near Liberec, left everybody breathless, especially those who witnessed its unveiling on the evening of May Day, 1955. Václav Kopecký — Uncle Miloš Havel's foe — the Deputy Prime Minister and the hyper-Stalinist overlord of film, art, and public propaganda, otherwise known as the Minister of Information, even bragged in his pompous unveiling speech that the statue was proof positive that socialism was winning the struggle with capitalism. He made no mention of Švec. He was silent about the workers who had lost their lives in accidents during construction. Comrade Kopecký spoke only of the need to recall that this was the tenth anniversary of 'the glorious liberation of Czechoslovakia' by Generalissimo Stalin. He lambasted 'German fascism' and Western 'imperialism' and reminded his listeners of 'the strong friendship which today binds the Czechoslovak and Soviet peoples'. 'It is a granite-strong friendship!' he added, without a grain of irony. He went on to express, on behalf of the Czechoslovak people, 'our unconditional loyalty and our burning love for our brotherly Soviet Union, our great ally, our powerful support, and our shining example'.
The hand-picked crowd assembled at the foot of the floodlit statue waved flags and cheered as Kopecký declared the monument open with a string of slogans. 'Glory to the Soviet liberators of our country!' he shouted into the evening spring air. 'Glory for ever to the memory of Generalissimo Josef Vissarionovich Stalin! Long live the strong and growing eternal friendship of the nations of Czechoslovakia and the nations of the Soviet Union!' After quick follow-up speeches by the Czech-speaking Soviet Ambassador and the Mayor of Prague, cannon fired into the night against the backdrop music of the Soviet and Czechoslovak anthems. Régime poets like Vítězslav Nezval were ecstatic. 'He, the victor, standing tall above Letná, will succour Prague for ever', he wrote. 'For ever he will stand guard over the happiness of humanity living in peace. For ever he will be among us, he will be ours.'
A bitter irony: at the very moment that Prague was wrapping Stalin in eulogies, Moscow was busily derobing the cult of the personality. So that when the Czechoslovak Party finally decided to get in step again by issuing a demolition order, The Thing, full of the arrogance of the vain survivor, brought nothing but headaches to its deconstructors. Given the fanfare at its unveiling, the matter of its dismantling seven years later was sensitive. The whole affair was potentially embarrassing to the Party, and it was therefore unsurprising that the constant stream of interested citizens who went to take a look with their own eyes at the hushed-up preparations had to be shooed away by plainclothes policemen.But keeping private the public destruction of the Biggest Stalin in the world was only one battle to be fought. The far bigger problem was technical in nature. The Party liquidators were informed by engineers that one big bang would directly damage parts of the Old Town of Prague and likely cover it under a scree of clifftop rubble produced by the blast. So the fireworks master Jan Příhoda decided to wrap the monument with pipes and blast by numbers.
Poor old Stalin and his comrades were first loosened up on 17-18 October 1962, just before the Month of Czechoslovak-Soviet Friendship. The writer Bohumil Hrabal noted that after the first remarkable show of flashing lights, clouds of smoke and flying pipes the statue 'stood untouched, seemingly stronger and bigger than ever before'. Some wags claimed that Stalin's smile had widened. But the truth was that the first round of mini-explosions transformed him and his comrades from socialist-realist icons into rather modernist figures. There were further blasts a week later. They left the statue looking like a grotesque carcass sculptured by Giacometti. Workers meanwhile beheaded Stalin, then smashed into the stump of the statue with heavy steel sledgehammers in preparation for the final blasts, which commenced (here there was a sweet irony unknown to the Czechs) on Guy Fawkes Day, 5 November. Stalin and his supporters were no more. The rubble was then cleared, and the concrete plinth on which The Thing had rested was repaired, eventually, for lovers and strollers and skateboarders to frequent, under the shadow of a huge metronome, a symbol of the passing of time.
The trouble was that clock time and political time refused to hold hands. Many observers — Havel included — wished secretly that the demolition of political Stalinism could have proceeded as swiftly as the destruction of Švec's monument. It was not to be. After Stalin's death in March 1953, the Czechoslovak Communist Party demonstrated in words and deeds that it was not for turning. It pursued a tough line against liberalization, or what elsewhere was being called 'de-Stalinization', mainly because its whole identity — above all, its power — had been shaped by the hammer and sickle of Stalinism. After coming to power through a _coup d'état,_ the Party consistently undertook the most ruthless purges and trials in central-eastern Europe, quickly developing in the process a reputation as the most dogmatic sergeant in the socialist barracks. And so although it is customary to describe 1956 as the year of the beginning of the thaw within the Soviet empire, the year zero in which de-Stalinization and Malenkov's 'New Course' began, no such development took place in Havel's homeland. Frightened that disturbances of the Hungarian kind might spread to their own territory, the Party tightened the screws of political repression. At home, it lashed out with all fours against 'mistakes' and 'incorrect opinions', as if the whole population was potentially or actually guilty. In the world of geopolitics, the Party gave strong backing to the goal of holding the fort of Soviet hegemony throughout central-eastern Europe. It hit out at 'National Communism' and 'revisionism' in both its Yugoslav and Polish form. It loudly backed Kádár and the new Hungarian regime, and naturally it took sides with Moscow in the emerging conflict with Peking.
There were admittedly some changes that followed the death of Josef Vissarionovich Stalin. The Party hierarchy began to stress the importance of collective leadership. There were signs of restraint in the public praise for Stalin. Many imprisoned during the show trials of the early 1950s were released. For a brief period during 1956 — as Havel's public performance at Dobříš demonstrated — a minor thaw occurred in the frozen world of official culture. Forceful speeches were made. Bold articles and suppressed manuscripts were published. Greater Slovak autonomy was promised. At the Second Congress of Czechoslovak Writers, in April 1956, reformists managed to gain control of the union. On May Day, during their traditional _Majales_ (May Festival) parade, students in Bratislava and Prague even chanted slogans and unfurled banners calling for liberalization: freedom of speech, access to the West, and freedom of assembly.
Such scattered resistances were exceptional interludes within a neo-Stalinist immorality play. From the death of Stalin until the eventual demolition of the tyrant's statue on the banks of the Vltava River, nine years later, the Party did everything within its power to ignore Malenkov's New Course, to treat it as a boring comedy that could be 'sat through', sniggering. After the death of Antonín Zápotocký in November 1957, Novotný inherited the supreme Party and state posts of First Secretary and President without a power struggle. The man who triumphed by working his way up through the apparat, contributing to the Slánský trials along the way, insisted publicly that 'the ambiguous word "de-Stalinization"' was a synonym for 'the idea of weakening and giving way to the forces of reaction'. And so the Party closed ranks. No Khrushchev-style figure emerged at or near its summits. No 'revelations' or purges were allowed to surface. Treading the path cut by the Barak commission, which reaffirmed the guilt of Slánský in October 1957, no new Czechoslovak 'scapegoats' were allowed. Even Gottwald was spared. A militant purge of state organs got under way. The cardinal principle of the leading role of the Party was fostered in every nook and cranny of life. There was a vigorous and harsh new drive towards collectivized property and industrialization. Religious believers, journalists, writers, dramatists, Slovaks, academics, youth were constantly accused of 'mistakes' and 'false opinions'. The students were told that from here on they were banned from holding their festival. At Party conferences and at Writers' Union gatherings, organized attacks were launched on 'deviationists' of 'bourgeois' and 'liberal' persuasion.
The whole trend was confirmed by the bold optimism of the special Party conference of July 1960. It approved the Third Five-Year Plan (1961-1966) and agreed the text of a new constitution. Framed in 'the spirit of the scientific world outlook, Marxism-Leninism', the 1960 constitution declared Czechoslovakia to have passed the threshold of socialism _en route_ to full Communism. Novotný welcomed and summarily defended the legal blessing given to the victory over modern capitalism. Aping the previous year's announcement in Moscow — where it was said that the struggle for socialism had been completed, and that the transition to Communism had begun — Novotný declared that socialist Czechoslovakia had taken a giant's step upwards and forwards in the world-historical route-march towards Communism. Capitalism had been consigned once and for all to the dustbin of history. But there were still some remaining obstacles along the path to Communism. The new constitution, he concluded, was designed to 'cleanse our state of various "birthmarks", comprehensible in a transitional period'. The overtaking of the West — that meant capitalism — required above all that the whole socialist bloc draw together more tightly the threads binding the Party and the state. The Party must be respected as the leading force in all policy matters. One particularly ugly 'birthmark' therefore needed to be erased urgently: what Novotný called 'liberal pseudo-democratic principles of the division of power'.
### **To Barracks**
Havel was among those who clung to the old-fashioned 'bourgeois' principle of power-sharing, but throughout his teenage years he managed, protected by the political privilege of youth, to escape the direct hand of the state. It first clawed at him during the year 1957, when he was drafted for two years into the Czechoslovak army. Going into uniform was not foreordained — against his mother's wishes, Havel deliberately gave up being a laboratory assistant and studying chemistry at the Technical University in Prague — but whatever unhappiness that resulted from his declining interest in the natural sciences was not washed away by army life. After completing induction and basic training, he was assigned to a regiment of sappers within the Fifteenth Motorized Artillery Division, based in České Budějovice, south of Prague. As a black sheep of 'bourgeois' origins — a 'member of old Prague's dynasty' — the crew-cut Havel found himself among other young men branded with various black marks. The point of the assignment — that they were considered by the officer class as dregs and potential cannon fodder — quickly dawned on each of them. The Czechoslovak army 'borrowed from the Soviets the tradition of sending the less worthwhile elements of the population to serve with the sappers', said Havel later, 'because in any action the sappers go in first and lose a higher percentage of men'.
The realization that others thought him dispensable, coupled with his intense dislike of boondoggling — lugging around a bazooka, barracks routine, petty discipline, and the meaningless tomfoolery of mess-hall culture — prompted Havel to complain bitterly about army life, especially to his trusted girlfriend, vivacious and beautiful Olga šplíchalová. The pair had first met in 1953, thanks to a mutual friend named Zdena Tichá, at the well-known Prague writers' hangout on the embankment, the Café Slavia. Havel was struck by her natural beauty and was attracted as well to her mature confidence — she was three years older than him — and to her self-taught interest in the arts. She had already tried her hand at co-writing a television script version of Jane Austen's _Pride and Prejudice._ She was interested in the history of painting, liked to go to the cinema and to read novels (her favourite authors were Hemingway, Steinbeck, and Faulkner), and she loved and lived for theatre. At the time Havel laid eyes on her, she was taking private acting lessons with the drama teacher Ludmila Wegenerova, and was soon to make her stage debut — as the lead role of Cinderella in a performance for children at the Mÿj Theatre in Vinohrady. For her part, Olga was especially attracted to the seventeen-year-old Havel's way with words. She thought him impractical, yet the chubby, blond-haired, boyish-looking young man seemed highly educated and immensely clever, and she was most impressed that he was already writing poems, one of which he dedicated to her. It redescribes their place of first meeting:
Beyond the window of the café sleet is raging
We are silent with the desired cigarettes, I don't know
how one could imagine us without them.
It is hard to explain.
what we're observing in ourselves without defences.
It's growing dark, on the lookout tower a red star shines,
for lovers in happy moments
Words join to express his feelings of mystery, exoticism, strangeness in Olga's presence:
Your soul is a suburb full
of smoky roads, muddy paths,
walls, cemeteries and telegraph poles
full of life's dramas
of people living somewhere on the edge of our
strange era. You read verse,
you'd like to be an actress and you say
that you're as cruel as the scourge of God.
And strangeness put more directly, but in hope:
It took half a day before we could really communicate.
You, Žižkov's daughter, I, still an inexperienced
habitué of writers' cafés. The two of us,
somewhere on the edge of spring.
Yet not quite springtime. More like unconsummated desire:
Day is dawning, the frogs in the pond at your place
are croaking furiously, quiet, not a soul anywhere.
We're standing by the wall, which is set
with shards of glass
to make life difficult for thieves.
I'm struck by comparisons with myself — a thief,
and with your face — a wall with shards to make
the way to your soul more complicated for me.
Havel's comparison of himself to a burglar and Olga to a wall covered in broken glass was perhaps understandable, given that when they first met she was seeing someone else, so that it took him three years to pluck up the courage to ask her out. Alas, the times were such that not even serious romance was safe from the clutches of arbitrary state power. Havel's bellyaching to Olga about life in the army brought her instant trouble. Strolling one day down Wenceslas Square, Olga was telling a girlfriend just how 'awful' Václav was finding his treatment. All of a sudden, out of thin air, a man began to chase them, calling out menacingly, 'Comrade, what did you say? What was that?' They ran as fast as they could, and fortunately managed to give him the slip.
When Havel heard this story from Olga, he was uncowed. Olga toughened his views. Born in Žižkov, one of the roughest working-class districts of Prague, Olga šplíchalová was a strong woman with radical views that harboured no sympathy for Communist nonsense. As a young girl, she had refused to join the Pioneers and the Czechoslovak Youth Union and, from the early 1950s, Olga always referred to the Communists as 'Bolsheviks', and as 'cheats' and 'criminals'. She had been raised by her mother, to whom she was so close that fiery disagreements between them were common. The fires were fuelled by the fact that Olga's mother had joined the Party immediately after the military defeat of the Nazis. As a strong-headed sixteen year old, Olga quarrelled with her about the trainload of gifts dispatched by Prague workers to Stalin in 1949, in time for his 70th birthday. Olga also found repugnant her mother's shy defence of the execution, during the following year, of the former member of parliament, Milada Horáková, whose trial on trumped-up charges of leadership of the subversive conspiracy against the Republic' was broadcast live over street amplifiers in Prague. The biggest row followed her mother's decoration of one of their flat's window-ledges with metal portrait reliefs of Beneš, Stalin and Gottwald. One morning, during an argument, teenage Olga took aim with a hammer and knocked all the great men down. Her mother grew so furious that she threw every bit of Olga's clothing out the window into the courtyard below. Olga retaliated by locking herself in the toilet for the rest of the day.
Havel meanwhile began planning another act of 'dissidence', as it would later be called. He fought back quietly against barracks discipline by banding with an army buddy named Karel Brynda. Both privates were interested in literature and one evening, over beer, it occurred to them that it just might be possible to lighten their parade-ground and training duties and cheer themselves up by writing about the absurdity of their army lives. The regiment had a theatre troupe, which was pretty second-rate. Both men were also aware that there was something of a tradition, or at least a precedent for, plays being written for and about army life. So during the first year of service, Brynda and Havel got permission from the regiment commander to cut their teeth on a staged performance of Pavel Kohout's _September Nights_ (1955). Set within the army, itself seen as a microcosm of the contemporary Czechoslovak regime, the drama tracks the fate of Major Cibulka, the officer in charge of political affairs. He is a well-meaning, dull-witted ideologue whose efforts to manage men result in the serious demoralization of the whole regiment. He has some potential officer rivals, including the ambitious First Lieutenant škrovánek, played by Havel, but the interesting thing about the play is its break with socialist stereotypes. The officer rivals for Cibulka's post are not pictured as class enemies, which leaves the audience free — for a time — to question and judge the characters' motives and even to wonder whether the system itself fails to recognize merit and so produces incompetents like Cibulka.
Havel and Brynda's version of _September Nights_ retained Kohout's scripted resolution of the drama by introducing the _deus ex machina_ figure of Colonel Sova, a wise man who in his capacity as Cibulka's superior has the good sense to recognize the damage he is inflicting upon the regiment and to sack him from his post. Sova could have been seen by the audience as something of a Good Man Khrushchev or a Good Communist Novotný, or perhaps both. In this respect, Havel and Brynda's production trod a difficult path between praise and criticism of the system, but the odd thing was that Havel himself aroused the suspicions of his company commander, who accused him of playing the role of škrovánek so convincingly that he had revealed his own personal designs on the post of company commander! Havel was demoted on the spot to a mere footsoldier. He was amused by the absurdity — and delighted to relinquish his bazooka, which was in any case heavy and needed to be cleaned every Saturday.
The demotion gave Havel more idle time, which he put to good use sketching fragments of a play in preparation for an all-army theatre-festival competition, to be held in Mariánské Lázně, a town west of Prague, on the German border. With the assistance of Brynda, he wrote and staged his first-ever piece, called _You've Got Your Whole Life Ahead of You (Život p řed sebou_[1959]). The script produced by the two budding playwrights — Brynda recalled — was simple and entertaining, but carefully constructed for a purpose. 'That ridiculous little play was simply what we army boys called a piss-take _(vychcanost)_ ,' he said. 'We did it to be cheeky to the authorities. It was a reaction to the stupid situation we found ourselves in, and nothing more.'
Set within a small regiment, the amusing drama centres on Private Pavel Maršík, who falls asleep one night while on guard duty after having been out on the razzle. He is rudely awakened by gunfire. An intruding civilian lies on the ground, wounded by shots fired from the rifle owned by Maršík. He is suddenly in trouble: asleep on duty and without possession of his weapon, which had been mistakenly taken by the officer on duty, Corporal Jan (Honza) Kubeš, who actually did the shooting. The two men secretly agree that it is in their mutual interest to cover each other's backs. Maršík is quickly rewarded for his duplicity. He is written up in the local newspaper, congratulated by his officers, and promoted to lance-corporal. But undeserved success gnaws at his conscience, even though his mates try hard to convince him that everything means nothing and therefore anything goes. 'Is it really such a big deal, getting promoted to lance-corporal?' sneers a buddy. 'Or do you mean that little item in the newspaper? Hmm. Today they write about you, and tomorrow there'll be an article about a milkmaid and the day after tomorrow about the guy who slops the pigs. You don't really believe anybody reads that, do you?' The same buddy threatens blackmail. That makes Maršík fret and fume, but his moment of reckoning soon arrives: he is asked to join the Party. He accepts, following the company commander's reminder to him that his whole life is in front of him, and that he should not ruin it through senseless posturing. In the final scene of _You've Got Your Whole Life Ahead of You_ the induction meeting is convened. Lavishly wooden speeches supporting Maršík's candidacy are given. He then begins his acceptance speech... during the course of which he surprises and embarrasses everybody gathered by slowing down, falling silent and staring into the distance. Maršik has refused temptation. His reputation is probably ruined, but his future is now wide open. He has made the essential gesture of resistance to untruth, amorality and duplicity.
Although the commanders of Havel's regiment were not themselves experts in matters of theatre, they shared a native dislike of the play, initially because they could not accept that Czechoslovak soldiers, even rookies, fall asleep on duty. Behind their disapprobation stood the suspicion that this was army theatre with a difference, which it most certainly was. The play is simply structured, so simply in fact that it is easy to discern within it some of the standard theatrical tropes for which, within a few years, Havel would become a world-famous playwright. It is true that the dozen or more plays that Havel subsequently wrote during the next thirty years can be clumped into several different categories. There are plays that are nominally based on, and in content redolent of, other plays written earlier by others. The _Beggar's Opera (Žebráckáopera_ [1975]) is an example of his rather conventional attempt to use well-known plays as a vehicle for Havelian ideas. So is his last-ever script, _King Lear_ (1989), which examines the extent to which the world of powerful people collapses when they are driven from their positions of power.
Then, at the opposite extreme, there are plays which are written so as to be unperformable. Like _The Mountain Hotel_ ( _Horský hotel_ [1981]), they are an exercise in twisting and stretching the conventional structures of theatre into something entirely unrecognizable, even at the risk of bringing theatrical forms to breaking point. These are plays which are so abstract that they resemble formal experiments that have little or no chance of being staged successfully. In between is a variety of plays that are 'political', in that they take a stand against the dominant power structures by raising uncomfortable questions about how lives are malformed and misshapen by those structures. Some of these political plays concentrate on the deeply personal aspects of unequal and dominating power relationships. An example is _Audience (Audience_ [1975]), a treatment of a fictional character, a brewery worker named Ferdinand Vaněk, whose drunken conversations with his beer-swilling, burping, bullshitting, belligerent, bosom-buddy boss have much that is perspicuous to say about inequalities of power in 'the world as it is'. Other plays within this political category concentrate more on the structures through which power is exercised over individuals. _The Garden Party (Zahradní slavnost_ [1963]) falls within this group. It is a play that concentrates especially on the power effects of language, including the structural mechanisms — of syntax and vocabulary — that enable distorted language to colonize and deform the lives of individuals. The same theme is central to _The Increased Difficulty of Concentration (Ztížena možnost sousl ředění_ [1968]) in which a computer named Puzuk displays a good deal more emotion than any human being.
Through these different — arbitrarily defined — categories run several threads that are common to the plays that Havel wrote from the time of his days in the barracks. The plays normally probe the tortuous world of some bureaucratic organization in order to uncover its vastly complex, but standardized, patterns of interaction. The organization usually resembles two worlds fused into one: the world of Franz Kafka, choking on metaphysical anguish, and the world of Jaroslav Hašek, populated with low-life clowns. Few, if any, references are made to the world outside, but rather like the plays of Harold Pinter, which also confine themselves to a single setting, a whiff of threatened violence — as in _You've Got Your Whole Life Ahead of You —_ is constantly in the air. The organizations being probed are barren — like Beckett's stage — and oppressive. Like Kafka's buildings, these functional organizations are purposeless, even though they exercise immense power over the lives of those who live and work within them.
Havel's probes into the world of pointless bureaucracy, in which everything is 'just the way it was planned', poke fun at its fastidious rituals, its confusions, dark sides, neurotic compulsions, and its hidden and open conflicts. The language games played within it are the special target of Havel, who has been described, correctly, as a 'master juggler of words'. Conversation between characters — as in _The Memorandum (Vyrozum ění_ [1965]) — is reduced to mechanical phrases, as if language were now computerized-clichés. Behind Havel's mockery of vacuous bureaucratic language _(kecy)_ there usually stands the plight of the Ordinary Individual, normally a man, who finds himself caught up within, and struggling against, a vast spider's web of power and intrigue.
The struggle for identity, for recognition and power, resembles life — the struggle is endless, full of setbacks, and usually doesn't succeed — except that it is worth noting that in Havel's plays the divided and dominated individuals never band together in groups to resist and overcome their powerlessness. Like the Chief Censor Aram in _The Conspirators (Spiklenci_ [1970]), an official who compulsively munches sandwiches with monstrous punctuality, individuals are alone, very often twisted and deformed by the power that is exercised over them. Havel dispenses with the masks and costumes of classical tragedy. His characters are obviously in an advanced state of confused disintegration. Havel usually develops this depressing point at length, and in so doing tries to prevent his audiences from prematurely taking sides, for or against a would-be hero. His plays in fact contain no heroes because they desist from all forms of moralizing and political propaganda. Havel describes himself as a 'sarcastic critic of all arrogant explainers of the world'. He therefore rejects as mistaken all ideas of so-called 'political theatre'. He explains that 'the theatre shows the truth about politics not because it has a political aim. The theatre can depict politics precisely because it has no political aim.' The techniques of emplotment of the plays try to ensure this by relying upon liberal uses of irony, the parroting of almost identical clichéd words and phrases, often in entirely different contexts, and of inverted repetition. And Havel's characters — unlike Beckett's, for whom there are questions without answers — provide answers without being asked any questions.
The combined effect of these techniques is to work against the immediate and 'automatic' bonding between play and audience. Audiences are rather encouraged to see the absurdity of normal situations. Havel's aim is to make the play exceed its author, so that it is 'cleverer than he is', so that through the mediation of the play — no matter what Havel was consciously intending — audiences come to grasp some deeper truths about their times. The feeling of absurdity experienced by the audience, says Havel of his plays, results from the sense of estrangement _(ozvláštn ění)_ which 'turns into nonsense that which made sense before, it denies the given situation, reverses and negates it'. So spectators are held back from identifying easily with the action on stage, and this has the paradoxical effect, or so Havel intends, of increasing the 'involvement' of the audience with the play. Theatre should 'provoke the audience, stimulate their fantasies, put questions before them, force them to find their own answers — to motivate them into not forgetting everything about the play by the time they reach the foyer'. The audience are not patronized as idiots incapable of judging for themselves what the play or its particular characters 'mean'. They are not on the receiving end of sermons delivered from the playwright's pulpit. Audiences instead find themselves drawn into the intrigues of the open-ended, puzzling, sometimes riotously funny plot, in consequence of which they are gently but surely forced to become active _interpreters_ of the webs of stories that comprise the play. They are themselves cast in the role of co-determiners of its meaning. It might even be said that they become part of the play — that they not only understand but _overstand_ the play, thereby transforming the physical place of the theatre building into a shared public space, within which basic questions about the contemporary human condition are raised, worked through, but not easily answered.
### **Socialist Realism**
Havel's whole approach was at right-angles to the official aesthetic dogma known as 'socialist realism'. After the _coup d'état_ of 1948, this dogma became part of the arsenal of the organized attempts to turn the theatre into a political instrument of Marxism-Leninism. The stage was required to defend the new totalitarian order, initially by discrediting the power and ideology of its 'class enemies', the 'bourgeoisie', whose agents were seen to be operating both within and without the country. The theatre was required as well to propagate positive images of the present and future. Its job was to help spread the Truth of Marxism-Leninism, to endorse specific policy decisions of the government, and above all to sing praise to the Party and its world-historic hero-leaders.
In practice, the official cultivation of socialist realism required the education and re-education of new dramatic cadres untainted by 'bourgeois' prehistory. They were required to see that artistic criteria were nothing: Communist principles were everything. The time frames of the plays varied. Some plays concentrated on the 'bourgeois' past. Vojtěch Cach's _The Viaduct at Duchcov_ (1950) featured the bloody confrontation between striking workers and the Czechoslovak militia during the Masaryk period of bourgeois 'pseudo-democracy'. Other plays concentrated on the present. An example was Otto šafránek's _The Honour of Lieutenant Baker_ (1950), which tracked the fate of an American pilot who had been on board the fighter plane from which the atomic bomb had been dropped on Hiroshima. Shortly after leaving the armed forces, Baker had become unemployed, the sharp experience of which opened his eyes to the evils of capitalism and the necessity of Communism. During Havel's teenage years, the title of many of the most respected socialist-realist productions — Jaroslav Nezval's adaptation of President Zápotocký's _When the New Warriors Will Rise_ (1949), Ilja Bart's _Coal is Mining Man_ (1950) and Karel Stanislav's _Built by Bricklayers_ (1950) — give a flavour of what was expected by the commissars of culture. The model play of this period was usually about a project important for the building of socialism, in which a worker or the working class were as a rule treated positively as heroes standing up for socialist virtues. The stage was filled with shirt-sleeved men, women clad in bright-red dresses, singing and chortling children. Usually a 'class enemy' or two stood in their way. And the plot was often thickened by the presence of foreign spies and conspirators. The drive towards socialism was sometimes seen to fall into difficulties. This was not because of saboteurs or divided and twisted characters, but due to insufficient morale among some workers. But it was supposed that even they grasp that all problems are ultimately solved by the wise application of the scientific homilies of Marxism-Leninism. So they ultimately rise to the occasion, leaving the play to work towards an obligatory happy ending that again proves the triumphant march of socialism into the world. All this is typically a cause for celebration. As the plot unfolds, audiences are encouraged to split their sides in laughter. The standard-formula socialist-realist play was a comedy, since this genre best reflected the official optimism of the Party about the march of history upwards and forwards into the future.
For Havel, socialist realism was no laughing matter. The whole genre of socialist realism was tedious and tiresome — and philosophically mistaken. So he set about proving that it was possible to sustain a different — more exciting, unpreaching — genre of theatre that could both expose the limits of socialist realism and push beyond its narrow horizons, so as to enable theatre to speak to its audience in radically more concrete and vibrant ways. The whole aim was to do theatre well without taking itself too seriously. This at least was the instinct that developed during his army days, so that while still in uniform Havel decided to sit the entrance exams to allow him to study dramaturgy at the theatre department of AMU. Required to write under examination conditions an analysis of a play called _The Eccentric,_ by Nazim Hikmet, Havel produced a well-written hyper-Marxist interpretation that concluded that the narrative contained the basic laws of dialectical materialism. It was a skittish attempt to practise the art of deception, but it failed. The admissions board smelled a rat and rejected him.
So Havel had no choice but to fall back upon family connections to find his way into the official world of theatre. His father was an old friend of the performer, entertainer and playwright Jan Werich. Werich, who was about to retire, offered him a job as a stage-hand at Prague's ABC Theatre. Built in 1928 by the architect O. Polívka and situated in a labyrinth of passages that linked up with the Lucerna complex that was once owned by the Havel family, the ABC Theatre was the site of Havel's emotional conversion to the stage. He dropped the commonplace prejudice that a theatre is the mechanical sum of its plays, booking office, ushers, actors, auditoriums, toilets, and audiences. 'It was there I came to understand,' he later reflected, 'that theatre doesn't have to be just a factory for the production of plays.' His time with Werich was inspiring. He adored watching Werich perform — the famous dialogues _(forbíny)_ between Werich and Horníček in front of the curtain during intermission Havel found unforgettable — so much so that they convinced him that the theatre could be 'a place for social self-awareness, a vanishing point where all the lines of force of the age meet, a seismograph of the times, a space, an area of freedom, an instrument of human liberation. I realized that every performance can be a living and unrepeatable social event, transcending in far-reaching ways what seems, at first sight, to be its significance.'
Each evening at the ABC Theatre, Havel eagerly pitched in with the practical work of creating the special magnetic field that develops around a successful playhouse. In his spare time he also wrote a few theoretical articles for the theatre magazine _Divadlo._ He turned his hand as well to writing another play, initially for himself. It was crafted in the style of Ionesco and called _An Evening with the Family (Rodinný ve Čer_ [1959]). Although it wasn't performed at the theatre, it was good enough to land him a job offer, in the summer of 1960, at Prague's Theatre on the Balustrade _(Divadlo Na zábradlí)._ A converted former warehouse located just near the River Vltava in cobblestoned old Prague, the Balustrade had been founded two years earlier by Ivan Vyskočil and Ji ří Suchý following a split that developed among the organizers of another small theatre called Reduta, which had until then been the pioneering small theatre in the Prague scene. The Balustrade Theatre was typical of the small theatres springing up at the time, and although (as Havel wrote in a letter to Werich) he had been profoundly satisfied by his time at the ABC, he instantly felt more at home at the Balustrade. He liked the head of its drama section, Ivan Vyskočil, who was a multi-talented 'hands-on' figure who did everything from playwrighting to acting and directing. The people working at the theatre were also closer in age to Havel; and he found that they were less interested in reviving plays from the past than in creating something new.
Something of the spirit of the early Balustrade is evident in _Hitchhiking (Autostop_ [1961]), the first-ever Havel play written (with the help of Vyskočil) and performed there. It is an absurdist satire of the automobile, which is represented as an icon of the burgeoning conspicuous consumption of modern societies, both of the capitalist and socialist variety. In effect, the play tries to plant the idea that what Marx called the fetishism of commodities is not just a chronic feature of 'bourgeois' societies, but of socialism as well. The play contains three loosely related parts. _Hitchhiking_ uses a variety of absurdist verbal gags to explore the theme of the obsession with owning a car, which was a prominent and growing status symbol in Czechoslovakia in the late 1950s and early 1960s, that is, during and after the official declaration that the country had at last achieved socialism. The play tells of the good fortune of an unadventurous and pudding-headed young man who wins an automobile in a lottery and is catapulted overnight into a sought-after society idol. The theme of the second part of the play is strikingly similar to Ionesco's _Le Salon de l' Automobile_ (1953), in that it relies on the device of bringing inanimate objects to life to the point where they come to dominate and deaden living human beings. Ionesco tells of a buyer riding away in a newly acquired vehicle that is female, and that he decides to marry. Havel shows how people obsessed with owning or driving cars begin to speak in sounds resembling their engines. Human feet start to look like car wheels. Some individual car-lovers are even transformed into cars. In contrast to the grotesque and dark atmosphere within many Ionesco plays, _Hitchhiking_ is rollicking fun. For those who don't find it so, or don't get the point, a university professor (originally played by Vyskočil himself) steps into the car-crazed culture to deliver a mock lecture on the historic transformation of people into automobiles. The didacticism grows during the last part of the play, when the degree and scope of the reigning automobile craze is tested scientifically according to the criterion of hitchhiking: the reaction of individual car-owners when asked for a lift reveals the degree to which they have been either dehumanized or retain a few sparks of humanity in an age of commodity fetishism.
### **Garden Party**
**_Hitchhiking_** was the accomplished work of a talented twenty-four year old. But like another short play called _The Best 'Rock' Years of Mrs Hermanová (Nejlepší Rocky paní Hermanová_ [1960]), co-written with Miloš Macourek and performed the following year, the satire on the automobile was very much a 'transitional' work. Both plays revealed the considerable — but temporary — influence at the Balustrade Theatre of Vyskočil. He was its _spiritus movens_ during its first several years. He encouraged collective authorship of plays and he appeared to favour satirical theatre — the blending of a literary text with improvisational acting, loosely connected by the story of an allegorical character — very much in the style originally championed by Voskovec and Werich ('V + W'). Vyskočil strongly emphasized as well the importance of engaging audiences not by means of 'plays' but by posing questions, conflicts, and problems in need of urgent consideration. The distinctive feature of the Balustrade Theatre, he used to say to Havel, was its reliance upon the _'appeal' (apet)_ to the gathered public to enter into a silent dialogue with the performance during or after its staging. 'The theatre of "appeals" does not wrap a problem in the confines of a story or of an image but restates it in such a way that it directly confronts the spectator's experience,' he once wrote. By asking questions, theatre tries to 'engage the intellect and the imagination of the spectator who is then forced to agree, disagree, compare and view a subject from various angles.'
The principle that plays should be open-ended dialogues was to make its mark permanently on Havel's understanding of drama. But the departure of Vyskočil from the Balustrade Theatre during 1963 made room for Havel to experiment with dramatic form. Under the new leadership of the famed critic and dramaturg and director Jan Grossman, the small theatre quickly developed a European-wide reputation as the showplace of the so-called 'drama of the absurd', both foreign and domestic. For the first time, all within the year 1964, Prague audiences were shown Eugène Ionesco's _The Bald Prima Donna,_ Samuel Beckett's _Waiting for Godot_ and Alfred Jarry's _Ubu Roi._ It was an exciting period for Havel. He was now sure that the theatre was for him, and so all remaining thoughts of pursuing formal education were finally abandoned. While his mother wasn't pleased, Olga was. She actively supported his judgement, even making the big decision herself to harmonize her life with his by working nights at the Balustrade Theatre as an usherette. She was serious about their relationship. Having a daytime job with nights off would have meant permanent separation from Havel — and would have left him alone to the temptations of the theatre dressing rooms.
Havel reciprocated by accepting Olga's proposal of marriage, knowing full well that their decision would spark his mother's further resentment. Božena was already upset about her older son's 'bohemianism'. For years, he had developed the bad habits of staying out late and keeping company with friends of questionable social background. He had failed to excel academically ... and now, he was marrying a tough-minded, chimney-smoking, spirit-drinking girl from working-class Prague. 'Miss,' said curt Božena to Olga during a visit to see Havel when he was still in service, 'I wish you could mix dumplings as well as you shuffle cards [to mix dumplings and to shuffle cards is the same verb in Czech, _míchat].'_ Olga gave as good as she got. Although she was very fond of Havel's father, she found Božena stuffy, obsessed with keeping alive bourgeois culture in her household, despite the painful fact that the Havel family had lost most of its property since 1948. Olga occasionally went out of her way to remind class-conscious Božena — 'Mrs Havlová' she called her — that she already had a mother, and didn't need another. So on 9 July 1964 — two days before Olga's thirty-first birthday — the two theatre-lovers married in secret in a civil ceremony held at Žižkov Town Hall. Olga was unveiled, carried no flowers, and the couple didn't exchange rings with their promises. Accompanied by the official witnesses — Jan Grossman and Libor Fára — they went to lunch afterwards at the Moskva restaurant, ate and drank well, then returned that evening to work at the Balustrade Theatre.
The newlywed Thespians threw themselves eagerly at the experiment that Grossman had launched. He was down-to-earth and highly skilled at motivating others. Under his guidance, the tiny Balustrade Theatre on Anenské Square became renowned for its experimentation and excellence. Although the authorities left the theatre alone — probably because it was full of young people, who were assumed to be unthreatening to the regime — everyone at the Balustrade Theatre, like the characters in Ivan Klíma's play _Games,_ soon found themselves to be treading not just on a theatre stage, but on political ground. The atmosphere was egalitarian and fearless. After queuing for tickets, audiences gathered in the open-air courtyard for a drink or entered a smoke-filled foyer decorated (stylishly for this period) with fake-leather armchairs and formica-topped, metal-legged tables. The popular drinks were cola _(kofola)_ and a fizzy soft drink called _amara,_ both served with rum for a few extra hellers. The theatre itself felt a bit like a living room in an apartment block: the stage was only 4½ metres wide, the audience's chairs were tightly packed together, and in winter they were kept warm by a coal-fired heater. It was a youthful place in which fresh thinking was encouraged, personal rivalries discouraged, audiences were warmly welcomed, and in which the rehearsal and production of plays — _The Times_ of London noted in March 1965 — was considered an act of co-operation. 'Each stage performance is discussed in detail and carefully prepared by all members of the group, from director to usherette, long before the first rehearsals. Everyone is engaged in stage performance. Hierarchical divisions of roles don't exist, as in the case of other theatrical groups. Grossman actually leads, rather than fights, with the talented people with whom he's surrounded himself. He's simultaneously a catalyst and generator of ideas.'
Grossman thought highly of Havel, and gave him enough space and resources to enable him to become the theatre's most important resident playwright — and a star of the Prague scene. The arrangement quickly resulted in _The Garden Party,_ whose première during 1964 marks the beginning of authentic absurdist drama in Czechoslovakia. _The Garden Party_ has been described above as an 'unperformable' play, in no small measure because the story it tells lacks a story. That made it all the funnier. Audiences at the Theatre on the Balustrade typically chuckled through the whole performance — which was very rare at the time. The action, although the right word might be inaction, centres on a young good-for-nothing man named Hugo Pludek. His ambitious father is so perturbed by his son's wistfulness that he arranges for him to land a respectable job at the Liquidation Office by making contact with one of its chief officials, who happens as well to be an old acquaintance. Hugo is supposed to meet him at a Liquidation Office garden party, but the official doesn't show. The young good-for-nothing Hugo nevertheless rebounds by taking advantage of a developing rift between the Liquidation Office and the rival Inauguration Office. He curries favour with the Liquidation Office officials and soon finds himself appointed to the post of liquidator of the Liquidation Office.
At this point, Pludek's career takes off. After working his way skilfully into the rival Inauguration Office, he becomes head of a brand-new, all-powerful body called the Central Commission for Inauguration and Liquidation. His rapid rise to power takes its personal toll by transforming Pludek into an unlimited conformist. He is an unbreakably plastic character. He seems able to adapt to any situation, to the point where in fact he wilfully becomes a nobody. Not even his parents can recognize him any longer. The personality of the good-for-nothing turned careerist constantly slips out of gear. He has no personality. He is a self-less creature incapable of speaking, judging and acting for himself — he is what the ancient Greeks would have called an _idiot._
The theme of the decomposition of Pludek's character (contrary to literal-minded interpretations of the play) does not prove that Havel had a 'pessimistic vision of modern society'. _The Garden Party_ in fact parodies more conventional narrative versions of the same psychodramatic theme, so that it is not, say, a variation on Kafka's _Metamorphosis_. Like absurdist playwrights before him — Havel was especially familiar at this point with the works of Ionesco and Beckett — _The Garden Party_ develops the theme of depersonalization _ad absurdum_. It does this by encouraging the audience to concentrate upon a spectacle of words that drown out any real plot, or conflict, or psychodrama. The play is about nothing else but words — words that do not play the role of 'neutral' conduits of meaning, that is, of expressing the ideas and emotions of characters interacting on a stage. Precisely the opposite role of language is highlighted. The characters, Pludek in particular, become the deformed medium of a deformed and deforming language.
Havel's aim here is not to repeat the point — which has become heavily clichéd since Lord Acton's _Historical Essays and Studies_ (1907) coined it in this way — that power tends to corrupt individuals, absolutely so when they exercise absolute power over others. _The Garden Party works_ up the more profound point, sometimes in riotously witty ways, that _language can corrupt and disempower the_ individuals who speak it, and that _corrupted language corrupts and disempowers them absolutely_. Havel, playing the role of parodist playwright, experiments in various ways with underlining and then flinging back the debased language into the faces of the audience. There are moments in the play, for instance, when the language of the so-called characters degenerates into dry-as-dust, pseudo-precise, belaboured bureaucratic memoranda. Consider the exchange about facilities between the She-Secretary and the He-Secretary, two Liquidation Office employees, who are seated at the entrance to the garden party at a desk covered with rubber stamps and heaps of paper:
SHE-SECRETARY: You are at present at the main entrance B13. You can buy here a general admission card, one which will provide you with the right of free movement throughout the entire topographical extent of the garden as well as with the right of visitation to all attractions organized within the framework of the garden party of the Liquidation Office—
HE-SECRETARY: There is, for instance, the discussion with the Chairman of the Development Department concerning liquidation methods, which is conducted in the area of the Little Pond.
SHE-SECRETARY: An entertaining Quiz Programme on the history of the Liquidation Office, conducted in Pavilion No. 3 —
HE-SECRETARY: Or the programme of humorous stories from the liquidation practice of Section 5 that were recorded and will be narrated by the Head of Section 5.
The so-called dialogue elsewhere in the play is no less counterfeit. Mechanical repetition is common, as when there are verbal duels between speakers repeating identical words or phrases. Purely grammatical combinations of words — an example is the tedious extended conversation between the Director of the Liquidation Office and the She-Secretary, using derivatives of four words: delimitation, liquidation, form and norm. Then there are the nonsense proverbs, which upon closer examination turn out to be mere slag heaps of semantically unrelated words. 'Dear son! Life is a struggle!' says Pludek's father, as if he were a speaking automaton. 'Stone walls do not an iron bar! To be or not, aye there's the rub! Consider the lilies of the valley, they spoil not, neither do they tin. You are my son!' In such instances, language seems to be destroyed not only by otherwise grammatically 'correct' sentences that unfold randomly. The meaning of the language is also destroyed from within: the proverbs have all the formal characteristics of proverbs, including the right intonation and rhythm, but the bizarre combinations and sequences of words are merely mechanical. _The Garden Party_ also contains plenty of nonsense disputes, as when an absurd disagreement erupts over whether the Large Dancing Floor is larger than the Small Dancing Floor.
The bizarre language that is burlesqued in these exchanges among individuals reveals that their capacity for communication has nearly been destroyed. The destruction is much more radical than in a drama by Chekhov, say. In Havel's hands, people do not communicate with each other. They do not even understand each other. They simply have nothing to say. They no longer even think. True, they talk at each other in prefabricated clichés that are repeated over and over again and sometimes twist and intertwine. They stride around the world, cushioned by words. Pludek even acts confidently in the world: his posture is self-assured and his carefully crafted sentences seem to be living proof that he trusts in the observations he makes and the ideals he espouses. He is the sort of character (as the director Andrej Krob says) who not only is a master of chess, but probably knows all the world's telephone directories by heart. Lacking an identity, he possesses absolute certainty about everything. He even knows the craft of saying something at odds with what he really thinks.
The trouble is that Pludek's decency is a synonym for stupidity. He is self-nullifying. He is everybody and nobody. Not only does he say nothing. His language, thanks to Havel's touch, is so hyperbolized that it is utterly absurd. Bureaucratic terminology, mechanical repetition, prefabricated platitudes abound. It is little wonder that nonsense proverbs and nonsense disputes result. Equally disturbing is the way in which false syllogisms and circular illogic abound to the point where the so-called conversations lose their veracity and spiral into nothingness. Its low point is the absurd autobiographical monologue — which rather resembles a lecture that lampoons Marxist-Leninist dialectics — delivered by Hugo during his homecoming. 'Me! You mean who I am?' he begins: 'Now look here, I don't like this one-sided way of putting questions, I really don't! You think one can ask in this simplified way? No matter how one answers this sort of question, one can never encompass the whole truth, but only one of its many limited parts. What a rich thing is man, how complicated, changeable, and multiform — there's no word, no sentence, no book, nothing that could describe and contain him in his whole extent. In man there's nothing permanent, eternal, absolute; man is a continuous change — a change with a proud ring to it, of course! Today the time of static and unchangeable categories is past, the time when A was only A, and B always only B is gone; today we all know very well that A may be often B as well as A; that B may just as well be A; that B may be B, but equally it may be A and C; just as C may be not only C, but also A, B, and D; and in certain circumstances even F may become Q, Y, and perhaps also H.'
### **The Crises**
Equations suggesting that A may be B as well as A, and that A is B and C ... as well as D were meanwhile appearing in the force-field of Czechoslovak politics. Despite the official declaration that the world-historic phase of socialism had been reached, and that the final struggle for Communism had begun, the Communist Party slowly lost its grip upon power. Signs of crisis within the regime began to appear everywhere. 'Crisis' is admittedly a strong word that has been polluted of late by overuse, especially within the worlds of advertising and everyday life. There it pops up regularly to describe everything from having a flat tyre and losing one's wallet to the resignation of a football coach or a government minister. The more precise — originally Greek — meaning of the term refers more narrowly to an extended sequence of events disfigured by self-paralysis. A crisis is a turning point, an interregnum during which what has existed for some time begins to fade, or to die away. Everybody caught up within the crisis feels (and is) less powerful. Their capacity to act is impaired. They live together in the subjunctive tense. They know that things could soon be otherwise, that everything in future depends on what now happens. That is why some, not surprisingly, summon up courage to act to resolve the crisis in positive ways. But the crisis also makes many others feel enervated, and in consequence some others react morbidly.
The morbid symptoms of crisis appeared in force in the Czechoslovak system during the years 1963 and 1964, when for the first time since the _coup d'état_ the regime began seriously to malfunction, to the point where the world seemed out of joint and nobody seemed confident enough to diagnose, let alone heal, the problems. The feeling of growing powerlessness in the face of this self-paralysis was compounded by the multiple roots of the crisis, all of which were however traceable in one way or another to the totalitarian state structures. The 1960 constitution had codified the leading role of the Party — Czechoslovakia was the first regime in the world to do so — which had the effect of legitimating the undesirable concentration of power within the upper echelons of the Party led by Novotný. Reliable maps of the pyramidal structure of decision-making power are hard to draw, but estimates suggest that most of the 300,000 members of various Party committees from the local level upwards had little power to determine anything except local supplies and deliveries of goods and services. These Party members — the nomenklatura — naturally were privileged by comparison with the huge majority of the population who remained outside the Party structures. But the reality was that state power was overwhelmingly concentrated in the hands of the 8,500 employees of the national Party apparatus; in the hands of the 750 apparatchiks who ran the Party at its very centre; and above all in the hands of the supreme organ of the Party, the Presidium.
The privileges — related to such resources as sex, luxury goods, vacations, and housing — accorded those who clung to the pinnacles of state power are legendary. Less well known are the administrative burdens that so enveloped the ruling oligarchy that even they began to sense the need to 'offload' the piles of paperwork on to others, and to call it decentralization of power. Whereas in the year of the _coup d'état,_ the average Presidium meeting dealt with a handful of items, by the early 1960s paperwork business emanating from the Party's Central Committee, government ministries or research teams had increased four-fold. Each week, the average Presidium member received some 500 pages of briefing materials relevant for the scheduled Tuesday meeting. Whether intended or not, paper in this quantity had an intimidating effect upon Presidium members, who uttered platitudes or simply kept their mouths shut for fear of making themselves look like the ignorant idiots many of them were. So as each item on the agenda of the Tuesday meetings was concluded, the First Secretary tried to take account of every speaker's point by verbally proposing a compromise resolution _(usnesení)._ No vote was subsequently taken to confirm the proposed decree, and indeed the final written version, which was drafted afterwards by the First Secretary and his staff, often bore no relationship at all to what had been discussed and verbally agreed.
The disempowerment and overburdening of officials in the alpine regions of the Party was compounded during this period by the sense that all was not well in the green fields of state investment, production, trade and consumption. It is misleading to speak of 'the economy' as an independent source of crisis within the Czechoslovak socialist regime, simply because an economy in the strict sense didn't exist. Everything from wage rates and international trade to the price of bread and condoms and bananas, or even whether they were obtainable at all, was decided by the Party-dominated institutions of the state. The state's elimination of an independently functioning 'economy' certainly confirmed the principle that socialism would abolish commodity production and exchange, but the price that had to be paid was high. Right at the beginning of the third Five-Year Plan (1961-1965), the robust industrialized production system that had hitherto been the showcase of the Communist world began to fall apart. The Sino-Soviet dispute and the dramatic confrontations in Berlin and Cuba meant a downturn in exports. There was a string of poor harvests. Capital equipment (like factory machinery) and office administration were often of poor quality and, above all, investment policy and management decisions were frequently senseless. The disturbing result, especially from the point of view of the trumpeters of Communism, was that during 1963 alone national output declined by at least 2 per cent. The Five-Year Plan was by then scrapped, the inflated presumption that the transition to Communism would accelerate the onset of material abundance was pricked, and Czechoslovakia, which had been ruthlessly exploited by its Comecon partners by making it dependent upon heavy industrial exports to pay for its fuel, foodstuffs and raw materials, found itself tightening its belts.
The resulting squeeze on the population was aggravated by the lack of intermediate groups and self-help organizations standing between the individual and the Party-dominated state. When times are hard, such social organs sometimes mean the difference between life and death, or between comfort and misery. _Corps intermediares —_ free trade unions, charitable organizations, self-help circles like the Thirty-Sixers — are barriers against the destruction of people's identities and, conversely, vital conditions of their ability to act in and on the world. Their absence in Havel's homeland was striking — it was a determinant feature of the totalitarian system — and it meant that, when frustrations began to build, as they did during the early 1960s, individuals had virtually nowhere outside their households and district Party headquarters to turn. There were no spaces in which, even in the face of adversity, they could feel themselves more or less free. Such _prostory,_ as the Czechs call them, had been badly damaged by the Reichsprotektorat and total war and the post-war disruption and hardship, but the 1948 _coup d'état_ and totalitarian rule that followed had a devastating impact upon the patterns of social self-organization, whose roots were often traceable back to the First Republic, and beyond.
The Communist seizure of power effectively demolished the rural and urban middle classes along with their associations, so that for instance in the decade after 1948 the number of craftsmen's studios and privately owned shops declined dramatically from 250,000 to a mere 6,553. The shocking effects upon the whole social structure were compounded by the systematic uprooting and disorientating effects of state policy, which used every means possible to prepare the way for 'socialism'. After the _coup d'état,_ thousands of 'bourgeois' professors and students were hounded out of the universities. The Augean world of newspaper and radio journalism was scrubbed clean. At least 300,000 people of the wrong class background — the young Havel, as we have seen, was one of them — were immediately kicked downstairs, or sideways into other official institutions. They were replaced by over a quarter of a million mostly young working-class people aged between twenty-five and thirty. These nomenklatura, whose ranks soon swelled, were hastily trained and promoted within the dominating power structures, even though they were only there thanks to Party patronage. Managerial competence was in short supply: by the early 1960s, it is estimated that nearly half a million men and women of the nomenklatura occupied key decision-making positions, particularly in the management of enterprises, for which they were formally unqualified.
The combined consequence of these various structural problems of the socialist state — unqualified leadership, administrative bottlenecks, economic stagnation, the absence of social 'shock-absorbers' — was to encourage a faction of the ruling oligarchy to embark on a dangerous journey called liberalization. At first there was no detailed or coherent programme, only random policy suggestions and an emerging sentiment that the present wasn't workable, that something needed to be done, and that the rulers themselves might well have to defer to experts and clients to find solutions. Power relations within the regime consequently began to feel less totalitarian — a regime of command and obedience in the grip of a Party monopoly — and more like an approximation, so it was said officially, of the ideal of power as a property of the system as a whole, as the making and use of authoritative decisions by the Party to mobilize commitments and obligations for the purpose of furthering the effective pursuit of collective socialist goals, without conflicts of interest, coercion and the use of force. It was exactly this momentary faltering in the onward march of socialism, its attempt to switch from bossing to persuasive bargaining, that provided a breathing space in which official ideas and initiatives in favour of liberalization could be proposed and tried. In theory, the Party was from here on supposed to win the trust and loyalty of the population — to earn its leading role — by persuading others, setting examples, and compromising for the sake of building socialism. In practice, the proposed reforms, and the resulting hopes and fears and confusions they generated, lifted the lid on the public expression of dissatisfaction — along with ballooning popular expectations. By early 1967, noted Alexander Dubček, the Party leadership had 'learned from reports of the district Party committees that the public mood in both Slovakia and the Czech lands was increasingly impatient and in favour of change.'
Isolated group initiatives had actually begun to spring up well before then. There was active discontent in Slovakia, directed especially at alleged Czech bigotry and the under-representation of Slovaks within the trade unions, cultural associations and other state institutions. Many students voiced dissatisfaction with poor dormitory conditions, restrictions on foreign travel, and the compulsory boredom induced by courses in Marxism-Leninism. Within the artistic field, theatre for instance, the centre of gravity moved during this period from large established state organizations towards smaller experimental institutions. Similar pressures for innovation became evident in the field of publishing, as was evident in the feverish tensions that built up during 1966—67 within the Writers' Union. Denounced by one of its senior apparatchiks as a 'bourgeois brat', Havel spent much time lobbying and petitioning and pestering officials in support of the goals of liberalization. He was heavily involved in the case of the writer Jan Beneš, whose arrest and conviction for sending articles to the Paris-based _émigré_ journal _Sv ědectví_ ( _Witness)_ resulted in moves to expel him from the Writers' Union. According to its by-laws, the case was cut-and-dried: a member convicted of anti-state activity was expelled automatically. At a rowdy all-day meeting lubricated by beer, the members eventually voted by a big majority in favour of Beneš's expulsion, but only after one of the most devoted Party members angrily exclaimed, 'Comrades! If you do not expel this Beneš, I will cancel my membership of the Union.' In a tiny minority, Havel raised his hand and voted against, with a few other writers like Josef Škvorecký abstaining.
The prelude to these battles was the controversy hovering over the monthly magazine for young writers, called _Tvá ř(The Face)._ Havel was invited on to its editorial board in the spring of 1965, just as it was about to be threatened with closure. For a while, the controversial contents of the journal — a translated excerpt of Heidegger's in the first issue, pieces by T. S. Eliot, Eugène Ionesco, and Alain Robbe-Grillet in the fourth, for instance — had seemed to escape official disapprobation from the Writers' Union. Everything initially was played out behind the scenes, after the fact. The Party censors made it known that they objected to 'non-socialist' foreign translations and previously banned Czech authors, like Jan Hanč from the Group 42. Soon the Party's slow-footed censorship found its stride. The editors got hell for what was about to appear. Then they were not allowed to print certain things. Then, in June 1965, the Writers' Union moved to shut down the whole journal.
The editors decided to fight the decision by circulating among people in the arts a petition against the ban. After enough signatures had been collected in Bohemia and Moravia, Havel, accompanied by the editor, volunteeered to take it to Slovakia. The trip was eventful from the moment they set off from Wilson Station, where two Party writers, Antonín Brousek and Jiří Gruša, tried unsuccessfully to stop them physically from climbing aboard the overnight express to Bratislava. Havel and Nedvěd talked their way through the blockade, to arrive next morning in good time for a meeting to discuss the matter convened by the Union of Slovak Writers. 'Václav went there [alone] and turned the meeting upside down,' recalled Nedvěd, 'and returned from it with some important signatures.' For the next few days, the two young rebel writers flitted like butterflies from flower to flower, usually — but not always — with success. They tried to get in touch with the dramatist and novelist, Peter Karvaš, who lived in a villa surrounded by a tall fence. For some reason, his doorbell wasn't working, so it was up and over the fence the hard way. Chubby Havel, complaining that his trousers were 'too modern', got stuck during the climb. Nedvěd eventually bunted him over, to be greeted by a surly dramaturg well known for his two recent plays, _The Scar_ (1963) and _The Great Wig_ (1965). The conversation with the intruders started badly, and didn't ever improve. Karvaš refused to sign.
Havel's politicking in support of what he affectionately called 'the tiny oasis of _Tvá ř'_ was the opening round in a battle with the Party state that lasted nearly a quarter of a century. His editorial work for the journal was certainly important. It kept him abreast of current literary trends, and confirmed his dislike of ideological prejudice in literary matters. _Tvá ř_ was intolerant of Marxism, but it was so exactly because its editors objected to the principle and practice of judging literature according to some ideological line or another. The later vicious attack on Havel by _Trud,_ the Soviet trade-union newspaper, understood well what was at stake. Havel was indeed working for the depoliticization of culture, that is, 'full freedom for any views, including anti-socialist ones, and no obligation on writers to defend proletarian ideology'. _Tvá ř_ also proved to be a forum in which he could experiment with the art of essay-writing, as evidenced by the success of the well-crafted 'Notes on Being Half-Educated', which generated considerable discussion of its insistence that the younger generation deserved tough criticism for failing to educate itself properly.
So the literary importance of _Tvá ř_ to Havel was clear. Of greater significance was the fact that the petition taught him several political lessons. Vigilance in the face of dirty tricks: likening himself to the poor Gascon gentleman d'Artagnan (in Alexandre Dumas's _The Three Musketeers)_ who comes to Paris in the reign of Louis XIII, only to be persecuted by him for duelling with some of his musketeers, Havel made duplicate lists of the signatures before returning with Nedvěd to Prague from Bratislava, just in case he was caught. His concern about police harassment was not misplaced. Shortly afterwards, he found a wad of anti-state leaflets stuffed in his home mailbox. He was convinced they were bogus, and perhaps even printed by the state authorities themselves. He reacted swiftly by telling his friends of the trap that had been set and reporting the whole matter to the local police station. He was rewarded with a secret-police file that listed him as 'an anti-socialist collaborator'. And he was savagely criticized in the official media, for the first time, by the Head of the Ideological Department of the Central Committee of the Communist Party of Czechoslovakia, František Havlíček, who denounced him as a 'bourgeois' writer whose family had owned various businesses, including the Barrandov studios. Temptation: at one point in the struggle between the editors of the journal and the Writers' Union, Havel was taken aside by the boss of the Cultural Department of the Party's Central Committee, Pavel Auersperg, and secretly offered the chance of starting up his own magazine, with the editorial right to commission pieces from the editorial board of _Tvá ř,_ which was earmarked for redundancy. Havel had heard that Auersperg, behind his back, had described him as 'a dangerous fellow', which drove home the point that Auersperg's offer was a clear attempt at _divide et impera_ by a Party hack. Not wanting to 'get mixed up in back-room wheeling and dealing', and feeling that 'a new and fresher wind was blowing', Havel flatly rejected the offer. There was also a lesson in civic initiative: the petition was so successful — over 600 signatures were collected — that a plan was hatched to widen the basis of support for _Tvá ř_ by creating a group of people around the journal, who would seek to shield it from further harassment. Leadership: the resulting supporters' network was named the Young Persons' Action Group, with Havel as its first chairman. He was an obvious choice, especially after delivering a swingeing attack on the 'evasive thinking' of the delegates attending the conference of the Union of Czechoslovak Writers — and getting roundly applauded by the very same delegates whom he accused of not 'defending the right of literature to be literature'. Criticism: Havel agreed to act as the mediator between the editorial board and the Writers' Union. Several times during 1965 he negotiated a compromise position with the Writers' Union, only to be rebuffed for his plasticity by the majority of the board, led by Emanuel Mandler. Havel later claimed that _Tvá ř_ had its dogmatic 'inner sanctum', and that its sectarianism proved the truth of Eugene O'Neill's famous maxim: 'We fought so long against small things that we became small ourselves.' Whatever the truth, Havel's perceived mishandling of the negotiations caused acrimony within the board, so that at one point a mutual acquaintance, the playwright Pavel Kohout, was asked to sort Havel out. He did — by arranging to pick Havel up in his Volga one afternoon, and then driving around Prague, all the while trying to drum into Havel that there should be no retreat, and that he and others must never give up. And failure: although the whole action seems to have prolonged the life of _Tvá ř_ for about six months, the Party rounded on it at the end of 1965. The tenth and final issue, which included contributions by the German social psychologist Erich Fromm and the century's greatest Czech philosopher, Jan Patočka, appeared in December of that year.
Then there was the experience of learning to live with defeat: various members of the circle of supporters of the banned journal, including Havel, were profoundly impressed by their reading of Dietrich Bonhöffer's famous prison letters, and it is therefore not surprising that the spirit of resistance pervading those letters steeled the _Tvá ř_ group in fighting for its life. Havel and others — including some of his friends like Věra Linhartová and Josef Topol — continued for the next eighteen months or so to meet regularly, in defiance of the authorities, at various venues, including (it was a standing joke) the loft of the building of the Union of Soviet—Czechoslovak Friendship. These and other sweet ironies of defeat were appreciated by everybody who was involved, and this in turn reinforced the fun and games that were played throughout the whole saga of the banning of _Tvá ř._
Shortly after its closure, Havel and other members of the editorial board organized a wake. It took the form of a drunken crawl through a handful of Prague's night-clubs. From several, Havel and his friends were thrown out for being improperly dressed, so they moved on eventually to the Kravín wine bar, where they spent a good part of an evening. On their way home from there, lurching down Vinohrady Street, they stumbled into the grounds of St Ludmila's Church, where they happened upon a pile of freshly cut Christmas trees. They naturally helped themselves to the collective wealth produced by socialism and, each with a tree in hand, resumed their journey towards Karlovo náměstí. They were suddenly stopped by a police patrol. 'Where are the receipts for these trees?' a stern officer asked. Of course, Havel and the rest of the group had none. But just at that moment someone in the group (Jan Lopatka) pulled out a press pass. The officer studied the pass, and then replied: 'You mind your business, and we'll mind ours!' And so Havel did — but not for long.
### **The Memorandum**
The Party's decision to liquidate _Tvá ř_ was officially justified as an exercise in 'improving the journal'. The hypocrisy was typical of the times, as Havel had emphasized in his attack on 'evasive thinking'. It was epitomized by a recent tragi-comical incident in Prague's Vodičkova Street, where a loose stone window-ledge happened to fall below on to a woman pedestrian, whose instant death caused a local scandal, which was then reported officially as proof that socialism was making enormous progress. That is to say, the combined effect of the pressures from above and below to liberalize the crisis-ridden regime led by President Novotný was to produce much confused double-talk, especially so within the thawing alpine regions of the Party hierarchy. The criticisms and reform proposals of the liberalizers — 'the antidogmatics' Havel called them — were for instance still normally labelled by their defenders as 'socialist'. They were mainly articulated through the mainstream official channels, which meant that — just like their 'establishment' opponents — they carried the birthmarks of inflexible and intolerant ideological thinking. And the reform proposals often came from the very same lips of journalists, scholars and writers who, not much more than ten years ago, had sung sweet songs of praise to Stalin and did everything they could to hound 'bourgeois' opinion out of the ranks of the nomenklatura.
The air was so ripe with whiffs of confused hypocrisy that Havel decided to make it the target of his wonderfully absurdist satire _The Memorandum._ The ribald two-part, twelve-scene drama unfolds within the offices of a large department that is somehow connected to a larger, undefined, bleak bureaucracy. The stage set of Jan Grossman's first production of the play at the Theatre on the Balustrade included special fire extinguishers with removable coats of arms, one for each new director; filing cabinets containing nothing but clerks' cutlery, wrapped in plastic bags, withdrawn and replaced with chronometric precision; an empty can, front stage, into which water drips with deadening regularity; and contrastingly loud snatches of bouncy music, resembling some terrible mixture of _Nabucco_ and _Lohengrin,_ designed as a counterpoint, to make the audience laugh. Laugh it certainly did when the department director, Josef Gross, discovers in his morning mail a memorandum written in a strangely jumbled language. He is surprised to find that his subordinates already know that the language exists. It is called Ptydepe. So Gross tries to have the memorandum translated, without success. His secretary hasn't yet grasped the grammar of Ptydepe, while his other subordinates haven't been authorized to attempt the translation. Entangled in red tape, feeling ever more isolated, Gross slowly realizes that he has been disempowered within his department, that there has been a plot behind his back, and that his deputy, Baláš, is responsible for the introduction of the strange new _lingua franca._
The bewildered Gross, hanging on for dear life to his director's post, finds that the stated aim of the newly circulating language is to improve the efficiency and effectiveness of the organization by eliminating imprecision of meaning. Whereas the old natural language produced misunderstanding and inaccuracy, the new language of Ptydepe is supposed to usher in transparent communication. Its grammatical rules are straightforward. It is said to be a 'strictly scientific ... thoroughly exact' language blessed with an 'unusually broad' vocabulary and a grammar constructed with 'maximum rationality'. Similarity among words is purposefully minimized. Professor Perina, the organization's language expert and teacher, explains that 'words must be formed by the least probable combination of letters'. Here the so-called principle of 60 per cent dissimilarity comes to the rescue. 60 per cent of the letters in any word in Ptydepe must be different from any other word of the same length. The vocabulary of Ptydepe is built on another logical principle as well: the more commonly used a word, the shorter it is. In Ptydepe, the word for wombat has 319 letters. At the other extreme, a word like 'whatever' — a favourite of amoral cynics — is the second shortest word, 'gh'. The 'f' word, we are told, is being held in reserve, just in case science should discover a term more commonly used than 'whatever'.
It is easy to see that _The Memorandum_ is a satirical attack on an imaginary world — a world only a few notches away from Havel's current reality — defined by the absence of communicative interaction and the complete destruction of freely expressed public opinion, that is, a pure totalitarian order in which the exercise of power no longer needs to be legitimated because nobody is capable of speaking and interacting with others. Ptydepe's rules of vocabulary and usage are based ultimately on the principle that language itself should become obsolete in human affairs. 'The greater the redundancy of a language,' says the wise professor, 'the more reliable it is, because the smaller is the possibility that by an exchange of a letter, by an oversight or a typing error, the meaning of the text could be altered.' Ptydepe is more than a super — new and improved — synthetic language. It is an anti-language, for it seeks to reduce its speakers to mechanical creatures who have neither ethical self-awareness nor even the capacity to distinguish between the language itself and the context in which it is embedded.
Little wonder, then, that throughout the play Gross's secretary sits at her desk, props up a mirror on her typewriter, and combs and teases her hair; or that Gross is constantly precluded from communicating with anybody else, or that the secretary of the Translation Centre has no contact with the outside world except for her shopping trips in search of lemons, melons and onions, and the continual ironing of the Chairman's underwear. Ptydepe is admittedly a rigorous language. It is designed to eliminate the need for communication. From here on, says the deputy director, no one will be led to think that being injured is the same as being helped. But it has several disadvantages. First reports received from the pilot projects where it had already been introduced showed that the trouble with Ptydepe was that it soon began to assume some of the degenerate characteristics of a natural language: various imprecisions, ambiguities, emotional overtones. Then there was the close-to-home difficulty of figuring out its grammar and vocabulary. Although Ptydepe classes had been set up for the employees, almost everybody found it utterly baffling. Only the departmental teacher and the staff of the Translation Centre understand its intricacies — although even the Head of the Translation Centre confesses that progress is slow, and that he's only on his second translation.
During the first part of the play, Gross — who resembles a Communist of the 1948 generation and repeats several times that he'd like to be a little boy again so that he could live his life differently, and claims as well that he is unfriendly towards Ptydepe because he is a humanist believer in Man — suffers defeat at the hands of the amalgam of words called Ptydepe. Gross, who received at the outset a text from the authorities in Ptydepe explaining their ruling that the language was from here on the official one, is victimized by the authorities' supplementary ruling that no person can be granted a translation of a memorandum in Ptydepe text until his or her own memorandum has been translated. Gross is subsequently kicked downstairs to the post of staff watcher.
Yet towards the end of the second part there is an apparent reversal of power relations within the organization. Havel here uses the circular structural pattern typical of absurdist plays to drive home the point that everybody in the play is caught up in the amoral tumble and scramble of the organization. The authorities order the liquidation of Ptydepe. A new and improved synthetic language called Chorukor is invented. Its aim is to put a stop to the unreliability of communication caused by Ptydepe's strenuous pursuit of words as dissimilar from each other as possible. Chorukor tries to achieve this through the — opposite — rule that the more similar words are, the closer their meaning. So Monday in Chorukor is 'ilopagar'; Tuesday is 'ilopager'; Wednesday is 'ilopagur'; 'ilopagir' is Thursday; Friday is 'ilopageur', while Saturday is 'ilopagoor' and Sunday is 'ilopagor'. But won't words intermingle, or get mixed up? And won't confusion result? The recipe is flawless, the consequences quite predictable, Professor Perina says reassuringly. Perfect interaction will result. And if a typist asked to arrange a staff meeting makes a mistake, then no harm will result. In typing 'ilopager' instead of 'ilopageur', all that will happen is that the meeting takes place earlier than expected — on Tuesday, rather than on Friday — so allowing business to be worked through well ahead of schedule.
### **Summer Friendship**
The early hot spring and summer of 1968 meant various things to different people, but for Havel it was a time of being surrounded by friends. It all began with a delicious surprise. On his way from Prague to New York in early May, accompanied by his wife Olga, he had a scheduled two-hour stopover at Charles de Gaulle airport in Paris. Taking advantage of the political thaw in Prague, Havel had telephoned in advance a man named Pavel Tigrid, who lived in Paris as editor of the most important Czech _émigré_ literary quarterly journal, _Sv ědectví (Witness)._ Havel yearned to greet him for the first time. Not only did he want to talk face-to-face with the editor to whose magazíne he had contributed some pieces in recent years. Havel was also busily collecting material for a series of radio programmes on Czech _émigrés,_ and Pavel Tigrid was an important part of the story of the tragic scattering of Czech talent around the world by twentieth-century power politics. The editor of _Svédectví_ had not only seen a good deal of life on both sides of the Iron Curtain. His life was coterminous with the twentieth century. Born in 1917, he had grown up in the new Republic of Czechoslovakia, only to witness its destruction while studying at Charles University. He first went into exile during the Nazi occupation, to Britain, where in London he spent the war years working as a radio journalist for the BBC. Tigrid — affectionately codenamed 'the old man' _(nestor)_ by Havel in their subterranean correspondence — returned home in 1945, to become editor of a national weekly. But in 1948, after the _coup de Prague,_ he moved to West Germany, then to the United States, and then finally to Paris, the base from which he devoted his time to spinning the precious gossamer threads connecting otherwise isolated writers who represented what remained of independently-minded Czech and Slovak literary culture. KGB agents described him as a 'reactionary American agent'; naturally, they kept him under their magnifying glass.
Havel had no knowledge of the geography of Charles de Gaulle airport. Nor did he have a visa to allow him to exit into the main terminal building. The wise Tigrid had promised Havel on the telephone that he would do everything to ensure that they met. He had instructed Havel to stay in the transit lounge. 'Make yourself visible to people waiting in the arrivals section of the airport, and keep your eyes open,' he had said. And suddenly there he stood. Thirty metres away, separated by security barriers, immigration officials and thick plate-glass windows, the short, greying, bearded editor smiled and waved, his delighted eyes fixed on the denim-jacketed, long-haired young playwright. The pair briefly put on a mime show, with the desperate Tigrid gesturing to the Havels to stay put. He then hurried to the nearby Air France sales desk, to join a queue of ticket-purchasers.
Time was preciously short. Only one hour before the Havels were to set off for Prague, perhaps never to return. Tigrid acted fast. He had brought enough cash to buy a ticket to ride — out of the country to nearby Brussels, or to Amsterdam, or Zurich. The destination was irrelevant. So was the price. It was not even a question of paying a price worth paying. Friendship was after all at stake. There is a saying that a friend in the market is better than money in the chest, which is to say that friendship is more and other than a monetary matter. Genuine friendship does not know the rules of selfish calculation. Friends have no interest in profit. Friends prove their friendship in times of need. They share all things in common. Friends are sincere with each other; they are a second self; they are generous; their requests do not wait until tomorrow to be satisfied; they are not vain. Friends are certainly a source of disagreement, sorrow, bitterness. But friendship ends when those qualities triumph; that is to say, friendship is an elixir of civility. Friends are non-identical, pure equals. Friendship is a relationship of mutual empowerment. It is not built on unequal power. 'Friends are an aid to the young, to guard them from error,' wrote Aristotle, 'to the elderly, to attend to their wants, and to supplement their failing power of action; to those in the prime of life, to assist them to noble deeds.' And all this is chosen. Relatives are bound together by nature and saddled with fate, but friends make themselves by choice. Friendship is a form of public freedom.
Tigrid moved towards the head of the queue. He would have to explain quickly, cut the chortle, race through immigration, and make a mercy dash to the transit terminal, with luck into the arms of strangers. Imagine then his bewilderment when, at precisely that moment, the officials behind the Air France desk slapped a 'Closed' sign on the counter and began turning off lights, locking doors, picking up bags, and walking off the job. So did all the other officials in the nearby airport departments. Even the immigration section stopped guarding the arrival and departure gates. Suddenly the barriers between East and West collapsed. Travellers and well-wishers alike were magically free to move wherever they liked. Borders were meaningless. Identity papers were obsolete. Surveillance was just a word. Nobody asked questions. The distinction between citizen and alien, between insider and outsider, was struck down. Everybody was equal. Havel and his editor were free to lock together in a warm embrace. It was a meeting whose time and place were to be noted and never to be forgotten. It was the early morning of Monday, 13 May in the international transit lounge of Charles de Gaulle airport. It was the first day of a half-planned, half-spontaneous general work stoppage organized by the left-wing parties and such trade unions as the CGT, the CFDT, and the FEN (National Federation of Education). The glorious May Days had begun.
During the next few days, as guest of Tigrid and his wife, Havel breathed the spring air of free and independent Czech culture in exile. It was thrilling to discuss Kafka and čapek and Seifert in exotic circumstances. Paris was in a state of pre-revolutionary upheaval, and through their hosts' eyes, and with their help as translators from French into Czech, the Havels witnessed breathtaking scenes and events, mainly on television. On the afternoon of their arrival, between 600,000 and 1 million demonstrators (the estimates were always contested politically) marched their way across the city. At various rally points, speaker after speaker denounced the government's deaf ears and heavy hands and accused the riot police of provoking the worst street-fighting witnessed by Parisians this century. There were graphic descriptions of the use of toxic grenades, of innocents torn from their cars and from cafés and beaten, of several women raped by police in the streets. Speakers described how, in recent days, students had fought back by building the first barricades seen in Paris since 1944, and by forming thousands of _comités d'action,_ whose aim was to establish counter-institutions of grassroots democracy outside the existing political structures. The huge crowds jeered when speakers quoted the week-old words of the Minister of Education, who had claimed that the disorder was caused by 'students playing at revolution'. Mention in public of the ORTF (the French equivalent of the BBC) produced scowling talk of ignorance and bias. There was wild applause at the announcement that its technicians had just joined the general strike. But — this reaction on the streets was telling of the wider mood of insurrection — the loudest hoots of irreverent laughter were reserved for the oft-repeated words of Georges Pompidou, the Prime Minister. Two days earlier he had addressed the country: 'Iask everyone,' he had pleaded, 'and in particular those who are leaders of representative student organizations, to reject the provocations of a few professional agitators and to co-operate.' He had added: 'For my part, I am ready for peace.'
That evening, as the Havels feasted on a home-cooked meal of venison, red cabbage and dumplings with their new friends, students armed with red flags settled into their occupation of the Sorbonne, which was declared open to the people, no longer a hierarchical institution, a place where 'labourers and workers are invited to come and discuss their common problems with the university students'. From this time the Sorbonne became the shop window of the uprising. It was the front line (as Daniel Cohn-Bendit said) against the France of Aunt Yvonne — enclosed, conservative, unable to understand that the world around it was changing. The Sorbonne housed many of the action committees set up by the general assembly of students, which met nightly in the courtyard to take decisions. Permanent teach-ins, debates and entertainment were organized. The style of action soon spread. During their week in Paris, the Havels witnessed the occupation of nearly every university in the country. Many university administrators threatened to resign unless the government stopped interfering and guaranteed full university autonomy. Two-thirds of _lycées_ in Paris went on strike. Many regional towns experienced the first-ever demonstrations since the Liberation. _Comités d'action_ were set up in the Renault plants, Citroën, Air-France, Rhône-Poulenc and the RATP (Parisian underground). Some workers and trade-union branches began to prepare for a long strike, and street battles with the police became commonplace. The École Nationale des Beaux-Arts and the Conservatoire Nationale de Musique in Paris were occupied. For the first time, the ORTF workers voted for a total strike against government interference and in support of the principle of public-service broadcasting. And (Havel noted) the Odéon, the national theatre, was occupied by demonstrators who declared it open to the public for discussion and cultural expression and as a meeting place for artists, students, and workers.
Despite the near-paralysis of public transport in strike-bound Paris — the government and CGT-led crackdown on the rebellion was yet to come — Pavel Tigrid managed to get his friends safely to the airport in time to catch their Czechoslovak Airlines flight on to the United States. It was a tearful ending, succoured only by the thought that friendship is more easily kept than it is made. Then came New York. There he walked the streets, listened to 'beat music', grew his sandy hair, sported an 'Elect Robert Kennedy' badge, and made more friends. In Jackson Heights, he was invited to the apartment of the famous pipe-smoking Czech journalist, Ferdinand Peroutka. They argued about the Prague Spring — Peroutka advised Havel to go slowly, and not to irritate the Russians — and attended the première of Havel's _Memorandum._ He also gave an interview to _The New York Times,_ in which he called for Czechoslovak legislation 'to remove censorship and guarantee freedom of speech and freedom of assembly', and reportedly said that 'swift political action by liberals in Czechoslovakia is necessary now, while the opportunity exists to make the country more democratic'. He followed up these remarks in London a few weeks later in an impressive BBC _Late Night Line Up_ interview with Joan Bakewell. Dressed in a turtleneck jumper, looking well fed and squeaky-clean, he told her that for him personally it was a good period, and that more freedom — probably — was coming to his country.
Havel returned to Prague during the last week of June, in time for an address to the Fourth Czechoslovak Writers' Congress, during which he praised the 'supreme, self-reliant poise' of Alexander Solzhenitsyn and warned that 'instead of uttering a thousand bold words, of which a hundred are later gradually retracted, it is always better to utter only a hundred, but to stand behind them to the bitter end'. Havel was clearly exhilarated, both by his taste of the West and his return to the East. But he was exhausted by his travels, which is why he wanted most of all to spend the rest of the summer relaxing in the countryside. The previous year Havel had bought a house and some land in the village of Hrádeček, near Trutnov, near the Polish border, 130 kilometres north-east of Prague. Hrádeček took its name from the nearby ruined small castle called Břecštejn. The village comprised a dozen or so houses. The ethnic Germans who had originally lived there were cruelly removed during the pogroms that swept through the country following the military defeat of Nazism. Among the new, Czech occupants was Mr Kulhának, who by 1967 wanted to sell the farmlet, where for four decades he had raised rabbits and goats for local sale. Through Andrej Krob, Kulhának's next-door neighbour, the deal was struck — with Havel, for the relatively modest sum of 24,000 crowns, some part of which probably was paid out of his foreign-currency earnings.
Havel was keen (perhaps to keep the authorities off his back) to hang the sign of modesty on his new purchase. He always subsequently spoke of his new purchase as a 'cottage', but the small castle in name was in reality grander than that. It rather resembled 'a little country estate' (said his good friend Jan Tříska, who spent the whole summer of 1968 there). Havel employed a live-in servant, a simple young man named Karel švorčík (nicknamed Kešot), who looked like a bearded Russian peasant, drank rum by the litre, and worked quietly as a handyman, sous-chef, waiter, and loyal Czech bodyguard. The little estate also included an orchard, which yielded good crops of apples, plums and pears, and a large stand of century-old beech trees, some of them measuring three hands in circumference. The main house, which included Havel's study that opened out on to the orchard, was flanked by a robust barn and a good-sized stable, and the whole property was surrounded by rolling wooded hills and, during summertime, meadows carpeted in blackberry and gooseberry bushes, burdock and sweet-smelling flowers.
Hrádeček needed some immediate refurbishment, and that summer, after planting some front lawn with Olga, Havel himself carefully designed and built a flat-stone pathway leading through the garden from the front door — even working by torchlight well into the night so as to complete the job before new guests arrived from Prague. A multitude of friends there was that summer. Friends came as individuals and in groups, in all shapes and sizes, sometimes overlapping so that the property bulged with housewarming well-wishers. Each person arriving was welcomed with a blast from the Hrádeček hi-fi set of the Bee Gees' love song 'Massachusetts'. It had been a big hit in America and England, and Václav adored its soft guitar and classical sounds and carefully crafted vocals; perhaps its sentimental talk of love, hitching a ride to San Francisco, and coming home also convinced him to use it as a stirring anthem for the new summer retreat. Havel — the compulsive dramatist — played the role of a generous and charming host who attended to the _mise-en-scène._
For some guests, the daily routine began at sunrise. Others preferred to sleep in, and then, encouraged by splendid weather, to sit lazily in garden chairs in front of the house, in the shade, sipping cups of black tea, or coffee, or morning glasses of Pilsener beer, story-telling, laughing, and discussing philosophy, art and politics. During the daytime, there was plenty of tomfoolery. Havel and Tříska, for example, spun elaborate jokes about the fact that their idiosyncratic fathers had each owned a thermometer containing three scales (Fahrenheit, Celsius, and Réaumur); and they decided to found the International Organization for Rescuing René Antoine Ferchauld de Réaumur from the Abyss of Condemnation by Science, with Havel as its elected president. The new incumbent (Havel) jokily pressed the point that Réaumur had been hard done by. 'Just because water boils at 80 degrees on the Réaumur scale is no reason to discriminate against him,' he would say, all the while cautioning against conspiracy theories. 'Celsius was Swedish. Fahrenheit was a German born in Poland. And our Monsieur Réaumur was French. So there's no reason to suspect that he was the victim of an extreme nationalist plot..,'
There was reportedly much serious interaction as well. Conversations were 'sharp, competent, inspiring, noteworthy, even educational'. And there was tranquillity. Olga would often appear later than the rest. She would wander outside silently, aloof from the others' good mornings, unlit cigarette and box of matches in separate hands. During the day, friends chatted with the Havels, helped tidy up, odd-jobbed around the property, played music — a large collection of LPs had been brought back from America and England — drank wine, went swimming in local ponds or walking in nearby woods, or made love quietly in some tight corner.
The evening dinners — Havel called them jolly parties'( _veselé ve čírky) —_ were definitely the highlight of the day. Havel did most of the cooking — Olga always confessed her preference for theoretical cooking and reading recipe books — and by all reports he tried to show off by preparing 'interesting' dishes. Grilled chicken was always popular; his penchant for spicy food, like devil's goulash and tangy sauerkraut, was the source of some jesting and quipping. There was usually a banquet setting, with a large lace tablecloth, candles, frivolous dressing and mock speeches. The cellar at Hrádeček was stocked full of luscious Moravian wine, and so naturally was the dinner table. There was polite conversation, gossip, loud laughter, drunken prattle, seduction, talk of art. And the guest named politics naturally dined at the table.
After several hard years of writing and literary politicking, Havel felt like a rest from official politics that summer. It wasn't to be. He shared in the widespread hope that the Czechoslovak Communist Party would show its human face, and, political animal to the core, he was therefore naturally reluctant to ignore the dozens of political stories and rumours delivered first-hand from Prague. He suspected (and top-secret records subsequently showed) that he was under surveillance, that along with Milan Kundera and others he was being described as a conspirator in an 'underground anti-Party group' that was hell-bent on undermining the foundations of socialism in the čSSR, and turning 'the country gradually on to the path of capitalist development'. The description resembled the most wooden of lines from one of his absurdist plays, which is perhaps why he found it impossible that summer to ignore the political thunderstorms that became world-wide media events.' We were self-confident, rebellious and intensely happy... everything seemed so simple', recalled his principal guest. But it so happened that this summer of 1968 was the moment of birth of a global public sphere that linked together, for the first time, by means of jet aircraft and print and electronic media like the telephone, radio and television, millions of unrelated people in many different countries. This fledgling public sphere moulded them into interested witnesses of spectacular media events. It endowed them as audiences with the feeling that they were living in the subjunctive tense. It made them feel that the existing 'laws' of society and power politics were far from 'natural'. It even convinced some of them, Havel included, that the future shape of the world was dependent at least in part on current public efforts to contest and refashion it, according to new and different criteria.
Havel's sense of living suspended in the subjunctive tense had been reinforced by his travels to France, America and England. It was confirmed by the nightly broadcasts of Radio Free Europe and the BBC World Service. Through these channels, he learned at least some details of the violent disturbances that swept through the United States following the earlier shooting dead in Memphis, Tennessee of Martin Luther King, the man whose funeral eulogy stressed that he 'gave his life for love'. There was the gathering global controversy produced by the vicious fighting in Vietnam following the NLF Tet Offensive against American forces and their South Vietnamese allies. There was the aftermath of _le joli mai_ in France and continuous stories from London, cast as a sensual, exotic playground where artistic extremes were initiated and driven forwards by an uneasy alliance of hippies, artists, students, youth, rock musicians and political activists, united in their fight against a collective enemy — the supporters of the war in Vietnam. There were also the widely circulated images that quickly turned into clichés: long hair and blue jeans; Dionysian talk of turning on, tuning in, and dropping out; clenched fists at rock concerts; and apprehensive hippies tentatively offering flowers to impassive policemen. There were love-ins and die-ins; Jimi Hendrix waving high his 'freak flag'; the street chants of 'Ho, Ho, Ho Chi Minh! We will fight, we will win!' Then there was 'Jumpin' Jack Flash', the mid-summer smash hit by the Rolling Stones. Stories of John Lennon living in India, learning the art of transcendental meditation and composing the song 'Revolution'. Bob Dylan. The Pope's public refusal of concessions to liberal opinion on birth control. The first anniversary of the Six Day War between Israel and its Arab neighbours. The death of Senator Robert F. Kennedy, shot by a Palestinian Arab immigrant, Sirhan Sirhan, only hours after winning the California primary election. And there was Prague.
### **Mid-Summer's Night**
The lush Prague spring and early summer of 1968 seemed to unfold naturally, in harmony with the local soil, seeds, trees, birds and animals. There were no flowers of evil, only the flowers of Strahov, the chestnuts of Žofín, the gulls hovering over Jirásek Bridge — and the rebirth of socialism. Socialism with a human face, it was called, especially by Dubček and the new group of Communists who had arrived, with no blood on their hands, at the top of the Party hierarchy. The change had begun on 5 January 1968, amidst sensational rumours of the uncovering of a 'hostile faction' within the Party. There was talk of the need for drastic intervention, perhaps by Moscow, or by the Czechoslovak armed and police forces, whose officers, interestingly, had just received a 1,000-crown bonus.
After an all-night, bad-tempered struggle within the top echelons of the Czechoslovak Communist Party, Alexander Dubček was voted in unanimously to replace Antonín Novotný as First Secretary. A vain man for whom power was an aphrodisiac, Novotný had for months resisted the proposal to split off his office of Party First Secretary from his other, combined positions as President of the Republic, Supreme Commander of the Armed Forces and Commander of the so-called People's Militia (armed units of the Party, known as the 'iron fist of the working class'). At the last minute, he changed his mind. Novotný calculated that the election of the Slovak Dubček would produce a backlash among the Czech members of the Central Committee. Some would say that Dubček's candidacy was 'inappropriate'; others that he was too radical; still others would denounce him as a weakling unsuited to resolving the crisis. So the dispute would drag on, providing cover for Novotný supporters' further manoeuvring. Alas, comrade Novotný miscalculated. The red-eyed Central Committee unanimously elected Dubček, who proceeded to give a short speech of thanks. In it, he highlighted the need for 'all-round reinforcement of relations with the Soviet Communist Party and the parties of the other countries in the socialist camp'; he stressed as well that he would personally 'exert every possible effort to work towards the aims which the Central Committee has always held under the leadership of comrade Novotný'. After concluding business, reactionaries and reformers rose together to sing The Internationale. An early summer of tragic ironies had begun.
Although Havel could not be described as a Dubček man in any simple sense, ever since his election to the post of First Secretary Havel often brimmed with enthusiasm for what the new leadership was achieving. It was symbolized that year by the May Day parade in Wenceslas Square, Prague's historic avenue. Havel was there to witness the endless procession of people, flags and enthusiastic chants. 'Of our own free will, for the first time!' read a prominent banner. 'Our Party draws its strength not from its power, but from the truth,' read another. A thrilled Dubček perched on a rostrum watched the glorious procession, occasionally improvising a loudhailer with his hands to respond to well-wishers. 'Carnations, roses, tulips, sweet-smelling sprigs of lilac and lily of the valley were thrown at the rostrum,' reported _Rudé právo_ next day. 'This is the spring of our new existence.' Havel shared similar feelings. 'Just think of it', he said later. 'Suddenly you could breathe freely, people could associate freely, fear vanished, taboos were swept away, social conflicts could be openly named and described, a wide variety of interests could be expressed, the mass media once again began to do their proper job, civic self-confidence grew: in short, the ice began to melt and the windows began to open.'
From the time Dubček was elected as First Secretary, Havel had been struck by the contradictoriness of the reforms. Havel said that he had 'agonizing doubts and hesitations' about the shaky entitlements of the non-Communist majority of the population, especially because the Party leadership, which still believed that Communists were always right, refused to put into question the principle of the leading role of the Party. The related principle of political pluralism, he noted, 'was simply beyond the leadership's power to comprehend'. And nobody in the Dubček group had yet dared to grasp the twin nettles of the immovable masses of Stalinists in the state security forces and the possibility of military intervention ordered by the Kremlin.
Above all, Havel worried about the schizoid reactions of the Party leadership. They were clearly in a good mood, as he discovered first hand when attending a lively public meeting — a question-and-answer session organized by 'the men of January' — held at Prague's House of Slavs. 'Suddenly these people were enjoying spontaneous support and sympathy, something none of them had ever experienced before, because the only kind of support they had ever known was organized from above,' he commented. But popularity bred fear, he added. The Party leadership felt itself to be swamped by the rising tide of social expectations that otherwise kept it afloat. It didn't understand its various currents of opinion, let alone the wider sea, whose rising waters it tried hard to dam up for the sake of a brighter socialist tomorrow. There were moments when watching the Party leaders cope with their own confusions made Havel feel a strange sadness. 'Again and again they were caught off guard, because things began to happen and demands began to be made which were sometimes incomprehensible, even terrifying, given how far they overstepped the limits of the "possible" and the "admissible".'
Havel summarized these various points in a widely discussed essay 'On the Theme of an Opposition', which appeared in a Spring 1968 edition _of Literárnílisty,_ the successor to _Literárnínoviny_ and the most influential weekly at the time in Czechoslovakia. Beginning from the premise that 'power only really listens to power', the essay argued that the combined democratic tasks of keeping a government on its toes, improving its performance, and making it conform to certain ethical standards required permanent public threats, not only to its reputation — through the free expression of public opinion — but also periodically to its very existence. The essence of democratic government is that organized public opinion can help kick it out of office at election time. Democratic government 'assumes the existence of at least two commensurable alternatives,' he wrote, 'that is, two autonomous and mutually independent political forces enjoying equal rights and the equal opportunity to become the leading force in the country, should the people so decide'.
Havel's reasoning was not especially original, being a familiar axiom of modern political thought in the Atlantic region, and certainly in Czech political culture during the First Republic; and despite its warning against the dangers of 'suprapersonal categories' in political life it still clung dogmatically to the old First Principle of 'the people' and its sovereign power. In the context of the Prague Spring, it is true, his reasoning served as a canny but sympathetic critique of the ideal of 'socialism with a human face'. A two-party system was now required in Czechoslovakia, he concluded. Did that require the Communist Party to lose its leading role, his readers might have asked? Well, yes and no, he replied. The activities of the Communist Party should be supplemented by a new 'democratic party', which would revive the 'Czechoslovak democratic and humanistic tradition'. That would then enable a 'moral reawakening of the nation' and help along the task of 'redefining human dignity' and placing emphasis on such values as 'conscience, love of one's neighbour, compassion, trust, understanding'. At a minimum, this would require a 'comprehensive rehabilitation' of all non-Communists 'who were made to suffer for years because they knew certain things before the Communists got around to figuring them out'. The Communist _coup d'état_ of February 1948 would need to be put behind everybody. The two parties would then function as partners in a coalition. Their respective names, conjoined, would symbolize the 'two poles' of the global political project facing the country: 'the creation of democratic socialism'. There was only one catch. Since classes had been abolished, Havel argued, the two parties by definition would not compete and clash along class lines. That implied as well that they should work to preserve the 'socialist social structure', and that both parties should therefore enter a legally binding pact containing 'an agreement on the basic outlines of their common goal, which would be the humane, socially just, and civilized self-realization of the nation on the way to democratic socialism'.
It is unclear whether Havel's patriotic democratic socialism was heartfelt. He had certainly absorbed from his father a principled affection for freedom, social equality and solidarity. In the spring of 1968, along these lines, he signed a declaration issued by the Club of Committed Non-Party Members (KAN), in support of the task of combining 'the socialist system, the democratic exercise of power, and freedom of the individual'. But it is puzzling that at precisely the moment when the iceberg of Bolshevism had begun to crack and thaw he was arguing the formula, Social Justice + Individual Freedom = Communism. It is most likely that he had not thought through deeply enough the _social_ preconditions of political democracy. 'Political programmes,' he did admit, 'are not born at writers' desks, but only in the everyday political activity of those who carry them out.' It is also likely that his call for a 'democratic party' was principally a tactical manoeuvre designed to consolidate the process of liberalization — and perhaps even a move to make a name for himself as a writer by angling for the political middle ground among the intellectuals.
Whatever the case, he had a chance to air these same ideas at his one and only meeting with the new leaders of the reforms. Shortly after his visit to the West, in early July 1968, he was invited by Premier Černík to a drinks party at Prague's ornate Hrzánský Palace, organized by the Party for the purpose of bringing together its new leadership and young artists who were stirring passions in the burgeoning world of independent art. Havel eagerly accepted. He wasn't disappointed. The Renaissance beauty of the Palace setting was matched by a mid-summer spirit of friendliness; the cheese and canapés _(jednohubky)_ were delicious; the wine and spirits flowed freely. And since the literati and apparatchiki had another thing in common — their late-night staying power — guests mingled unhurriedly with the 'men of January' until just before dawn. Everybody who counted was there, including leading writers like Josef škvorecký, Pavel Kohout and Ludvík Vaculík, and such key politicians as First Secretary Dubček, Premier Černik, the Minister of Culture Galuška, and a quiet man named Gustáv Husák.
After plying himself with a cognac — this was the first time he had met heads of government — Havel sidled up to the First Secretary, Alexander Dubček, to tell him personally a few things. On a terrace bathed in the light of a mid-summer's moon, the floodlit stars-and-stripes flag of the nearby American Embassy fluttering above the tree tops in the warm breeze, the unhurried Havel and Dubček chatted about the future of socialism. Havel performed the old art of _ketman_ (from the Arabic: _kitman,_ concealment): simulating adherence to a prevailing political doctrine which conflicted with much of what he believed to be true, all the while taking some self-mocking pleasure in practising the techniques of concealment. Seated on a low wall, surrounded by a cluster of admirers, the First Secretary did most of the listening.
'I assure you, Mr Secretary,' said the long-haired, denim-clad playwright, 'practically everybody who lives in this country supports socialism.' 'Do you think so?' replied the small First Secretary with a large nose tailor-made for caricaturists. He seemed for an instant to twinge with the discomfort caused by the unfamiliar 'Mr' and by the smart new silver-patterned summer suit chosen for him by his advisers. 'Most certainly!' continued the playwright. 'Look at me, for example. My father was a millionaire, and some might therefore say that I would gain a lot from the restoration of capitalism. But believe me, Mr Secretary, I've never ever had such thoughts. I'm not interested in accumulating property. I'm a man of the theatre — and theatre, potentially at least, fares better under socialism.'
The frowning First Secretary's attention seemed to fix on the souvenir dangling around the playwright's neck, a brass peace symbol on a leather chain acquired during the recent trip to America. 'Are you really sure that socialism has such support?' he asked again, adding: 'Perhaps it seems so to you because of your talents. You find full satisfaction in your work, and so do I. But not everyone can or does. You and I believe in socialism. The fundamental question is whether others do as well. Even those who have no artistic talent.' Sucking up, the playwright grew more emphatic. 'An absolute majority believes!' he said. 'Socialism is the _epitheton constans_ of the modern world.' 'Do you think so?' asked the First Secretary, for the last time.
### **A Politician of Retreat**
Amini-skirted waitress resembling a Carnaby Street mod, juggling drinks and snacks on a platter, cut short the conversation, but years later Havel still recalled being impressed by Dubček's capacity to listen and to ask questions. Such openness, he said, 'is not at all common among politicians, especially Communists, because they are too busy churning out their own phrases and clichés to listen to anyone'.
Uncommon the First Secretary was, but arguably the flattered young playwright's enamoured description of him was a trifle too simple. Dubček was indeed a rare species of political animal — a _politician of retreat,_ let us call him. To understand him well involves taking issue with the dominant habit within modern political philosophy to concentrate either upon the arts of capturing and maintaining the key resources of power (examples include Machiavelli's _Il principe_ or Carl Schmitt's _Die Diktatur);_ or upon the process of limiting, controlling, and apportioning state power (an example of which is _The Federalist,_ drafted by James Madison and others). Although the two standpoints remain indispensable to mapping and measuring the mechanics of power, they are in fact complementary, since each presumes that the lust for political power is both polymorphous and universal. Edmund Burke expressed this conventional point succinctly in _A Letter to a Member of the National Assembly_ : 'Those who have been once intoxicated with power, and have derived any kind of emolument from it, even though but for one year, can never willingly abandon it.' In the century before, Thomas Hobbes's _Leviathan_ put the same point more pithily: 'Kings, whose power is greatest, turn their endeavours to the assuring it at home by Lawes, or abroad by Wars: and when that is done, there succeedeth a new desire; in some, of Fame from new Conquest; in others, of ease and sensuall pleasure; in others, of admiration, or being flattered for excellence in some art, or other ability of the mind.' The flipside of such reasoning was well put three centuries later by the Czech humorist and friend of the Havel family Jan Werich. The struggle against the stupidity of those who exercise power, he liked to say, is the only human struggle that is as futile as it is permanently necessary.
What such modern commentaries on power have failed to grasp is that there are political contexts defined mainly by the logic of _retreat from power._ Dubček was one of a crop of political leaders during the second half of the twentieth century — a century, it should not be forgotten, dominated by various kinds of state-enforced 'moral projects' — whose chief role is to have contributed to the (temporary) _dismantling_ of a despotic political system. Latin American observers long ago recognized the importance of 'state-led liberalization from above', but in European political thinking this process has rarely been discussed, despite a succession of political figures who have tried their hands at de-concentrating power: Adolfo Suárez, who forced through a democratic constitution upon becoming Spanish Prime Minister after Franco's death; János Kádár, who survived the fall of Khrushchev and eventually helped prepare the way for market reforms and a multi-party system in Hungary; Constantine Karamanlis, who with high-ranking military support facilitated the dismantling of the 'regime of the colonels' in Greece; Wojciech Jaruzelski, who eventually colluded with the formation of the first Solidarność-led government in Poland; Milan Kučan, the protagonist of constitutional reform in Slovenia; Mikhail Gorbachev, who walked in the footsteps of Nikita Khrushchev, the first leader to attempt to dismantle the Soviet system from above; and the man who tried to wear Khrushchev's shoes, Alexander Dubček, the chief symbol of reform Communism and 'socialism with a human face' during the 1960s.
Like all politicians of retreat, Dubček had been schooled in the arts of conventional politics. His career began in the corridors and committee rooms of state power. Born on 27 November 1921 at Uhrovec, a tiny village in western Slovakia, he spent his early years in the Soviet Union with his father, a joiner, who was among the first members of the Czechoslovak Communist Party. Dubček himself joined the Slovak Communist Party when he was eighteen, and after fighting for a partisan brigade in western Slovakia, and living as a manual labourer and regional Party organizer, became a full-time Party official in 1949. Shortly after Stalin's death, he was drafted to the advanced Party school attached to the Central Committee of the Soviet Communist Party in Moscow, to perfect himself politically. After spending three years there and returning home his promotion was rapid. In 1960 he was elected to the Secretariat of the Czechoslovak Communist Party; in 1963 to the Presidium; and in 1963 he replaced the Stalinist, Karol Bacílek, as First Secretary of the Slovak Party.
Despite his irresistible rise to power, Dubček was not a strong-willed, charismatic and (potentially) iron-fisted figure — like, say, Woodrow Wilson, Mussolini, Roosevelt, Churchill, Stalin, Hitler, Adenauer, and de Gaulle before him. Everybody who knew him well commented upon his tendency to indecision, a quality quickly branded as weakness in conventional politics. Immediately after he had replaced Novotny as head of the Czechoslovak Communist Party, it became an open secret in the Presidium of the Party, in the Secretariat and the Central Committee, that Dubček was an 'innocent', a 'hesitater', a 'decent fellow who does not like drastic measures', while Jiří Hendrych, Novotný's right-hand man, said that 'Dubček is an honest man, but he is indecisive'. Such remarks pointed to the fact, especially evident after becoming First Secretary, that Dubček was not to devote his remaining life and political career to the task of preserving or expanding his state's integrity at home and abroad.
It was not that he was a weak leader. It was rather that he — like Suarez, Karamanlis and Gorbachev who followed him — was caught up in a bundle of contradictions related to the politics of retreat. As a _Communist,_ he criticized, with enthusiasm, the Communist creation for which he continued to stand; he worked for the liberalization of a regime that in his youth seemed to be the pride of anti-liberal forces in the world; and he tried to breathe life into 'bourgeois' principles, like freedom of expression and assembly, that he once spoke of as mere 'bourgeois relics' of a bygone era. Such contradictions normally dog politicians of retreat. Rather than being driven by lust for power or visions of grand victories through conquest, Dubček was instead forced, by dint of circumstance and choice, into becoming a practitioner of the difficult art of unscrewing the lids of despotism. He withdrew and retreated from unworkable political positions. He worked hard to forge new compromises between state actors and their subjects. He thereby enabled the growth, out from underneath the edifices of state power, of the first tender shoots of social life.
Dubček learned this art belatedly, when the process of dismantling in which he was embroiled had already begun. This is unsurprising, since the art of retreat, as von Clausewitz explained in his essay 'Vom Kriege', is the most difficult of all political skills to learn. It requires an ability to know the difference between foolishness and magnanimity. It entails knowing how to spot jiggery-pokery and when and how to blow the whistle on (potential) opponents; it demands the guts to abandon untenable positions, and to slip through the loopholes of retreat. It sometimes necessitates surrendering the middle ground and it always requires mettle, acumen, nerve, toughness, and patience. The politics of retreat is naturally a delicate and dangerous process. As Dubček quickly found, its protagonists get trapped in quicksands. He risked his career and life at every step, surrounded at all times by enemies lurking in the shadowy corners of state power. Ingratitude of his rivals and subjects was to be his ultimate fate. Although his well-known unshakeable faith in socialism sometimes got the best of him, and even though he was therefore not among the wisest politicians of retreat, Dubček eventually learned that he had to be ruined for the good of others.
That ruin stemmed partly from the fact that, unlike early modern enlightened bureaucrat reformers who aimed to strengthen society without initiating political reforms, he was a politician of retreat who worked for the disintegration of the existing Stalinist regime. He therewith threatened certain individuals and groups whose power base lay within the _ancien régime._ Dubček, like other politicians of retreat, suffered unpopularity in the ruling Novotnyite and Brezhnevite circles because he insisted on doing without certain privileges or customary routines — like unconditional observance of the principle that Communists were never wrong. Certainly, his actions helped dramatically to widen the political spectrum, even to the point where public opinions, independently formed, began to be expressed. But this was not to everyone's liking, or full satisfaction. Not only did Dubček's actions breed the uncertainty, disorientation and confusion typical among people who have just come from prison — what Havel later called 'post-prison psychosis'. Politicians of retreat like Dubček usually do not offer immediate positive benefits to their supporters. Although they know one thing best — that despotic regimes can die from swallowing their own lies and arrogance, and that fear and demoralization cannot govern for ever — they tend to speak the language of future gains, described in abstract terms.
Politicians of retreat also often lead a tenuous — and usually short — existence because their actions have the unintended consequence of fostering the growth of _social_ power groups acting at a distance from the despotic state which they help to dismantle. In helping to disarm the Leviathan, the politicians of retreat encourage the growth of a self-organizing civil society, whose chattering, conflicts and rebellions unnerve them. They learn too slowly that effective government requires winning the trust of citizens, and that this involves more than dismantling or scheming, rapacity, peacockery, and shouting orders. For all these reasons, but especially because they play the role of midwives of civil society, the politicians of retreat typically sow the seeds of their own downfall. Comrade Tito, who was given a tumultuous public welcome in Prague in early August, warned Dubček privately of this. He spoke from experience. In domestic matters, he said, the Czechoslovak leadership should advance cautiously towards its goal of decentralization so as not to 'weaken the influence of the Party'. Decentralization required a 'strengthening of the centre from which all power emanated'. He reportedly gave examples. Abolishing pre-publication censorship was a step in the right direction, but the Party had to be sure that its men and women were in charge of news and entertainment; and although a resolute fight against conservatives and hardliners was necessary, Tito warned Dubček, the 'excesses of the reformists' and 'the danger of "social-democratism"' should never be underestimated. Tito was right, if for the wrong reasons. In the end, Dubček proved a poor match at home for the political and social forces which he had helped to unleash. Like all politicians of retreat, he fell victim to his own success.
Some politicians of retreat suffer bitter disappointment when their reforms prove to be stillborn. Others have the cold comfort of knowing that their experiments with the status quo lead to consolidated reforms. Some politicians of retreat find that their efforts breed revolution. Dubček was less lucky, for his liberalizing reforms resulted in a full-scale military crackdown, the dramatic force of which he had not anticipated. In his heart, the First Secretary had never believed in the possibility of an outside military invasion of a friendly socialist country; he was convinced Communists would never commit that kind of treachery. During the summer of 1968, besides, the Dubček group did everything it could to behave itself in the company of geopolitics. Its so-called Action Programme, presented by Dubček to the Central Committee on 5 April as a working blueprint for 'our socialist homeland', bowed and scraped to the Soviet Union. And as tensions mounted within the country, Dubček and his friends consistently played their strongest card: since January, they insisted, Prague's foreign policy hadn't changed; her loyalty to the Warsaw Pact, Comecon and the Soviet Union remained steadfast; and no future changes would take place. Even Dubček's speeches were peppered with attacks on 'imperialist reaction', calls to fight 'neo-Nazi and revanchist tendencies' in the Bundesrepublik, and other run-of-the-mill phrases from the lexicon of Novotný.
Moscow was not much impressed. Brezhnev and others there correctly spotted that Prague's stated allegiance to the hammer and sickle was contradicted by developments _inside_ the country. The point was simple: regardless of whether or not it was viable, a 'new model of socialism', the realization of Dubček's final vision of a more open and just system, was ultimately impossible without revising Czechoslovak relations with the Soviet Union. There was mounting evidence of this, Moscow observed. There were clear signs of the public contestation of the 'leading role' of the Party (meaning its absolute power). Czechoslovak newspapers, radio and television were spreading reports 'both incorrect and outside Party control'. A mid-summer's purge of the Soviet security forces — many of them kicked upstairs and paid not to do their quisling jobs — was being carried out by the Minister of the Interior, Josef Pavel. And the Soviet marshals were uneasy about parallel reforms being carried out by General Dzúr in the Czechoslovak army. So it was concluded that the Soviet trap had to be set, leaving enough room to catch the mouse.
The open-ended July manoeuvres of the Warsaw Pact armies on Czechoslovak soil opened the trap. The exercises were designed to exert pressure on the Dubček leadership, even to get the population used to foreign occupation, which lifted only after a conference resulted in the signing of the Treaty of Bratislava on 8 August. The mouse was drawn into the trap at these talks at the railwaymen's clubhouse in the eastern Slovakian border village of Čierna nad Tisou, where the Soviet delegates, led by Brezhnev, arrived on the morning of Monday, 29 July in a special armoured train with bullet-proof glass and its own radio link. The Soviets (to recall Hegel's description of Napoleon) acted like history on horseback. They instantly went on the attack, beginning with Brezhnev's abusive four-hour monologue, in which he issued sour-faced denunciations of various 'counterrevolutionaries' and quoted extensively from the Czechoslovak media to prove that Dubček was losing control of the situation. Much of the four-day meeting resembled a dialogue of the bad-tempered deaf, who sat as two teams on opposite sides of a long table, refused to dine with each other, interrupted, spoke excitedly out of turn, and exchanged insults. The worst moment came when Aleksei Kosygin — who had earlier grunted that 'if we wanted to, we could occupy your entire country in the course of twenty-four hours' — grilled one of the Czech delegates. 'Who is this Kriegel? Is he a Czech at all? Is he not a Galician Jew?' František Kriegel politely enquired why he was objectionable. The Ukrainian Petr Shelest shouted: 'You just _are_ — we don't have to explain why!' Dubček instantly stepped in, banging the table with his fist and shouting in Russian: 'You're not going to treat _us_ as underlings, comrades!' 'You'll get used to it, Alexander,' snapped his friend, the Czechoslovak President Ludvík Svoboda. 'Marshal Koniev treated me as an underling all through the war.'
Throughout the Cierna talks, the Soviets tried to prove that political power ultimately grows from the barrel of guns. The railwaymen's club, located 150 metres from the railway station, was surrounded by Soviet guards with hand-grenades in their pockets; a division of Soviet troops was on standby 5 kilometres from the frontier, on Soviet territory; each night, the Soviets in their special train pulled back across the border, 300 metres away, on to Soviet territory. Although the Cierna talks ended with an agreement and a one-day summit meeting in Bratislava, the Czechoslovak delegates were made constantly to feel trapped. Even their private telephone line to Prague was bugged by the Russians. The point is that it would have been possible to arrest and kidnap Dubček and his team in Cierna, but the Soviets prudently waited, all the while carefully preparing the final details and assessing the risks of intervention.
They did not wait for long. Hours after the Dubček leadership published (on 10 August) draft Party statutes guaranteeing such principles as the separation of state and Party power, a Party 'controlled by the people', the protection of minority opinions, and limited tenure of offices, the final decision to invade was taken. Havel happened during that period to be in the northern Bohemian town of Liberec, visiting friends. During the warm, sleepy night of 20-21 August, he was awakened by the steady noise of low-flying planes. Lights went on in the town and his telephone started to ring. Unmarked soldier-loaded trucks, tanks and armoured cars were pouring across the border with the German Democratic Republic, he was told. One caller described the tank column wending its way through the streets of Prague, guided by a Soviet Embassy car, bound for the building of the Central Committee of the Czechoslovak Communist Party. Another rang to tell of the occupation of Prague airport, where huge Antonov transport planes were landing at sixty-second intervals.
At four-thirty on the morning of 21 August, Havel heard Radio Prague confirm the invasion and call upon citizens not to resist. As the Czechs say, the truth had prevailed, but this time in cruel and surprising ways. Five Communist countries wielding twenty-nine divisions, 7,500 tanks and 1,000 planes had begun the invasion of a sixth Communist country in the name of 'international proletarian solidarity'. The beautiful summer that had begun early in May 1968 had ended abruptly. Yet something new had been conceived; the present was now pregnant with a different future. Thanks to the Prague events, the arrows of socialism, like those of Nimrod, had been hurled at the sky, only to fall back to earth, stained with infamy and blood. The Soviet empire was now fated to suffer terminal decline; the word 'socialism' was soon to be discredited; and Havel's career as a world-class playwright would collapse, ironically leaving him free to become a serious political essayist and to fight his way into political life, equipped with an entirely new vision of the Czechs' — and the other Europe's — place in the world.
## **_Late-Socialism_**
## **_(1969-1989)_**
### **Normalization**
The invading armies soon smashed their way into the town of Liberec. Hours after the Prague Radio announcement, Havel witnessed unforgettable scenes of violence. Warsaw Pact tanks crashed through arcades near the main square, burying several people under the rubble. Trucks, weaponry, heavy equipment, jeeps, troops felt omnipresent. And, at one point, a tank commander, armed with a sub-machine gun and perched on his turret, opened fire into a crowd, badly injuring several people. The situation — guns, tears, dust, diesel fumes — felt hopeless. Grown men cried. Women wailed. Children had fear etched on their faces. Protest was out of season. It seemed imperative that everybody observe the maxim, reportedly formulated by Favorinus when yielding to the Emperor Hadrian, that it is ill arguing with the master of thirty legions.
Havel barricaded himself in the local 'free' radio station with Jan Tříska. The building was protected against the invading troops by the efforts of local workers, who moved swiftly to ring the site with huge transport trucks loaded down with massive cement blocks. Disguised in blue overalls, unshaven, and carrying a fake identity pass supplied by the manager of a local factory concerned to help him escape from any personal danger, Havel worked for a week as a resistance journalist. He and Tříska appeared on local television, in a studio rigged up on nearby Ještěd Hill. Working into the wee hours of the morning, Havel also ghost-wrote speeches for the chairman of the National Committee, and crafted as well declarations for various organs of the Communist Party. Havel listed involvement in the town's National Committee, the District Committee of the National Front, the Communist Party's District Committee and its District National Committee, for each of whom during that week he prepared poster material that was pasted up on the walls of Liberec, or for whom he wrote commentaries broadcast to the local population over street loudspeakers.
Havel also wrote at least five radio commentaries that were read out on air by Tříska, who later described Havel's texts as 'inflammatory' and his own performances as 'tongue-tied' and 'jabbered'. 'The country is brimming with thousands of lads from the Ukraine and Kazakhstan who aren't quite sure what country they're in, don't understand the local language, and can't figure out why it is that, wherever they go, people are shaking fists at them', ran one Swiftian broadcast, which then added, cheekily: 'Mr Brezhnev is sitting in the Kremlin over a glass of vodka and is fuming.' Another resembled a message in a bottle tossed with a prayer into stormy seas. It appealed for support from a long list of literary figures, including Kingsley Amis, Samuel Beckett, Günter Grass, Eugène Ionesco, Arthur Miller, John Osborne, and Jean-Paul Sartre. Still another, likening the resistance to that of David to Goliath, spoke the language of anarchism: 'Search for new ideas about how to fight! Organize yourselves, ensure contact between each other, establish action cells and co-ordinate their activity, establish a network of contacts, approach things in an organized way. Join forces!' Throughout, the broadcasts called for the triumph of 'conscience' and 'humanity' over 'beastliness' and 'the pistol'. They also forecast possible cloudbursts of violence: 'We could lose our free transmitter any moment. So we can't allow ourselves to lose contact with each other. Any minute, soldiers with machine guns might be walking through the town square, firing at anybody from the town who is wearing the tricolour. Any moment they could arrest our principal city politicians and the head workers in the factories.'
It was what might be called a Greek experiment — an exercise, attempted in classical Greece, in the political art of using public words against the power of violence. After Soviet agents and Czech conspirators shut down the country's transmitters on the night of the invasion, in order to put on air a more powerful propaganda station called 'Vltava', thousands of clandestine radio and television studios, calling themselves 'free' and 'legal' stations, sprang up. They had a single aim: not to let an army of a quarter of a million men kill the spoken, written, and televised word. The studios' calls for help were on air twenty-four hours a day. They may have bordered on the editorially primitive and improvised — surviving transcripts and secret-police records show — but they propped up an extraordinary seven days of government by microphone. For the first time in the history of modern telecommunications, spirited broadcasts of the Liberec kind assumed all the normal functions of a clandestine 'government' bent on waging non-violent resistance to an occupying power. 'The mass media,' Havel recalled, 'outwitted the occupiers and moved and mobilized the entire society against the powerful will of the aggressors and some of their helpers at the time. The country simply refused to pay attention to the occupation.' The new media government's appeals for help — spread by transistors, television sets and word of mouth — brought prompt responses; its orders were swiftly executed. The townspeople of Liberec, responding to 'free' radio appeals, actively resisted the invading 'fraternal' armies. Wrong directions and information about the town's buildings were given systematically, helping to foil the invaders, forcing them to retrace their steps, and even on one occasion to fire on themselves. Secret-police cars were immediately identified and permanently tailed. Within the town, a long-haired youth group called the Tramps volunteered for civic duties. During the first night of occupation, they carefully removed all street signs and neatly stacked them in front of the town hall. The group was subsequently invited by the mayor to wear armbands of the auxiliary guard, and to provide extra protection for civilians by accompanying the local policeman on duty. The town hall, a key symbol of the local civic resistance, was protected by sentries twenty-four hours a day. At one point, Havel recalled, the mayor's own office was guarded by the long-haired Tramps. These 'troops' wielded guitars and sang the Bee Gees' 'Massachusetts', against a backup band of revving tanks.
For a brief while, government by microphone proved immensely popular. It again demonstrated to Havel, as it had done in Paris in May '68, the importance of a form of power that is often underestimated: what is sometimes called people power. Roman political thinkers referred to _potestas in populo,_ by which they meant that without a people or group there can be no power. The old insight remains important, for there are times — the Czechoslovak people's reaction during the first week of the Soviet invasion is exemplary — when it becomes clear that the power to act in and on the world is primarily not the property of an individual, or the isolated leaders of an institution like an army or government bureaucracy, and that power derives instead from the group which acts in concert for some felt or stated purpose. In these circumstances, it is people's support or resistance that empowers or disempowers others — military generals, politicians, administrators — and forces them, without using guns or shouted orders, to take note of their external dependence upon others. Those 'in power' are compelled to recognize, if only for a fleeting moment, that whatever power they have to act in fact derives from others, in whose name they are empowered to act. This is what was meant by a host of eighteenth-century political thinkers (James Madison, David Hume and others) when they remarked that all governments rest on opinion.
As if they had grasped this rule, the residents of Liberec stuck together. They tried to demonstrate that the resort to violence can result in a loss of power, that guns alone could not decide things — or, as Talleyrand famously remarked, that armies cannot expect to rest their weight upon their own bayonets. The strong display of public solidarity in Liberec, Havel recalled, 'showed how helpless military power is when confronted by an opponent unlike any that power has been trained to confront; it showed how hard it is to govern a country in which, though it may not defend itself militarily, all the civil structures simply turn their backs on the aggressors'. He was right. Liberec locals showered their new disc jockey with flowers, food, medicine, and good wishes. Whenever broadcasts were temporarily stopped because of transmission problems, fatigue, or lack of material, hundreds of telephone callers inundated the station to find out if Havel and Tříska were all right. Olga pitched in as well. Her speciality each day was to keep up the radio station's morale by raiding the local bakeries and fetching biscuits and sweets.
But popular power under difficult circumstances has its limits. A week after the Soviet armies invaded Czechoslovakia, the spontaneous resistance from below began to falter. Like many other activists, Havel began to feel exhausted — even to feel that the resistance wasn't working, as if the summery world of nature was totally indifferent to the wintery despair felt by Czechs and Slovaks. It was the beginning of the end of ideals, especially socialist ideals; decay from disillusion and inefficiency would destroy the felt need for solidarity, leaving behind only the common-sense conviction that from here on the 'powerless' were in the jaws of the all-powerful. Things were not helped by the lame reactions of the Dubček government. The full-scale military invasion forced it to live a daily contradiction: it was compelled to serve its masters in Moscow while demonstrating at home that it remained loyal to its citizens. Paralysis resulted. Since it had believed all along that the application of military force by Moscow was an improbable option that in any event could be averted by last-minute negotiation, the Dubček government initially dithered. 'I, who have devoted my whole life to collaboration with the Soviet Union, now they do this to me!' stuttered Dubček, as if struck by lightning from a blue sky. 'This is the tragedy of my life!' It vaguely followed that his country had no choice but to decide against resisting a vastly superior aggressor. He thus began to think that it was imperative to avoid battles that it would surely lose in advance. The decision came slowly. During the first few hours of the invasion, the Czechoslovak armed forces remained without orders; not until one o'clock in the morning of 21 August did the Presidium finally instruct the armed forces to remain in their barracks.
Just imagine the extended political farce that followed: a group of former Communist revolutionaries, once the representatives of the supreme power in their own country, now trapped in a dire emergency, in a state of permanent shock and resentment at the betrayal by 'class friends', attempting to come to terms with military occupation by convening meetings of the National Assembly, of the government, and of the Central Committee. During the first few days of occupation, it is true, the tactic of handling the crisis exclusively in a legal-democratic way seemed to wrong-foot the occupying forces. When the Soviet Ambassador Chervonenko went to Prague Castle to persuade the President of the Republic to nominate a new 'revolutionary workers' and peasants' government' so as to 'avoid the worst', President Svoboda sent him packing. He refused to negotiate, and asked politely that he leave the building at once. Then at midday, still on the first day of occupation, a general strike began. An hour later, 'free radio' broadcast a declaration, signed by a clear majority of government members, condemning the occupation and calling for the rule of law. Meanwhile, Soviet agents failed to win control of the Ministry of the Interior, thanks to 'free-radio' broadcasts of their car registration numbers that led quickly to their detection and arrest. And the Fourteenth Extraordinary Congress of the Czechoslovak Communist Party, meeting in best James Bond-style in a factory at Vysočany, confirmed that there was no split in its ranks. By the evening of 22 August, Brezhnev, sitting at the end of a telephone in Moscow, was forced to recognize that successful military occupation was producing political defeat, and that something dramatic had to be done.
The whole country watched and listened breathless next morning as news leaked out that the holders of power had been kidnapped and brought by plane to Moscow to be taught a lesson in international workers' solidarity. The Czechoslovak leadership, including President Svoboda and First Secretary Dubček, received a grand reception. They were promptly whisked away in polished black cars to the Kremlin, behind whose closed doors their smiling hosts quickly turned into fanged interrogators. At such talks at a 'summit level', the Soviets were experts at the art of sickling their opponents to pieces and then hammering them into the ground, like small wooden stakes. A key member of the Czechoslovak Presidium, Josef Smrkovský, confessed later that he would rather commit suicide than repeat the Moscow experience of being 'humiliated and insulted'.
Dubček told friends that after being wrapped in handcuffs and adbucted to Moscow, he gave up all hopes of returning home.On the verge of a nervous breakdown, he fainted twice during the interrogations. Like the others, he was cut off from outside information, kept isolated, the aim being to break his and his comrades' wills, to make them pliable in the hands of power, shatter their nerves, reduce their capacity for making shrewd political judgements to mere fawning capitulation. During the four days and nights of bullying, letters and telephone calls to and from Prague were banned. The delegation saw nobody except their interrogators. Not even Khrushchev — who emerged from retirement and came excitedly to the Kremlin on the second day to urge Brezhnev not to compromise or use half-measures against his victims — was allowed to see them. Any thoughts among the kidnapped that they might at some point be able to escape back to Prague, even to have an agreement ratified by the government and the National Assembly, were crushed with threats and insults. 'We have already got the better of other little nations, so why not yours too?' Brezhnev shouted at one point, vodka in hand, quickly adding a reference to class enemies like Havel. 'As for the intellectuals,' he burped, 'put your minds at rest, in fifty years there will be a new generation, healthier than this one!'
At midnight on 26 August 1968, after four torturous days and nights, the capitulation document — later called the Moscow Protocol — was signed by the Czechoslovaks, with only one dissenter: 'the Galician Jew', František Kriegel. He was missing from their delegation as it assembled on the tarmac at Vnukovo airport, and for two hours Dubček and his friends refused to board any aircraft until the Soviet partisans of Aryan purity backed away from their plan to keep him in reserve for a possible show trial of 'Zionists' and other Czechoslovak 'deviationists'. The Soviets capitulated, reluctantly, so permitting the whole delegation to arrive back in Prague at dawn, incognito. No crowds, no journalists, no officialdom awaited the capitulators, who retreated directly to the Prague Castle, where they rested for a few hours and worried their heads about who would say what and when to the country.
Mid-afternoon that same day, the official radio broadcast a communiqué on the Moscow agreement. After the voice of a frail President Svoboda sounding like Hacha speaking about the Munich disaster came on air, it was Dubček's turn. His speech was among the unforgettable moments of the twentieth century. Punctuated by long lapses and loud sobbing, Dubček's words moved millions to tears. They managed to conceal the worst possible news in the optimistic assurance, repeated again and again in the rambling sentences of a man verging on a nervous breakdown, that the Moscow agreement was based on the 'progressive withdrawal of the five countries' troops from our territories'. 'Our ultimate aim,' he said, 'is the complete retreat of these troops, to be effected as quickly as possible.'
Although it seems improbable that Dubček deliberately lied to his audience, there is no doubt that his chronic Communist optimism got the better of him. It concealed the bitter truth: the fifteen-point Moscow Protocol legitimated exactly the opposite outcome. The top-secret document stated that the recent Fourteenth Extraordinary Congress was 'invalid', and that a new congress would be convened when the situation in the Party and the country was 'normalized'. The document left no doubts about the meaning of 'normalization'. It confirmed both parties' commitment to purging from office everybody who failed to promote 'the imperative task of reinforcing the leading role of the working class and of the Communist Party'. The communications media were singled out for harsh criticism of their 'openly anti-socialist standpoints', and the Bolshevik question of what was to be done was answered in pure Bolshevik terms. 'A re-allotment of leading posts in the press, radio and television is inevitable,' it said. As for the matter of the socialist troops in socialist Czechoslovakia, it was not quite true that the parties agreed to their 'progressive withdrawal', as Dubček claimed. The agreement made it clear that the withdrawal was utterly conditional on satisfying other criteria. It could begin only when 'the threat to socialism in Czechoslovakia and to the security of the socialist countries has passed'. The agreement also emphasized the thorny problem of securing the country's border with the Federal Republic of Germany, the front line of 'aggressive plots of imperialism'. And it highlighted the primacy of rebuilding and maintaining what it described as 'Soviet-Czechoslovak friendship'. The final clause of the document — by implication — left no doubt that the troops might be there for quite a while. 'Both sides pledged in the name of their parties and governments to promote all efforts of the Soviet Communist Party and the Czechoslovak Communist Party and the governments of their respective countries to intensify both the traditional friendship between the peoples of both countries and their fraternal ties,' it read. It added just two final words: 'for eternity'.
### **Late-Socialism**
Havel, along with millions of other Czechs, was pushed sideways and downwards by the pledge to retain socialism, if necessary by armed force. Perhaps that is why the surviving fragments of his life during the first twelve months or so following the occupation suggest hesitation, even incoherence. Whereas before and immediately after the invasion he had been a driving intellectual force by calling for an opposition party and citizens' involvement in political opposition, he now began to react with some uncertainty about what to do. The key political question was whether to submit to 'realism', or whether the process of normalization required and even facilitated greater political radicalism. 'Realism' meant accepting whatever measures the invading power and their quislings decided upon, hoping perhaps that the restoration of order might take the foreign heat off the country, and thus enable a further phase of liberalization to take place, as appeared to be happening in neighbouring Hungary under the leadership of Kádár. The option of 'radicalism', by contrast, supposed that no good could come from the invasion. The pacifiers had to be resisted non-violently — through strikes, petitions, protest letters, street demonstrations — for that was the only way that the liberalizing achievements of the Prague Spring could be rescued, and perhaps developed further.
There were fleeting moments — around the time (17 April 1969) that Gustáv Husák was appointed as First Secretary of the Central Committee of the Communist Party — when Havel may have thought that the 'realist' option of getting rid of Dubček, the politician of retreat, was necessary for promoting much-needed political order. The secret-police claim to have recorded a conversation in which Havel observed that 'the situation in the state needed a firm hand. Dubček wasn't up to it, because he is a dreamer and a lyric poet.' Havel apparently went on to favour Gustáv Husák, who was at the time (because he worried about a split in the Party) posing as a friend of the Prague Spring, and whom Havel considered to be the only person 'who has a genuinely firm vision and can lead the people out of this crisis situation'. In an interview around the same time, he suggested that Husák's appointment was 'not a bad thing' since it would clarify the lines of power and subordination. He made it clear that Husák was no friend. 'He will rule dictatorially,' he said.
Then there were moments when Havel seemed to waver, and bend back towards the option of supporting Dubček, in the hope that he might speak out actively for resistance to the occupation — and for continuing liberalization. A few days before Dubček's dumping, Havel addressed a huge meeting at the Arts Faculty of Charles University, attended by about 1,200 students. Turning to several members of the Central Committee who were also on the podium, Havel urged everybody to stand behind Dubček. 'We must ask for progressive members to fight harder — to fight on small issues as well as big ones,' he said. Two weeks before the first anniversary of the Soviet invasion, he wrote a private letter to Dubček appealing to him to walk out from 'this dark and tangled wood into the light of what we might call "simple human reasoning". To think the way every ordinary, decent person thinks.' Havel said that he feared that the ruling authorities were preparing to pressure Dubček into making a public confession in favour of occupation. It would be a set-piece speech, in which Dubček acknowledged the failings of his leadership, fully endorsed the Soviet view of things, and confessed that with hindsight he had come to realize that the Soviet leadership should be thanked for their 'fraternal assistance' in sending planes and tanks to preserve socialism against counter-revolution.
Havel warned that if Dubček gave such a speech, then it would deal a terrible blow to the population's morale — by fostering the collective depression, indifference and cynicism that would be required for Soviet-style 'normalization' to succeed. It was therefore imperative, argued Havel, that Dubček take a moral stand. His stated support for democratization might well be misused by the ruling authorities to justify further repression. So be it, for the moral significance of taking a stand in support of the highest ideals of the Prague Spring would be threefold. The 'prestige of Czechoslovakia's struggle in the eyes of the world' would be enhanced. The stand would keep alive the ideal of democratizing socialism, which Havel described as 'one of the more positive aspects of the Communist movement'. Above all, Dubček had the chance of acting as an ethical mirror before the eyes of the population. His words of support for continuing democratization would have immeasurable ethical significance. 'People would realize that it is always possible to preserve one's ideals and one's backbone,' wrote Havel. They would be reminded 'that one can stand up to lies; that there are values worth struggling for; that there are still trustworthy leaders; and that no political defeat justifies complete historical scepticism as long as the victims manage to bear their defeat with dignity.'
It cannot be ruled out that the letter to Dubček was Havel's first calculated move towards assuming leadership of the moral opposition to the abnormalities of normalization. The thought may not have occurred to Havel, certainly. But equally certain is that the letter initiated that effect. The tone and content established a pattern that was to be repeated often during the years to come. The letter was notably tough on Dubček's doings prior to the invasion. 'I must say,' Havel wrote, 'I am convinced that you must share some of the blame for your present situation.' He especially laid into Dubček for signing the Moscow agreement, whose effect was to provide the illusion of success when in fact they merely postponed the decision explicitly to say 'yes' or 'no' to intervention — thus failing to take advantage of the other fact that the Soviet leadership was initially wrong-footed and embarrassed by the local (if uncoordinated) resistance to invasion. What is also interesting about Havel's letter was its anticipation of Dubček's skulking off into the oblivion of silence. Havel noted that if Dubček behaved like Švejk and pretended that he could fool everybody by quietly slipping unscathed out of the crisis, then Dubček would draw fire from both sides. The Party would quickly get rid of him. The population would dismiss him as a schmuck. That of course is precisely what happened. Dubček gave up without a fight, and a month after Havel sent off the letter, he was removed from the Presidium and then, in January 1970, expelled from the Communist Party.
Dubček's capitulation confirmed Havel's hunch about the importance of long-term moral resistance. The need for such resistance had surfaced some months earlier in a public tussle with Milan Kundera, whose strange essay called 'The Czech Lot' ( _Č eský úd_ěl) had aroused much controversy after its publication in mid-December 1968. Kundera suggested that the long-term significance of the Czechoslovak autumn would outweigh that of the Czechoslovak spring. The two periods, despite appearances to the contrary, were on a positive continuum. The attempt to build humane socialism was now being reinforced by the dignified — and successful — resistance to the invasion. The reform policies and their underlying principles remained intact, and no police state had been installed. Everybody should cheer up. Those who had fled the country, or who remained abroad after the invasion, should return. 'People who are today falling into depression and defeatism,' he wrote, 'who are commenting that there is an absence of guarantees, that everything could end badly, that we might again slide into a marasmus of censorship and trials, that this or that might happen, are simply weak people, who know how to live only in the illusions of certainty.'
Writing in February 1969, Havel strongly objected to Kundera's view that things weren't so bad. It rested upon the mythopoeic presumption that the small nation of Czechs was fated to be the creator of big values, not a nation of exploiters. Kundera's position, he argued, exuded a form of typically Czech passive patriotism that served to rationalize away a disaster as a moral victory. It also suffered from a typically nostalgic form of Czech myopia, argued Havel. It was easy to celebrate imagined past glories — imagining 'how good we were before August and how marvellous we were in August (when those bad guys came to get us)' — all the while forgetting about present-day needs. Kundera could accuse him of 'moral exhibitionism'. He could insinuate that Havel was suffering from the 'illness of people anxious to prove their integrity'. Yet the harsh reality was that there was now an urgent need 'to examine what we are like now, who among us is still good and who not at all, and what must be done so that we are true to our previously earned merits'.
The defiant tone of Havel's remarks was foreshadowed a few weeks earlier in tough replies to the questions put by a journalist from _Sv ět ν obrazech_ (The World in Pictures). He criticized the current government's reassurances that the 'springtime of politics' would mature into summer, despite the arrival of thousands of Warsaw Pact troops. He noted that the government's talk of democratizing the system was contradicted by the reintroduction of censorship. He said he feared that the ethos of the springtime was suffering liquidation, and that therefore stiff civic resistance was required. In a democracy, said Havel, the aim of citizens should be to 'make life more complicated for its government' by expressing their opinions openly about its aims, methods, and policies. 'I am for democracy,' he said in the old spirit of Dobříš, 'and so I am also for a maximum amount of freedom of information, because such freedom is the first condition of democracy: in order that people truly keep tabs on their government and influence it, they must perforce know what the government is doing and why, and they must have the right to express themselves freely about what it does.' Havel said he intended to use responsibly to the full the existing freedoms. He was currently working with Jan Němec on a screenplay on the theme of the swindling of 'ordinary people' by 'the international establishment'. He also reported that he was sketching a new play called _The Wedding (Svatba):_ It was to be a portrait of a convivial wedding reception. At one point during the celebration, one of the newlyweds' relatives suddenly interrupts the chatting and laughter with a straightforward burst of honesty about the marriage. The relative is pounced upon and beaten up by her husband. Nobody comes to her rescue. Everybody feels sorry for her. But then she falls silent, and everybody resumes their feast of small talk, sprinkled with laughter.
_The Wedding_ ended up in the dustbin. A script written with Jan Němec and called _Heart Beat,_ about the international mafia trade in human hearts, went unfilmed. Under the weight of military occupation, Havel instead wrote the dark and depressing play _The Conspirators (Spiklenci)._ It proved not to be among his favourites. He later complained, harshly, that it was the first of his plays to be 'forbidden', that it had been conceived in times suffering from 'lack of air and senselessness', and that the play consequently felt (to him) 'lifeless, over-organized, bloodless, lacking humour as well as mystery'. It resembled 'a cake that has been left in the oven too long and has completely dried out'. Posterity may draw that same conclusion. Yet _The Conspirators_ reveals — in fifteen precisely structured scenes — Havel's ongoing preoccupation with the subject of political power, and its corrupting effects. A revolution erupts. Student demonstrators in Concord Square call for freedom and justice, above all for the immediate release of a political prisoner, Alfred Stein, an individual loved for his honesty, his passion for philosophy, his desire to live quietly with his cat. Public joy floods through the streets of the capital. Cries of 'Long live the revolution!' signal the end of the bloody despotism of Olah. But behind the scenes, four conspirators set to work. Parroting slogans like 'Freedom and Democracy!', warning of the 'evils of anarchy' and the need for 'unifying action', they jostle for control over the revolution. Like swine before slop, their greed before power proves limitless. Two conspirators — the weakling Commander-in-Chief of the Armed Forces, and the Chief Censor Aram, an idiot who can only think after denouncing others — are quickly shoved out of the way. That leaves two figures locked in a Hobbesian struggle for state power: Chief Prosecutor Dykl and Chief of Police Moher. As menacing crowds gather in Concord Square, this time to demand the return of the exiled despot Olah, the much-loved political prisoner, who has been tortured into making diametrically opposed confessions of guilt, commits suicide in his cell. The two conspirators try to outmanoeuvre each other, without success. Incapable of absolute victory, they end their struggle in stalemate. So Chief of Police Moher gets to the point. 'My friends, let us finally stop beating about the bush! After all, everyone knows that one man is capable of establishing order here, to return the nation to the path of disciplined work ... and a future of genuine freedom and democracy.' He continues, in twisted logic: 'Seriously, my friends: if we do not want the leadership qualities of this man to be misused against the people, why could we not also use them for the benefit of the people?' The soliloquy is interrupted by a phone call from Monte Carlo. The curtain falls — with the Chief of Police striding towards the telephone, to invite back the despot to take charge of the new revolution.
Legislative Measure Number 99/1969 turned _The Conspirators_ into a 'forbidden' work. On the late afternoon of 22 August 1969, as street battles raged in several cities, especially in Brno, the Presidium of the Federal Assembly passed legislation by this name. It was presented by Gustáv Husák and signed by three of the principal proponents of the Prague Spring, including Alexander Dubček, who later claimed (typically) that he did so only because he had his arm twisted. Passed in the absence of the Federal Asembly, Legislative Measure 99/1969 in effect cleared the way for a permanent state of emergency. It provided for steep fines and imprisonment for those involved in public disturbances. Crimes of a political nature, including defamation either of the Republic and its representatives or of any state in the international socialist system and its representatives, were from here on punishable with increased sentences. Criminal proceedings related to political violations were to be expedited: pre-trial proceedings were scrapped, one-man tribunals were introduced, the right to defence was limited, and the maximum period of detention without trial was extended from forty-eight hours to three weeks. The legislation also took aim at trade unions and other (potential) civil associations by restricting or disbanding volunteer and other organizations. And it prepared the way, within such bodies as schools, universities, theatres, the academies of science, and the state ministries, for mass purges of 'untrustworthy' individuals suspected of having 'disturbed the socialist social order'.
Born of street protests crushed by water cannon, truncheons and firearms, Legislative Measure 99/1969 contained the basic elements of the late-socialist regime of power all Czechs and Slovaks would have to live with for the next twenty years. Late-socialism admittedly had older roots — traceable to the Bolshevik Revolution, and deeper still to the practice of party discipline, the calculated use of promotions, demotions and expulsions, and the life-and-death struggles for organizational control within the oppositional socialist parties of the nineteenth and early twentieth centuries. Late-socialism — as Havel himself was to point out — also preserved certain characteristics from the regime built from the _coup de Prague._ But the type of state that was born of the military invasion was nevertheless a new and distinctive system of power. Although the Communist Party continued to rely ultimately upon government by fear and brutal repression, it did so in considerably more anonymous, selective and calculated form. Violence was from here on 'targeted' against the unlucky few who 'disrespected public officials' or engaged in 'acts against the Republic'. Big show trials became a thing of the past. The Party's utter disregard for efficiency, characteristic of the delirium of the Stalin period, was also abandoned. Especially in matters of administration and production, much emphasis was given to innovation, productivity and the need for permanent reform. There were novelties as well in the field of communications. While the Party still attempted to contain everything that was said within an ideological tent of words and images covering the past, present and future worlds, almost nobody — probably not even senior Party apparatchiks — believed any longer in their pantomime of ritualized claims. Finally, the late-socialist regime abandoned the old totalitarian formula, _L'état, c'est nous._ The state no longer strived to control fully the bodies and souls of its subjects, to embrace everything in depth, to magnetize everyone so as to produce a single will, focused upon the Great Leader. Late-socialism was instead largely content with the regulation and control of _apparent_ behaviour. So long as its subjects forgot the past, quietly conformed and merely grumbled among themselves, they were probably safe.
To this list of novelties of late-socialism should be added another: the painful disruption caused to many Czechs and Slovaks during the drastic transition to late-socialism during the years 1969-1971. Among the paradoxes of late-socialism was the fact that it was able to tolerate the quiet conformity of its subjects only after it had rummaged through their personal and working lives to an unprecedented degree. In the name of eliminating 'right-wing' and 'anti-socialist' forces, a mass purge of the population was carried out. The Communist Party of Czechoslovakia was designated as the major force of cleansing and regeneration, but the key problem was that the Party was internally divided, with a clear majority of its members and officials opposed to winding back the political clock. So the Party had to be rebuilt — around what was called the 'sound core' of Communist officials and members who believed that the most dangerous enemy was to be found within its own ranks.
The scale of the autumn cleaning was inversely proportional to the defeats inflicted on Party unity in the spring years. During the two-year period following Legislative Measure 99/1969, at least three-quarters of a million citizens of the country, or about 2 million people if their households are included, lost their jobs or were demoted or seriously discriminated against — rarely with a punch in the mouth, usually with a frown or a warning, and quite often over a cup of coffee, or with a smile or a shrug of the shoulders, or a handshake from the perpetrators. The 'civilized violence' of the purges was felt in every nook and cranny of the regime. Far-reaching changes in the supreme legislative bodies were enforced. Three-quarters of the ministers and all of the premiers (including Dubček) of the federal and two national (i.e., Czech and Slovak) governments were dismissed. The same proportion of leading diplomats was replaced. The entire top team at the Czechoslovak General Prosecutor's Office was sacked. There were sweeping changes as well in the field of production and commerce. The whole management of the major banks — the State Bank and the Commercial Bank — was removed. More than two-thirds of directors of national enterprises and foreign trade corporations were dismissed. More than a third of a million management officials were screened at least once, while workers' councils, which had sprung up during the Prague Spring, were entirely liquidated. 'Normalization' in the trade unions meanwhile meant the total reorganization of their committees and councils and the dismissal of 125,000 officials. In the field of education the story was much the same. Hundreds of headmasters and their deputies and thousands of teachers at the secondary and primary levels were dismissed or removed to more remote localities and disqualified from teaching political subjects. The Union of University Students was liquidated. Some 2,000 university teachers were forced out of their posts.
The purges were especially harsh in the field of media and cultural policy. Most film and television directors, actors, cameramen, music-hall artists, script-writers, painters and sculptors were screened and re-screened and then forced on to a long-term treadmill of persecution. 475 of the 590 members of the Czech Writers' Union were removed, while 130 writers, among them Havel, were put on the blacklist and had their earlier editions removed from public libraries. The entire management and senior editorial staff of television, radio and the news agency were booted out. Out of forty influential dailies and weeklies, thirty-seven editors were replaced. Nearly 40 per cent of all journalists were forced to resign, their jobs being filled especially by young people lured by increased salaries. The autumn purges also extended into the mass 'front' organizations which functioned like flesh on the bones of the Party. The changes were especially harsh within those front organizations considered strategically vital, such as the peace committees, the Association for Co-operation with the Army, and the organizations of youth, women, and co-operative farmers. But even the 'non-political' organizations suffered. Sackings, warnings and demotions were commonplace in such bodies as sporting clubs, the Red Cross, local fire brigades, and associations of huntsmen and beekeepers.
The fear and disruption produced by the purges was well worth it. Late-socialism became renowned world-wide as a system of state power structured by the grey and dreary principle of the leading role of the Party. Under late-socialist conditions, the Party was sovereign — it was the central nervous system of the political order, so that all important powers of making and administering decisions were concentrated in its hands. The Party organization itself was pyramid-shaped. All Party members were formally equal, but the upper echelons — the senior nomenklatura — were definitely more equal than the rest. Having carefully climbed the ladders of power within the Party, they enjoyed wide-ranging privileges, including a special kind of non-monetary wealth attached to their leadership roles.
The sovereign powers of the ruling group within the Party ran wide and deep. Leading members of the Party chose the Party membership, and also structured the outcomes of the Party Congress. Constitutional changes had to be approved by the Party leadership before going through the mere formality of acceptance by the Party-dominated parliamentary bodies. The Party executive suppressed market mechanisms by monopolizing key decisions concerning investment, production and consumption. In matters of law, court decisions were also supervised closely by the Party executive, especially in sensitive cases, when the courts functioned as executive bodies. The army and police and secret police — the beating heart of the Party, Czechs said — were also supervised closely by the Party leadership, even with direct assistance of their Party-controlled Soviet counterparts. In the field of communications media, the hand of the Party leadership was omnipresent as well. The Party sought to entomb the whole population within an ideological pyramid of clichéd and often bizarre language. 'Socialism is a young, dynamic social order,' said Gustáv Husák at one point, typically, 'which is seeking and testing in its stride ways of making even better use of its advantages, of organizing and controlling social development most efficiently.'
The monopoly powers of the Party leadership in matters of state policy-making and administration, production and consumption, communications, law and policing led unavoidably to arbitrary decision-making. It also produced a constant widening of the discretionary powers of the Party authorities. The line of the Party leadership was always correct — even when it contradicted itself, or changed course markedly. Party had a sibylline quality. It represented itself as wise and omniscient Its 'scientific' pronouncements were presumed to be incontrovertible, even if onlookers often found them mysterious, confused, unfathomable. The standpoint of the Party, especially! its leadership, seemed synonymous with life itself.
The overall function of the Party and its leading echelons was to determine the substantive aims and formal methods to be followed by all subsidiary organizations and personnel. The upper layers of the Party aimed to penetrate, strictly subordinate and centrally unify the vast labyrinth of state ministries, which perforce had distinct chains of bureaucratic command, interact with each other at various levels, and develop and defend (partially) divergent interests. In this task of centrally co-ordinating and synthesizing the various state bureaucracies, the sovereign Party leadership was reinforced by a complex network of subordinate Party structures — trade unions, youth and women's and writers' organizations, for instance — staffed by middle- and lower-level Party members. The task of these ancillary Party organizations was to enforce the primary objectives of the ruling pinnacle of the Party and, thereby, to monitor, regulate and discipline each and every organization within the political order.
Their function was also to keep the Party's firm grip on each and every individual citizen. Since proportionately few citizens were Party members, the vast majority of the population were considered second-class citizens. The life chances of a young person who refused to join the Party, for instance, were extremely limited, for she or he in effect refused to accept the principle that only Party members can and should govern. That person also refused to acknowledge the converse of this principle: that the programmes and actions of the Party were always binding upon its individual subjects, who therefore had to be prevented systematically from developing alternative policies, organizations and forms of expression in matters of politics, production and culture. These policy areas were deemed the exclusive prerogative of the Party, its ministries and ancillary organizations. Their goal was 'socialism' — meaning unchallenged rule, the complete subordination and incorporation of all individuals into the crystalline structures of the Party-dominated state. The vast majority of the citizenry of late-socialist regimes had no say at all — not even legally — in the decisive question of who would rule them. This question was always answered in advance. Since the Party was always right, even retroactively, it was obliged to lead, limit and teach its citizens. The one-party system of late-socialism was in this precise sense totalitarian: democratic pluralism was outlawed.
Under the conditions of post-Stalinism, in other words, the citizens of late-socialism were expected to join what Havel's friend Ivan Klíma called the 'community of the defeated', and to abide by its basic rules: that there would only ever be one governing party, to which everything, including truth itself, belonged; that the world was divided into enemies and friends of the Party and, accordingly, that compliance with Party policies was rewarded, dissent penalized; and, finally, that the Party no longer required the complete devotion of its subjects, only the quiet acceptance of its dictates. This meant that the Party emphasized discipline, caution, respectability, self-censorship, resignation, and moral flaccidity among its subjects ('far better not to know and not to think'). Conversely, the Party feared and actively discouraged independence of mind and judgement, excellence, boldness, perspicacity, courage, public commitment to democratic principles and the pagan mistrust of official jargon and bureaucratic regulations.
These basic unwritten rules of late-socialism implied that no subject was ever fully innocent before the Party apparatus. In effect, this apparatus subjected each individual to a form of permanent internment. Life was made to feel like one big grey dreary depressing prison. And since the Party was always right about everything, even retroactively, those individuals who ceased to be humble and obedient Party followers were automatically considered to be its deserters and, therefore, enemies of socialism. Citizen opposition to the Party was always regarded by its top echelons as 'decadent' and seditious, which is why the (potential) opponents of the Party were to be found not only among intellectuals like Havel, but also in every pub, café, street queue, factory, church and theatre.
### **Beggars' Opera**
A tall man with a menacing face stepped front stage from behind the drawn curtain. Artfully, in slow motion, he lit a cigarette, which glowed brightly in the darkness of the makeshift theatre. The invited audience of 300 people — painters, writers, actors, relatives, even Havel's ageing father — stilled. The speechless man carefully aimed a smoke ring in their direction, then began eyeing them defiantly. Nobody laughed. Nobody smiled. The man's face began slowly to resemble that of a psychopath. He stared coldly at each person below and beyond the stage, beginning with the first row and working his way gradually sideways and backwards, one person at a time. There followed a second puff of smoke, accompanied this time by menacing glances directed like darts at every single member of the audience in the middle distance. By the time the third smoke ring circled overhead, everybody present had the feeling that something was amiss. It seemed that trouble had entered the theatre — even that they might well each have to pay a heavy price for choosing that night to drive to Horní Počernice, on the outskirts of east Prague, and to huddle, nervous and sweating, in a pub restaurant called U Celikovských, whose biggest room had been converted into a theatre sealed off with mattresses to hamper police entry and to muffle the roar of scruffy drunks in the adjoining bar.
The man completed his sinister inspection, then slipped silently behind the curtain. Time seemed to stop, as if fate's turn had now come. The hearts of the audience thumped. Their brows sweated, their bottoms remained riveted to the creaky chairs. The tense atmosphere was toughened by the knowledge, shared by actors and audience alike, of just how dangerous the whole performance was. The play that was about to be performed had originally been written three years earlier, in 1972, for the Činoherní klub in Prague, but the crackdown after the Prague Spring had prevented its performance. Havel's next-door neighbour at Hrádeček, the actor and director Andrej Krob — the man with the sinister face — proposed doing it by subterfuge. Havel agreed, and Krob set about pulling together a makeshift troupe of actors and stage-hands, who spent the next eighteen months rehearsing. So as not to be caught by the StB, the performers — Jan Kašpar, Lída Michalová, Jana Tůmová, Viktor Spousta among them — moved around from apartment to apartment. Krob, one of those figures who lived life seriously without taking it seriously, proved demanding. He always said, like Molière, that he'd like to die on stage.
Others regarded his despotic intensity with trepidation. 'As a person, he's wonderful,' remarked Kašpar, 'but as a director he's awful.' Lída Michalová also found him 'terrible, intolerant, selfish'. Personalities aside, nobody really thought that a performance was possible, but everybody battled on, trying to improve the dialogue and to perfect the blocking and rhythm. A rehearsal was brought to Hrádeček, and soon after Havel wrote to Krob with his criticisms and advice: 'You have chosen one of the most difficult plays,' he reflected. 'Every sentence must be precise; it must have an exact meaning. It may not be important in some realist-psychological play if Nora says to Ingrid "You are evil", "You are cruel", or "Ingrid, you piss me off". But here, the whole effect stands and falls on language, its exactness, the logic of its syntax, its melody and rhythm. Every word is important, no word can be omitted or altered. If you do, the situation immediately loses its spark and becomes just a story.' Havel added a paragraph of warm praise. 'Regardless of whether you get through to the end and what the outcome is, I think it's great that you are searching together for something, that you are able to find time and energy for something which is burdensome and will not bring you any profit. It seems to me that it is something unique, good and meaningful in today's earth-bound world.'
Havel and his old theatre friend Jan Grossman came to see the dress rehearsal. The two masters of contemporary Czech theatre gave their seal of approval, and young bearded Viktor Spousta, who was to play a lead role in the play, set about finding a place for the performance. It had to be accessible to the audience but inaccessible to the police. U Čelikovských, the pub restaurant in Horní Počernice, seemed perfect. Costs were covered by selling a limited number of tickets. Havel, hitherto bewildered, grew excited. He was about to see the only one of his plays ever to be performed under late-socialist conditions. Others doubted that it would happen. An hour before the performance was due to start, only a handful of relatives had taken their seats. Everybody presumed the worst: that the StB had got wind of the event and had already begun roadblocks and arrests.
A chink of light, then a curtain suddenly opening to reveal a stage, costumed actors, a table, chairs, movement, expression, and words. Catharsis: the first and only performance of _The Beggar's Opera_ had begun. For the next two hours, the audience grinned, laughed and clapped its way through Havel's adaptation of John Gay's early eighteenth-century musical play. Through his anglophile friend and literary scholar, Zdeněk Urbánek, Havel had discovered some years earlier Gay's work, whose central character is Captain Macheath, a highwayman and lighthearted winner of women's hearts. Macheath falls in love and marries Polly, but her father, a receiver of stolen goods who also makes a living by informing on his clients, is not pleased. Furious at her folly, he decides to spoil the marriage by grassing on Macheath, with the aim of elevating his daughter into the 'comfortable estate of widowhood', Macheath is arrested and sent to Newgate prison, where, awaiting execution, he manages to conquer the heart of a woman named Lucy. Polly and Lucy subsequently do battle for the affection of the swashbuckling Macheath, who shows no remorse ('How happy could I be with either, Were t'other dear charmer away!') as he makes his escape from prison.
Havel's emplotment of _The Beggar's Opera_ runs a different course. There is no music and no singing — the opera form is stripped bare — and no happy or charming endings. It is nonetheless a comic treatment of a world in which each individual cheats on every other individual. Even the notion of honour among thieves is exposed as romantic nonsense. Everybody behaves selfishly. Selfishness is 'reality', and there appears to be no alternative but to act 'realistically', which means accepting that the system encourages and depends upon chronic lying, double-crossing, back-stabbing, trickery, the greedy pursuit of self-interest as it is defined at that particular moment. To act in contrary ways, for instance to embrace precepts like honesty or care for others, would amount to pure foolishness that would then simply play into the hands of others. In any event, acting according to those old-fashioned precepts doesn't occur to anybody. Individuals' power to act on the world has been reduced to pure manipulation and self-manipulation. Moral thinking as such, the habit of examining people and events in terms of means and ends, has disappeared. The small evils of knavery have become utterly banal. Language itself is corrupted. Sentences are no longer means of communication. Words have become mere tools of manipulation.
William Peachum, the boss of a thieves' network, is locked in battle with Macheath, the chief crook of a competing crime syndicate. Peachum tries everything to outsmart his rival. He is naturally delighted at the news that his daughter Polly has secretly been having an affair with Macheath. Peachum has plans for her. He also manages to recruit Harry Filch, a freelance pickpocket and former employee of Macheath. Peachum does business as well with Madame Diana, who runs an up-market brothel. She needs precious objects like silver cutlery, a few candelabras, and a few yards of brocade for some new curtains, and in return offers to supply Peachum with one of her best girls. Mrs Peachum agrees that her husband, in order to outcompete the swashbuckling Macheath, needs to improve his ways with women. For Macheath has a superior reputation in this field. He is renowned as a powerful desperado, a _bon vivant,_ a physically attractive man of gall and charm and seduction. His formula for success is simple: his strategy with women is to simulate an inferiority complex because (he says) 'women love to help someone and to save someone'. Macheath, who likes to calculate gains and losses, admits that things are a bit more complex than that. Inexperienced 'nice' women, for instance, are exciting to seduce and they offer their services free. But, lacking erotic experience, they are seldom physically satisfying and, besides, their seduction sometimes takes up precious time that could be better spent making money. They also have a nasty habit of falling in love. So, Macheath reasons, prostitutes are a better bargain. 'Agreement is quick,' he says, 'shame does not prevent them from co-operating with any of your desires. And the act itself does not complicate your life with their feelings or demands.' If for any reason a prostitute does try to cling on, he concludes, getting rid of her is simple. 'Either behave towards such a person so despicably that her lingering dignity prevents her from maintaining an interest... Or the second possibility is simply to marry her.'
Macheath speaks from experience. It transpires that he is a bigamist and is already married to Polly, Peachum's daughter. When he finds that out, Peachum instructs her to become his secret agent inside Macheath's organization — with the aim of liquidating it. The same thought occurs to Macheath, who soon receives a visit from Polly, who betrays her father's trust by confessing to her husband that her father is preparing a plan that will send him to the scaffold. Macheath no sooner berates her for not uncovering the precise details of his fate than he is lured into the arms of an old lover who now works at Madame Diana's establishment. The prostitute cries rape, Macheath is arrested by the police, and promptly carted off to prison. Peachum's plan has worked — with the help of the Chief of Police, Lockit.
The Chief of Police is a calculating knave and although working for Peachum tries to recruit Macheath into his own network of crime-fighting criminals. Lockit is unaware that his daughter Lucy is married to Macheath, whom she helps to escape with a hacksaw. But Macheath doesn't last long on the outside. He is arrested in Madame Diana's establishment while hiding out there, but a worse fate follows. His two wives finally catch up with him. He tries to rescue his reputation with oratory. 'No, girls, if I was to best fulfil my responsibility towards you,' he says, reminding them that in hours he might be on the scaffold, 'I could not follow other men in this matter, but had to follow my own path, maybe untrodden, but decidedly more moral — that is, the path which gives you equally the same measure of legitimacy and dignity.' On goes the duplicity. On and on. Lockit has Filch arrested and executed after he refuses to co-operate with the racketeering of the police. The key characters — Madame Diana, Peachum, Lockit, Macheath — resort ever more to clichés. So does the sleeping drunk who, appearing in several scenes, rouses himself to shout, 'Long live freedom of the press!' The amorality and bowdlerization of language intensifies. Peachum at one point protests against the whole trend. 'Do you at all understand what it is to wear two faces for such a long time, to live two lives, to think in two ways, from morning till night to guard oneself, to masquerade, to conceal some things and pretend others, to adapt yourself constantly to the world which you condemn and forswear the world to which you really belong?' Fine words — but he too eventually succumbs to the universal corruption, and in a most spectacular way. He proposes to the Chief of Police the formation of a new crime cartel. It is accepted by Macheath, in writing. Lockit is ecstatic. 'From this moment on, our organization controls practically all of the underworld,' he declares. The Chief of Police has finally become the chief swindler-in-charge — and nobody else knows, even though everybody serves him.
### **Charter 77**
The miserable ending of _The Beggar's Opera_ posed a fundamental political question: How is it all possible to keep alive personal integrity in a world that pays no dues to the fine points of humanity? Andrej Krob, the director who played the role of Chief of Police Lockit, had an answer. He admitted that he was thrown forwards and upwards by the performance of _The Beggar's Opera,_ despite all the technical hitches. 'For me it was a mess of fuck-ups — curtains opened poorly, slips of the tongue, sweating faces. But with the passage of time, I realize it wasn't a matter of a theatrical performance at all, but of something that managed to happen under absolutely incredible circumstances.' Everybody who was there thought it a happening. Havel certainly felt triumphant. At the party after the performance, held at U Medvídků, a restaurant just around the corner from Prague's police headquarters on Bartolomějská Street, he told the troupe that the performance had brought him more personal joy than any of the foreign premières of his plays, 'from New York to Tokyo'.
All hell broke loose when the surprise news of the performance reached the authorities. They went on the warpath to ensure that the one performance (as Krob put it) was the première and dernière. Havel was brought in for questioning. Dozens of other interrogations took place. Ministry of Culture bureaucrats spread the word that there would be a tightening of policy towards the theatres, and that Havel should be blamed for the setback. The threats worked in some parts of the theatre world. 'Many a shallow-minded actor fell for it,' reported Havel later, 'and got very upset with me and my amateur actors for frustrating their artistic ambition, by which, of course, they meant their well-paid sprints from job to job — in dubbing, theatre, television, and film — that is, from one centre for befuddling the public to another. But that wasn't the point.' The point was that the success of _The Beggar's Opera_ encouraged* Havel to go further. His boldly worded open letter to Husák, which was circulated underground, published abroad and broadcast back into Prague by Western radio stations, several of which likened Havel to Alexander Solzhenitsyn, had also persuaded him a few months earlier that forms of resistance to late-socialism might be possible. Around the same time, the completion of the one-act play _Audience_ had a similar effect, even though it was not performed. But _The Beggar's Opera_ had a special impact. After a seven-year interruption, it made him see with his own blue eyes that he could still write performable plays. It convinced him that he was not burned out. It gave him courage, and made him feel that he had energy for further projects.
Just around the corner, although he didn't yet know it, was the biggest and most important project of his life so far. Its beginning resembled the climax of a cheap television police drama. A rusted-out getaway white Saab, stuffed with boxes of sealed envelopes and documents and three scruffy men bound for the Federal Assembly building in central Prague, was chased into the district of Dejvice. It was then trapped in a railway underpass by a squad of police cars, screaming sirens, bright-orange lights flashing in the gloom of midday winter darkness. There was a squeal of tyres and the slamming of doors. Then followed sounds of scuffling bodies and scraping feet — the sounds of the three conspirators, the playwright-driver Pavel Landovský and his two passengers, Ludvík Vaculík and Václav Havel. The men were promptly bundled at gunpoint into separate patrol cars before setting off at high speed to police headquarters on Bartolomějská Street.
The authorities' arrest and all-night interrogation of Havel and his colleagues and the confiscation and careful inspection of their booty — which included a three-page document that was immediately stamped, in red ink, POZOR: DAKTYLOSKOPICKÝ MATERIÁL! NEVYJÍMAT Z OCHRANNÝCH OBALŮ (Caution: fingerprint material! Do not remove from the protective wrappers) — failed to suppress the story. Next morning, 7 January 1977, the day on which Havel was rearrested for a second round of questioning, the whole world awoke to hear the extraordinary news that a petition with the simple title of Charter 77 had been launched in Prague by several hundred prominent 'Czechoslovak dissidents'. The story was in the front section of newspapers like _Le Monde,_ the _Frankfurter Allgemeine Zeitung_ (which published the text in full), and _The Times_ of London, which described the document as 'not the work of a Machiavellian secret policeman concocting evidence against dissident intellectuals', but 'a remarkable gesture of courage' signed by 'the flowers of the Czechoslovak intelligentsia', including 'Mr Václav Havel, a prominent playwright.' The document was headlined by the Voice of America, and mentioned by tens of thousands of radio and television programmes scattered around the world.
The text of the appeal was short, and easy to report accurately. Charter 77 pointed to the discrepancy between law and reality in socialist Czechoslovakia. At the 1975 gathering of state representatives in Helsinki, it claimed, the Czechoslovak political authorities had signed up to both the International Covenant on Civil and Political Rights and the International Covenant on Economic, Social and Cultural Rights. Those covenants, Charter 77 pointed out, had come into force during the past year (23 March 1976), and were now in effect binding upon both the Czechoslovak Socialist Republic and its citizens. This constitutional change was to be welcomed, it said. The human rights and freedoms underwritten by these covenants were preconditions of a 'civilized life' and 'the development of a humane society' in which the exercise of power is publicly controlled. But — here the Charter used the intellectual strategy of immanently criticizing reality, using the law as an Archimedean lever against state power — these 'basic rights in our country exist, regrettably, on paper only'.
According to the Charter, tens of thousands of citizens were denied the right of free public expression and were victimized by a system of 'virtual apartheid' administered by the dominant Party, which harassed and discriminated against them simply because they held views that were out of step with those of the authorities. Hundreds of thousands of other citizens were denied the right to live in freedom from fear. Many young people were prevented from studying because of their, or their parents', views. Workers and others were unable to protect their interests through the unrestricted right to form trade unions and other organizations. The legally guaranteed right of free religious expression was systematically curtailed by various methods, ranging from direct interference with the activities of believers to constraints on religious training. The centralized control of communications media meant that 'no open criticism can be made of abnormal social phenomena', or of false accusations or unjust and illegal prosecutions. The freedom of movement of citizens to and fro across Czechoslovak borders was consistently violated, for instance through the biased system of granting entry and exit permits. The freedom of citizens from 'arbitrary interference with privacy, family, home or correspondence' was daily undermined by bugging telephones and houses, opening mail, house searches, and shadowing suspects. And networks of neighbourhood informers, often using illicit threats and promises, added to the pressures of daily harassment.
The Charter's allegations were serious. The Czechoslovak Socialist Republic, supposedly on the road to a free and classless society, was in effect a lawless Leviathan, whose subjects were permanently held hostage by an unchecked Party-state apparatus. It admitted that the responsibility for maintaining civil and human rights ultimately rested with the political authorities. But the Charter insisted that citizenship — the entitlement of all individuals to enjoy certain rights and to observe certain duties within a political community — also required the vigilance of the citizenry. Those who exercise power over others cannot be expected to exercise power over themselves. Within any state, the saplings of liberty must be watered constantly with the independent efforts of its citizens. 'It is this sense of co-responsibility,' it said, 'our belief in the meaning of voluntary citizens' involvement and the general need to give it new and more effective expression, that led us to the idea of creating Charter 77, whose inception we today publicly announce.' It went on to emphasize that Charter 77 was _not_ to be understood as a revolutionary organization planning and plotting to seize state power, by cunning or strength. Charter 77 would instead aim to function as a citizens' initiative. It had been formed out of like-minded circles of friends and acquaintances, many of whom had been shaken by the recent trial of the rock band called the Plastic People of the Universe. The Charter comprised people who from here on were concerned to work for 'the general public interest'. The Charter was not an organization. And it was not — as Havel had argued successfully during the drafting process — a committee that would function as something like the Czechoslovak sister group of the Helsinki Human Rights Group recently established in Moscow. The new initiative had no rules, permanent organization or formal membership. Charter 77 — the following words drafted by Havel would quickly become world-famous — was best considered as 'a free, informal, open community of people of different convictions, different faiths and different professions united by the will to strive, individually and collectively, for the respect of civic and human rights in our own country and throughout the world'.
The timing of the launch of the Charter during the first week of January 1977 had been carefully devised. Nine years earlier — Havel felt it to be a lifetime — the Prague Spring had begun in the month of January. It was also the start of the year proclaimed as the Year of Political Prisoners, and in a few months a potentially important conference was to be held in Belgrade to review the implementation of the obligations assumed by Czechoslovakia and other states at the Helsinki Conference on Security and Co-operation in Europe. Then there was the practical consideration that the last-minute tweaking of the document and its circulation among potential signatories was best done during the Christmas/New Year break, when cold weather, gathered families, and merry-making, even within the ranks of the secret police, made it easier to slip through the nets of state surveillance.
The schedule for finalizing the text, collecting signatures, and dealing with other remaining matters was tailored accordingly. Havel, who wrote the first draft of the declaration, worked closely with Zdeněk Mlynář to produce a redrafted version. The playwright Pavel Kohout thought up the name Charter 77. The threesome decided that the text should be anonymous. 'It didn't seem appropriate to emphasize authorship,' Havel later said, 'not because it would have been too dangerous, but because after all everyone was responsible for the Charter by signing it.'Two handfuls of people, co-ordinated by Havel, did the rounds in search of potential signatories. Considering the restrictions imposed by time and secret police, the response was good, although unevenly distributed. 243 signatures were collected, of whom nearly 90 per cent were from Prague, with only 1 (Dominik Tatarka) from Slovakia, 1 from northern Moravia, and 17 from Brno. The collection point was the Havels' embankment flat. There the signatures were put in alphabetical order, Bohemian champagne drunk and, at a meeting that followed, Havel was elected ring-leader of the two other first spokesmen, Jiří Hájek, Dubček's Foreign Minister in 1968, and Professor Jan Patočka, the country's leading philosopher.
So the struggle with the authorities began. It has been said that the petition 'generated a vibrant response in a country still deep in the slough of despondency resulting from the invasion in August 1968'. Despondency was certainly widespread, but since there was no freely accessible public sphere in existence and, hence, no public opinion, it is impossible to say just how many Czechs and Slovaks knew about the Charter or, if they did, what were their reactions around meal tables, in pubs, or at work. Having launched a life-raft upon an eerie sea of silence, Havel and the other signatories could only ask themselves whether (as the best contemporary Czech historian put it at the time) the Charter would prove to be a catalyst of 'a new national and democratic revival _[obrození_ ]' comparable to the early nineteenth-century renaissance that ended a long period of darkness _(temno),_ or whether the civic initiative would be stillborn, leaving despair and misery untouched rulers of the people's hearts.
It was too early to tell, but the positive reaction of the world's press certainly buoyed the spirits of the drafters and signatories. Havel moved quickly to harness such responses. The cleancut, good-looking playwright actively tried to direct the international media's interests with upbeat soundbites and intelligent commentaries that not only turned the heads of many journalists, but also captured the ears of thousands of listeners and readers in dozens of countries outside the Soviet empire. The Charter performance was good for his political career. Slowly but surely, Václav Havel was becoming an international media celebrity, and certainly the best-known Chartist outside the country. Within the first year of the Charter's life he told a BBC interviewer that his support for the principles and moral rightness of the Charter was unwavering, and he claimed even that the initiative was beginning to have a visible impact upon the Czechoslovak population. 'We are no longer divided into a few habitual dissidents and the rest of the population,' he said, adding that 'society's conscience' had begun to awaken, and that 'the ice barrier of apathy' had begun to crumble. A few months later, he told the Vienna daily newspaper _Kurier_ that the Charter had a fundamentally moral quality, and that no matter what happened it would continue to play a vital role in the resistance to totalitarian power.
The authorities acted quickly to dampen such civic enthusiasm. The text of the appeal reached the desk of white-haired, bespectacled President Husák on 8 January. He studied it carefully, and even took the trouble to underline in black ink certain passages, such as the claims about the lack of freedom of religion, the right of free speech, and the restrictions on what young people could study. The care he took was the clumsy care of the closed-minded ideologue bent on inflicting revenge, which came fast, in rough-edged dollops. Three weeks later, following his instruction that everyone had to pitch in to defeat the _Charta,_ a packed Prague meeting of well-dressed and famous artists declared their loyal support for socialism. It was the solidarity of believers and those afraid not to believe. The television cameras caught glimpses of the guitarist and composer Jiří Brabec, the pop singer Marie Rottrová, and the Golden Nightingale award-winner, pop artist Karel Gott.
The cameramen couldn't take their lenses off the actress Jiřina Švorcová, who was warmly applauded by the delegates for a red-hot propaganda speech, in which she said that she was disgusted by people — Havel's name was surely on the tip of her tongue — who acted as if they were 'the chosen', but who were in fact traitors, mere isolates, enemies of humanism and peace, worshippers of money, imperialist agents, and the source of hatred among nations. After her speech, other actresses, joined by television personalities, journalists, painters, musicians and entertainers, including Jan Werich, an old friend of the Havel family, queued up to sign a declaration in favour of 'New Creative Works in the Name of Socialism and Peace'.
President Husák personally supported this so-called Anti-Charter. He went on the warpath. At a press conference held shortly after the launch of the Charter, he pointed out that vigilance was required, that nobody should underestimate its campaign to undermine the socialist countries. 'But history teaches us,' he said, 'that all campaigns based on lies and lacking links to the life and consciousness of the people will collapse, and that all the hired puppets of these campaigns will end up in the dustbin of history.' Exactly one week after the launch of the Charter, the Communist Party's leading newspaper, _Rudé právo,_ in conjunction with Bratislava's _Pravda,_ reinforced the point by running a headline (that rhymes in Czech) about 'The Shipwrecked and the Self-Appointed' _(Ztroskotanci a samozvanci)_. The newspaper started a campaign against named Chartists and began to carry stories of prominent sportsmen, artists, and other public figures who opposed the initiative. Czechoslovak television filmed workers (most of whom had never seen the text of the _Charta)_ denouncing the enemies of order and socialism. The Party also leaned heavily on prominent waverers like Cardinal František Tomášek, who responded by issuing a signed declaration explaining that the representatives of the Church had not signed the Charter. The declaration called for universal peace, justice and love; expressed concern about the disturbances of the peace caused by the _Charta_ initiative; reiterated that nobody else could speak on behalf of the trusted Holy Roman Church; and left readers breathless from the crooked logic of the document to ponder exactly what it might be saying.
Havel was also leaned on heavily, so heavily in fact that he issued a statement which revealed his concern that the authorities now suspected him of being 'the main initiator and organizer of Charter 77'. Bugging devices began gathering evidence later used to prove that he was part of 'a counter-revolution'. He was soon attacked officially from all directions. _Rudé právo_ denounced him as an 'inveterate anti-socialist'. He was accused of being in the pay of the 'well-known agent of the CIA' Pavel Tigrid (his friend and editor of the Paris-based _Sv ědectví_) and the recipient of funds directly provided by American, West German and other intelligence services. His past was thoroughly muck-raked. Havel was described as a millionaire's son who was a second-rate poet and who had, in his plays, called into question 'the very essence of the socialist order'. He had been involved with the magazine _Tvá ř,_' the voice of ideas absolutely foreign to socialism', and he had spent a lifetime fruitlessly trying to rehabilitate various reactionary 'bourgeois' ideas, such as those of Masaryk. Czechoslovak Radio chimed in with a programme called _Who is Václav Havel? (Kdo je Václav Havel?),_ the text of which was published in full or as excerpts in virtually all the daily newspapers in the country. It described him as 'extremely conceited', as an arrogant nobody who held 'everybody around him in contempt'.
The authorities made two initial strategic mistakes in their anti-Charter campaigns. More minor was the fact that they had initially suspected that the launch of Charter 77 was the work (as _Rudé právo_ put it) of anti-Communist and Zionist 'centres' in the West. This paranoia of the Party leadership about counter-revolutionary subversion from abroad granted the signatories and their spokesmen a small breathing space, an interregnum of comparatively nonviolent harassment, within which the Chartists could steady themselves. So, during the first several days after the launch of the Charter on 6 January, those who had been questioned by the StB met every evening at Havel's flat — he and Olga were temporarily resident in the district of Dejvice — to explain what had happened to them and what the police wanted to know. The sessions were attended by foreign journalists, who were thus able to act as on-the-spot reporters of the _Charta_ initiative, providing it with the very global coverage that the Party most feared, and certainly had wanted to suppress.
The Party's other tactical mistake was inadvertently to give the advantage of publicity to its opponents. Low-cost modems, satellite-linked telephones, the affordable photocopier, and electronic mail were not yet available. But the Chartists certainly understood the potential power of communications media such as the land-linked telephone, radio and television to publicize their initiative. The Party did not, and not only because since the military crushing of the Prague Spring it had become relatively unfamiliar with dealing with civic initiatives of the kind Havel had helped to organize, helped along by his earlier experiences stretching back to the Dobříš gathering and the Thirty-Sixers. The Party leadership did not grasp at the outset that by 'going public' about the _Charta_ it not only provided it with free publicity. It also placed itself on a level playing field — the battle for public opinion through reasoned argument and rhetorical controversy — with which it wasn't familiar, and on which it had trouble winning against its opponents.
### **Violence**
That left the Party with the option of using the one resource over which they did exercise a monopoly: the means of violence. In practice, late-socialist power brought to completion the monarchic state doctrine of sovereignty, according to which no human society is possible without government, just as no government is possible unless it possesses the ultimate capacity to have the last word in deciding who gets what, when and how, if need be through violent means. Viewed in this way, sovereign power is necessary to protect the state against its enemies. It is ultimately indivisible. When the crunch comes, and especially when normal conditions are threatened by an erupting crisis, the sovereign decision-makers must insist that all other members of the body politic are decision-takers. 'All the characteristics of sovereignty are contained in this,' wrote Jean Bodin, among the inventors of the modern doctrine of sovereign power, 'to have power to give laws to each and every one of his subjects, and to receive none from them'. Sovereign government must be supreme. Those who rule must wisely bear in mind the constant possibility of deception, cunning and violent opposition from their opponents. The rulers must be granted the plenitude of power and insist that the _maxime unum_ is the _maxime bonum._ Sovereign power enjoys the _jus belli._ It is entitled to invoke all measures deemed necessary for the preservation or restoration of order, including suspension of the constitution and the liberties it protects. The sovereign state can and must act as a dictator. It must be intolerant of voluntary associations, regarding them (as Thomas Hobbes said) as treasonous, as nothing better than 'worms within the entrails' of the body politic.
The violent capacity of the state to kill off the worms in its entrails was displayed during the last days on earth of Havel's close colleague, philosophical mentor, and co-spokesman of the Charter, Professor Jan Patočka. More than 1,000 people, flanked by 100 police, paid their last respects to Patocka at Břevnov cemetery in Prague. The mourners were frisked, some friends and Chartists were turned away at the entrance gates, while others were detained for questioning. Police cameras filmed and photographed everybody, even at the graveside. The service was interrupted, and the priest's funeral oration drowned out, by a military helicopter circling overhead and the heavy revving of police motorcycles at a nearby racetrack. Havel's face, like most in attendance, showed signs of deep strain as two members of the band Plastic People of the Universe placed a crown of thorns on Patočka's grave.
From the time of the launch of the Charter, Havel had numerous brushes with state violence. For the first time in his life, he felt continuously gripped by the shadowy hand of the secret police. After signing the second document released by the Charter on 8 January, protesting police measures against the signatories, he was interrogated by the StB almost daily. He received threatening letters and anonymous telephone calls. His life began to feel as if it was one continuous round of threats, bright lights, padded doors, wooden desks, sliding chairs, handcuffs, truncheons that pointed to a limited future. When it became clear to the authorities that the man was not for giving up, and that the Charter activists could only be forcibly silenced, Havel was arrested, charged (under Section 98) with committing 'serious crimes against the basic principles of the Republic'. He was confined without trial 'in total isolation' for four and a half months in Ruzyně prison.
During this time, he managed to write an open letter (dated 13 March 1977) to the editors of all the newspapers that had published 'Who is Václav Havel?', calling on them publicly to issue retractions. To ward off the 'depressive emptiness and hopeless inner solitude' of gloomy Ruzyně prison, he also penned an eloquent obituary for Professor Patočka, whose modesty, penetrating philosophical intellect, quiet sense of humour and 'inconspicuous moral greatness' he praised. The obituary also contained a philosophical twist. Surrounded by violence and mourning the loss of a key Chartist and friend, Havel confessed that he was perplexed by a strange double injustice within the human condition. Not only does 'death even come to people who have spent their entire lives thinking about death', he wrote. It is also a fact that such 'people who understand so much about death and its meaning ... seem to be the ones to whom death pays most attention, perhaps out of fear that they might finally reveal her mystery after all — she hurries to get them, often before the others'.
His reflections on death provided a clue that the authorities were playing dirty, and perhaps even that he was anxious about his safety. Ignorant about the Charter's current activities — and denied even the heartening news of the daring release on 20 April of a large flotilla of brightly coloured children's balloons in Wenceslas Square, accompanied by leaflets publicly demanding his release — Havel was interrogated constantly about its organization, signatories and leadership. The indictment the authorities drew up made no mention at all of the Charter, but on the day of his release (on 20 May 1977) they issued an official statement in which Havel was reported to have said that his actions as a Chartist had 'not always been correct' and that his statements had been 'tendentiously interpreted by the foreign press and misused against Czechoslovakia'. Most importantly, it was claimed that Havel had agreed to resign as Charter spokesman. It was said that he had vowed 'to avoid all activity which could be classed as criminal' and given his word not to 'participate in any action which could be misused for a campaign against the ČSSR'.
The heavy-handed tactics of detention and disinformation were the cause of trembling within the ranks of the Chartists. Havel tried to stand firm. In a carefully worded statement, issued to correct the official 'distortions', he confirmed that he was indeed relinquishing his position as Charter spokesman. But he said categorically that he would remain defiant in the face of state intimidation. He would not withdraw his name from the list of Charter signatories. He would stand by 'the moral obligation' it implied. And he would do everything within the law to come to the assistance of the victims of political injustice. It was in this spirit of acting as if the rule of law existed that, ten days after his release from prison, he bravely called on the District Prosecutor's office in Prague 2 to initiate proceedings against the writer, Tomáš Řezáč, who was originally responsible for slandering him in 'Who is Václav Havel?'. In quick succession, he hosted a small celebration, with Chartist friends, to mark the appearance of the volume _Hry 1970-1976 (Plays 1970-1976),_ published by Zdena Škvorecká's and her husband Josef's Sixty-Eight Publishers in Toronto; gave an interview, published in London, about Charter 77 and independent culture; and (on 1 October 1977) helped demonstrate the meaning of cultural independence by hosting an autumn music festival at his country retreat at Hrádeček. Exactly the same spirit of acting as if he were a citizen living in freedom under the rule of law was again displayed less than three weeks later in his concluding address to the Prague city court hearing the charge of 'serious crimes against the basic principles of the Republic'.
The judge was so unpersuaded by the address that he dispensed with ceremony to sentence Havel to fourteen months, suspended for a period of three years. Havel had damaged the sovereign interests of Czechoslovakia and justice had been seen as done. Now it was to be done in fact. The secret police readied their weapons. On the evening of 28 January 1978, they carefully set a trap for him and other Chartists outside the Railwaymen's House of Culture building in the Prague district of Vinohrady. It had been a custom in Bohemia since the turn of the century that organizations arranged balls and sold tickets to non-members. Aware of this old custom, several women within Chartist circles had spontaneously thought up plans for Chartists and their friends to join the annual ball held at the Railwaymen's House. 'It's politics all the time. We have the right to entertainment too,' they agreed, without resistance, certainly not from Havel, who (as the Americans say) had always liked being shown a good time. A crumpled black-and-white photograph shows him on the way to the ball, grinning, dressed in a dinner jacket, looking every bit the dandy, or perhaps the ladies' man, Anna Šabatová draped over one arm and another woman over the other.
The evening quickly turned into an unrelaxing episode resembling the final murder scene in Dürrenmatt's play _Visit of an Old Lady._ At the entrance to the building, state security police masquerading as railway workers dressed in black politely greeted Havel and others, then announced with a snarl that they were unwelcome guests at the ball. Truncheons suddenly cracked heads. Havel and others fell involuntarily on to the frozen pavement, stunned, bleeding. Several women in evening dress were kicked, and the word 'whore' shouted repeatedly. Someone cried out for help. Uniformed police were instantly on the scene. They were instructed by the black-suited security police to take Havel and several others straight to the clinic for alcoholics, claiming in the process that the agitators who had been hit were actually dead drunk.
The uniformed police had the sense to take them instead to a casualty ward, in precariously slow time. Had Havel and his colleagues (Pavel Landovský and Jaroslav Kukal) been suffering brain damage, they may well have drawn their last breath during the journey. _En route_ to the hospital, they were stopped and detained for ten minutes by another police patrol. After checking their identity papers and taking down their names, the police then tailed the threesome at every turn for the rest of the evening. Around midnight, after a doctor administering a blood test laughed in his face when asked for guarantees that the sample would not be exchanged, Havel was formally charged with obstructing and attacking a public official in the course of duty. He was carted off to Ruzyně prison, where he was to spend the next six weeks, pending a trial that never took place.
One evening just before lights-out, halfway through his ordeal, sitting upright on his bed, nursing a recurrent headache caused by crunching truncheons, Havel heard a man's voice calling out down the prison corridor. 'Is there anybody here from the committee to defend Václav Havel, Pavel Landovský and Jaroslav Kukal?' 'Yes!' replied an anonymous voice. 'Well then, do something,' said the first man's voice, 'I'm Jarda Kukal!'
### **Courage**
It was obvious to the signatories and friends of the Charter that the initiative was an act of courage. Courage is a key source of citizens' power to act in the world, the necessary and indispensable propolis of citizenship, and it is therefore unsurprising — given the stresses and strains of acting under great pressure — that the meaning of courage and whether and under what conditions it could be sustained under duress quickly became a topic for debate within Chartist circles. It was the doing of one of its first signatories, the moustached, black-rim-spectacled writer Ludvík Vaculík — the author of the famous '2,000 Words' manifesto that called for faster and more comprehensive de-Stalinization at the height of the Prague Spring — who used a three-page feuilleton publicly to pick a fight with the Charter's basic principle of non-violent, open resistance against a regime that was systematically violating its own constitutional precepts.
Vaculík began without mincing words. 'I sometimes wonder whether I'm mature enough for prison. It frightens me,' wrote the man who, together with Havel and others, was almost sent to prison in 1969 for writing the 'Ten Point Manifesto'. He admitted that he may be an unusually weak and fearful character, but insisted that everybody who is confronted with possible imprisonment because of their moral commitment has the duty to reflect on whether that price to pay is too high. The presumption that prison is always worth risking is peacockery, he argued, for taking a 'courageous' stand against the politically powerful is not always effective, and sometimes foolish. It is very often full of contradictions. For instance, risking prison drags friends, family and other contacts into the same magnetic field of force, regardless of whether they want to take the risk. Courage is not a trusted friend of freedom; it may even be the latter's enemy, as for example 'when someone provokes someone else to do something which they are then unable to retract without loss of pride, prestige or authority'. Vaculík also tried gallantly to stick up for the silent majority of non-Chartists by defending their so-called apathy. He did so by highlighting the well-known problem, facing everyone who was actually or potentially in contact with Charter 77, that those who watch others take risks easily see that the whole business of activism is so physically and emotionally exhausting that they — sanely — avoid it. The so-called uncourageous individual in fact acts cautiously and prudently by shunning so-called heroism and asking: Is it worth going through with it to the death? and looks for a way to retreat. The reason is clear. 'No psychologist or politician would expect heroism in public life from people except when the atmosphere is literally ionized by radiation from some powerful source. Heroism is alien to daily life.' That is why most of the population 'can less and less see anything in the even more heroic deeds of the declining number of warriors other than a personal hobby'. The encouraging fact, he warned, is that most people 'are well aware of their own limits and only do things whose consequences they are ready to take. Anyone who urges people when times are rough to do things beyond their capacity shouldn't be surprised if they get clobbered.' Here, down-to-earth Vaculík began to sound like the good soldier Švejk. Normal people living in unexceptional circumstances wisely 'stick to their good habits and virtues; they have irreducible standards and will stop them from being degraded. They don't like it when they see someone defiantly taking great risks, but like to say that honest work in peace is best, even if it isn't particularly well rewarded, and that decent behaviour will find a decent response'.
It also has to be said, continued Vaculík, that there are times when the sentenced are publicly forgotten before the sentence is ended, in which case taking a moral stand and flirting thereby with prison turns out to be a sad swan song. Vaculík charged the unofficial campaign, led by Jiří Müller and others, to boycott the 1972 elections with this weakness. He went on to insinuate that the Charter may well turn out to be performing a similar kind of swan song. 'Nobody can give a convincing answer to the question of whether Charter 77 has made things better or worse or what things would look like if it had not happened. In the answers we get,' he taunted, 'moral impulses seem to be out of step with political opinions, and the strongest positions arise from character rather than intellectual orientation.' And there is one final point, Vaculík wrote. Chartists should be honest enough to admit — or mature enough to recognize — that acting with 'courage' and ending up in prison can have long-term destructive effects upon the individual's character. Courage, he concluded, is a term best applied to those who manage to survive prison and especially the painful period of self-destructive post-prison blues that inevitably follows.
So, people outside should be careful and not get themselves locked up. They should even be courageous enough to say no to so-called courage. They should be bold enough to ask the questions forbidden in Chartist circles: Are Chartists really heroes whose convictions have unfortunately landed them in prison? Are Chartists better described as fools who are taking risks for things that are not worth taking risks for? Or even as agents provocateurs of a regime that 'does not want to give publicity to any heroes' and is probably disposed to administer 'measured doses of repression'?
Vaculík is not a writer of common sense and conventional taste, a man without originality and political courage. He acts the part of a curmudgeon and in fact later willingly confessed his awareness that his own argument was intentionally trapped in a literary contradiction. His 'Notes on Courage' was a courageous warning about the potential folly of courage but, like Goedel's maxim that not even mathematics can save itself from the quagmire of inconsistency, Vaculík's inconsistent argument had a stimulating effect upon its readers. Written in spare, angular prose, it was driven by the conviction that its tongue-in-cheek claims would shock and outrage quite a few Chartists, who understood him to be saying, or implying, that Charter 77 ought to cease all its activities forthwith — that it was time to quit the make-believe game of constructing what Václav Benda, a fellow Chartist, called a parallel polis. 'Notes on Courage' was vintage Vaculík: an overstated act of lyric _Verfremdung_ from an old cuss intent on prodding and poking and rolling over on to its back the taken-for-granted principle of courage, for the ultimate purpose of highlighting the need to make judgements about the meaning and utility — and limits — of courage. The emphasis on judgement explains why Vaculík never assumed that his was the last word on the subject of courage, and why, under trying circumstances, he was calling in effect for more reflection and discussion of the topic. And doing so in the manner of a writer who assigns a special role to irony in an age inclined to over-seriousness.
There was certainly plenty of room for contesting Vaculík's unfashionable claims, as many Charter supporters and signatories, including Havel himself, saw quickly. Vaculík reported that 'Remarks on Courage' caused a stir. At first, he told others that 'everyone agreed with my piece and some even congratulated me on it', but his tune changed when the first criticisms reached his ears. Many others followed. Someone said that Vaculík had become demoralized. Others said that his piece relied upon the same base journalistic techniques used by _Rudé právo_ against the Charter. A friend took a copy away to read, fell silent, then one day said: 'Listen, chum, some people have got serious reservations about it and quite rightly, too!' Others reported that the StB was probably monitoring the quarrels — and rubbing their hands together as they waited for the spoils. Vaculík was unrepentant. He made it known that since Chartists had defined themselves as free people by signing the Charter they should act freely — which included freely expressing their views, regardless of whether or not that pleased the secret police. As for the insinuation that he was acting as an unpaid agent of the secret police, that was worthy only of satire. 'Apparently I should not have spoken about heroes,' he said, 'but gone right ahead and said "a handful of self-appointed has-beens", and the sensible, normal people I spoke of are no more than the "honest working people led by the Party". And when I advocate "courageous honest work", what is it but the "honest co-operation" required by the state and the police... ?'
Others were unsatisfied, and some took umbrage. Havel was among the irritated. He wasted no time drafting a reply to Vaculík's leading question: Is anything the Charter has embarked upon worth going to prison for, perhaps for several years or more? The tone of his answers was impatient, and tough. He began by attacking Vaculík's suggestion that so-called dissidents are out to get something by cunning, as if they were potential shoplifters in an Eastern supermarket, rationally weighing up their chances of getting caught, of being punished, or of being left alone.
According to Havel, the luxury of calculating whether being arrested and punished is worth the risk was denied to Chartists. True, they could legitimately minimize such risk by dropping out of the parallel polis, although even then they would not necessarily be rescued from the 'silent and unspectacular degradation' inflicted by the post-totalitarian regime upon 'thousands of anonymous people'. True, the act of signing the Charter was dangerous, inasmuch as it brought the individual into the front line of police activity against all 'enemies' of 'socialism'. From that moment on, there was a marked increase in the chances of that individual being followed, threatened, beaten, imprisoned, or forced into exile with nightmares in their head. But Vaculík's call for individual dissenters to weigh up their acts in terms of their consequences, especially the probability of imprisonment, was utterly misleading, Havel insisted. It amounted to the view that 'nothing is worth it'.
Chartists who chose to remain Chartists indeed put themselves on the path leading toward confrontation with the regime. But as the fate of the Plastic People of the Universe revealed, whether or not they were arrested or punished was not necessarily correlated directly with their intended doings. 'The people whom you call heroes, and suggest are eccentric,' wrote Havel, 'did not go to prison out of a desire to become martyrs but because of the "indecency" of those who go around imprisoning people for writing novels or playing tapes of unofficial songs.' The indecency of the political authorities had something of a random — terroristic — quality to it, Havel went on to argue. 'People who are decent and do not go to jail are lucky.' Consider the different fates of Vaculík's _The Guinea Pigs_ (1970), which landed the author in no immediate trouble, and the award of a handsome prison sentence to Jiří Gruša for writing _The Questionnaire_ (1975). 'You know as well as anyone,' Havel said, 'that the decision as to whether to imprison Gruša or Vaculík has nothing to do with who weighed up the risks most accurately, but is the result of cold and cynical calculation. At one time it might be better tactics to imprison Gruša and attempt in this way to intimidate Vaculík, at another it might be cleverer to imprison Vaculík and try in this way to intimidate Gruša.'
Havel's point was double-barrelled. Under post-totalitarian conditions, the question of whether or not to act with courage as a citizen could and should never be decided by calculations about the risks of imprisonment. Some things, as Jan Patočka had said repeatedly, were worth struggling and suffering for. But more importantly: courage itself is not subject to calculation. If the courage to act against unfreedom is boiled down to mere calculations of risk, then courage ceases to be courage. In effect, Havel charged Vaculík with misrepresenting courage — and, inadvertently, of calling upon citizens to lay down their arms, not to behave heroically, and to stay out of jail. 'To be a hero is to be unsociable,' wrote Havel in unusually sarcastic sentences: 'It is something other than that good honest work which decent people like so much and which keeps society going; it repels and appals people. In any case, heroes are dangerous because they make things worse. It is true that the people up there are well behaved when one treats them decently. Why provoke them with novels, music, or sending books abroad? Such things force these nice people to beat up women and drag our comrades into dark woods and kick them in the stomach. We must respect their prestige and not go around provocatively waving a wad of International Agreements or even insolently making copies of various writings by Černý, Vaculík, Havel, etc'
Havel's mood was defiant. It was as if he had decided that the act of writing about courage needed to display courage, beginning with the elementary point that courage (from the Latin, _cor,_ heart) is always ultimately a matter of a prior felt commitment to embark upon a certain course of action within a field of power. 'We never decided that we would go to jail,' he wrote. 'In fact, we never decided to become dissidents. We have been transformed into them, without quite knowing how, and sometimes we have ended up in prison without precisely knowing how. We simply went ahead and did certain things that we felt we ought to do, and that seemed to us decent to do, nothing more nor less.' Havel in effect insisted that, especially under difficult circumstances — war, repression, unemployment, murder, theft — this feeling of courage is a basic precondition of the individual's ability to act upon the world. Courage is the felt will _not_ to be afraid of acting against considerable odds. Fear is its key enemy. Fear eats up the souls of citizens. It destroys courage by corrupting and weakening those who try to act upon the world, turning them into faint-hearted subjects. Havel grasped the converse of this rule: since fearlessness is not a naturally occurring substance, a personal effort must be made to shake it off. Fearlessness is the special ingredient of courage. It is the will to act gracefully under pressure that develops wherever victims of manipulation, lying and bullying make a personal effort to throw off the habit of letting fear dictate their actions as citizens.
Havel's tactic involved turning Vaculík against Vaculík. The agreed point that nobody wants to go to jail because imprisonment is frightening implied the need of citizens to demonstrate their fearlessness by exercising their courage against those who jail others illegally, against their will. Havel openly acknowledged that he could well understand the flagging enthusiasm of Chartist advocates of human and civil rights. 'Everyone has the right, when they have had enough, to retreat into the background, to stop doing certain things, to take a rest or even emigrate. This is entirely understandable, normal and human, and I would be the last to resent it,' he wrote. But to understand why activists withdraw from the parallel polis, to appreciate why they use their legs instead of courage, must not slide into sordid broadsides against the principle of courage. Figures such as Vaculík actually know better than to do that. 'I do resent it,' he said, sharply, 'when such people do not tell the truth, and on this occasion — don't get angry — you are not telling the truth.'
The sentiments Havel expressed sounded almost classical. After the high Roman fashion, perhaps without knowing it, he was repeating the maxims that the philosophers, playwrights and poets of ancient Greece and Rome had long ago insisted were vital preconditions of citizenship. Under entirely different political circumstances, and using different words, Havel was saying to Vaculík that courage is generosity of the highest order, for the brave are prodigal of the most precious things. Courage is to be preferred to grovelling, love of riches, greed, violence, or selfish calculation. Courage shuns baseness. It avoids stupidity and irrationality. It is unselfish and unheroic. True courage does not require witnesses, even when it leavens actions destined for the public or world stage. Courage never leaves the world untouched. It transforms the individual citizen. Courage scorns death by reaching for the stars. It can even break the grip of bad luck. Courage takes the knocks, buoys the spirits, puts a new face on everything, and even gives physical strength to the body. Courage in distress can stop armies from marching to success. Courage is that virtue which champions the cause of right. It loves mercy. It delights in rescuing others. It encourages others. Courage breeds courage. But courage is also modest. Courage in conflict is half the battle, but only half. It senses the dangers of pig-headedness and knows that victory is never guaranteed, that defeat is a companion of courage. The greatest test of courage is to suffer defeat without giving up. 'Some of us have passed the last two years, others ten years, and still others their whole life in a tough and depressing confrontation with the secret police,' confessed Havel. 'Nobody enjoys it. None of us know how long we can keep it up.' He took it as read that courageous are those who neither seek popular applause nor under pressure desert their cause. The remaining question for him personally was whether or not he could screw his courage to the sticking-place — without buckling under the weight of suspicion, surveillance, and further threats of arrest and imprisonment.
### **The Powerless**
The subject of how best to resist late-socialism preoccupied Havel after the launch of Charter 77. It was at the heart of an essay — 'The Power of the Powerless' _('Moc bezmocn ýdi) —_ that soon became one of those rare pieces of political reflection that outlive their time of birth and come to be regarded as classics. Written shortly after the launch of Charter 77 and just prior to the birth of Solidarnosc in Poland, it was arguably among the most original and compelling pieces of political writing that emerged from central and eastern Europe during the whole of the Communist period.
The essay was the fruit of a 1978 initiative of Czechoslovak and Polish intellectuals committed to the defence of civil rights. In that year, they had prepared a joint seminar on the aims, problems and possibilities of their respective initiatives. Havel had agreed to write a discussion paper. He did so 'quickly' (he later said). The text was then made available to the other contributors, who were asked in turn to respond to the many questions raised by Havel about the potential power of the powerless under 'post-totalitarian' conditions. The whole original plan was flung into confusion by the arrest, in May 1979, of ten members of VONS (the Czechoslovak Committee for the Defence of the Unjustly Prosecuted). The original project had to be fast-forwarded, and it was decided by the authors to publish the Czechoslovak contributions separately as _On Freedom and Power,_ a collection of eleven pieces introduced by Havel's extended essay. Compellingly structured and written in crisp prose, the essay probably ranks as Havel's finest literary intervention in the world of politics. It is haunted by the general feeling (shared by Milan Kundera) that central-eastern Europe was under siege, that its whole identity was being strangled slowly to death — and, more immediately, by the pain caused by the recent death of his friend Jan Patočka, to whose memory it is dedicated.
The immediate aim of 'The Power of the Powerless' was to explain the significance of Charter 77 to its (potential) supporters within Czechoslovakia, and to give courage to the opponents of late-socialism elsewhere in the Soviet block. The essay works with a fairly standard conception of power as the ability of (certain) humans to exercise their will over and against others, even despite their resistance, and it reveals no broader concern with surveying the kaleidoscope of previous conflicting definitions of power. Yet the striking feature of Havel's treatment of power is its lack of deference towards the powerful. It was uninterested in copying previous manuals of statecraft (like Machiavelli's _Il principe)_ written primarily for rulers. It was also not a grammar of obedience written for subjects, like Thomas Hobbes's _De Cive._ And — perhaps more radical still — Havel's attitude to power and powerlessness also rejected the view that the subject of power is a lost cause, the view buried in the well-known contemporary joke about the two Czechs travelling by train from Brno to Prague, one of whom groans constantly, apparently in pain, until his companion loses patience, and erupts: 'Quiet! Can't you talk about anything else but politics?!' 'The Power of the Powerless' questions the cynicism of those whose encounter with the absurd unrealities of life leads them to abjure action, stand aside from life, and drift with the tide. Havel also questions the anti-political attitude of the wry-faced cynic, who curses that all rulers are bastards and concludes that the downtrodden should either smile knowingly into their beards, or soldier on, turn the other cheek, or cheat and lie and steal their way through life, or entertain or drink themselves into oblivion. 'The Power of the Powerless' is certainly not attracted by institutional politics, but its core idea is much more original than the standard middle-European version of anti-politics. The essay could even be called subversive. 'Men at some time are masters of their fates,' Cassius tells Brutus in Shakespeare's _Julius Caesar._ 'The fault... is not in our stars, But in ourselves, that we are underlings.' The idea is repeated in Havel's essay. It proposes that under any circumstances the downtrodden always contain _within themselves_ the power to remedy their own powerlessness, and that, consequently, they are the ultimate cause of their own continuing subordination.
The continuing intolerance of opposition, lingering insecurity, and especially the subordination produced by the late-socialist regime (Havel called it 'the post-totalitarian system') convinced him that the system was too ossified to be reformed from within — as Dubček and his supporters had tried to do in 1968 — and that there was consequently a need for more imaginative and radical ways of defeating it. Here the idea of _the power of the powerless_ served him well. The oxymoron was not an exercise in clever writing — not a play on words by a playwright teasing an audience. It was rather driven by the conviction that all attempts to resist democratically the pressures of late-socialism have their essential beginnings in the extra-state areas of everyday life. The centre of gravity of potential resistance is what he called 'the existential dimension of the world', or what Edmund Husserl, the most famous Moravian philosopher of the First Republic, called the _Lebenswelt._ Here a different life — what Havel called 'living in the truth' and would later call 'anti-political politics' — can be lived, and the self-sustaining aspects of the system, its presence within each individual, can be shaken off. In effect, Havel's call for dissent involved turning the system's basic logic of subordination against itself. 'This system serves people only to the extent necessary to ensure that people will serve it,' he wrote. 'Anything beyond this, that is to say, anything which leads people to overstep their predetermined roles is regarded by the system as an attack upon itself. And in this respect it is correct: every instance of such transgression is a genuine denial of the system.' In other words: individuals need to understand that so long as they act as if they accept the system then they will continue to confirm the system. They will continue to make the system, to _be_ the system — until the moment that they decide enough is enough.
Havel's thesis necessarily involved something of a Copernican Revolution in the way that power is conceived. It upended the presumption that people who command states and therefore have at their disposal the accoutrements of power — spies, weapons, bureaucrats, propagandists, even the means of production — have things all their own way, at least if they play their cards right. Havel was adamant that those who speak of the sovereign power of the state should not have the last word in politics. Sovereignty may be an appealing word. Those who present themselves as 'realists' may sound convincing when they insist that the politically wise are those who bear in mind the constant possibility of deception, cunning and violent opposition from their opponents, that armed conflict against enemies is the ultimate political event. Those who speak of the need for sovereignty also seem to have tradition on their side, beginning with Jean Bodin's classic insistence that those who rule through the state are required, especially in emergencies and periods of disorder, to make _final_ decisions about what is to be done, including what is to be done against the enemies of the state. It seems plain common sense that those who rule politically enjoy _the jus belli —_ the unlimited right to define the domestic or foreign enemy, as well as to fight and destroy that enemy with all the available resources of state power. What could be more obviously true than the proposition that political power confers upon its holders an awful prerogative — the unrestricted power to wage war and, hence, to rob others of their lives?
Havel rejected the originally monarchic doctrine of sovereign state power. Although he didn't quite put it this way, he was in effect saying that under certain circumstances _the powerful are powerless._ Power is certainly the process of affecting the actions of others with the help of (threatened) severe punishment for non-conformity to the wishes of the powerful. The powerful may even rule others by means of 'non-decision-making', that is, by effectively limiting the scope of decisions and by preventing certain felt grievances from developing into full-fledged disputes that call for decisions. But there are times when the powerful are like the little Dutch boy with his finger in the dyke. The more real power they seem to enjoy, the less they can afford to throw it around, to exercise it over others.
The powerlessness of the powerful is traceable mainly to five related factors, or so Havel argued. To begin with, he emphasized the fundamental inability of rulers to control the micro-movements of their subjects. In every nook and cranny of life — on the job, in the apartment, the kindergarten or school or university, in the pub or restaurant, in the fields of newspaper production, radio and television programming — the rulers of late-socialism may well reduce individuals 'to little more than tiny cogs in an enormous mechanism'. But the rulers themselves tend to be pudding-heads, stupid men with conservative instincts. Their minions are no better; working within and for a system that disallows individualism, they tend to be 'faceless people, puppets', mere 'uniformed flunkeys of the rituals and routines of power'. Those who govern at various levels are not able to free themselves from the clutches of the unthinking obsequiousness of the system they direct, which has the effect of dulling their ability to govern the ship of state intelligently, including their ability to monitor, let alone motivate its subjects. Power over others breeds blindness and loopholes, hence, the possibility of crawling through them.
Secondly, Havel argued, this possibility is enhanced by the perverse tendency of the whole power structure to depend upon ideological rituals that are ever less credible, exactly because they are untested by public discussion and controversy. In systems that enjoy public competitions for power and office, there is naturally public monitoring of the ways in which power tries to legitimate itself before others. The tendency of power to wrap itself in alibis and false claims — declared by early modern thinkers like Niccolò Machiavelli and Thomas Hobbes as an active ingredient of good government — is potentially stoppable. Under late-socialist conditions, by contrast, there is nothing to prevent ideology from becoming ever more removed from the reality of circumstances. So ideology becomes 'a world of appearances, a mere ritual, a formalized language deprived of semantic contact with reality'. Most people take no notice of it, but they know it is there, always in the background, sometimes in the foreground, at all times serving as a reminder of where they are living and what is expected of them. This domination of ritual not only has the paradoxical effect of tempting power to believe its own rituals and thereby serve the ruling ideology, as if the ritualized ideology were sacrosanct, even at the highest levels of state. The _'diktat_ of the empty phrase' also comes to be seen by the ruled as empty, as unbelievable, as a mere façade of the all-embracing system of power. Ideological ritual is sensed to be a crude substitute for public debate and controversies among parties and politicians, which are officially banned.
Here a third consideration arises: the possibility that some will call the ideology a lie and declare the emperor naked is nurtured by the _ontological_ fact that 'the everyday, thankless, and never-ending struggle of human beings to live more freely, truthfully, and in quiet dignity' is ultimately not fully repressible. At least some individuals will resist, if only because their very identity depends upon it. Having become fed up with stagnation, having grown tired of years of waiting, of apathy and scepticism, they feel that they cannot live otherwise. They know (as Havel's friend Patočka liked to say) that the most interesting thing about responsibility is that individuals carry it around with them everywhere they go. Those who strive to live truthfully therefore simply refuse any longer to be watched by the police, to be humiliated by their superiors, or to put up with a constant feeling of insecurity before the law. They know that the possibility of freedom depends upon shaking off the presence of the one-party system within themselves by altering the relations of power 'closest' to them. They have grasped, as Havel put it, that 'life, in its essence, moves towards plurality, diversity, independent self-constitution, and self-organization, in short, towards the fulfilment of its own freedom'.
Fourth, the ontological check upon totalitarian power is nurtured by the fact that, among those who think about their situation, a felt need develops for serious reflection upon the nature and limits of the system. It is as if misery nips at the heels of imagination, forcing the mind towards concern with the human condition. They feel compelled to examine the deeper coherences of their situation, to consider how it came to assume the form that it has, and whether there are any ways of preventing themselves and their world from wasting away to nothing, or, like Gadarene swine, rushing headlong over a cliff into the sea. 'There are times,' Havel wrote, 'when we must sink to the bottom of our misery to understand truth, just as we must descend to the bottom of a well to see the stars in broad daylight.'
Finally, these individuals who 'live in the truth' reject the innocent fiction that power is a thing to be grasped or abolished. It is customary to say that this or that person or group or institution 'has power', which implies that power, like wealth, is a possession, which enables its owner to dictate some future goal. But, according to Havel, power is relational, not possessive or substantive. Within any regime, power relations are not reducible to the instruments of power. And certainly within the late-socialist system, power is never owned or concentrated in a single space, such as the leading echelons of the Communist Party or the ruling class. It is never imposed upon one group by another and never divided between those who have power and those who are powerless. Within the system, every individual is entrapped within a dense network of the state's governing instruments — a 'complex machinery of units, hierarchies, transmission belts, and indirect instruments of manipulation' — themselves legitimated by a flexible but comprehensive ideology, a 'secularized religion', that offers a ready answer to any question whatsoever. It is as if each individual is trapped within a tomb within a tomb within a tomb, and it is therefore necessary to see, argued Havel, that power relations within the late-socialist system are best described as a labyrinth of influence, repression, fear and self-censorship which swallows up everyone within it, at the very least by rendering them silent, stultified and marked by some undesirable prejudices of the powerful. The lines of power permeate the entire system; in consequence, every person is both its victim and a supporter — and potential opponent.
Since the lines of organized power within the system pass like low-current electricity through all its subjects, the latter can defend themselves against it only by being different in the most radical sense, that is, by insulating themselves against the system and preventing it from ruining their own personal lives. Those who choose to live in the truth effect something of an 'existential revolution'. They agree that 'there are some things worth suffering for', the words used by Professor Patočka shortly before his death, and they are prepared to say aloud and do what many others only think in silence. Their actions can take many forms — an open letter written by intellectuals, workers' refusal to work, the holding of a rock concert, a student demonstration, a hard-hitting public speech, the decision to go on a hunger strike — but in every case their actions rely initially on the courage and determination of existential choices made by thinking, acting individuals. Their effective power cannot be measured in terms of numbers of disciples or loyal voters, infantry divisions, or sizeable crowds of demonstrators. Living in the truth is a risky business. Its consequences for the individual are wholly unclear, and yet although it is something of an all-or-nothing gamble it can be surprisingly effective — like a bacterial weapon, said Havel, it can be used by 'a single civilian to disarm an entire division'. It is true that divisions of well-armed troops and other political authorities can succeed in crushing those who live truthfully, like insects undeserving of life. They can be dragged from their beds in the middle of the night, beaten silly, judged insane and carted off to institutions or treated as professional malcontents and labelled 'counter-revolutionaries', 'backsliders', and 'dissidents'. They can be murdered, even. But such tactics (Havel cited the case of the hunting and hounding of Solzhenitsyn out of Russia) prove the point: the powerless have within themselves the power to obstruct normality, to embarrass the authorities, to point to the possibility of living life differently — according to values like trust, openness, responsibility, solidarity, love.
Living in the truth operates initially and primarily at the existential level. Although it can manifest itself in publicly visible collective actions — a street demonstration or citizens' association, for instance — it is essentially local, invisible, anti-political. It is uninterested, say, in forming and leading a vanguard, or writing a new programme for a political party or working for the replacement of party-appointed officials by a government or head of state elected once every few years. The strategy and goal of living in the truth tries to be acephalous. It is concerned not to define itself too quickly into rigid and highly visible institutional forms, which can be spotted, 'decapitated', and eliminated easily by the political authorities, who are specialists in the art of eliminating competing political organizations. Under the extremely adverse conditions of late-socialism, living in the truth minimizes the likelihood of a crushing, total defeat and, conversely, it maximizes the chances of 'victories in defeat'. Living in the truth is for this reason also most ethically effective when it keeps its distance from formal politics. The powerless must understand that '[a]ny eventual political articulation of the movements that grow out of this "pre-political" hinterland is secondary'. They must grasp that a better system will not ensure a better life, that the opposite is true: 'Only by creating a better life can a better system be developed.' Living in the truth requires the cultivation of mechanisms of individuation, self-protection and co-operation in areas 'underneath' and beyond the reach of the state — within the household, among friends, at the office, within the parallel economy and sphere of unofficial culture, in citizens' initiatives like Charter 77. In a phrase, the empowerment of the powerless first and foremost requires individuals to build open, flexible structures of resistance that run parallel to and underneath the late-socialist state. This is best done from below, by means of what Tomáš Masaryk called small-scale initiatives _(drobná práce)_. But such initiatives can thrive only if individuals recognize that the system has frustrated and flung Masaryk's original principle into a profound crisis, that it is now harder but therefore more imperative to take a stand and to renew daily the existential commitment to break the rules of the game, to disrupt the game as such, to expose it relentlessly as a mere game.
### **The Victim**
It is easy to pick holes in Havel's arguments, for instance in his Panglossian confidence in the probable harmony among differing interpretations of what it means 'to live in the truth'. Havel dodged not only differences of political opinion, declaring the need to 'shed the burden of traditional political categories and habits', but also difficult questions about such tensions within the human condition as trust and betrayal, love and suspicion, faith and despair, creativity and destruction. Aside from moral appeals and exemplary actions, Havel's essay also offered little consolation to individuals who choose to live in the truth, and who suffer injuries when the sky falls down on them, as often it does. Havel simply _supposed_ that, despite everything, individuals 'by nature' want to live in the truth, a supposition that mistakes ontology for history. The point is that we feel ourselves to be responsible individuals who want to keep our spines straight and live in dignity in the world thanks to the survival of tradition, for instance, because we have inherited such a disposition from Christian-influenced traditions, as his friend Jan Patočka was fond of pointing out. That point begs a series of hard questions about the problem of deaf ears and hostile minds and hearts. Havel was aware, of course, that the origins of our capacity for action in the world as individuals are necessarily shrouded in some mystery: if the existential roots of individuality were graspable, then the tender plant of individuality would die. But it has to be said that, although in particular contexts at particular points in time some people are inclined to live truthfully, we are not 'by nature' lovers of truthful living. 'The Power of the Powerless' thus failed to propose a way of breaking the hypnotic effects of a system of power that, as he admits in one passage, offers to people who feel lost and humiliated 'an immediately available home: all one has to do is accept it, and suddenly everything becomes clear once more, life takes on new meaning, and all mysteries, unanswered questions, anxiety, and loneliness vanish'.
The same point about the limits of Havel's ontological account of living in the truth can be put in a different way and with different implications. Whether intended or not, Havel's belief in the ontological principle of living in the truth encouraged the abandonment of politics — the often messy and always complicated activity of collectively encouraging individuals 'to live in the truth' and thereby to decide who gets what, when and how. Havel's account _supposed_ that the good society is one that recognizes and gives expression to its most secure foundation, the individual living in truth. Expressed differently again, Havel's defence of living in the truth rests upon a species of what his Hungarian colleague György Konrád later called anti-politics. It _supposed_ that politics is a type of impersonal and unprincipled activity that reaches its zenith in the figure of the grey-suited Party apparatchik, generals with tinted shades, leather-jacketed secret policemen, military-uniformed bureaucrats, and other cogs in the late-socialist state; that politics is shrewdness, manipulation, unfreedom, the struggle of some to exercise power over others; that politics is inherently absolutist, in that its field of operation, human beings living together in complex societies, is infinitely deep and wide, and that therefore the hunger of those politicians who politically seduce, manipulate and subsume others is never fully satisfiable.
Havel's essay admittedly contained a few passing references to the importance of such procedural arrangements as the rule of law and the necessity of defending human and civil rights, as specified in the constitutions of particular states, the Universal Declaration of Human Rights, the International Covenant on Human Rights, and the Concluding Act of the Helsinki Agreement. But nowhere did the text mention politics as a form of collectively based speech and interaction orientated to the attainment of the good life (as in the Aristotelian tradition). The text also eschewed talk of parliaments, armies, police forces, the civil service, local government, as if these institutions were somehow unnecessary or secondary or optional or ultimately dispensable procedures, or what Havel called 'dry' mechanisms, since they cramp the truthfully-living individual. Talk of synergies between individuals and organizations should be suspected, he implied. There is always a zero-sum power relationship between subjects who think and act in the truth and their institutional environment. Havel's statement about the primacy of the individual's existence over the institutional frameworks within which they live made this point clear. 'It is of great importance,' he wrote, 'that the main thing — the everyday, thankless, and never-ending struggle of human beings to live more freely, truthfully, and in quiet dignity — never impose any limits on itself, never be halfhearted, inconsistent, never trap itself in political tactics, speculating on the outcome of its actions or entertaining fantasies about the future. The purity of this struggle,' he concluded, 'is the best guarantee of optimum results'.
The limitations of an ontology of individualism, and especially its strange other-worldly unconcern with the institutional _preconditions_ of liberty, would later become evident in the political battles sparked by Havel's penchant for acting as a prima donna, surrounding himself with hand-picked appointees, and his maverick appeals to 'the citizens' over the heads of parliament and the courts of law. 'The Power of the Powerless' was equally unconcerned with the philosophical limits of individualism. Indeed, it concealed these limits through literary skill, that is, by attempting to divine _individual_ readers' sympathy through the sheer rhetorical force of his text, for instance in its bold appeal to shed the burden of all inherited political thought and political habits, or in its comparison of living for the truth with the act of surfacing from darkness into the light of day. Its provocative summary of the significance of Charter 77 was also exemplary of its rhetorical force: 'The confrontation between a thousand Chartists and the post-totalitarian system,' wrote Havel, 'would appear to be politically hopeless. This is true, of course, if we look at it through the traditional lens of the open political system, in which, quite naturally, every political force is measured chiefly in terms of the positions it holds on the level of real power. Given that perspective, a mini-party like the Charter would certainly not stand a chance. If, however, this confrontation is seen against the background of what we know about power in the post-totalitarian system, it appears in a fundamentally different light. For the time being, it is impossible to say with any precision what impact the appearance of Charter 77, its existence and its work has had in the hidden sphere, and how the Charter's attempt to rekindle civic self-awareness and confidence is regarded there. Whether, when, and how this investment will eventually produce dividends in the form of specific political changes is even less possible to predict. But that, of course, is all part of living within the truth. As an existential solution, it takes individuals back to the solid ground of their own identity; as politics, it throws them into a game of chance where the stakes are all or nothing.'
Powerful rhetoric of this kind was eventually to move millions of people to clap and cheer Havel. Even at the time it seemed to work small wonders. Retyped by loyal fingers, it was read to shreds by hundreds, perhaps thousands who found the essay brilliantly persuasive. There were some who reacted with hostility — the little-known Charter 77 group around Emanuel Mandler fiercely criticized Havel's unrealistic defence of a political theory and strategy that set itself up as a 'moral judge' of society, served in practice to deepen the division between 'normal' citizens and 'dissidents', and thereby exposed the opponents of the regime to state repression. The Czech dissident scholar Václav Černý reportedly also bitterly attacked the essay as the 'horribly superficial, shallow' work of a figure who was 'pathologically conceited, pathologically ambitious'. Yet many more Czechs and Slovaks found the essay enlightening. Even dough-faced Party bureaucrats read and discussed its themes. Foreign translations of the essay also sometimes caused a minor sensation, as in Italy, where the tiny Bologna publisher CSEO sold more than 30,000 copies in quick time. The essay also earned handsome praise wherever it appeared in the Soviet block. The Polish reaction was not atypical. The Polish writer Stanislaw Barańczak recalled how the underground translation of the essay produced 'broad-based popularity and unanimous respect' for Havel within the ranks of the opposition during the late 1970s. The remark of the Polish Solidarity leader Zbigniew Bujak also captured something of the way the essay engendered the joy of 'living in the truth' among its first, otherwise deflated readers within the Soviet block. 'This essay reached us in the Ursus factory in 1979 at a point when we felt we were at the end of the road,' said Bujak: 'Inspired by KOR [the Polish Workers' Defence Committee], we had been speaking on the shop floor, talking to people, participating in public meetings, trying to speak the truth about the factory, the country, and politics. There came a moment when people thought we were crazy. Why were we doing this? Why were we taking such risks? Not seeing any immediate and tangible results, we began to doubt the purposefulness of what we were doing. Shouldn't we be coming up with other methods, other ways?' Bujak continued: 'Then came the essay by Havel. Reading it gave us the theoretical underpinnings for our activity. It maintained our spirits; we did not give up, and a year later — in August 1980 — it became clear that the party apparatus and the factory management were afraid of us. We mattered.' Bujak added: 'When I look at the victories of Solidarity, and of Charter 77, I see in them an astonishing fulfilment of the prophecies and knowledge contained in Havel's essay.'
It could even be said that the act of writing the essay was an exemplary case of the civil resistance to power — a small-scale initiative — that it advocated. Despite everything that was to follow this act of resistance, two major things were permanently achieved by 'The Power of the Powerless'. To begin with, Havel's rough treatment at the hands of the authorities illustrated to everybody with eyes that could see that the regime's propensity to violence highlighted the need to find peaceful alternatives — just as the essay had proposed. 'The Power of the Powerless' rejected Sorelian-type myths of brave and heroic violence. Havel admitted that there are times, during the build-up to the Second World War, for instance, when the use of violence must be regarded as a necessary evil. In these 'extreme situations' violence must sometimes be met with violence, for otherwise remaining passive effectively works against decency and in favour of the rule of violence. But the trouble with violence, he argued, is that it is the extreme case of the instrumentalization of concrete human beings, often for some abstract, spurious and ill-defined better future. Violence is the antithesis of living in the truth. It follows that 'a future secured by violence might actually be worse than what exists now'. Havel insisted that those who live in truth 'do not shy away from the idea of violent political overthrow because the idea seems too radical, but on the contrary, because it does not seem radical enough'.
The non-violent sentiment of 'The Power of the Powerless' resonated with the fact that the heavily armed late-socialist regime ensured that surveillance, military parades, prison and fears of random violence were constant everyday companions of the whole population, who understandably felt a deep antipathy towards the use of violence as a tactic of resistance. In opposition to the traditional left and right, the essay associated bravery not with heroic acts of violence, such as terrorism, assassinations or kidnappings, against perceived enemies. Bravery is rather seen as the civilized patience of citizens who seek to live decently in an indecent regime and, therefore, remain unmoved by acts of violence directed against them. Havel supposed an inner connection between violence and state-centred politics, and he therefore (implicitly) rejected Marx's well-known view that Violence is the midwife of every society pregnant with a new one'. According to Havel, violence is the enemy of all societies, old and new. Compared with the (calculated) impatience of revolutionaries and revolutionary politics, Havel's account of power was imbued with a fundamentally different sense of time. It rejected fantasies of apocalyptic revolution because it supposed that 'living in the truth' requires citizens to acquire the art of patience. It further supposed that acts of living in the truth could not succeed in days, weeks or months; that there is no such thing as total defeat; and that, if necessary, citizens must wait a very long time and be prepared to endure harsh setbacks. In short, Havel envisaged a peaceful abolition of the late-socialist system by means of a _slow fermentation_ of opposition underneath, and in opposition to, the edifice of state power.
The proposed theory of living in the truth was more than simply an attack upon late-socialism. From under the rubble of that system, it was something of a parable about the dangers of all forms of concentrated power. It therefore necessarily involved a challenge to the whole of modern political thought's preoccupation with the sovereign power of the territorial state. Without saying so in exactly these words, Havel's essay proposed lopping off the head of sovereign power. It breathed new life into the maxim that the struggle against stupidity is the only human struggle that is always in vain, but can never be relinquished. More than that — this was its second major achievement — the essay proposed a new practical solution to the age-old problem of finding a remedy for the hubris of political power.
The problem of _hybris_ was first formulated by classical Greek thinkers and historians like Herodotus and Thucydides, for whom the ambitious desire to have more than one's share of power is a necessary feature of political life and one that inevitably produces disastrous effects. From Thucydides and others, there is no good news for us. The Greek analysts of power warned that power breeds overconfidence and imprudence. _Hybris_ is the progeny of high position, as Euripedes explained, in a famous passage in the _Suppliant Women,_ where it is said that the conqueror 'is like a poor man who has just become rich: he commits _hybris,_ and his _hybris_ causes him to be ruined in his turn'. _Hybris,_ we are told, is also fed by the need of the powerful to shield themselves against the aggression of the powerless, whose oppression breeds fear. Power is sometimes despised by those who don't have it and those who exercise command over others become the object of fear and hostility or even hatred, which is why the powerful tend to act imprudently. They are prone to paranoia, plotting and flattery of their subjects, which prompted Pericles to say that he feared before everything else the city of Athens' arrogant mistakes, such as refusing the offer of peace during the time of Pylos, acting cruelly against other cities, and initiating new conquests, especially in Sicily. Finally, our Greek ancestors warned, _hybris_ breeds _hybris._ Power leads to increases in power because powerful rulers have to act that way. As things plummet out of control, the path of prudence, the acquired skill of judging 'what is best', as the Greeks loved to say, gets ever narrower... and it becomes narrower still, as Isocrates, Demosthenes and Pericles in his Epitaphios all emphasized, because of the decline of civic morality among both rulers and ruled, the final effect of which is discord, _stasis._
The originally Greek idea that _hybris_ and its dangerous effect are rooted in the very nature of power over others survived into modern times — think of the various accounts of the rise and fall of the Roman empire by writers such as Polybius, Livy, Sallust, Florus, Montesquieu and Gibbon. The theme of _hybris_ left a bad taste in the mouths of all those who knew that modern forms of state power were prone to corruption. Unfortunately, the analysts of _hybris_ gave a Greek gift to the modern world, in that they provided no permanent remedy for the dangers of _hybris,_ except for the thought that it is punishable by the gods, who so hate the wish to have more than a fair share of power that they are prone to turn against mortals, as Herodotus reports Artabanus to have warned Xerxes before he finally made the decision to attack Greece: 'You see the biggest creatures, how God crushes them with his thunder, and doesn't allow them to make a show of their great size. But the small ones don't trouble him. You see how he always directs his blows towards the highest houses and the highest trees. God indeed abases anything that grows above the rest... For God doesn't allow high-mindedness in others but himself.'
Except in millenarian circles, warnings about divine intervention against the powerful ring hollow in our times, and so it can be said, from the perspective of the ancients, that we moderns have been bequeathed what might be described as an _aporia,_ an extremely difficult perennial problem that seems virtually insoluble. The problem is this: given the tendency in the world of politics towards _hybris,_ how can its disastrous effects be overcome? How, in other words, can citizens be liberated from the permanent dangers of corruption and the infernal rise and fall of states? Can human beings find other ways of organizing power that would release them from _hybris?_ Or must we reckon with the ultimate impossibility of containing _hybris?_ Is life nothing more an endless struggle for power that comes to rest only at the point of death? Or can only divine intervention now rescue us from the trials and tribulations caused by our own hubris?
In 'The Power of the Powerless', interestingly, Havel's response to these questions cross-referred to the German philosopher and critic, Martin Heidegger. In a famous interview with _Der Spiegel_ published only after his death, Heidegger discussed the problem of whether any political system, including democracy, can reverse the hubris of our technological age. The essence of modern technology is its imprisonment of Man within a Frame-Work _(Ge-stell)_ that puts men and women in their place, assigns them tasks, and calls them to order, all the while crushing their existent individualities by means of abstractions, thus rendering them powerless. 'I don't know whether you're frightened,' Heidegger remarked to his interviewers. 'I am when I see TV transmissions of the earth from the moon. We don't need an atom bomb. Man has already been uprooted from the earth. What's left are purely technical relations. Where man lives today is no longer an earth.'
So what is to be done? Is there any solution to this problematic hubris of modern times? Heidegger's reply is as striking as it is unsatisfactory. 'Only a God can save us now,' he says, using words that Havel's 'The Power of the Powerless' repeats, with a twist. Heidegger's polemics against the modern world led him to urge others to step away from the 'noise' of the world, to withdraw so as to allow individuals in their concrete being-there to listen thoughtfully to the call of Being. Concrete individuals should actively strive to be passive, that is, to engage in the contemplation of the present, to prepare expectations or, as Heidegger puts it, 'to prepare to be prepared for the manifestation of God, or for the absence of God as things go downhill all the way'.
In broad outline, Havel accepted Heidegger's diagnosis of the crisis of modern technological society. Late-socialism is seen by Havel to be a thoroughly _modern_ regime which, contrary to being a regression or mutant, is in fact both 'an inflated caricature of modern life in general' and the possible shape of things to come. Late-socialism was the most complete and devilish expression so far of modern attempts to transform citizens into subjects who are compelled to act as if they were mere casts of extras in a fully politicized stage performance directed from above. The Soviet-type system of late-socialism is 'a kind of warning to the West, revealing its own latent tendencies'. Havel also acknowledged Heidegger's observation that there appears to be no way out of the powerlessness produced by modern regimes of power. We seem to be condemned to look on helplessly at the coldly functioning organizations that engulf us by tearing us away from both our natural habitats and fellow human beings. 'We have no idea and no faith, and even less do we have a political conception to help us bring things back under human control.' That leaves only one possible earthly weapon against hubris. Heidegger missed it: the cultivation, from below and against all odds, of institutions that can develop 'the independent life of society' and thereby empower the powerless, even preventing them from ever becoming new masters of others. Tentatively, and in clumsy language, Havel called this new and desperate possibility 'social self-organization'. With greater confidence and precision — and political implications of the most dramatic type — it would soon be called _civil society._
### **Prison**
The StB came for him at five o'clock in the morning of 29 May 1979. The swoop was quick and quiet. He was bundled, half-asleep in a state of controlled panic, into the back of a van, handcuffed, clutching only his favourite bundle of belongings — an emergency kit containing a toothbrush, razor, nail clippers, deodorant, brush and comb, a few sticking plasters. As the sun rose he was unloaded into the sable corridors of Ruzyně prison and, along with ten other members of the Committee to Defend the Unjustly Prosecuted (VONS), charged under Article 98 of the Criminal Code for 'subversion', a crime against the state that carried a penalty of up to ten years' imprisonment.
So began a desperate personal experiment in the related arts of improving his physical health, steadying his nerves, and breathing meaning into his own existence. Havel initially spoke of it as a struggle for 'self-consolidation'. He likened his imprisonment, minus the drama and deep religiosity, to the inner commitment and outward struggle of Dostoevsky's heroes, as they go off to prison, to be themselves in a better way. Havel refused easy solutions, bolting for the emergency exits of false confessions or emigration, for instance, and he was confident that his refusal would give him the permanent strength of knowing that he had not shied away from the basic task of self-improvement. It was as if he wanted to follow the script outlined in 'The Power of the Powerless', as his first letter to Olga from Ruzyně prison on 4 June of the year 1979 records: 'It appears the astrologers were right when they predicted prison for me again this year and when they said the summer would be a hot one', he wrote. 'As a matter of fact, it's stifling hot here, like being in a perpetual sauna. I feel sorry about the many complications my new stint in jail will probably cause you... I don't know, of course, how long this trip will last; I'm not harbouring any illusions, and in fact I hardly think about it at all.' He concluded: 'Prison, of course, is a terrible bore; it's no fun staring at the walls day after day, but with each stay I find it easier to bear because a lot that I once found disturbing no longer surprises or upsets me.'
In fact, Havel's time in prison proved a good deal more personally threatening than the phrases 'living in the truth' or 'self-consolidation' implied. His stint in prison is better described as a power struggle of the most primordial kind: a struggle against the inevitability of powerlessness. He was fated to suffer a profound crisis of identity — the same profound crisis of identity represented within virtually every one of his plays — in which his own sense of self began to crumble, leaving in its trail the rubble of everything that endows human existence with a meaningful sense of order, continuity and change. Under prison conditions that resembled a 'pure' or 'concentrated' form of late-socialism, he was forced to battle with the realization of just how fragile and contingent and destructible the human personality is.
The human personality, Havel had always argued, has no guaranteed, fixed essence. It is 'a large set of possibilities, potentials, perspectives, relationships, demands, opinions and anticipated responses; it is something open, always actual'. The personality resembles an unfinished play but, like all plays, its attempted or actual completion and production may end in failure. Havel, drawing on the language of existentialism, called this 'nothingness', a condition in which the human personality is virtually dissolved into its surroundings. 'If nothingness wins out,' he wrote, 'man surrenders to apathy, and faith and meaning exist only as a backdrop against which others become aware of his fall.' Prison threatened him with such decline and decay into 'nothingness' — into a 170-pound lump of organic matter — and posed to him the only other realistic alternative: the struggle, against great odds, to establish (here Havel drew on Patočka) a self capable of acting responsibly in the world.
Prison hammered into Havel's hide the painful realization that responsibility is the key to human identity. 'The secret of man is the secret of his responsibility,' he concluded. By this he meant that individuals' faith in their own power to live in the world is constitutive of their capacity to thrive in the world. Conversely, the disintegration of the human personality always entails the destruction of the power of the individual to carry on in the world. Responsibility is the centre of gravity of the self. It has a relational quality, in that it requires the existence of a person who is responsible and someone or something for whom or for which that person is responsible. Responsibility orientates the self within an infinitely wider and longer landscape. It endows that self with the power to confer meaning on its relations with the wider world. The substance of the meaning so conferred can be and usually is multiplicitous. Some interpret responsibility in terms of love and sacrifice; others see it as a matter of instinctual self-preservation; still others consider responsibility as a relationship to the sacred; some treat it as a phantom from past times when people still feared gods. In each case, however, responsibility ultimately makes possible the creative 'separation' of the self from the world by enabling the self to become an independently thinking, judging, acting being. That means that the struggle to establish and cultivate responsibility is a life-and-death struggle to survive as a human being. Life is constantly threatened by nothingness. Responsibility is thus the prize in the contest between the individual and the world; the power of individuals to survive in the world, their ability to fend off nothingness, depends upon their skilled cultivation of their capacity for responsibility.
The punishing prison conditions tested Havel's capacity for responsibility. 'I would say that responsibility for oneself is a knife we use to carve out our own inimitable features in the panorama of Being,' he remarked eighteen months into his sentence.The tone of philosophical defiance built into the remark was double-edged. It testified to his rebelliousness in the face of nihilism, the stubbornness of his personal efforts to stand out and stand up to the crushing pressure of a prison world wrapped in barbed wire. But the remark also revealed his personal desperation in the face of a system that aimed to harass, manipulate, repress, and de-individualize his daily life and nightly dreams, even to offer the prospect of death.
Pushed to the edge of the world, Havel's daily life was reduced to frustrated basic wants, half-satisfied needs, yearnings, compensatory reflections, weird happenings. Like being shaved bald and noticing for the first time the contrast between his smooth skull and wrinkled face. Or coming to terms with the lack of light by day, the lack of darkness at night. Living in the same space with people who swiped his cigarette butts. Getting used to a wide assortment of pollyannas, perverts, miserable and desperate men, some of them scoundrels. Adjusting to shortages (or the outright banning) of items he craved most: Stuyvesant cigarettes, powdered juice, lemons, plums, apples, perfumed Kleenex, toothpicks, cheese slices, instant cocoa, strawberry jam, tea, cigars. Intense homesickness for the permitted minor pleasures of late-socialism: sleeping in his own bed wearing his own pyjamas; drinking strong coffee in the morning; strolling through Malá Strana; sweating in the sauna; eating crab cocktail, steak, and cake topped with whipped cream in a restaurant; watching good movies; gathering with artist friends in bars, studios, and galleries; lying in the sun on the lawn; barbecuing chicken at Hrádeček; making the tartar sauce to go with it while sipping white wine and listening to Pink Floyd and the Stones.
Feeling with increasing intensity that prison is an institution designed to rob inmates of free time. Grasping a line in Shakespeare's _Richard II:_ 'Grief makes one hour ten.' Attempting to study English. Hoping to learn German. Being victimized by his constant compulsion to reconsider things. Witnessing and hearing buggery. Reading a queer variety of (sometimes bad) books, despite the enveloping hubbub: _Aurelien_ by Aragon; a crime novel by Ed McBain; _The Pickwick Papers;_ Max Brod's biography of Kafka; Hemingway's _To Have and Have Not;_ biographies of Muhammad, Toulouse-Lautrec, and Karl Hermann Frank; _The Triumph_ (a look from behind the scenes at American foreign policy); a little book on the Watergate scandal by Václav Borovička; _Treasure Island; The Financier_ by Dreiser; a novel about capital punishment by the Czech author Jaroslav Maria, _The Sword and the Scales;_ Ratzinger's _Introduction to Christianity;_ Malaparte's _Kaput;_ Stendhal's _Lucien Leuwen;_ Saul Bellow's _Herzog;_ an autobiographical account by Byrd of living alone for six months at the South Pole. Rescued by the cultivated and clever language of Musil. Pondering _The Stranger_ by Camus. Battling with Heidegger's _Sein und Zeit._ Strenuous efforts to counteract hopelessness by doing yoga. Poring over _Rudé právo_ the whole day, in effect performing textual analyses by distinguishing what is said from what is not said.
Yearning to hear things once more called by their proper names. Worrying about growing into a humourless old man with no sense of irony. Playing chess with a partner too good for him, and not enjoying it. Fraught attempts to imagine new plays and to analyse the most incredible events and characters of his dreams. Experiencing everything more intensely — and paying more intensely for it. Repeated vivid dreams of women like the VONS activist Jarmila Bělíková and the mysterious 'Andulka', 'who appears to me by day and in my dreams'; old theatre friends like Andulka's ex-husband, Pavel Kohout. Other lavish dreams stained with traces of prison power: being visited by Gert Bastian, former General in the Bundeswehr, dismissed for his opposition to Nato deployment of nuclear weapons; and filming in America with the lucky and successful — and free — Miloš Forman. Suddenly becoming full of energy and élan, gripped by the feeling that there is hope because fundamentally one's life is meaningful.
Good health fertilized by the absence of complications, self-confidence, even the feeling of being able to express things coherently, with a touch of wit. Moved after six months' pre-trial detention from Ruzyně to Heřmanice. After nineteen months, from there to Plzeň-Bory for another thirteen unlucky months, followed by another few months elsewhere. Watching others exhilarated after hitting up with whatever they could manage to get their hands on. Convinced that the tragedy of modern man is not that he knows less and less about the meaning of his life, but that he just doesn't give a toss. Darkness and empty boredom. No sounds of children playing outside his window. No shaking hands, indeed, no physical contact with anybody, except when accidentally bumping into someone or when visited, a few times each year, by Olga and Ivan. Inmates' constant natter about women. Struggling with the burden of inventing a different concept of time. Discovering one way of shortening it: by imagining that one has just been sentenced, only to the time that actually remains. The strange feeling of dependency upon the one-dimensional surroundings of prison. Waving goodbye to the complexity of the outside world, giving up the corresponding art of living responsibly by making decisive judgements about matters like appointments and deadlines. Childish delight in small achievements like overcoming anger, darning a hole in a sock, or finding a quiet physical space to write. Discovering that writing, like a good night's sleep, is a biological necessity. Gripped constantly by the feeling that letter-writing to immediate relatives — the only writing permitted by the authorities — is an unsatisfying form of soliloquy addressed to a world that is ever receding over the horizon. Enduring the strictest prison rules of correspondence. No more than one four-page letter per week. No copies of the letters to be retained. No letters to anybody but immediate family. No mention of prison conditions, or politics. No underlining. No scratching out or correction. No illegible handwriting. No quotation marks. No foreign words or expressions. No humour.
Feeling ill. Sinking into hibernation, dragged down by the sweet mental lethargy induced by the oppressive routines of prison life. Cold and sad reveries about autumn leaves. Winter darkness and gloom. Craving alcohol and settling for Earl Grey tea. Toasting the end and arrival of yet another year with prisoners' champagne: a powdered fizzy orange drink called (impressively) Celaskon Effervescens. Celebrating the world première of _The Mountain Hotel,_ performed at the Akademietheater Wien, with an American cigarette and a cup of hot powdered milk. Looking forward to travelling by bus, at gunpoint, each day, to work in the nearby Vítkovice Ironworks, near Ostrava. Learning to be a welder. Washing and ironing sheets stained with millions of unborn children. Practising the art of self-control. Astonishment at discovering that shouting at a fellow prisoner relieves tension.
Certain that mental stupidity — forgetfulness, shrinking horizons, losing the knack of writing — is setting in. Shattered by exhaustion, aches and pains at the end of the working week. Craving sweet-tasting foods, like chocolate or crown mints. Six-monthly visits to the prison dentist. The satisfaction of having tartar removed from grimy teeth. Aching gums. Lancing pus with a needle sterilized in a flame. Getting new and stronger lenses in old glass frames. Searching for 'anchor points' — an approaching spring, a visit from Olga and Ivan, the sight of a tree, a warm gesture from a tattooed inmate. Undermined by hearing of the death of an old friend, the free-spirited anti-Chartist Jan Werich, an icon of the cultural confidence of the First Republic. Weighing the remark of Alexandre Dumas — ' _A_ kind word in prison is worth more than the most expensive gift in freedom' — against the vile prison reality of permanent conflict, tension, and stress, some of it caused by tough-guy neighbours called 'kings'. Endless waiting for letters, some of which are not handed over because of something written in English, or because the text was deemed to contain hints, codes or cross-references, or because the prison authorities objected to the name 'Václav Havel' written on the envelope. Savouring brother Ivan's reflections on modern physics. Feeling mentally fit, even enlivened by the clutter of interesting experiences and characters. Terrified by the reality of being inside for several more years. Always keeping an eye on personal belongings. Always chasing something, making arrangements, fearing for something. Otherwise feeling despondent, distracted, uneasy, inattentive, derailed. Bombardment with inmates' talk of how people are naturally lying, selfish bastards who are not worth helping. Learning that other people are indeed hell. Smoking in front of a mirror. Trying hard not to be turned into a curmudgeon. Practising the art of not yielding an inch to the unprincipled hatred of others.
Unlimited time for thinking coupled with the realization, amidst the clutter and lack of interaction with the outside world, of the impossibility of coming up with any decent ideas at all. The impossibility of writing about prison in prison. Struggling for trivial concessions like more sunlight. Daydreaming the first moments of release: telling stories to Olga; sweating it all out in a sauna; waltzing to the theme of the film _Doctor Zhivago;_ having good dinners and parties with friends, who will laugh with tears in their eyes; listening to favourite tapes and records; drinking good coffee and rum for breakfast; dropping in on brother Ivan and hugging oldest friends like Zdeněk Urbánek; drinking beer at The Two Suns; paying respects to Egon Bondy; walking dogs through the splendid orchard on Petřín Hill; bumping into conformists unsure of which way they should look; strolling through the Wallenstein Garden; admiring a large pool containing goldfish, gurgling water nymphs, a statue of St George wrestling a dragon; going for a swim at Podolí; praying not to sink like a stone to the bottom.
Then two disturbing questions: What then? What next? The gnawing pain of lumbago. Another hernia. Tennis elbows. Longing for injections to kill pain. Disciplinary punishments. Chasing ideas around the head, all the while worrying about the danger of succumbing to prison psychosis. Fantasizing a natty new suit hand-tailored from dark-brown corduroy cloth. Knowing that a rich meal of grilled chicken, home-made tartar sauce, and white wine would now induce vomit. Comforting colleagues struck down by tears after receiving a letter from home. Battling all day, every day, with the burden of reconciling the need to get along with everyone and the impossibility of suppressing angry emotions against another inmate in a hellishly cramped cell measuring 6 metres square. Experimenting (unsuccessfully) with the art of establishing telepathic contact with others on the outside. Vividly sensual, almost hallucinatory memories — of boarding school in Poděbrady, Ajda shaking the water from her fur after dipping in a pond, the feel and smell of musty old theatre costumes impregnated with make-up powder at the Theatre on the Balustrade. Yet more intense daydreams about the first few days after release. Coping bodily with the impossibility of concentration by becoming bone-lazy and passive. Getting no pleasure out of exercising, losing weight, studying, thinking. Tumbling into a state of profound numbness and fatigue induced by nervous strain. Remembering Franz Kafka: 'Man is an eternal rebel.' Realizing that the source of hope is not outside, in objects or events for instance, but inside. Discovering and being repulsed by a certain type of prisoner, who on the outside is big-talking, bossy, selfish, cynical and interested only in getting rich at others' expense, while on the inside becomes a chronically simpering, self-pitying hypochondriac forever pinning the blame for everything indiscriminately on to others within reach.
Cheered by the sound and smell of rain. Yearning for the return of spring buds, flowers and perfume to the prison courtyard. Eating bread with margarine and garlic. Watching television — a good American documentary on Martin Luther King, even — and suddenly realizing that the outside 'normal' world actually exists, that it is not just a dream or a memory. Watching with delight a variety show put on by prisoners for prisoners. Prison muzak, once in a while good enough to attract dancing inmates under loudspeakers. Looking on, overcome with mounting depression at the pointlessness — and Orwellianism — of it all. Coping with an atmosphere that contains nothing pretty, pure, moving. Observing how many prisoners are grumpy hedgehogs who become irritated or fall into a vile temper by any disturbance of their precise and somnolent daily routines. Facing the grim probability that after calmly falling off to sleep, one will be awakened by a razor-sharp pang of resentment, followed by anger that abates only after arising from bed, furiously scribbling several pages of nonsense in the dark, pigging out on sweets, and smoking three cigarettes. Fearing that release will result in another lock-up.
Looking in the mirror, disgusted, to see only a double chin, baggy eyes, a filthy sagging face, crumpled wrinkles. Haemorrhoids. Always haemorrhoids, so bloody and painful that the prison doctor is summoned and, with luck, agrees to consign the sufferer to bed for days, with the added privilege of long warm baths and perhaps the good news that no tumour has been found. Experiencing the worst bad moods all in a row. Melancholy. Alienation. Hopelessness. Wild anger. Fear. Apathy. Self-doubt. Drawing the conclusion: that everything seems pointless, hopeless and sad, that one is good for nothing else but rotting in prison, that perhaps prison has been deserved. Battling colds and influenza. Bothered by not being able to go for a walk. Bothered more by the emotional incapacity to go for a walk. The fear, felt by everyone who senses the danger of metamorphosis, of being transformed into a tiny, helpless insect. Illness again: sore throats, aching joints, crippled arms, needles, headaches, pills, clogged lungs, and, worst of all, the unspecific prison-fever. Feeling shivery, slight headache, watery eyes, always tired, groggy and weak, feeling brain-dead, nervous and absent-minded, compounded by nothing going right and nothing giving pleasure. After all these years, a bowel operation. No cigarettes for weeks. Sleeping off depression. Gaining weight. Staring out of the window. Diagnostic tests. Catheters. Fever. Pain. More pain.
Havel's prison ordeal dragged on until the last week of January 1983. One fateful Sunday afternoon, his body suddenly collapsed under the nerve-wracking weight of the past 189 weeks. Convulsed by a wildly beating heart and a raging fever well off the thermometer scale, he caused his bed to shake so loudly that it kept neighbouring prisoners awake all night. Havel became convinced of the arrival of the grim reaper. Worried that the death in custody of a world-famous rebel might produce an international scandal, his jailers panicked. After administering aspirin, then antiobiotics, and X-raying his lungs — Havel was sure that he was suffering acute pneumonia — the authorities arranged for his transfer by ambulance, in pyjamas, handcuffed, back to Prague's Pankrác prison. There was talk of complications, even of some kind of bubble in his lungs. Havel went for broke. Although feeling ghastly, he summoned up enough energy to write a detailed account of his plight to Olga, hoping that the laxer censorship at Pankrác combined with his expressed anxiety that he might be dying would together ensure that his letter from the prison hospital cell just might get through. It did.
Olga, accompanied by Zdeněk Urbánek, rushed to the prison. They demanded to see Havel, to learn details of his condition, even to leave some fruit for the patient. The authorities refused each request, adding only that Havel was alive and his condition stable. Olga exploded. She rushed home and rang Pavel Kohout, now an _émigré_ in Vienna. He spent several days and nights telephoning the offices of various notables and heads of state throughout Western Europe, urging them to intervene. Messages on his behalf soon began arriving from all over the world, with quick effect. 'One evening, which I shall never forget,' Havel recalled, 'just as I was getting ready to go to sleep, into my cell there suddenly stepped several guards, a doctor, and a woman official of some kind, who informed me that the District Court of Prague 4 was terminating my sentence.' He was so flabbergasted, even overcome with fear of freedom, that he begged to spend one more night in prison. He was told by the official that that was impossible because he was now a civilian, that without delay he should gather his few belongings, since an ambulance was waiting to take him in his pyjamas to Pod Petřinem civilian hospital.
By the time he reached the intensive-care unit, Havel was in a state of euphoric shock. People were calling him 'Mr Havel' (instead of the impolite 'Havel'). He was no longer handcuffed. Gone were the burly policemen armed with pistols and panting, snarling dogs. He was even able to pick up the phone. Within the hour, Olga, Ivan and Ivan's then wife Květa had arrived, wielding flowers, oranges, sweets, cigarettes, newspapers, photographs, clothes. The distinguished playwright Josef Topol soon joined them, clutching a chrysanthemum, tears in his eyes, shocked upon hugging Havel that his thin body now flinched at human contact. Everybody then cried, including some of the nurses and doctors. News of his release was broadcast by the serendipitous Voice of America — just one day after it had broadcast a Charter 77 appeal for his release. At the flick of a microphone switch, a panicked regime hoping to unburden itself of a sick dissident by parading itself internationally as liberal found itself represented as having buckled under the moral pressure of democratic forces at home and abroad.
Havel's condition quickly improved. It felt like the happiest time of his life. 'Released from the burden of prison, but not yet encumbered by the burden of freedom, I lived like a king,' he recalled. Holding court from his bed, sometimes on the telephone, he welcomed friends all day long, every day, for a month. He seemed not to need sleep. Samizdat texts piled up on his bedside tables. Flowers and salutations and gifts arrived from all over the world. Cameras clicked. Olga brought him a bottle of gin a day, and Havel the brewmaster quickly perfected the art of converting tinned fruit gifts into fruit punches. These he drank by night either chatting up the young female nurses or alone, propped up on pillows reading Ludvík Vaculík's _Czech Dream-book,_ the most talked about literary work in the contemporary Prague scene. Havel himself appears as a character within the text — as a brave non-conformist — which seemed a fitting tribute after all that he had been through.
Everything considered, his life seemed normal once again, perhaps even better than normal. The baleful omnipresence of the state had receded. The secret police visiting his bedside spoke with honey tongues. They apologized, politely nodded, and thanked him for continuing to refrain from speaking with foreign journalists, and from making international calls. The hospital staff were kind. No visiting hours applied. Smiling, chatting well-wishers of every description freely came and went. Havel laughed for the first time for years. He had only rights, and no duties. He felt unconditionally free. Even his body again felt refreshed, light, effervescent. Everything somehow represented a triumph over the evil of arbitrary power — except for the profound personal crisis that he was soon to suffer.
### **Largo Desolato**
The day came when he had to return to the world as it was. Released from Pod Petřínem hospital during the first week of March 1983, he was driven to his family apartment house on the embankment on Rašínovo nábřeží, where he hoped and expected — as he had made clear in a reverie from prison — to spend time with Olga, to renew and develop what he called at one point during his sentence their 'two-in-one identity'. During one sweet fantasy about life after prison, Havel imagined going to a sauna, combining it with swimming and sunbathing, then going home for a snooze, then in the evening putting on some nice clothes and going out with Olga to a good restaurant and eating and drinking to their hearts' content. Within another reverie he re-enacted his favourite morning routine of sleeping late, drinking good coffee and rum, listening to tapes and records, then soaking in the bath, with Olga sitting beside him, on a bathroom stool, summarizing the large pile of newspapers that every morning she and he had once loved to devour together.
These sweet fantasies were entirely understandable. Not only had their relationship survived unbroken since the 1950s. During the past three years, the more pertinent fact was that Havel had come to regard Olga as his anchor-hold, or 'point of stability'. Awash in transience, blown here and there by political storms, culminating in prison, Havel regarded her as the main addressee of his communications with the outside world. Whenever something good, or absurd, or heartbreaking happened to him, and whenever he mulled it over in his mind, which he often did, he would issue a report to her, as it were. Olga honoured his wish. She was always the first to open the letters when they arrived. She would either read them alone, or aloud to friends (like Zdeněk Urbánek) who were with her at the time. Then she would pass each letter to Ivan, who for safe-keeping would make two or three copies on the typewriter. Olga was his penfriend. So it seemed only fitting that after release Havel decided to assemble and publish the letters under the title _Dopisy Olze (Letters to Olga)._ 'It's true that you won't find many heartfelt, personal passages specifically addressed to my wife in my prison letters,' he later said. 'Even so, I think that Olga is their main hero, though admittedly hidden. That is why I put her name in the title of the book. Doesn't that endless search for a firm point, for certainty, for an absolute horizon that fills those letters say something, in itself, to confirm that?'
_Letters to Olga_ is a sad but inspiring work, especially for personally troubled or melancholy readers. Its chosen title was calculated by Havel — with an eye on his public image — to bless the letters with a touch of romantic love. There are certainly plenty of passages in the letters that lend credence to that image Havel desired. 'Last night I dreamt about you. We had rented a palazzo in Venice!' he wrote. 'I'm worried about you!' runs another passage. 'Don't walk over bridges alone at night, and don't go anywhere alone, if possible.' There were also many passages of heartfelt concern. 'I'm really sorry you feel depressions coming on. But you can't afford to have depressions now — wait till I come home! Be cheerful, sociable, active, brave and prudent (but mainly prudent).' And there were the lover's passages: 'I appreciated your saying in one of them that you love me. It's been a long time since you've told me that!'
The interesting thing about these passages in _Letters to Olga_ is just how exceptional they are. Those who read the letters as confirmation of a relationship of romantic love battered by months and years of separation in effect have blind eyes for the friction manifested in dozens of contrary passages within the text. We do not know what Olga wrote to her husband — the letters were confiscated by the secret police during a house search, and reportedly went missing — but we do know that her letters did not always win his approval. 'You said you were not sending me a kiss and that I knew why,' he wrote six weeks into his detention. 'I don't know why! I do know, however, that you mustn't write such things to me — I felt miserable for several days. These letters are all one has here. You read them a dozen times, turn them over in your mind, every detail is either a delight or a torment and makes you aware of how helpless you are. In other words, you must write me nice letters.' The demand made of his lover-wife seemed reasonable enough, but in the next breath he issued a string of commands and a reprimand that both contradicted his own principle of romantic civility and revealed some hidden anger at his wife. 'And number them, put the date on them and above all, be as exhaustive as you can and write legibly. After all, it's not so difficult to sit down at a typewriter once in a while and write about everything you're up to.'
Aggression poked its way up between his lines like nettles repeatedly during the next three years. On and on and on _and on_ he went about how Olga didn't write enough to him. He often claimed she had 'orphaned' him and regularly signed off by saying that he had run out of paper, as if to remind and chide her that her occasional postcard or one side of a single sheet of paper was thoughtless. At one stage, he wrote in exasperation: 'WRITE MORE OFTEN! WRITE MORE DETAILS! WRITE MORE!' He grumbled constantly, even to the point of nicknaming her The Grumbler. He also chastised her often for not observing the ever-changing rules of prison correspondence: 'I was informed last night that another letter from you had arrived,' he wrote eighteen months into his sentence, adding that the authorities had confiscated it 'because there are greetings from various friends in it, and I am allowed to receive messages and greetings only from relatives. I wasn't even given the photos you included. A pity. It's the third time this has happened.'
Even in the trying circumstances, Havel's reaction was anomalous, considering that he knew Olga actually loved to write. Crafting little plays for fun at the kitchen table in Hrádeček, for instance, was among her favourite activities. She wrote quickly, so quickly in fact that Václav was envious. Her infrequent communication clearly had other and deeper roots, though they seemed lost on Havel at the time. He took little account of the interfering tricks played by the prison authorities on their attempts to synchronize letters. Olga understood the point instinctively: 'Sometimes I would get three at once. Sometimes he would not get my replies before he sent another letter. It was a method they used to make people nervous — psychological pressure.' Havel also underestimated Olga's unshakeable commitment to the marriage. He therefore misunderstood her belief that detailed letter-writing was an exercise in pointlessness, especially since the prison-letter rules dictated that she could only pen the same clichés over and over, which is why she sometimes asked Havel's good friend Zdeněk Urbánek to write on her behalf. Havel's grumbles also overlooked the difficult point that letter-writing meant fundamentally different things to each of them. For him, each one of the 144 letters from prison that he wrote was a matter of life-or-death, a tactic of elementary survival against immense pain. The ensemble of letters resembled Janáček's _From the House of the Dead:_ lacking any real plot, the four-page letters read like determined monologues from individual members of a prison chorus who step forward to tell their desperate story before melting back into invisibility. Olga's experience was the inverse: each letter or postcard that she attempted to write induced a great quantity of inner pain. 'Those were letters that were awfully hard for me to write,' she later said. 'I broke down even over the address where you had to write "the accused" and eventually "the convicted".'
Havel also tried to get at Olga in other ways. He managed to master the art of completing compliments with put-downs, sarcasm and pickiness over details. 'I think of you with tenderness,' runs one letter's ending, 'and I even accept with tenderness the fact that you don't write, that you don't do what I ask or respond to my letters (do you at least read them carefully?)'. And another: 'I have an idea for an excellent Christmas gift you might give me: you could write me a long letter at last. Perhaps you could spend one of the holidays writing it.' He added, 'I'd appreciate it if you would answer at least some of the countless questions I've flooded you with in the last six months. Would it be asking too much, for instance, for you to tell me what state you left Hrádeček in, what work you did, and did not, manage to get done, how you're living in Prague, what your plans are, etc. etc.?' And yet another: 'I forgot to tell you I loved the way you looked,' he wrote tetchily after a visit. 'You were smartly dressed and very chic. Even your hair looks good that way (it has, as you know, a tendency to look like spikes or straw — but it didn't during the visit).' Havel occasionally patronized her. 'It seems that this time, being a grass widow has been good for you,' he once wrote after she visited him in Ruzyně, adding: 'But of course I am happiest of all to see that you are living and acting — if I may put it this way — "in my spirit" and that you are effectively standing in for me.'
Havel also seemed to have taken some misanthropic delight in hinting at his extra-marital affairs. 'Greetings to all my friends, kisses to my girlfriends (if I still have any)', he once wrote, as if seeking to annoy Olga. In one of her rare letters, Olga replied by telling her husband of a dream in which she found him in bed with a mutual friend. 'I don't quite understand why your dream pushed me into bed with Markéta, of all people,' he replied cockily. 'She is one of the few beings with whom I have not only, in all politeness, avoided such a possibility, but absolutely forbidden it to myself, even for the future.' Yet there were plenty of other punishing mentions of girlfriends, real and imagined. 'I am not at all surprised,' he wrote at one point, 'that in my dreams (and when I am awake too) various girlfriends appear and try, in all sorts of clever ways, to seduce me (a while ago, for instance, it was Běla. Give her my greetings!).'
Havel's sexual fantasies and actual affairs were an open secret both before and after he left prison. Asked later by the _Magazín Lidových novin_ about his 'amorous adventures' he replied, playfully: 'I don't consider myself a Casanova, and I'm not aware that my life has been attended by so-called forays. On the other hand, I do not conceal the fact that I'm a normal man who doesn't shun the world of women. I don't think I have anything either to hide or to publish.' The interviewer then asked: 'When was the last time you told a lie?' Havel replied: 'When answering the last question.' A Casanova in prude's disguise? Like his father, who had had mistresses and two wives? A secret emulator of an early Kundera hero, whose endless copulations amount to sex as amnesia? Improbably the latter, but Havel left his readers guessing, even though there is no doubt that his 'zipper problem' posed problems for his philosophy of living responsibly, in the truth.
Havel's 'amorous forays' — even the one with Anna Kohoutová (the blonde ex-wife of his playwright friend-in-exile Pavel Kohout) on the night he was arrested — were well known. Olga had to 'reconcile herself to them'. The manner in which she did so reveals much about both the personal politics of Havel and Olga's perception of him as a man. Olga could certainly not be described as a subservient woman who ignored the lines of power around her and adored her man through thick and thin. Nor was she looking for a man who adored and loved her until divided by death. Olga was the kind of woman, as the Czechs say, you can't get drunk on a bun. Everybody who knew her well admired her hard-nosed, levelling realism in matters of power, in whatever sphere she moved. She was a typical girl from the poor neighbourhood of Žižkov, where life was frank and not easy, and whining a foreign word. She managed to get through life without bourgeois self-confidence.
The good-looking, blue-eyed butcher's daughter with a gruff voice despised pretension. She was often sarcastic, and normally knew what she wanted and knew how to get it. Whereas her husband was sometimes obsessional about technical details, measuring everything millimetre by millimetre, Olga concentrated more on the overall length and direction of things. She was curious and open-minded about life, but she was not a know-all, even though (according to her friend Dana Němcová) she was impatient with 'intellectual puzzles'. She always knew whether she was for or against something, and acted accordingly, and (like her husband) had a tendency to uncompromising pig-headedness. She always meant what she said. Some mistook this as contemptuousness for others. 'I like personalities, people who are individuals, but I can't stand people who have no spine, try to suck up to the powerful, and are arrogant towards people who have no standing,' she once remarked.
Courage in the face of despair and defeat was one of her most striking qualities. The Havels' friend Zdeněk Urbánek spoke of her as 'the bravest woman among those who took part in defying totalitarianism', and with good reason. 'You shouldn't tell them anything, not even the name of our dogs,' she once said angrily to her husband, after he soft-heartedly invited in for coffee two StB agents standing outside their flat on duty in sub-zero conditions. 'I wouldn't even throw them food for their dogs,' she added. Olga often warned him against being too kind to those who didn't deserve it. She was on the lookout especially for sycophants and self-servers. 'I just can't stand the kind of people we in Žižkov used to call "grubbers'", she once said. 'The sort who think only about themselves and don't care about anything around them. They calculate how much they're making, how they spend it, what to buy, where to go next.'
In contrast to her husband, Olga did not depend upon sexual adventures. If at times strangely embarrassed about her slimness (she didn't like to swim for this reason) and although in public she concealed her left hand (due to the loss of four fingertips in an industrial accident at a state-run Bat'a factory when she was sixteen), Olga was certainly sensuous. She simply disliked burdening others with such private details, and was at ease with her body, even in matters of pregnancy and childbirth. In response to prying questions about why she and Václav had never had children, her response was typically frank. He would say: 'I wanted to have children, but God didn't want me to. I have now come to terms with that. Anyway, God probably knows what he's doing. My children wouldn't have had an easy life.' She would say: 'We never tried not to have children, but unfortunately it happens that some people have children and others don't.'
Her matter-of-factness attracted men's eyes. Some (the playwright Josef Topol, for example) thought that she looked and acted like an aristocrat. She was tall, dignified, easily commanded respect from others, and moved gracefully. She had a ready but unillusioned smile, lots of natural charm, and some men thought of her as sexy. But she had no time for those who talked of orgiastic prowess and she disliked intensely the use of sex as a bargaining chip. She couldn't stand sexual narcissism and (as her secret wedding to Václav revealed) she had the feeling that sacred-sounding promises of love, fidelity and sacrifice were actually selfish displays of raw possession, cleverly disguised but nonetheless fraudulent, deceiving of oneself and others. Despite constant and vigorous denials that she wasn't a feminist, she always said that she considered most men unreliable. She also said that she considered women equal to men, and that in any relationship the two sexes should add to and complement each other's efforts. She certainly considered Václav her equal, and she was convinced that he found her egalitarian independence among her most attractive qualities.
His imprisonment undoubtedly strengthened her sense of independence. She had plenty to do, and lived life to the full, despite huge personal difficulties. She worked long hours preparing manuscripts with Ivan Havel for the samizdat publishing project, Edice Expedice. She tried to keep in touch with people who were going through hard times. Olga also distributed letters, played ping-pong and bridge, walked the dogs Ajda and Golda every day, and trained up a newly acquired German Shepherd guard dog. She liked to go to parties, where she loved to smoke and drink and chat, and (friends noted) would often choose to dance alone. She hatched plans to set up a samizdat project that would later be called _The Original Videojournal,_ which tried to capture on film, and distribute video cassettes of, the realities of life in socialist Czechoslovakia. If there was any remaining spare time, she occupied herself with little things that meant a lot in the prevailing circumstances, like shopping, gardening at Hrádeček, mushroom and raspberry picking in nearby forests, collecting books, imagining recipes, browsing antique shops for things art nouveau (her favourite style) that she could use to decorate the embankment apartment or Hrádeček, or (among her favourite activities) rummaging through the rubbish tips at Barrandov film studios, which were richly stocked with bits 'n pieces tossed away by people she denounced as 'unimaginative'.
Olga also started up a reading group, mainly for women. She described it as a 'society of prison widows' and named it 'The Tomb' _(hrobka),_ partly because it held its weekly meetings in a dank, dark room in Prague's Old Town, and partly because of the group's passion for reading and discussing trashy erotic and Gothic novels by banned authors (Olga's favourites included _Monsters of Dr Gagra_ and _Strange Mandarin_ by Sláva Jelínek).The Tomb group tried to live fearlessly. It organized fancy-dress balls, parties and weekends at Hrádeček, and published its own typewritten magazine. The group lived on the edge, with constant secret-police harassment. Many of its core members suffered police threats and violence, and quite a few were forced subsequently into exile.
Olga had her share of dealing directly, and alone, with the secret police. Her movements were constantly monitored, and there were plenty of ugly incidents to handle coolly. When Havel was moved to Plzeň-Bory at the end of July 1981, the StB offered her (and Havel) a passport to enable her to emigrate 'without any problems' to the Federal Republic of Germany. She flatly refused. On another occasion, she was taken into custody for four days (with Ivan) and interrogated about their publishing and book-smuggling activities linked to the Edice Expedice series. She refused to say a word, and was accused of subversion of the state. Then there were the repeated house searches, some of which smacked of sexual harassment, as when two dumpling-headed StB agents, after searching through her belongings, ordered her to go for dinner with them. Typically, cunningly, Olga extracted her revenge by embarrassing them by ordering one clove brandy after another, loudly pointing out to everybody within the restaurant that the public security agents were breaching their own code of conduct. After cutting short the dinner and paying the bill, the red-faced, red-epauletted officers left.
Olga's steely independence reinforced the mild contempt she expressed for her husband's dalliances. They were a source of tension and noisy arguments with him, even though she knew that Václav always confessed that life without her would be unthinkable. Ever since they had been married, she had sensed his capacity for infidelity. Her radars were certainly trained on rambunctiously sexist men — Pavel Landovský, for instance — whom she dismissed as womanizers capable of leading Havel down the path of good times and easy women. In one way or another, she always found out (or was told) about her husband's affairs, and she consistently made it clear to him that she didn't like them. She also disliked the tendency among Charter 77 men to treat Havel's affairs as the butt of back-slapping jokes ('I hear you're at it again!'), sometimes within earshot of Olga. She didn't even approve of his habit of babbling into the ears of women about himself after a few drinks — the habit, as he put it, of being a '"merry drinking companion", a carouser, a bit of a high-stepper, even, some suspect, with inclinations to Don Juanism'. Olga was consistently tough on her version of the proverbial heartless and impious seducer who delights in succumbing to the women he meets. But she didn't take revenge or punish him, in part because she regarded his escapades as harmless juvenile behaviour and partly, some of her close girlfriends thought, because she regarded them with the same ambivalence as a mother does towards her son's sexual experimentations. But although Olga tolerated these affairs, she used her razor-sharp senses to draw the line at sexual encounters that she knew would prove dangerous to their own relationship.
The one she most worried about was Havel's ongoing relationship with Jitka Vodňanská. A trained social psychologist with a young son named Tomáš, Jitka first met Havel just before his long spell in prison. Their affair began immediately after his release, when Havel's skirt-chasing was at its most intense. Although it seemed as if he was simply wanting a fling to punish Olga for 'orphaning' him — or as if all the libidinal energy of the past four years simply had to be discharged in the quickest time possible — Havel soon found himself in a lustful relationship that lasted six years, after which it turned into a good friendship, with occasional sex on the side. After the misery of prison, he felt uplifted by Jitka's sparkling eyes and wicked sense of humour. Her words were certainly balm to his soul. He wrote to her nearly every day, usually on the back of postcards marked with an artistic or philosophical bent. He loved to let her talk about his character, and he told her often that her astute observations had helped him crawl out from under a big, heavy stone. 'Dear Jitka,' runs one of his early lover's postcards, 'Thank you for your letter and for the very germane analysis of my personality. Except for two details, it's precise. One of them, concerning women, is not exactly a stereotype. I've always been attracted to otherness and unrepeatability. After the good advice, I'm looking forward to seeing you here. You'll be with me in a fortnight. Yours, Václav.'
Jitka's broad view — it was shared by Olga and several of her friends — was that Havel was attracted to strong women to whom he could not or would not make a long-lasting commitment. It was as if he craved hyperprotective women — 'Habsburg' women, Jitka called them — who exercised considerable power over him in order to justify his own need to resist their towering strength. Such resistance came in various forms of active rebelliousness, as when Havel first began to irritate his mother by staying out until all hours of the morning. According to Jitka, his decision to marry Olga carried on this old habit. It was a protest against the dynamic and attractive mother whom he loved, but whom he found both overbearing and distant, especially during those periods when she delegated her son to governesses who made him feel that too much of his childhood was spent doing such things as 'learning how to button up shirts'.
Much the same 'hurtful' emotional protest was now being waged against Olga, Jitka told him. The advice highlighted the abstract point — crucial for understanding childhood — that when power is exercised over us, for instance by our mother, we do not simply 'internalize' or accept its terms and conditions, on our knees. We may do that, of course. Power is indeed sometimes that unequal relationship that presses down on us from the outside, only to relegate us as inferiors to a lower order. But in childhood, power in this sense often only functions as such because it _forms_ us. We accept its terms of reference. We treat them as the very precondition of our existence, as part of ourselves, and in this way the relationship of power that subordinates us also _empowers_ us to act in and upon the world. It turns out that power — in this case, that of Havel's mother over her first-born son — assumes a psychic form. It does not simply press-gang us into submission. Power rather forms our own identity. It renders us into a subject capable of certain forms of action. We then carry that power relationship around with us in later life. If we have lucky childhoods, we are permanently strengthened by its effects, like the strong belief in ourselves or confidence in our own ability to make bold judgements in the company of others. But power also often marks us with its more troubling effects, like regrets, unsatisfiable longings, unrealistic hopes, unfounded fears — and, as as Jitka said of her man Havel, deeply ambivalent, sweet-and-sour feelings for strong women.
In context, of course, Jitka's advice to Havel had different, more carnal meanings. Perhaps the advice was offered simply as a lover's gift. Perhaps it served as an elaborate justification of her own desire for him. Perhaps it simply took aim at knocking down his remaining defences. Whatever the case, the twosome were permanently excited in each other's presence. Freshly out of prison, Havel found she brought him joy through orgasm laced with words and wine. The two made love indiscriminately and often. Jitka quickly became pregnant. Suddenly everything changed. Olga generously proposed a _ménageátrois._ Jitka pointed out that Olga's maths were wrong — how young Tomáš would fit in was altogether unclear — and that from a child psychologist's standpoint life would be hell for the child. So Havel began to talk of divorcing Olga. Then he changed his mind. Jitka kept calm — she liked to remind the combatants that her father was named Václav and her mother was called Olga — but she had inner doubts about Havel's resilience under pressure. She guessed secretly that he hadn't much desire for a child. She noted his clumsiness towards children and his ambivalence towards Tomás. There were memorable moments, for instance when Havel secretly made a medal and presented it to the eight year old in honour of his efforts to gobble up all the dumplings on his plate. But Jitka also noted that Havel often seemed ill-at-ease with Tomáš. He sometimes treated him like a pupil in need of lectures on phenomenology. There were even touches of jealousy, for instance when Havel complained about Jitka taking up precious time to read fairy-tales to her 'spoiled' son.
Faced with such ambivalence, and not yet familiar with the lover with whom she had been sleeping for only a few months, Jitka wrote to Havel to tell him that she had decided to terminate her pregnancy. It was a decision that she subsequently regretted for the rest of her life — a choice she so bewailed that her body shook uncontrollably whenever she was reminded of what she had done. Her thwarting of the power of beginning had the short-term effect of shoring up the affair, even propelling it forwards into passionate love. Havel felt utterly free in her presence. 'Vašek Havel, writer and fat-arse,' began one of his regular postcards, 'sends greetings to his lover of many years and a lifetime — I hope — sweet girlfriend.'The photographs that have survived — Olga burned a pile in a rage — reveal traces of his exquisite happiness during this post-prison period. One image shows him cancan-ing the night away, wearing a big smile and a borrowed diamond brooch; another reveals his suntanned legs, dressed in shorts, as he hiked in the high Tatra mountains; yet another sees him celebrating his fiftieth birthday, Moravian wine in hand, nestled alongside beautiful Jitka.
It is said that nothing is happy in every way, and so it was with Havel, who was heading for a hiding. Olga's ongoing hostility to the affair began to worry him, and he responded by urging Jitka and Olga to meet, to try to resolve the growing tensions. The exercise in male diplomacy ended in a hopeless hangover. Olga was thoroughly fed up. So, over coffee one morning, choosing her moment, she said to Havel, with her usual candidness: 'It's good you have friends.' She paused, then added: 'I've got one, too.' The news of Olga's first-ever affair whistled like a bullet into Havel's spine. He fell speechless, then plummeted into prolonged silence, knowing that his point of anchorage in the world was now potentially smashed into small pieces. It transpired that during the latter part of his time behind bars Olga had become friendly and fallen in love with a young actor named Jan Kašpar. Born in 1953 — his curly-haired youthfulness bothered Havel — Kašpar was talented, good-looking, unmarried, and sometimes kind. He affectionately called Olga _'šejka_ (Boss); for parity's sake, he called Havel 'Boss' _(šejka)_ as well. Kašpar officially described himself as one of Olga's closest friends and as the 'friendly caretaker' at Hrádeček, but his good friends in Charter 77 knew that that was a euphemism for an affair of the most serious kind. It is unclear where the relationship would have led, but Olga chose to end it, and to move back in with Havel and to rescue their marriage, despite the fact that his affair with Jitka showed no sign of abating. In any event, fate was cruelly to decide things. After Kašpar's separation from Olga, he got married and spent several weeks' honeymoon with his new wife at her country cottage. While pruning a cherry tree, Kašpar slipped and fell to the ground, landing on a pick, severely damaging his spine. Paralysed from the waist down, he was for ever confined to a wheelchair.
It was bad luck that amounted to a personal tragedy, which for reasons of sympathy and guilt circled like an albatross over Havel's head for a long time. Struck down by the fact that Olga had nearly left him, aware that their relationship might now be terminally ill, Havel tumbled into a deep pit of post-prison blues. He had never experienced anything like it in his life, and although he'd half-anticipated their onset while still in prison, the daily reality of trying to cope with serious depression began slowly to destroy him. He drank heavily, slept badly, had no energy for sex, dragged himself everywhere, and slowly withdrew from the world. He began vaguely to resemble Dr Eduard Huml, the 'hero' of his play _The Increased Difficulty of Concentration,_ which premièred at the Theatre on the Balustrade in April 1969. Huml, a depressed, exhausted, scholarly writer, whose _magnum opus_ is a treatise on human happiness, is preoccupied with striking some balance between the demands of his wife, Vlasta, a manageress of a toy shop, and his girlfriend Renata, who keeps coming for lunch at Huml's flat and romping about in Vlasta's dressing gown. Each woman contrives to monopolize Huml: Renata wants him to get a divorce and marry her, while Vlasta insists that he should stop seeing Renata. Huml flounders. Unable to decide, he lives tediously, tenuously, pressured from all sides, unable to get off the treadmill of daily existence.
The depths to which Havel had plunged in this period are best revealed in _Largo desolato. 294_ Perched alone day and night in his study overlooking the Vltava River, guzzling brandy, listening to taped music, he found writing a crutch, a weapon of last resistance against an army poised to overrun his defences. He confessed to one or two friends that _Largo desolato_ would examine 'what happens when the personification of resistance finds himself at the end of his tether'. The final version was sometimes interpreted as the most autobiographical of his plays, but that is not strictly accurate. The key motifs and overall theme of the play were certainly inspired by his own experiences, more directly than in any other of his plays. 'When someone comes to write Havel's biography,' said Jan Grossman, 'they should pause when they come to this play, because it is very personal, self-critical, and in a certain sense a caricature of the dissident.' Seen in this way, _Largo desolato_ can be understood as a self-caricature of Havel's post-prison depression, but the very fact that he managed to write the play — and to write it as a satire on his own condition — indicates that it is not simply an 'autobiographical' work. _Largo desolato_ is better understood as a comic parable about the condition of powerlessness, about what life is like when the individual finally crumbles under the weight of all-consuming power — a chilling, tragi-comic picture of what happens when the power of the individual to think, speak and act in the world is utterly routed by personal and political failure.
At the centre of the narrative is Doctor Leopold Kopřiva, a philosopher who has fallen foul of the state authorities for writing books with titles like _Phenomenology of Responsibility, Love and Nothingness,_ and _Ontology of the Human Self_ Kopřiva is in an utter mess. His nerves are wracked by the random visits of the secret police. He fears that they will successfully tempt him into declaring that he is no longer himself, and that he will stoop to accepting their offers of freedom in return for signing a confession that he has acted as an 'intellectual hooligan', in breach of Paragraph 511 of the criminal code. Kopřiva is also paralysed by pressure from fairweather friends and supporters, who want him to speak out, to issue a declaration, to take a stand against despotic power. But Kopřiva has already buckled. He is tired, desiccated, broken. Frequently pacing the floors of his apartment like a prisoner pacing his cell, listening helplessly to the passing of time, he swills rum from morning to night, shakes, complains of the cold, eats a diet of onions and almonds only to stay alive, all the while sinking deeper and deeper into a void.
Kopřiva certainly talks repetitiously about human identity: how it resembles a pre-verbal existential space in which the individual can grasp the world through experiencing the presence of others; how the meaning of life has to be chosen by individuals themselves, in other words, that it is not something that can be summarized and handed over to another like an information sheet; and how he would rather die than abandon his own identity. But Kopřiva does nothing and no one can help him — not even two workers who arrive bearing gifts of writing paper stolen from their own factory, and not even an attractive young woman philosophy student, who after reluctantly agreeing to drink her fill of the philosopher's rum tells Kopřiva she loves him. The cruel fact is that Kopřiva is beyond writing and loving. He suffers more than writer's block. He has run out of good excuses for putting off writing. Surrounded by bookcases and walls of bookshelves, his thoughts go round in a loop and he is capable only of stumbling over banalities — pen or pencil? Which paper? First tidy the desk? Suicide by alcohol seems appealing. As for love, Kopřiva has no strength, no courage, no self-confidence, no joy, no appetite for life. His failed heart cannot be brought back to life. The curtain falls with Kopřiva collapsing on the floor, banging his fists, dragging himself to a sofa, where he sits half-drunk, staring at the front door, morose, waiting for the police to return.
### **Temptation**
Lead us not into temptation, but deliver us from evil: these ancient words still rumble like thunder through our hills and valleys, not least because the gluttonous act of giving in to enticements, initially against our will, is made to feel morally questionable by the survival deep in our hearts of the belief that we are mere mortal sons and daughters of a fallen apple-eater. Our imagery of temptation is originally religious. That is why the lingering association of temptation with evil has ensured it an important place in the world of power, despite various attempts to reduce the art of governing others to a merely technical or cynical art. Temptation is a thoroughly political matter. Everyone who mixes with power and its resources — property, fame, sex, advantage — knows temptation, whose eventual poisonous fruits are confusion, self-pity, corruption, ruined reputations. Less obviously, temptation is an important resource in the arsenal of those who exercise power over others. It has often been observed that those who rule over others do so by means of guns, money, charisma, sex or law. Missing from such lists is the quietest and often most effective ally of power: temptation.
Before the long spell in prison Havel had known his share of temptations, from cigarettes and booze to sexual infidelities. But more than anything else it was his two spells in prison — the brief one in 1977 and then the extended sentence from 1979 — that dragged him before the devil, threatening to transform him into a toad before power. The dynamics were complicated but they conformed exactly to the rules of temptation. Temptation is a game of seduction whose stakes are high. From the point of view of those who are exercising power, tempting others with advantage — a lighter than expected sentence or material privileges, for instance — must perforce be based on careful calculation. Tight reins must be kept on the advantage offered to the victim, for otherwise they might think that they have scored a victory. The whole point of tempting a victim is to victimize them or seduce them into conformity; in either case, they must be moved to do what they would otherwise not have done. The act of taking the king's shilling normally heaps anguish upon the tempted. They feel in two minds, stretched in several directions, sometimes to breaking point. Guilt and shame are their accomplices. If they succumb, they feel for ever haunted by their own duplicity. If they refuse temptation, then they are left with gnawing doubt about their own capacity for judgement under duress. They are gripped by the feeling that they have unwisely martyred themselves into disadvantage. Either way, the outcome feels unsatisfactory. Giving in to temptation involves cavorting with the devil. Yet the price of integrity is further suffering — and possibly even revenge by the powerful.
From the time of the launch of Charter 77, Havel found himself constantly haunted by this dilemma. His first spell in prison, which followed the launch of the Charter, was hard to bear. 'I didn't know what was happening outside, all I could see was the hysterical witch-hunt against Charter 77. I was deceived by my interrogators, and even by my own counsel. I fell victim to curious, almost psychotic moods.' He was wracked especially by the feeling that his defiance of the authorities made him directly responsible for the misery that now befell his fellow Chartists. 'It seemed to me that, as one of the initiators of the Charter, I had brought terrible misfortune on a large number of people. I of course was trying to shoulder an excessive responsibility, as if the others had not known what they were letting themselves in for, as if it was all just my fault.' Despondency nourished by guilt was fed by his growing awareness that the authorities were preparing a trap for him. During one of his appeals against detention he had made a casual remark about how he felt guilty for the harm he had brought to others — so implying that he regretted his role in Charter 77. The police instantly twisted and hurled it like a dagger back into his heart. Knowing their skill at ruining reputations, Havel panicked. He saw no way out of the trap that his own naivety had helped to set. He caught a glimpse of what it was like to be tempted. He even began to wrestle with the accusation, put about by the authorities, that he had actually succumbed to temptation. 'I had strange dreams and strange ideas. I felt I was being — quite physically — tempted by the devil, that I was in his clutches. I realised that I had somehow got tangled up with him. The fact that something I had written, something I had really thought and that was true, could be misused in this way brought it home to me yet again that the truth is not only that which one thinks, but also under what circumstances, to whom, why and how one says it.'
As if to pay penance for his brush with temptation — to spite the authorities' rumour that the world-famous playwright and dissident Václav Havel had accepted that his attempts to defy power were imprudent and ultimately futile — he wrote a new play called _Temptation (Pokoušení_ [1985]). The drafting process went slowly. Numerous fragments went into the bin. Whole sketches of the individual scenes — Havel's preferred way of writing plays — were also jettisoned. Suddenly, during October 1985, inspiration rushed through his fingers. The play took him only ten days to write, as if it was an act of self-preservation. Driven by the desire to shake off despair and to withdraw from the Faustian pact the authorities had prepared, he wrote 'in a state of increasing feverishness and impatience, you might almost say in a trance'. In prison, he had been sent a copy of Goethe's _Faust_ and Thomas Mann's novel on the same subject, _Dr Faustus,_ but the script he scribbled out feverishly was unique — and arguably one of Havel's very best.
The play, Havel later observed, is about 'structures' and the fate of people within them. It draws upon the old medieval legend of a man who sold his soul to the devil, and who became identified with a sixteenth-century necromancer named Dr Faustus, in order to tell the story of Dr Henry Foustka, a respected scientist working within a research institute. Life within the organization is all dull-grey ritual. Its white-coated staff are in the habit of hardly noticing one another. Their hearts seem blind. Their bodies are numbed by routine. Their brains are geared to the central task of producing and deploying and protecting the Truth, which contrasts oddly with the staff's immersion in an endless farrago of pointless chit-chat and joking, punctuated by requests for coffee and 'Did you sleep well?', the Director's preferred question of his staff. Bureaucratic thinking reigns, or so it seems. Until it is announced, to a flutter of controlled excitement, that there will be a staff social evening. But that event, and the preparations for it, serve as an absurd canvas on which Havel paints a profound crisis lurking within the organization itself.
The Director makes an official announcement, whose surprising content comes wrapped in language resembling anaesthetic before the knife. 'As you probably know,' he begins, 'there have lately cropped up complaints that our institute isn't fulfilling its tasks in keeping with the present situation.' He continues: 'We're being urged, with increasing insistence, that we go over to the offensive, that is, that we should at last somehow try to implement a programme of extensive educational, popular-scientific and individually therapeutic activity.' The arse-licking Deputy Director, always eager to impress, adds wisdom. He says that the programme should be firmly in the spirit of the scientific _Weltanschauung._ But he is cut short by his pompous superior, who continues to explain to his workers that these are modern times. He appeals to them 'to counter the isolated but nevertheless alarming expressions of various irrational viewpoints which can be discerned in particular in certain members of our younger generation and which owe their origin to the incorrect ... interpretation of the complexity of natural processes and the historical dynamism of human civilization, some of whose aspects are taken out of context, only to be interpreted, either in the light of pseudo-scientific theories ... or in the light of a whole range of mystic prejudices, superstitions, obscure teachings and practices spread by certain charlatans, psychopaths and members of the intelligentsia.'
The soliloquy is interrupted several times — by the late arrival to work of a breathless scientific worker carrying a bag of oranges, the Deputy's revelation that typewritten copies of the works of C. J. Jung are circulating among youth, plus a discussion of the daily soap ration. But the interruptions prepare the way for a scene in the dingy, book-lined apartment of Foustka, who is discovered kneeling in the middle of a dimly lit room, in his dressing gown, surrounded by burning candles, another in his left hand, while in his right is a piece of chalk with which he draws a circle round himself and the candles.
There is suddenly a knock at the door. It is Foustka's landlady, informing him that a stranger has come to see him. Foustka is instantly suspicious — his life outside the institute is evidently a risky business — but curiosity gets the upper hand. Enter Fistula, looking like a figure straight from a Beckett play, but actually a stool-pigeon, the secret agent of power who has come to tempt his victim. Fistula is a small, slender man with a limp caused by chronic athlete's foot, he clutches a paper bag containing a pair of slippers, and grins vacuously. Foustka, the secret opponent of the institute, its power over others and all that it symbolizes, stares at his surprise guest with a mixture of curiosity, suspicion and revulsion. So begins the sordid business of temptation.
Foustka reacts initially by scrambling to hide his private life from his unexpected guest: lights are switched on hurriedly, candles are removed, an attempt is made to rub out the chalk circle. Ritual _politesse_ is followed by a warning by the tempter Fistula, who is in the habit of grinning a lot, that the encounter should be kept a secret. Foustka is puzzled, then realizes quickly that his unsolicited visitor knows much about him, which makes him angry. 'Out!' he shouts. 'Leave my flat at once and never show your face here again.' Fistula rubs his hands together contentedly, sensing that Foustka's resistance is perhaps a prelude to co-operation. The cunning hunter tries to calm his victim by acknowledging that his host has every reason for suspecting that Fistula is an _agent provocateur._ Fistula, always on the move, then boldly confronts Foustka with three choices: 'You can continue to consider me an _agent provocateur_ and insist that I leave. Secondly: not to think of me in those terms but instead to trust me. Thirdly: not to make your mind up in this matter just yet and to adopt a waiting posture, which means not to throw me out but on the other hand to say nothing which, if I were an _agent provocateur,_ I might be able to use against you. If I may,' concluded the slippery Fistula, 'I'd recommend the third alternative...'
Foustka from here on makes a string of fatal mistakes common to all those who succumb to temptation: pacing up and down the room, he hesitates, then agrees reluctantly to the third possibility. He chooses to be 'flexible' — unwittingly he prepares to welcome the devil — and is greeted with the flattery of a fox. Fistula praises his caution, sharp intelligence, and ready wit, all of which, he goes on to explain, suggest that the two men can work well together. The suggestion upsets Foustka, who moves once again to shake off his tempter by denying he has anything to hide. 'I am a scientist and hold a scientific world view, working in a very responsible position in one of our foremost scientific institutes. If anyone comes to me with ideas that can be defined as an attempt to spread superstition, I shall be forced to act according to my scientific conscience.'
The tempted hangs on to respectability. Everything is at stake, but the unfolding hypocrisy subverts his claim to purity. Fistula, always looking for points of weakness to exploit, responds with riotous laughter, quickly apologizes so as not to repel his victim, then prepares the final trap by offering himself up to Foustka for scientific experiments designed to combat the spread of mysticism. Foustka agrees, then wriggles. The tempter in effect exposes the double standard of the tempted: at a certain stage in the process of temptation, the tempted is required to make the painful acknowledgement that he or she is a hypocrite. That Foustka does silently, at which point he becomes clay in the hands of his master. 'So what's to become of our agreement,' he asks Fistula sheepishly. 'That is entirely up to you,' replies the grinning Fistula.
Back in the company of his colleagues at the scientific institute, Foustka tries to recover his dignity by leading a normal life. He talks philosophy, charms a woman, acts politely in the company of the Director, whom he otherwise assiduously avoids. At one point, daringly, he even lectures the guests at the institute's social evening about the dangers of nihilism: 'When man drives God out of his heart, he makes way for the devil,' says Foustka. 'What else is this contemporary world of ours, with its blind, power-crazed rulers and its blind, powerless subjects, what else is the catastrophe that is being prepared under the banner of science — with us as its grotesque flag-bearers — what else is it other than the work of the devil? It is well known that the devil is a master of disguise. Can one imagine a more ingenious disguise than that offered him by our modern lack of faith? Doubtless he finds he can work best where people have stopped believing in him.' Foustka's talk of the devil is a moment of honesty. It is shortly afterwards followed by a private confession: 'Something is going on inside me — I feel I'd be capable of doing things that were always alien to me. As if something that had lain hidden deep inside me was suddenly floating to the surface.' He knows that those who sup with the devil must use a long spoon, and that his is too short. He grows angry with what he himself has done, brutally striking to the floor, and then kicking, a female colleague.
Honesty, confession, anger provide no hope for the tempted. The deed has been done, and only the public exposure of his temptation remains to be carried out. Like mice fondled by a hungry cat, the tempted are usually tormented by their tempter. So Foustka begins to feel fingers of power around his throat. The Director, reminding his colleagues that the institute is a lighthouse of true knowledge ('What we think today, others will live tomorrow!' he remarks), turns a finger in Foustka's direction, accusing him of indulging pre-scientific deviations, but promises that, since these are modern times, there will be no staged witch-hunts. 'Let the manner in which Dr Foustka's case is handled become a model of a truly scientific approach to facts, which will provide inspiration for us all. Truth must prevail,' he concludes, threateningly, 'whoever suffers in the process.'
The naive Foustka feels relieved. He tries to lie his way out of danger, claiming that he was only acting as a lone soldier doing battle against mysticism. Nobody believes him. He now knows that his days are numbered, and so he grows angry at his tempter, Fistula. 'You're a devil,' he shouts, 'and I don't want to have anything more to do with you.' Fistula replies that he has been no more than a catalyst, and that the honest truth is that in the final analysis Foustka himself _chose_ to be tempted. Foustka becomes morose. He confesses his 'unforgivable irresponsibility, for my having succumbed to temptation', but Fistula resorts to sarcasm, diagnosing his victim as suffering from the Smíchovský Compensation Syndrome: a 'hangover' of masochistic self-accusation and self-chastisement caused by the liquors of temptation.
None of this matters. Foustka is done for. He confesses to his indulgence of hermetic rituals; recognizes that he has been too clever by half, and that he has come a cropper by believing that he could play both ends of power against the middle and get away with it. He sees that, in the eyes of those who wield power within the organization, his ultimate crime can be summarized in the devilish maxim: To lie to a liar is fine; to lie to those who speak the truth is permissible; but to lie to the powers who ensure that we can lie with impunity — this is unacceptable and cannot go unpunished. The play does not reveal whether Foustka is promptly fired, made an example of, publicly disgraced, completely destroyed by his act of giving into temptation. He does sing a swan song of opposition to his opponents, railing against 'the destructive pride of intolerant, all-powerful and self-regarding power, which uses science as a handy bow with which to shoot down everything that might put it in jeopardy'. His speech is applauded sarcastically by the head of the organization, after which Foustka's clothes are set on fire, sending him running to and fro in panic across a stage quickly enveloped in smoke. The only player to take a bow is a fireman, fresh on the scene, fully uniformed, looking anxious, a fire extinguisher in hand.
### **Cliff-Hanging**
The assignment: to conduct a long, carefully prepared interview with the most famous 'dissident' in central Europe for London's _Times Literary Supplement._ Elaborate preparations have been made. My _nom-de-plume_ — Erica Blair — is to be used. Through the exile news agency Palach Press, permission is sought and received. 'Tell Miss Blair that I am happy to do it and I am awaiting her visit to Praha.' Exactly how we will meet — or whether Havel himself will be in prison — is unclear. A few days before the departure, my guide and translator, A. G. Brain — now Gerald Turner — telephones to say he has broken his right leg after slipping on black ice. That is exactly what we fear will happen to us once again after arriving in Prague, crutches in hand, pretending to be tourists. For two days, we split up and try to look inconspicuous, mainly by hiding out in the pubs and shops and safe apartments of the city. Then comes the prearranged moment of our first meeting with the man. Crammed around a dark corner table of a dingy pub on the Vltava embankment, Havel is gracious, offers us beer, cigarette in hand. We make final preparations for the following day. My host looks ill and exhausted from his long spell in prison, but he still manages to show his sense of humour. 'Umm, I am sorry,' he says in broken English, 'I had no opportunity to prepare my remarks because I was not today two hours in a prison.'
Next day's meeting made me tremble. Havel's fourth-floor embankment apartment in the heart of art nouveau Prague is a building site, its walls stripped bare in search of concealed microphones. Cigarette smoke blues the air. Havel fidgets constantly with his whisky glass, usually looking at the floor as he speaks. In the era of _glasnost,_ the tapped telephone rings often. Two StB policemen now stand guard across the street. Havel's dog, whose predecessor had been shot dead by the secret police on the doorstep, paces nervously at the front door, growling at every creak and thud in the building. The ugly atmosphere gets on my nerves, but my fidgety friend — as in our previous meetings — seems willing to speak with measured passion about his concerns, his tired face occasionally breaking into a warm smile. Short and slight with thinning sandy hair and a pouty moustache, he is described in police files as a 'subversive' and an 'anti-socialist element'; in situations like this, struggling to understand my English and random Czech, he seems shy, soft-spoken, sometimes with a slight lisp, the result of a prison beating, courageous, occasionally sanctimonious, and always stubborn under pressure — a rebel, one of the truly dangerous types, a subversive guided by civilized manners and a taste for freedom.
Time is precious. Olga brings Turkish coffee. Havel opens the bottle of Isle of Skye whisky I have brought him as a gift. There is no small talk. I kick off by asking him how, despite everything, he manages to keep his head above water. He quotes Franz Kafka: 'Why are you watching? Someone must watch, it is said. Someone must be there.' The watchman explains that totalitarian regimes such as Husák's Czechoslovakia and Honecker's GDR, although now on their last legs, are unique in human history. Using more civilized and sophisticated methods of control than the hack dictatorships of the Third World, they are all-embracing and spirit-destroying. 'These regimes get under society's skin,' Havel said. 'From morning to night, everything ordinary citizens do is in some way interfered with by the system. The regime leaves its mark on everything, from the way housing estates are built to the patterns of television programming.' The state is employer, policeman, social worker, judge and jailer rolled into one. It therefore pressures individuals to adapt and to capitulate, to reinforce the foundations of the very regime they spend time bellyaching about in the hidden corners of factories, kitchens, pubs and offices. Havel goes on to say that totalitarianism thereby heaps invisible violence upon everybody. It slowly destroys the individuality and basic human dignity of virtually every member of society, rulers and ruled alike.
Havel's words against the totalitarian regimes of the East are matched — surprisingly — by a deep suspicion of the West. He explains that he is not, and never has been, a professional anti-Communist. Both systems, he tells me, contain huge, faceless organisations which treat people as mere objects. 'The world is losing its human dimension,' he insists, Franz Kafka at his side. 'Self-propelling mega-machines, large-scale enterprises, faceless governments and other juggernauts of impersonal power represent the greatest threat to our present-day world. In the final analysis, totalitarianism is no more than an extreme expression of this threat.'
Havel reaches for another cigarette. Our conversation turns philosophical. We are slowly losing our grip on the world, he explains, precisely because we strive to be the supreme masters of ourselves and our universe. He points out that one of his favourite plays, _The Memorandum,_ satirizes this trend. Office workers are instructed by officials to learn a new 'strictly scientific' language, Ptydepe. It is supposed to eliminate misunderstandings by maximising the difference between words, so that no word can be mistaken for another, the length of the word being inversely proportional to its frequency of use (wombat has 319 letters, he reminds me). Ptydepe paralyses the office and baffles everybody who tries to learn it. So the bureaucracy introduces a new language that contains words so simple that they have virtually infinite meanings — and suitably disastrous consequences for the organisation. Havel admits that _The Memorandum_ is intended to be riotously funny — that it plays language games before audiences who are perforce confronted with players caught up in a power struggle for survival and self-recognition. 'In _The Memorandum_ I saw myself as a free-wheeling pop-art painter trying to take concrete segments of reality and then rearranging them in fantastic form,' he says. But he also insists that _The Memorandum_ well illustrates one of his most serious themes: our modernist attempt to know and to control everything — whether in scientific research, the development of technology, or politics — is slowly but surely paralysing our capacity as individuals to lead meaningful, independent human lives. Several times during our conversation, he mentions that the world is slipping through our fingers, and that this slippage cannot be prevented by grand leaps of faith into the future. He goes on to denounce Utopian visions, 'radiant tomorrows' he calls them. Life is ever-changing and lacking an essence. To try to master it fully, to clamp it down on to a drawing board and to blueprint its reconstruction, therefore always ends up strait-jacketing and destroying life. So Havel highlights a direct link between beautiful Utopias and the concentration camp. 'What is a concentration camp,' he asks, 'but an attempt by Utopians to dispose of those elements which don't fit into their Utopia?'
Havel's razor-sharp question reminds me why the West's enthusiasm for Gorbachev during the era of _perestroika_ was often considered naive, even disheartening, by many people in central and eastern Europe. The disgust produced by failed Utopias is something they feel acutely. Havel agrees that his plays aim to accentuate the aversion to radiant tomorrows. He says that they are inspired by the thought that theatre should question Utopias and encourage people to think and act less dogmatically. They deny that art is a refuge for moral Truth. Havel tells me that he rejects the common complaint of theatre reviewers — repeated at the time in England during Tom Stoppard's elegant adaptation of _Largo Desolato_ for the Bristol New Vic — that his own plays are tantalizing because they fail to grasp the moral nettles they themselves plant. Theatre, he insists, is an incomplete dialogue, the playwright essentially a witness to the times. Theatre shouldn't try to thrill or charm playgoers or make things easier for them by providing positive heroes. He admits that his plays provide warnings. But in the same breath he stresses that they don't arrogantly pretend to portray things as they 'really are'. They leave such sermonizing to Brecht and instead try to confront people with themselves — to make them think by prising open their awareness of the unresolved questions and problems facing them. Modern times are gripped by a permanent 'crisis of certainty', he says. Theatre should not pretend to know what is to be done. 'I try to fling my audiences into the heart of a problem that they can't avoid,' he says, pausing to light another cigarette. 'I try to push people's noses into our common wretchedness. Theatre should remind people that the time is getting on, that our situation is bad, and that there's no time to lose.'
Havel agrees to talk about how this idiosyncratic view of theatre as the adversary of totalitarian illusions has earned him considerable international acclaim. He describes how he began working in the theatre as a stage-hand, and how his 'bourgeois' origins excluded him from film school and university. He recalls how he soon became literary adviser at Prague's famous Theatre on the Balustrade, and how his first play there, _The Garden Party,_ brought him overnight fame in the early sixties with the tale of a regime racked and ruined by the struggle between the perfectionist Office of Liquidation and the modernising Office for Inauguration. Havel tells me that he mistrusts rigid categories, and that he does not like being pigeonholed as a master playwright of the Theatre of the Absurd. He says that his preferred authors are Hašek and Čapek, Beckett and Ionesco (whose influence is strong, he confesses, in one of his first plays, _An Evening with the Familý),_ and he acknowledges Kafka's decisive influence on his work. 'When I first read Kafka, I constantly had the feeling that I was writing it myself,' he tells me. 'It was as if I'd had a similar basic experience of the world.' We talk through some of his best-known plays, including _The Increased Difficulty of Concentration,_ an adaptation of _The Beggar's Opera_ and _Temptation,_ soon to be performed by the Royal Shakespeare Company at the Barbican in London. Havel quickly emphasizes that these accomplishments — he modestly declines to discuss his many literary awards, including the American Obie Prize for the best off-Broadway play and the 1986 Erasmus Prize — had had their painful side. His plays have not been performed in his own country for nearly twenty years, and during that time he has also been banned by the Czechoslovak authorities from producing or directing anything. He reminds me that his work did once slip through the net: an amateur production in 1975 of _The Beggar's Opera_ in a village near Prague. It led to a police raid, he says quietly, still looking down. All those who took part were interrogated and harassed. Such clampdowns visibly anguish Havel. Theatre needs a home, he says with a wince. A play which remains a mere script is only ever half-finished.
The point helps to explain why Havel, the playwright with an aversion to power-grabbing politicians, has been dragged into politics, apparently against his will, subsequently forcing him to make the best of fate by acting as if he were both playwright and performer in a political opera. He has paid the price: several prison sentences, and more to come. Yet Havel's taste of total power — remarkably — has not seemed to produce hunger for power over others. He appears to harbour no illusions about party politics and professional politicians. He tells me, reaching for another whisky, that he sees himself as an ordinary citizen, endowed with inalienable rights of self-determination. 'I favour a politics growing from the heart, not from a thesis,' he continues, insisting that politics 'from below' is indispensable if individual people are to seek and to protect a meaningful existence in a world threatened by impersonal organizations. Havel acknowledges that small-scale, local activity directed at such organizations is often ridiculed by Western politicians, who consider it as fanciful as the Lilliputians' attempts to tie down Gulliver from below by thousands of small threads. But he strongly disputes this view. 'It's becoming obvious,' he says with Lech Walesa and Solidarnošc in mind, 'that politics doesn't have to remain the affair of professionals and that one simple electrician, with his heart in the right place, can influence the history of an entire nation.'
During our five-hour discussion, Havel tries to emphasize several times that he is a reluctant political figure: he says that he wants above all to get back to writing plays and to have them performed in his own country. 'But whether you like it or not,' I reply, 'you are now a star performer in a theatre of opposition.' I add that political figures normally hate irony, which corrodes their own certainties by revealing the ways in which the world is full of ambiguity, and I remind him that in his play _Temptation_ a character says: 'I don't give any specific advice, and I don't fix anything for anyone. The most I do is to stimulate now and again.' Havel agrees that that line is his credo as a playwright — and he expresses the hope that it will serve as a future maxim of his own philosophy as a political writer and public figure.
We discuss how Havel's own civic activities have multiplied rapidly during recent years. He had been a founding spokesman for Charter 77 ('a community of people acting independently and trying to voice the truth') and a key figure in VONS, a citizens' group working for the protection of the unjustly prosecuted. At the end of the 1970s, he had been a key participant in the bacchanalian border meetings between the Czechoslovak and Polish democratic oppositions. In the early 1980s, he had conducted an important dialogue with the Western peace movement, urging its activists to swallow the bitter fact that 'peace', a pampered term in the prolespeak of the Communist Party, generated little enthusiasm in central and eastern Europe. This argument, expressed in a number of essays, produced another of the many ironies that had so far defined his life: the prestigious Olof Palme Peace Prize. At the time of our meeting, Havel was also busy with samizdat publishing and the emerging key figure in beleaguered 'dissident' circles.
Havel confesses as well that he has come to sympathize with green politics: 'The green movements have brought to the surface issues — such as whether there is any sense in threatening future generations by the constant drive for increased production — which the traditional political parties have neglected.' The greens' 'non-ideological stance and advocacy of non-violence are close to my own head and heart'. Havel reveals how profoundly he had been influenced as an early teenager by Josef Šafařík's _Seven Letters to Melin,_ in which an engineer defects to philosophy, blames modern science and technology for the contemporary crisis of humanity, and concludes that conclusions can only ever be tentative, and that each individual is ultimately responsible for co-determining with others how each shall live. We discuss the prominence of ecological images in his writings. He explains that among his strongest is a powerful boyhood memory of walking down a country lane from Havlov to school in the shadow of a huge munitions factory. 'The chimney spewed dense smoke and scattered it across the sky. Each time I saw it,' he says, 'I had an intense feeling that something was profoundly wrong, that human beings were fouling the heavens.'
Such powerful memories evidently feed Havel's philosophical conviction that the human will to master the world produces poisonous outcomes and that therefore the human species, to avoid disaster, should abandon our arrogant presumption that 'Man is capable of knowing everything, describing everything and doing everything'. We should instead let things be, he urges, all the while trying to nurture a sense of wonder and respect for the world. Havel insists that his call for human modesty is not a plea for apathy. At the end of our meeting, he acknowledges the pitfalls of nihilistic despair; he also stresses the inexhaustible strength that flows from sticking to principles and prodding and poking at the world around us. 'Only by "looking outward" and throwing ourselves repeatedly into the tumult of the world, with the intention of making our voices count — only in this way', he says, 'do we really become human beings.'
The words escaping his gritted teeth were poignant, especially considering that for nearly two decades Havel had been living under constant police watch, ever in danger of arbitrary arrest and imprisonment. His had been a hard and often discouraging life, as his letters from prison bear witness. He tells me that he has tried hard to master the difficult art of waiting patiently, and that nowadays nothing really surprises him. I reply by reminding him that the power of the unexpected can sometimes exceed that of the most powerful governments and politicians. What neither of us realizes is that in a matter of a few months after our meeting his stubborn, civilized patience was to be vindicated, then tested by the temptations of power. Massive crowds were soon to gather in the frozen rectangle called Wenceslas Square to exercise 'candle power' (as he later called it) or, emulating the storming of the Bastille, to jangle keys together — the keys of the Czechoslovak prison — while chanting 'Give the jesters their cap and bells'. The Party lies of 'normalization' would soon begin to collapse into a twisted heap of confusion. The riot police and water cannon would begin to flinch. Chants of 'Long Live Havel!' would echo through Prague's cobbled streets and narrow passageways. A big surprise indeed was just around the corner. Yet Havel's last words to me remained circumspect on the brink of political success. 'I'm full of hopes, doubts, determination, uncertainties, plans, fears,' he says with a wrinkled smile, gripping my hand to say goodbye. 'For the time being, I'm sure of only one thing: for me it will always be a cliff-hanger.'
## **_Velvet Revolution_**
## **_(1989)_**
### **Revolution**
Never mind cliff-hanging. It was now time for Havel to move to the streets of Prague. It is Friday, 17 November 1989: the first day of the Velvet Revolution. Nobody thought of it that way, of course. A hallmark of revolutionary alterations of power is that they are always unanticipated and unplanned. Revolutions are surprises on a grand scale. Initially, no one is in charge. They never obey the rules of the putsch. _Coups d'état,_ the Prague variety of 1948 for instance, are a type of carefully planned seizure of power. They entail elaborate preparations, usually in secret, and they are executed swiftly, often in the wee hours of the morning, when most of the population is in bed, asleep. Their effect is felt instantly: troops surround the central radio and television stations; the international airport is closed; bank accounts are frozen; new or reshuffled faces appear in the ruling group; government orders, instructions, and policies immediately reveal that things have changed, or not changed at all. Revolutions are not like this. They are not calculated in advance; and they may even be described as a long chain of unintended consequences. Revolutions consequently have no easily definable point of origin. And although they are not about trifles (as Aristotle observed) they often spring from what appear at the time to be trifles.
No one had anticipated that sometime during that dark and dreary mid-November day late-socialism in Czechoslovakia would begin to collapse. A crowd of some 15,000 students had gathered peacefully that afternoon outside the Pathology Institute to commemorate the death of Jan Opletal, a student victim of the Nazi occupation fifty years earlier. The commemoration had the Party's approval, and the list of speakers, both official and unofficial, had been organized by the university council of the Communist Youth Union. The students' request to walk on to Opletal Street near Wenceslas Square, after the rally, had been refused by the authorities, so an alternative was authorized. The students were to march to the cemetery in Vyšehrad, where they would gather at the graveside of the nineteenth-century poet, K. H. Mácha. And it was agreed with the authorities that the customary candles would be lit, wreaths and flowers would be laid, the national anthem would be sung, after which the procession was to disperse quietly.
Everything but the last clause in the contract was satisfied. Instead of dispersing tamely into the evening darkness, thousands of students, feeling their spines straightening, spontaneously began to march towards Wenceslas Square. Tension rose suddenly when the students were temporarily halted by the police at the Botanical Gardens. In the distance police orders were barked. The demonstrators began to sing the national anthem. A flying wedge of helmeted police wielding truncheons cut into their ranks. Scuffles broke out. Shouting and chanting erupted. The awful sound of clumping boots was temporarily drowned by cries of 'We are unarmed!' _(Mame prázdné ruce)_ and 'No Violence!' _(Nechceme násilí)._ The police with truncheons now pointing at the best brains in the country seemed hellbent on breaking up the demonstration. They began by swooping on a young bearded anarchist named John Bok. They had been looking for a pretext to arrest him for some time, and Bok, a man with unusually sharp senses, knew they were cutting through the crowd specifically to arrest him. 'Tell Vašek!... Get a message to him at Hrádeček!... Tell him what's happening! Quickly!' he shouted to his friends, gasping for air, as a clutch of mean-looking policemen headlocked him into arrest and dragged him, kicking back while being kicked, through the crowd and dumped him into a nearby van waiting to take him directly to prison.
Bok refused that afternoon to talk to his interrogators at Ruzyně prison. After being charged with assault of a public functionary, he was allowed one brief phone call to his wife, to whom he repeated the message that he had earlier gasped to his friends. 'Please make sure that Vašek, who is at his cottage, gets the message to return urgently to Prague. Something has changed. He needs to be back here. Fast.' Following those words, Bok was beaten, deprived of sleep, and tortured by pushing his body backwards over a chair, so that he couldn't properly breathe. The uncivil police methods presaged the fate of the remaining demonstrators. After losing Bok from their ranks, they marched on defiantly towards Wenceslas Square, edging along the banks of the Vltava River. Scores of curious bystanders, like monks coming to prayer, silently joined in. So did actors and theatre staff. Friday night patrons of the Café Slavia, located riverside just near the Havels' flat, downed their drinks and joined the throng. Outside the famous Klášterní vinárna (the Monastery Wine Bar), waiters and customers came outside on to the streets and called out to the young demonstrators, who by now had lost their fear. They were in a relaxed and cheerful mood, and repeatedly chanted out in defiant tones, 'Join us! Join us!' and 'The nation's helping itself! _[Národ sob ě]'_
Havel, who had gone into retreat at Hrádeček with Jitka Vodňanská, happy to be off 'the Prague merry-go-round', received Bok's message. He hurried back by car to Prague, where he arrived home around midnight. He heard from his brother Ivan, and from Olga, breathtaking news. At a performance of Ivan Kurz's _The Madman's News_ at Smetana Hall in Prague, the audience had cheered and applauded Václav Neumann, the director, and the members of the symphony orchestra, who had signed a petition protesting against Havel's most recent imprisonment. Olga reported the irony that during the performance of _The Madman's News_ the state television and radio stations had coldly issued a ČTK communiqué which stated that the day of remembrance had been 'hijacked by anti-social elements, well known to the police, and authors of various recent outrages'. The communiqué had denounced those who had chanted slogans hostile to the socialist state. It described them as uninterested in 'dialogue, reform, or democratization'. They were forces of instability, violence, and social destruction. 'Because of this,' it concluded, 'the forces of order were obliged to take necessary measures to restore peace and order.'
A different, but equally exaggerated, version of the events, Havel learned, had just been broadcast by West German television. It informed viewers that reports were being received that an insurrection was taking place in Prague, that its streets were full of young people, that the police were out in force, and that Prague Castle was surrounded by tanks. Something rather different had happened, in fact. After the arrest of John Bok, the originally smallish student demonstration had safely reached the National Theatre, where its numbers had mushroomed to over 50,000 people. At that point, everybody who had been present confirmed that all public places adjoining the demonstration were packed, as if, after all the years of isolation, people could not get enough of each other's company. The protest seemed to take on a life of its own, as if it had sprouted wings, which is perhaps why at around eight o'clock, as it snaked into Národní třida, it was suddenly greeted with walls of riot police.
Determined not to allow the marchers to reach Wenceslas Square, the commanders of the police operation ordered the leading demonstrators to disperse and simultaneously cut off their long tail of supporters with another thick wall of riot police. Suddenly the crowd realized that it had lost its escape route, and that it was surrounded. All hell broke loose. Many of the trapped and panicky demonstrators began to chant, 'No violence! No violence!' and 'We are unarmed!' Thinking that this might just be another temporary halt enforced by the police, some parts of the crowd called, 'We'll go home from Wenceslas Square! We'll go home from there! [Z _Václa váku dom_ ů]' Other demonstrators, sensing correctly that they were now at the mercy of the white-helmeted riot police, taunted them with shouts of 'Freedom! Freedom! _[Svoboda]'._ Still others bravely made fun of the President by calling him by his first name, and by mimicking his strange ungrammatical way of speaking, deliberately mispronouncing his name in a working-class drawl. 'Jakeš, Jakeš...' they called. 'We don't want Myloš! _[Nechceme Myloše]'._
Once again came the megaphoned order to disperse. The crowd now knew that this was a sick joke, since there was nowhere to go. Many trembled, sat down, then began to sing the national anthem, followed by 'We shall overcome'. Keys were jangled, and a handful of young women were seen giving flowers to the unsmiling police, fixing them on to their helmets and transparent shields. Hundreds of candles were lit. 'No violence! No violence!' the seated crowd again chanted, yellow light flickering on their faces. Some again called out, 'Freedom! Freedom!' The response was swift. Riot police charged from both sides into the trapped crowd. It began rising to its feet, only to be thrown violently against itself, then flung about, jumbled into confusion, and stampeded into the arcades next to the Reduta jazz club.
The crush was so great that individuals began to gasp for air. Many shrieked for help. Cameramen and photographers began to be manhandled out of the way. Then out of nowhere armoured personnel carriers, diesel engines revving, arrived on the scene. Out poured scores of grim-faced Red Berets, the feared Special Anti-Terrorist Forces, who instantly charged at the demonstrators, herding them back to the street, wielding long truncheons on men, women, and children, pushing and shoving each of them in the direction of a carefully prepared narrow path flanked on either side by riot police. The street was filled with sounds of ripping clothing. Glasses scrunched underfoot. Thudding truncheons. Heavy breathing. Screams. Confused shouts. Then shrieks of demonstrators being pushed in ones and twos through the police funnel. Each was punched, kicked or cracked over the head or shoulders. All came through the tunnel looking dazed. Some cursed. Most stumbled. Others crashed to the ground, stunned, bleeding. The lucky ones were dragged into side streets to safety by friends and helpers. The luckless lay there, kicked and struck into unconsciousness.
### **Velvet Power**
The Velvet Revolution that magically began that afternoon was to produce a fundamental change of governmental power, without sparking civil war. Like all revolutions, it triggered bitter public controversies about who gets what, when, and how. It tore apart the old political ruling class and invented new rules for new political actors. The revolution bestowed the power to govern on new decision-makers. It forged new policies for tackling local and national problems and for reacting with and against international swings and trends. But the revolution did something more basic than this. It also flung everybody temporarily into an everyday world marked by flux, ambiguity, contingency. No doubt, the revolution drew together clumps of previously divided citizens who shared new memories, values, aspirations. The revolution legitimated not only governments and policies — practical outcomes — but also new shared sets of symbolic meanings and emotional commitments. The revolution produced a collective feeling of solidarity of the previously powerless. But in granting citizens a new freedom to speak and act differently the revolution also forced everybody into a state of unease. It catapulted them into a subjunctive mood. All of a sudden, some things were no longer sacred or forbidden. Everything seemed to be in perpetual motion. Reality seemed to lose its reality. Unreality abounded. There was difference, openness, and constant competition among various power groups to produce and to control the definition of reality.
When millions of oppressed people are flung together into a subjunctive mood they naturally feel sensations of joy. Hope and history are words that seem to rhyme. 'Bliss was it in that dawn to be alive,' wrote Wordsworth, and so it usually is in all upheavals of a revolutionary kind. Revolution is a transformative experience. 'It was like a step into an unknown space,' said Havel, as if everybody was staging 'a play that was unfinished'. Revolution is an adventure of the heart and soul. Citizens initially feel personally strengthened by it. Their inner feelings of barrenness, emptiness, isolation momentarily disappear. They lose their fear. They feel lighter, joyful, more enthusiastic, even passionate about their family, friends, neighbours, acquaintances, and fellow citizens. They feel they have a future. Astonished, they discover boundless energies within themselves. They experience joy in their determination to act and to change the world. Their participation in the turbulent thrill of the revolution becomes a giddy exploration of the unknown. The Germans call this giddiness _Freude._ The French call it _jouissance._ The Spanish call it _alegria._ The Czechs call this state of intoxication _euforie._
All this is familiar. But it is equally clear that revolutions are also fickle events. Revolutions are times of condensed uncertainty. The joyful solidarity they produce is always countered by a shared sense of menace, danger, foreboding — of the sensed possibility that things will get worse, that evil will be the offspring of good. Revolutions disorientate people. They breed anxiety. Not only do many rediscover the obvious rule that the familiar normally serves as a comfortable home. They also learn at first hand that not everybody gains during revolutions, that indeed many lose out, and that everybody, through the course of revolutionary upheaval, fears to a greater or lesser extent that they will be pushed on to the side of the losers. The history of modern revolutions from the late eighteenth century onwards suggests that revolutions are never 'the irruption of the masses in their own destiny' (Trotsky), for the simple reason that they always — the Velvet Revolution was no exception — unleash the lust for power among jostling minorities of organized manipulators, who seek the ultimate prize: immense power over the lives of millions of others. During revolutions, that is to say, power struggles among political factions always break out. Within the old ruling groups, the knives are usually drawn. Groups of professional counter-revolutionaries are born. Within the ranks of the opposition, groups of professional revolutionaries possessed of great initiative, organizing talent and elaborate doctrines also make their appearance. At first, they appear to listen to their fellow citizens who are rebelling on the streets. Later, these revolutionary grouplets claim to represent them. Eventually, they supplant them, sometimes through violence. The professional revolutionists press home the need to avert counter-revolution and to revolutionize the revolution. The revolution is seen to be an irresistible necessity. This enables the revolutionaries to justify their actions, to sacrifice their victims to the great event, and to absolve in advance any guilt or crime that may be committed in the name of the revolution. Strangely, this idea of the necessity of the revolution is mixed up with the contrary presumption, among both the revolutionaries and their opponents, that human beings have absolute power over their destinies. And so revolutions are usually dangerous affairs. Revolutions are like hurricanes. Drawn into their forcefields, human beings find that it is possible to commit actions that posterity, out of sheer amazement and horror, finds it difficult to comprehend, let alone to justify.
The first day of the Velvet Revolution confirmed these maxims. Whatever observers may now think of the scale and causes of the events, the mayhem that followed undeniably scared many people, revolutionaries like Havel included. He noted that the authorities did their world-historical best to restore calm and to rebuild order and normality. On the morning after the events, on day two of the revolution, Communist Party newspapers reprinted the CTK communiqué, adding only that by ten o'clock in the evening the centre of Prague was peaceful again. The official press also reported some heavily doctored casualty figures: 7 policemen and 17 demonstrators had been injured; 143 people had been arrested and a further 9 detained for further questioning; 70 others had been caught _flagrante delicto_ disturbing the peace; 21 others had been fined and released.
Quite the opposite message had meanwhile spread like fire through Prague. The word 'massacre' began to be heard everywhere. Whoever invented it either committed an unintended exaggeration or deliberately produced a white lie. But its effect was to arouse public indignation against the whole Communist system. As each hour passed, talk of massacre ensured that the radical resistance that had sprung up in the university faculties and theatres quickly spread into the streets. Televisions set up in shop windows ran videotapes of the police brutality. At scores of unofficial meetings and in theatres, cafés and pubs all over the city people began to talk of the need to stand up to the Communists, even to defeat them, for instance through strike action and public hearings about police brutality. Inebriated by their own power, crowds began to deface statues, rename underground stations, tear down Communist Red stars. Some people began to hold all-day vigils, lighting hundreds of votive candles at bloodstained sites, and then standing back in silence, as if in prayer.
Whatever fear and vacillation remained on the second day of the revolution suddenly evaporated with the extraordinary news, based on Western media reports that evening, that Martin Šmíd, a young student at the faculty of mathematics and physics, had died from injuries received the previous night. It later transpired that the report was untrue. The standard story is that Havel's Trotskyite friend Petr Uhl had been approached by two StB agents who provided him with details of the death. Uhl was the director of a dissident press agency and in that capacity supplied Western agencies with the world-shattering news. Whether or not Uhl was handling the truth carelessly, or what the motives of the agents were, or why the dithering authorities subsequently spent a whole day searching for the supposed fatality, remains unclear to this day. It was subsequently alleged that an STB secret-police agent had infiltrated the demonstration, provoked it to change course, and then fell down, feigning death, to be carted away by an StB ambulance. The ploy was evidently backed by pro-Gorbachev Party bosses whose aim was to fire up the population, to discredit the hardliners, thus improving the chances of 'the moderates' retaining power. Whatever the case, the truth of the matter did not matter at the time. In thousands and thousands of minds, the death of a young student at the hands of the Communists during a demonstration to commemorate the death of a young student at the hands of the Nazis fifty years earlier proved that the two systems stood on the same continuum of intolerance, totalitarianism, violence.
With danger in the air, Havel was forced to grow concerned about his own personal safety. His friend John Bok especially criticized his habit of walking everywhere and of making his own way home at night after political meetings. He quickly convinced him of the need for protection. Several days into the revolution, long-haired, energetic Bok had organized a private police force to protect the body of the man who would prove to be its principal actor. The Force — 'the boys', Bok preferred to call them — operated from the outset according to the rules of military-police discipline. The thirty or so young men were not especially political. But they had grown tired of the Communist system and were alert to the high risks and dangers of this present moment in history, which their native intelligence told them was of historical significance. The Force was well briefed: their job was to protect the lilliputian figure, a man of the people, by operating in secret a rival force to that of the official StB, without it spotting and catching them. The Force looked and dressed like Czech athletes in training, which several of them were in fact. Full of energy, tall and physically agile, they wore track suits and trainers and were strictly forbidden to drink alcohol while on the job. They had excellent road sense and knew Prague like the backs of their big hands. Several were equipped with short-range walkie-talkies, which were used sparingly lest they were detected or monitored by the StB. All were skilled in the arts of seeing and shielding, without being seen.
The tasks of the Force were initially easy to execute: chauffeuring and ferrying Havel here and there all over Prague. Concealing his whereabouts. Keeping watch for the feared official police. Anticipating or foiling any plot they might be hatching to snatch and detain their man. Ushering Havel politely through small crowds of well-wishers. Making sure he shook and kissed hands in moderation, so that he could be on time for the next string of meetings. The problem of scheduling soon mushroomed in size and complexity. For the first time in his life, Havel found himself ever more trapped within a thickening forest of appointments. Individuals and groups, enjoying the new freedom to act with and against each other in opposition to the regime, wanted time with him, and he with them.
Gone for ever was the halcyon tranquillity of trilobite-hunting at Barrandov, peaceful walks through the woods at Hrádeček, long early-morning baths, sipping coffee laced with rum. Some mornings now began before first light. The days usually stretched unbroken beyond nightfall, and often well past midnight. The pace had to be quickened, kept up, quickened again. Amidst mounting chaos, appointments needed to be made and kept. Havel had to be reminded of them; alterations needed to be made; others had to be contacted as and when events demanded; routes and vehicles had to be co-ordinated; and, given the dangers of further police and army crackdowns, everything had to be executed quietly and invisibly.
The job of crowd control was not especially difficult at first. But the technique of gesturing Havel along his route with outstretched hands soon had to be replaced with flying wedges. As each day passed, and especially after the appearance of the first trolley cars adorned with banners reading _Havel na Hrad_ (Havel for President), the Force found itself up against thickening walls of people, whose good nature was overpowered by its heaving numbers and, hence, the growing probability that Havel would be mobbed, trapped, knocked down, trampled, injured, wilfully hurt, assassinated even. No one, and certainly not Havel himself, knew the authorities' intentions or tactics, especially after his daring act on the third evening of the revolution: to convene a meeting of citizens at theČinoherní klub theatre to discuss and to decide what now was to be done.
The wise political animal Havel did not know that the gathered group of revolutionaries was destined, in quick time, to lead the struggle against the old order, let alone that it would form itself into a shadow government. But he had the good sense to invite a broad and motley array of individuals and group representatives whose opinions captured something of the various hopes, fears, and angers sparked by the so-called massacre. The packed meeting included Charter 77 veterans, the Pen Club committee, members of groups like the Society for the Protection of the Unjustly Prosecuted (VONS), Art Forum, the Independent Students' Union, the Czechoslovak Helsinki Committee, the Circle of Independent Intellectuals, Renaissance _(Obroda),_ the Czechoslovak Democratic Initiative, and independent members of the churches, banned Christian and socialist parties, and other associations. That evening, on Sunday, 19 November 1989, at 11 p.m., after brief but spirited discussion, the meeting voted unanimously to form itself into a new citizens' umbrella group called Civic Forum _[Ob čanské fórum]._ In the early hours of the next morning, it issued a proclamation. Signed by Havel and seventeen other representatives, the toughly worded document aimed to bring to justice those responsible for the massacre. It sought to remind the population of the tragedy that befell them after capitulating silently in 1968. It aimed as well somehow to split the ruling Communist Party by identifying some of its hardliners. The proclamation called for the resignation of the current Federal Minister of the Interior, František Kind, and Miroslav Štěpán, as well as those Communist leaders (like Gustáv Husák and Miloš Jakeš) who had actively supported the Warsaw Pact invasion in 1968. It went on to propose the setting up of an independent Civic Forum commission chartered to investigate the massacre and to punish those responsible. And, as if to remind everybody of the need to lift their political sights, it called for the release of all political prisoners, including those (like Petr Uhl) who had been arrested that day.
It would have been easy for the authorities to pick off Havel and his Civic Forum colleagues. They instead kept their fingers off the trigger, probably because for the past two days, ever since the outbreak of the revolution, everything had gone badly for the Communist Party. The silent reprieve gave Havel courage that more could be done. He moved fast to seize the initiative, protected by the Force through all the confused twists and turns of the revolutionary maelstrom. From the moment Civic Forum was formed, Havel manifestly set his sights on becoming Leader of the Opposition. He busied himself initially in securing his immediate power base, for instance by helping to set up and monitor Civic Forum committees concerned with operations, technical advice, information, and planning of strategy. He paid special attention to keeping his fingers on the rapid pulse of events. His days were long and filled with scores of conversations, more or less confidential, laced with endless cigarettes, brandy and beer, snacks and cups of coffee. He quickly looked wrecked, as if to play the part of the rakish revolutionary leader burdened not by the weight of the past, but by the massive uncertainty about the fate of the present.
There are always moments in a revolution (as Jules Michelet pointed out) when actors feel as though normal mechanical time has vanished. This was certainly that moment. Sometimes Havel had the feeling that the revolution — he was now convinced that this was the right word to use — was moving too slowly, and at other times too fast. It never felt just right. Things often moved too slowly because people's actions, including his own, quickly became ensnared within thickening webs of relations, obligations, problems, misunderstandings, all of which gave him and those around him in Civic Forum the feeling that their efforts were being diverted, dissipated, or bogged down in details. Yet events also sometimes seemed to move too quickly. Things happened and disappeared so fast that everybody had to hurry in order just to experience them. The revolution seemed to hurtle forwards at breakneck speed, with such force in fact that the proliferation of surprises and unforeseen events induced flutters and fears in everybody's hearts. In either case, it felt to Havel as if the unfolding revolutionary events could not easily be brought to an end — neither that they could be halted nor that they pointed to a happy ending.
On board the revolution rollercoaster Havel worked hard through Civic Forum both to ensure its survival and to guarantee its role as the beating heart of the emerging opposition body. With his support, Civic Forum dispatched delegates all over the country with the aim of establishing brother and sister chapters. Attempts were also made to embarrass and paralyse the regime by sending delegations of Civic Forum representatives to visit all the strategically important state bodies, such as the Parliament, the Federal Government, the Czech Government, the Presidency, the Czech National Council, and the Ministry of the Interior. The delegations were typically met with sweet words or brick walls, but that did not matter because on each occasion the Civic Forum activists were chaperoned by cheering crowds, which gave the opposition the moral high ground and had the added effect of making the political authorities look as though they were paralysed by crisis. Havel, fearing that they would use violence, like cornered animals, lent his hand to the Forum's efforts to calm public nerves and to appeal for absolute physical restraint within the ranks of the demonstrators, despite police provocations and rumours.
Among the many paradoxes of the Velvet Revolution — its name was drawn from the 1960s New York experimental rock band, the Velvet Underground — is that it began violently and continued throughout to threaten to rain down violence on a torrential scale. Havel told friends that he found the whole saga nerve-wracking, for he knew that any attempt by the authorities to impose martial law would throw everything into the pot of jeopardy. He also knew that the persistent and ineradicable threats of violence — symbolized by the omnipresent walls of grim-faced police dressed in riot gear — might at any moment puff up the street crowds into violent explosions. Everything rested on a knife-edge, especially after hundreds of police moved in on the fifth day of the revolution (Tuesday, 21 November) to surround and protect the building of the Central Committee. The sinister symbolism of that move was compounded by next day's rumour, which ran hot through the street crowds, that all Prague schools and university faculties were being visited by security-police agents; that in nearby Pilsen militia leaders had urged Jakeš to 'stand firm and reject reforms' and to recognize that 'force should be met by force'; and that 40,000 troops were closing in on the city to prepare a Beijing-style crushing of the Czech democracy movement.
Havel hoped against hope that everything would turn out well. Measured calculations dictated the conclusion that the regime would not crack down violently on its opponents. Moscow might not approve. The western enclaves of the Soviet empire were anyway in an advanced state of collapse (Communism had already peacefully collapsed in Hungary and Poland, and neighbouring East Germany was in turmoil). Violence would hardly bring much-needed economic reform or solve any other structural problems of the regime. Violence might well make the country ungovernable. A military crackdown would surely breed resistance from the emerging civil society. There would also certainly be a huge international outcry against a repetition of the Prague Spring solution. And yet within a revolutionary crisis of this kind, Havel sensed, reasoned calculations could count for nothing in comparison with the authorities' fear-driven impulses. So he helped do some fire-fighting, as when he and Professor Jelínek from the Civic Forum leadership made several desperate telephone calls to the Pilsen militia leaders, who were indeed getting ready to issue live ammunition. The tactic of responsibly calling the militia's bluff and sending off a thousand demonstrators to their buildings worked.
The success convinced Havel that the chances of a non-violent or 'velvet' outcome would partly depend on his winning leadership of the opposition. Nothing was certain. But a week into the revolution he had begun to look and act like the moral and political leader of the resistance to late-socialism. The revolution itself was proving to be a great spectacle. It enchanted both observers and participants alike, and so Havel, a master dramatist and compulsive planner of his and others' moves, climbed eagerly on to a stage already clotted with countless actors. Edmund Burke's remark to Lord Charlemont during the French Revolution, 'What a play, what actors!', applied just as well 200 years later to the Velvet Revolution, and particularly to Havel himself. His public quest to confirm his leadership — a show _par excellence —_ began at the Prague theatre Laterna Magika. Havel chose that as the site to base the headquarters of Civic Forum, whose inner circles quickly began to function as a government in waiting.
There, in the smoky caverns of the Laterna Magika, he coordinated the huge task of drawing up blueprints for the future of the country, helped by a team of experts, including several frustrated _prognostiks_ (academic economists), to whom the Jakeš government had refused to listen when the time had come for _perestroika_ reforms: Dr Komárek, Dr Dlouhý, and his future enemy number one, Dr Klaus. Reporters from all over the world began to crowd into the theatre, hoping to get a glance or word from the becoming-famous playwright-leader. Havel tried to put some order into the chaos by organizing press conferences, among the first of which was held at 8.30 p.m. on 22 November. At an informal briefing beforehand, his furrowed face radiated confidence as he spoke of the past twenty years of post-totalitarian repression, the misuse of the word socialism, the organized lying about everything, including the Prague Spring and the recent massacre. He said that Civic Forum wanted to replace the powermongering, lies and corruption of the old order with a pluralist democracy. It wanted guarantees for independent economic activity, which was not the same as the restoration of capitalism.
Towards the end of the briefing, Havel said in jest to one reporter, Dana Emingerová, that if details of the briefing were published in the Czechoslovak press then he would pass on to her the prestigious Olof Palme Prize, which he had that day been awarded. In retrospect, the remark was highly revealing of the reigning ignorance within the opposition about the state of morale and fortitude within the upper ranks of the nomenklatura, who were now beginning to panic so wildly that they resembled the swine of Gadarene. Havel's last remark at the briefing reinforced this impression. A messenger had just informed him that a highly secret extraordinary session of the Central Committee had just voted out the compromised leaders in favour of a reformist faction led by Štrougal. 'This probable fall of the compromised calls for champagne,' said Havel with a grin, without knowing that the Party session was not so extraordinary — simply because the _whole_ of the Communist Party was in an advanced state of implosion.
Although it took several weeks for Havel and the rest of the inner circle of Civic Forum to realize that they had overestimated the power of the ruling party, he cunningly managed to manoeuvre it into its greatest public test of the revolution. The plan was to put the Party on trial before the emerging public opinion by inviting a senior Communist to address a public rally. The experience of addressing a public without rigging the setting, theme or outcome had almost been forgotten in Czechoslovakia since the military crushing of the Prague Spring. Havel reasoned that the Party leadership, well accustomed to deciding things in committees and behind closed doors, would probably be wrongfooted when exposed to the test of public-opinion-making. He personally had found unforgettable his public debut at Dobřís and more recently — eleven months ago, on 10 December 1988 — he had for the first time addressed a demonstration in Prague's Škroup Square (so named after the composer of the national anthem). Czechoslovak television and amateur video images of that rally show the wispy-haired Havel up on the podium, dressed in a black leather jacket and a brightly coloured scarf, speaking into two loudhailers, attended by a young student, poking fun at the authorities, singing praises to citizens, evidently enjoying the stage performance immensely.
Havel had the chance to repeat this kind of performance on a freezing but sunny Tuesday, 21 November 1989, this time before an immense crowd of over 200,000 demonstrators squeezed into Wenceslas Square. It was the first time Civic Forum figures like Václav Malý, Radim Palouš, Milan Hruška, Karel Sedláček and Havel himself had appeared before such a large crowd. Although earlier that day the air had been rife with rumours about martial law and Chinese-style massacres, the crowd defiantly took refuge in its size, cheering the speakers standing up on the balcony of the Melantrich building, the headquarters of the Socialist Party, whose general secretary, Jan Škoda — a schoolmate from Poděbrady — was a founding member of Civic Forum. The wildest cheers of all were reserved for the nervous Havel. He made a tremendous impression as well on the police, many of whom were spotted sporting the national colours on their lapels and cheering Havel. His political career as Leader of the Opposition was now much clearer, and it was confirmed within hours by a secret approach to him from a leading Communist, Evžen Erban, sent by Premier Adamec to propose that secret negotiations about the future of the country begin immediately.
Little is known about that first contact with the Party, but Havel's determination to look and act like the next leader of the country was revealed in the letters he immediately drafted on behalf of Civic Forum to Presidents Bush and Gorbachev. The letters aimed to inform them of the deep crisis in Czechoslovakia just before their planned talks in Malta. The quick unofficial replies he received made it crystal-clear not only that Bush favoured a breakthrough to political democracy, but also that Gorbachev, by refusing to back his Czechoslovak comrades with force, was _defacto_ of the same opinion. Havel and the rest of Civic Forum drew courage. Their foray into foreign policy, which is what it amounted to, combined with the approach from Premier Adamec, served as the immediate backdrop for Havel's direct backing for the Civic Forum plan to work towards a general strike by hosting a countrywide string of giant demonstrations designed to force the government on to its knees.
There were now large daily demonstrations in Prague, and a taste of things to come was provided by the next one after Havel's Melantrich appearance. An estimated half a million people crushed into Wenceslas Square, amidst extraordinary reports and rumours. News was received of growing confusion within the upper echelons of the Party and of support for Civic Forum from a wide variety of groups and organizations, including the Slavia football club, the Prague Lawyers' Association, the giant ČKD electronics plant, and Barrandov film studios, formerly the property of the Havel family. Demonstrators also knew of the demand for editorial freedom hurled by the employees of State Television at their Communist managers. And snippets of information were circulating fast about the unprecedented spreading of unrest to many towns outside Prague. In Bratislava, where the trial continued of Dr Čarnogurský, who was charged with defaming the socialist system by calling it totalitarian, up to 100,000 demonstrators, many of them workers from Slovnaft Petrol Complex, reportedly had turned out. In České Budějovice, 25,000 protestors braved pouring rain, while policemen searched student hostels for planted bombs. In Brno, perhaps 120,000 people came out in support of the local demand to widen the dialogue 'to involve civil society'. In some cities, like the north Bohemian industrial town of Most, the authorities had tried to prohibit demonstrations, which took place regardless. The significant news also reached Wenceslas Square of the 'disappearance' of seventeen coachloads of Moravian militiamen, newly arrived in Prague to relieve colleagues now exhausted by five days on duty guarding state buildings. Havel told reporters that the militiamen had not been told where they should report for duty — such was the chaos in the capital's police administration — and that consequently they had got lost in the huge crowd gathering for the 4 p.m. demonstration. The militiamen later tried to find accommodation, were refused everywhere they went, and presumably then found their own way back to Moravia, their ears ringing with the chief slogans chanted by the peaceful throng: 'The Soviet Union: Our Model at Last! [ _Sov ětský svaz, konečně náš vzor_]'; 'St Stephen's Day without Štěpán! [ _Na Št ěpána bez Štěpána_]'; 'Miloš Jakeš, it's all over! [ _Miloši kon číme_]'; and a chant that must have thrilled Civic Forum's leader, 'Play Havel's Plays! _[Hrajte Havla]'._
And so came the weekend of the biggest peaceful demonstrations of all. Moved for reasons of space at the last moment to Letná Plain, high above the Old Town Square, the planned demonstrations on Saturday and Sunday, 25 and 26 November attracted great excitement. The Civic Forum leadership smelled victory. Popular fears of violent counter-revolution were at their lowest ebb. And the Communist leaders, plugging wax in their ears and shading their eyes, pretended to be busy with their official duties. On the day before the Letná demonstrations, the ageing Jakeš had appeared so calm that some of his senior comrades became convinced that he was actually insane. At seven o'clock that evening, Jakeš replied by suddenly announcing that he and his secretariat and politburo were resigning. The news was instantly relayed, in the style of the ancient Greeks, by a journalist who sprinted to Wenceslas Square, where the crowds that were still gathered there greeted the revelations with a roar.
The resignation resembled collective suicide. It was an act of grave political stupidity, and it convinced Havel and his supporters, who immediately afterwards drank a champagne toast to 'A Free Czechoslovakia', that the Party was dissolving into chaos. That was certainly the feeling on Letná Plain, where on the Saturday 750,000 people assembled, some of them having come straight from attending a special mass marking the canonization of Agnes of Bohemia in the Prague Cathedral, celebrated by the ninety-year-old Cardinal Tomášek and shown live for the first time by state television. The Letná demonstrators did not know that Štěpán had just been forced to resign and that President Husák had just agreed to halt criminal proceedings against eight people, including Miroslav Kusý and Ján Čarnogurský. The crowd was nevertheless thrilled to hear speeches from Havel and various other celebrities, and it was agreed by an enormous forest of hands that another demonstration at Letná would take place the following day, at 2 p.m.
With the scent of political victory in the freezing air, nearly a million demonstrators returned on the Sunday to cheer, shout slogans, jangle their keys and listen to the speeches. The gigantic crowd was told through loudspeakers of the Communist counter-demonstration at Litoměřice, where some 1,800 faithful Communists had gathered with shouts of 'Long Live Socialism!', 'Long Live the Party!', 'Long Live the Army!', 'Long Live the Police!', 'We Shall Never Give Up!', and 'Who Is Havel?'. There were jeers and hoots of laughter, then respectful silence followed by some cheering and clapping as Alexander Dubček, the representative of both Slovak voices and of the aspirations of the Prague Spring, mounted the makeshift podium to speak of socialism with a human face and of the past twenty years as a period of national humiliation. There followed live music and a string of speakers, including police lieutenant Pinc. He received a mixed reception after apologizing personally to the crowd for police brutalities and trying to explain that the police themselves did not agree with the ruthless handling of the 17 November demonstration, and that they were only obeying orders. Student representatives replied by reading out a statement by the procurator-general, who acknowledged publicly that the police used excessive violence on the first day of the revolution. A large section of the crowd sounded amused, especially after a Charter 77 spokesman pointed out that not all political prisoners had yet been released. The chuckling turned into rapturous applause when it was announced that Petr Uhl — the first link in the chain of publicity of the massacre — had just arrived at the demonstration, straight from prison.
It was then Havel's turn to stand up before the vast tidal sea of expectant faces. Dressed in black, wearing reading glasses, rocking nervously, to and fro, on his left leg, the man of the people began. 'The Civic Forum wants to be a bridge between totalitarianism and a real, pluralistic democracy, which will subsequently be legitimized by a free election,' he shouted into the microphone. 'We want truth, humanity, freedom as well,' he added, enveloped instantly in a cloud of thunderous applause. After thirty seconds he continued: 'From here on we are all directing this country of ours and all of us bear responsibility for its fate.' Havel went on to announce that the Prime Minister of Czechoslovakia had been invited to speak to the crowd. Havel did not explain why, but those in the crowd who thought about it would have realized that the Civic Forum leadership had put their trust in Adamec as the only senior Communist leader whom they could trust. 'Adamec! Adamec!' some parts of the crowd began to chant, perhaps with the intention of exacting their pound of flesh.
Adamec initially lived up to Civic Forum's and Havel's expectations by telling the crowd politely that the government accepted all of their key demands. The crowd whistled. It roared with joy. But no sooner had Adamec performed well when he made the mistake of qualifying his opening statement. He revealed that he still knelt before the principle of the leading role of the Party by resorting to the ifs and buts for which he had always been famous. He was instantly repaid by the hostility of the demonstrators. Their sea of faces swelled up into a tsunami. It drowned out Adamec. They hissed and booed and heckled and taunted each sentence. Tension rose to the point where the Civic Forum marshals knew that either he was to be pulled from the podium or he would be swallowed up — suffocated, assaulted, even lynched — by the crowd. Adamec's hunch that he could solve the political crisis and save the Czechoslovak Communist Party by appearing at Letná had gone hopelessly wrong. His attempt to outwit Civic Forum had backfired. So too had Civic Forum's attempt to use the Party as a safe bridgehead into the post-Communist future. The revolution was now succeeding. 'Our jaws cannot drop any lower,' exclaimed Radio Free Europe. Communism's time was up. The events boastfully predicted in the Prague scene a few days earlier — a prediction made by British writer Timothy Garton Ash that many thought a wild exaggeration — had come to pass. The political job of getting rid of Communism had taken ten hard years in Poland. In Hungary it had taken ten months. In neighbouring East Germany the revolution had taken ten weeks. In Czechoslovakia it had indeed taken just ten days.
### **Machiavelli**
The end of Adamec led many Civic Forum supporters to conclude that Havel's candidacy for high office was now firmly secured. The inference was premature, but it quickly managed to harden into one of the biggest myths of the revolution. According to the conventional story, Havel was the 'natural candidate' for the country's presidency. This followed from the fact that for a long time — ever since Charter 77, some say — he had been admired and universally popular within the circles that later counted. His reputation seemed to grow unhindered even when he tomfooled around — as on New Year's Eve, 1988, when, less than a year before the outbreak of revolution, a photograph shows him at a 'Monarchy for All' party, happily sitting on a throne, crowned and drunk, swigging straight from a bottle of wine.
Havel's popularity became especially potent upon his arrest and imprisonment on the evening of 16 January 1989, after laying flowers in Wenceslas Square in memory of Jan Palach. His imprisonment sparked protests and led to a sudden mushrooming of his popularity outwards from narrow dissident circles. Even the Bundestag, in Bonn, passed a resolution, on 16 March 1989, condemning his sentence. A further round of international recognition also came his way, for instance in Toronto, where his friend Josef Škvorecký helped secure his nomination for the Robert F. Kennedy Human Rights Award. Meanwhile, the statesman Henry Kissinger described him as an 'inspirational personality who has shown that all great achievements have to be somebody's dream before they become a reality'. The single sentence uttered by Olga at his trial a month later seemed to capture the inexorable trend towards fame. 'If Václav Havel is sentenced,' she said to the stone-faced judge, 'then all who stand by him in our country, and abroad, including those who have nominated him for the Nobel Prize, will be sentenced along with him.'
His early release from prison, for the last time, on 17 May 1989, consolidated his fame. The welcome-home party held in his honour was attended by everyone who counted in the opposition, including Alexander Dubček. Those who believe the conventional story say that the warm welcome proved that he was now the unrivalled symbol of oppositional integrity, the personification of a principled life lived in the open, the good-looking man who had lost his fear, who always played clean and — despite shy protestations to the contrary — was good at politics. The unprecendented success of 'A Few Sentences' _(N ěkolik vět),_ a new petition that he drafted and helped circulate during the early summer of 1989, confirmed these qualities. So did the enormous success, on the Brno stage that same summer, of the last of his plays performed (anonymously) before the revolution, _Tomorrow the Balloon Goes Up (Zítra to spustíme_ [1989]). And so did his Paulskirche speech, 'A Word on Words', read out in Frankfurt, live on German television, by the actor-director Maximilian Schell to an audience that included André Glucksmann, President von Weizsäcker, and Chancellor Kohl. Or so the conventional tale, runs. Then serendipity intervened, it is said. The Party fell into confusion. The regime began to collapse. That left only one alternative to the filth and crumbling authority of the _ancien régime:_ the clean-living, smiling and waving Havel, the man who was a master of moral _mise-en-scène,_ the honest man of the streets, the political figure with an unblemished past who could, if offered the chance and so long as he accepted, lead the country back into the promised land of freedom.
The view that Havel was naturally destined to be King is fanciful. Its political naivety was obvious to him. Havel knew well that there are tides in political affairs, that good fortune results from catching them when they are rising to their highest. What he could not have known in advance is that before setting to sea he would be required, during the last five months of 1989, to fight his way through a Machiavellian obstacle course of death, intrigue, rivalry and trickery. A portent of things to come was offered by his astrologer friend Daniela Fischerová, whom he visited in early August, just before the twenty-first anniversary of the Prague Spring. It wasn't the first time he had seen her. When the going was rough, he, the embodiment of 'reason', found that he liked the momentary escape from the stress of everyday life into an occultish world with different prospects. Fischerová told him that his signs were most unfavourable. She said that he should take special care of himself. Perhaps this is one reason why he urged the ragged opposition grouplets in Prague not to provoke the authorities by holding demonstrations in memory of the Soviet invasion of the country, and why, during that week of August 1989, he retreated to Hrádeček to avoid being picked up yet again by the secret police. Perhaps as well it was unfavourable stars that convinced him, when at Hrádecek, to have the property privately filmed. Trailed by a crew of video film-makers, he moved slowly from room to room, describing the events that had happened there, prefacing his remarks by saying that he did not know what would now happen, and that in any event the film would serve as a record for posterity.
Havel soon grew less cautious. Death beckoned. During the first few days of September, he let his guard down completely when attending a gathering organized by the Jaroslav Hašek circle of literary friends at a picturesque countryside retreat in north Bohemia in Okrouhlice. It quickly degenerated into a bohemian razzle, and on the night of 3 September, dead drunk, following a performance by the rock 'n' roll band Sure Thing _(Jasná páka),_ he tried to stagger from an open-air fire to the house where he was sleeping, arm in arm with an equally pie-eyed accomplice. Eyewitnesses were uncertain who was the drunker, and who was really assisting whom. One thing only was certain. As they snaked past a water mill, the future political leader of the country tripped and then slipped into the ice-cold waters of the steep-sided millpond. Desperately trying to claw its stone sides, coughing and spluttering and grunting for help, he went under repeatedly for several minutes. A great panic ensued. Less inebriated friends hobbled to the pond. Several dived in but nobody could help Havel. Then someone managed to fish his almost lifeless body out with a ladder. Someone else ran for a car. At high speed, the waterlogged, vomiting Havel was taken to the local clinic, where he was plied with oxygen and had his chest massaged. Miraculously, he woke up next morning covered in scratches and bruises and suffering severe chest pains. Somehow, he was alive. Shortly afterwards, suffering from pneumonia, he rang his historian friend Vilém Prečan in Germany, to say that there was another fact for the archives. 'I was convinced that there was no hope,' said Havel, in the tone of a man born posthumously. 'I had given in.'
It is incredible to think that the leader of the political opposition nearly died only weeks before he became world-famous, but so it was. The stupidity, or near-tragedy, resembled a dreadful parody of an exchange in _Twelfth Night._ 'What's a drunken man like, fool?' it is asked. The answer: 'Like a drown'd man, a fool, and a madman: one draught above heat makes him a fool; the second mads him; and a third drowns him.' The episode had an immediate sobering effect on his judgements, as was evident in the various interviews he gave during the following weeks. Tail between legs, he told the samizdat cultural magazine _Sport_ that he had never had political ambitions and certainly didn't want to become a professional politician. 'I would quite enjoy being the kingmaker,' he said, using the English word, 'but I wouldn't enjoy being King.' The point was repeated shortly afterwards in the pages of _Lidové noviny._ He said that although he felt squeezed in the narrowing gap between his roles as 'a bankrupt' _(zkrachovanec)_ and 'a politician', he was most certainly not being dragged into politics against his will. He warned against false euphoria, cautioned the opposition against relying upon the tactic of pressuring the state authorities through street demonstrations, and (giving a twist to a famous expression used by Masaryk) urged others to give plenty of emphasis to 'small-scale political work' _(drobné práce politické). 316_ The advice placed him in some tension with Jan Ruml, Rudolf Battěk and others who favoured big pushes from the streets, but very soon neither his caution nor his resistance to official politics counted for much. The outbreak of the revolution and the birth of Civic Forum forced him, not entirely against his will, into playing the leading political role within the opposition.
But now for the moment of intrigue. Among the principal weak points of his efforts during the second half of November to manoeuvre himself into the dominant role within the opposition was his lack of reputation. He was already something of a hero within Civic Forum, of course, and the massive crowds who heard him speak — not very forcefully or plainly — at least now knew how to recognize him up on balconies at vast distances. But the plain truths were that the revolution was a media event, that very few people in the country had ever heard him speak, and that most did not even know who he was. This was acknowledged on the afternoon and evening of 5 December, during a fateful meeting in Prague of the so-called Crisis Headquarters of the Co-ordination Centre of Civic Forum _(Krizový štáb). 317_ The meeting had been called specifically to examine who would be nominated as Civic Forum's candidate for President. Havel's longtime friend Ladislav Lis began the discussion without beating around the bush. 'The whole nation is calling Havel! Havel!' he said, only to be contradicted by a variety of speakers who thought otherwise. Havel mostly sat in silence as various positions were outlined. Quite a number appealed for 'realism' after Petr Pithart, testing the waters, suggested that perhaps a Slovak like the intellectual Miroslav Kusý should be nominated. Heated cries of 'This is absurd!' and 'This gentleman could never get through!' served as a prelude to discussion of the more serious options. Zdeněk Jičinský spoke powerfully for the view that Alexander Dubček was obviously the only political candidate who was well known to both the Czechoslovak public and the international scene. Someone suggested that Civic Forum should perhaps 'try' the well-known Communist Adamec, who in recent days had confided in him that he wanted to be President. Havel's friend Jiří Dienstbier reported to the meeting that both Olga and the writer Eda Kriseová were backing the Brno left-winger Jaroslav Šabata. At that point, probably sensing that the discussion was slipping through his fingers, Havel felt compelled to intervene, perhaps even with a touch of wounded pride. 'I obviously don't want to be President', he said slowly. 'But if the situation sharpens in such a way that it would be in the interests of the country to have me as president for a short while, then I'm able to be President, since I have always subordinated my personal interest to the interests of the country. Otherwise I would not have gone to prison.' Dienstbier, revealing his true colours, jumped in at this point with the claim that it was unrealistic that his friend could be President 'for a short while', and that instead he should realize that millions of people in the squares would indeed support the slogan (he spoke in English at this point) 'Havel for President!'.
The doubts about whether Havel was famous enough to get elected nevertheless lingered. Well after midnight, the only worker representative at the meeting, Petr Miller, pointed out that most middle-aged workers didn't know anything about Havel, except that he was a dissident opposing things. A campaign in the factories would be needed, Miller added. Another passing remark by Zdeněk Jičínský — who pointed out that the Communist-dominated Federal Assembly would more likely support Havel if the proceedings were televised — hit the same sore point. So it was clear to Havel that he was no 'natural' winner of any political prizes, and that the immediate political task was to become popular. That would require opposition to any talk of a directly elected president — which he thought (correctly) that he would lose — and, at the same time, a direct massaging of the will of the parliament and the taking of his campaign for presidency to the country's living rooms and kitchens and pubs by the most powerful available medium of communication: television.
On the 10 December 1989, in the name of Civic Forum, Havel was nominated by his actor friend Jiří Bartoška as a candidate for the presidency. 'I thought it was out of the question that the Parliament we had inherited from the previous regime would elect me,' he recalled. The parliament was indeed hostile to his election. That is why a proposal to hold direct elections of the president immediately surfaced within the radical Democratic Forum grouping of the Communist Party. On 12 December, within the federal parliament, it was argued for forcefully by the Communist deputy Blažej. Havel and other Civic Forum leaders grew worried. Using various means, they spent the next five days trying to kill the proposal. At one point, Havel, watching a live television broadcast of parliament, tried to lobby its members by getting a message through by telephone. He didn't know which number to ring, so he and Petr Pithart leafed through the telephone book. Havel eventually got through to the cloakroom. Twenty minutes later, the two men watched someone deliver a letter to the chairman of the parliament. But nothing happened. Havel grew despondent. It is also possible, although still unproven, that during this period Havel put in telephone calls to lobby the student representatives who were at the time (mid-December) sitting on the Parliamentary Commission of Investigation of the Events of 17 November 1989. It was well known that student groups were opposed to the principle of directly electing the President — like Havel, they were convinced that the Party's chosen candidate, probably Adamec, would win a handsome victory, thanks to their choking control over the official media. It was not to be. Although the students sitting on the Parliamentary Commission were prevented from lobbying for Havel, the surprise resignation of Adamec eighteen days before Christmas was an early season's gift to Havel. With the Communist Party leaderless and in a state of collapse, parliament was the only forum in which properly the future President was to be chosen. So Havel now had to raise his profile on television. That meant dealing directly with the Director of Czechoslovak Television, Miroslav Pavel.
A secret meeting between the two men, arranged by Havel, was planned for four o'clock on Sunday afternoon, 16 December at the top-floor studio of artist Joska Skalník, where for the past few days Havel had been in seclusion. Pavel brought with him his newborn baby in a carry cot — his wife was ill — but the 'new man' image was deceptive. He was the former spokesman of Adamec's government, and was a tough and experienced operator. Havel expected trouble, and got it — in the face. Pavel told him that he was a minor political figure, and as such he was completely unprepared to give Civic Forum coverage in the early evening (7.30 p.m.) prime-time news slot. The best he could offer was a late-night slot — when of course most of the nation would be asleep. He smiled, glancing to check his sleeping infant. Havel instantly welled up with anger. He raised his voice, so sharply that Pavel's baby woke up and began to scream.
With that anger, at that moment, something changed in Václav Havel's life. The moment of big-time rivalry had arrived. He revealed that he was not prepared to back down in the confrontation with one of the two powerful men who now stood between him and sovereign power. For the next twenty minutes, the pair exchanged words like boxers exchanging punches. No progress was made, so Havel resorted to threats. 'You just wait until I become President,' he scowled, without the faintest note of irony, testing the rule that he who plunges the dagger never inherits the crown. 'You'll not last long. I'll make sure we get rid of you. You'll be nothing!' Havel went on to shout that Jiří Kantůrek, who was there by his side at that moment, would replace Pavel if he didn't back down. Pavel raised his voice. So did Havel. Someone leaned forward to restrain both men. 'All right, have it your way, arsehole!' snapped Pavel, sensing at that instant that the tide of history was flowing against him.
With that remark, he grabbed his baby and strode downstairs to get into his car parked outside. On the way out the door, Havel, acting the part of the victorious gentleman in a duel, handed his defeated opponent the tape recording of the meeting. Petr Pithart ran down five flights of stairs after him — not in honour of some prior gentlemanly agreement, but because Pithart was worried that Pavel might try to outfox his opponent with allegations of dirty tricks and unfair play. 'If he plays it on the radio, we're finished!' called Pithart to Havel. Just as Pithart got to the street, Pavel was driving off. Breathless Pithart chased him, banged with his fist on Pavel's car, and appealed for him to wind down the window, which he did. 'We agreed not to misuse the tape,' said Pithart. 'We can stick it down the nearest sewer,' he suggested. Pavel nodded, revving his engine impatiently. But no nearby open sewer could be found, anywhere. Pithart, the future Prime Minister of the country, ran back to the car. 'Look, you'd better take it,' he said. Replied Pavel, just before zooming off: 'No thanks. Stick it up your arse.'
That evening, the nervous-looking Havel, barely looking up at the camera, read out a statement during the seven-thirty evening news, live. Millions watched, but what they thought went unrecorded. More certain in retrospect was the way in which the incident leading up to the television appearance suggested a number of disquieting things about the phenomenon of power in human affairs: that the hunger for power over others is polymorphously perverse; that the process of coming to power is usually a costly business; that in the era of mass communications, one of the prizes and privileges of power is the freedom to define reality for others; and that in any conflict-ridden struggle to get the upper hand, good-natured conversational reason is always the loser to raised voices, threats, and outright bullying.
From the point of view of Havel's own stated commitment to living honestly in the truth, none of these things looked very pretty, but at least they had the effect of toughening him up for the coming moment of knavery. In his quest for sovereignty, it was obvious to him and plenty of others around him that by the middle of December there remained only one man potentially standing in his way. By 10 December 1989 — the day he announced that he would be a candidate for President — Havel had effectively won over a big majority of the inner governing circle _(rada)_ of Civic Forum. But everywhere there was still talk of another declared candidate named Alexander Dubček. The hurdle had to be jumped, and so the name of his potential opponent must have begun to ring in his ears and to cause him loss of sleep. There were some within Civic Forum, the historian Pavel Seifter for instance, who worried that a power vacuum would result from Havel's departure for the Castle, where in turn he might well fall prey to Dubček, who would wait in the wings for the inexperienced President to make fatal political mistakes. Things were not helped by the fact that Olga was against his candidacy, that Havel's own sister-in-law, Dagmar Havlová, had told him that she supported Dubček, and that the same plausible view had been put eloquently and forcefully within Civic Forum by Zdeněk Jičínský.
Dubček was indeed a threat. After Havel's television performance, Dubček still remained much more a household name than the dissident playwright proto-politician. It was also obvious that Dubček was, in the eyes of many, a bridge to the unfinished business of the Prague Spring. Although indecisive, he had learned a few hard lessons in the difficult art of dismantling the Communist system. Moreover, his election would send a powerful message of unity from Prague to Slovakia, and for exactly that reason he commanded enormous support within its population at large. It was also being said that President Dubček — the name sounded more familiar than President Havel — could better secure the loyalty of the nomenklatura amidst the disruptions caused by the revolution, thereby ensuring a smoother transition to free elections sometime during the next six months. And — the critical point — within the Federal Assembly, which was now poised to make the final decision about who was to be the next President, Dubček seemed much more likely to win the hearts of a clear majority of the hard-headed Communist deputies looking for a way to stem the anti-Communist tide.
So Havel had to get above him on the ladder to power, even if that meant trampling on not a few of his fingers. Dubček somehow had to be dealt with — in a civilized, but tough and effective manner, of course. Havel pushed for a solution in two separate, but overlapping, contexts. One of them was the round table, behind-closed-doors talks about the future government that began less than ten days after the outbreak of the revolution. Convened by a group called Most (Bridge) that was put together in the summer of 1989 by the journalist Michal Horáček and prominent rock musician and film-score composer, Michael Kocáb, the regime and Civic Forum and its allies played power games with each other for two weeks. The sometimes tense negotiations culminated in the formation of Marian Čalfa's Government of National Understanding. Havel later dubbed it the Government of National Sacrifice, but it is clear that at every stage his role was central to its formation, and to the negotiated end of Communism's grip on the presidency. The Communist negotiators' tactic of appealing for more time, in the hope that that would enable their survival, was countered by Havel's bold initial call for the resignation of President Husák by the end of 1989. Havel also pushed for a resolution that the Federal Prime Minister, Ladislav Adamec, be invited to address a Letná rally, perhaps with the expectation that Adamec could be used as his own personal Trojan Horse. When Adamec, freshly back from Moscow talks, shocked everybody by announcing that he would not head up the new federal government, so implying that he had his eyes on the presidency, he and Havel — on 5 December — met for a private discussion. Havel followed it up immediately with a letter to Adamec (co-signed by the actor Milan Kňažko, of the Public Against Violence) which said that while they saw Adamec as an important guarantor of political stability his proposed candidacy for president would be viewed unfavourably on the streets, and within Civic Forum itself. From there on, Havel used the tactic of putting himself at the centre of things. Like a head of state, he personally assured Vacek, the Minister of Defence, that the opposition trusted him personally and knew that the army would not resort to Tiananmen tactics. Havel also used the tactic of making haste. He repeated many times that any attempt to stall the negotiations about the future government and the next President would produce explosions on the streets. 'The public will overthrow us and nobody knows what will follow,' he said at one point. And Havel tried — but failed — to get agreement that the resignation of Husák now had priority over the formation of a new government. When the opposition's two lawyers (Petr Pithart and Pavel Rychetský) pointed out to him that that tactic would leave no constitutional body to appoint a legitimate government, he backed down. He then put his weight behind powerfully built, sandy-haired, smiling-eyes Marián Čalfa. Havel proposed that he should be the next Prime Minister, on two conditions: that the new cabinet to be formed should 'visibly' meet the opposition's demands, and that the next President should be a Czech who was a member of no political party.
So Adamec was pushed aside and the way cleared for Havel to become President. Dubček now had to be dealt with from within Civic Forum. A clue as to how that was to be done was provided by Havel himself on 5 December, well after midnight, during the long debate within Civic Forum about who would be their presidential candidate. There Havel proposed the principle of turn-taking: he would be willing to accept the candidacy, but on the condition that he would remain President only until free elections were held. This position had strong support both within Civic Forum and its counterpart in Slovakia, Public Against Violence. It was pointed out immediately by Zdeněk Jičínský, in reply, that the proposal was strictly speaking unconstitutional, since the term of office of the President was not tied to that of the parliament, and that presidents were normally elected for five years. But Havel persisted, and in his television appearance on 16 December he reiterated the proposed strategy. 'If it is in the general interest that I should accept the presidential office, then I will accept,' he said. 'But there are two conditions: that I would be temporarily in post as needed only until the one who sits in Masaryk's chair is chosen by a freely elected Federal Assembly. The second condition,' he said, pausing, 'is that by my side, in any post, will be Alexander Dubček.' Havel added: 'I will neither allow any dark powers to erect a barrier between him and me nor between our two nations.'
His audience did not know that on the day before, Havel had met in secret for one hour with the new Prime Minister, Marián Čalfa. In a carefully debugged room, the two men formulated a bold but simple plan. Čalfa promised that he would support Havel's candidacy and would deal with the parliament to ensure it voted that way, before the end of the year. Havel would take care of Dubčcek in his own way. The two men set to work. Čalfa wined and dined, lobbied and lectured, teased and threatened various groups and individuals 'to stop all unwanted initiatives in parliament'. On 19 December, just as agreed, he appeared before the parliament to appeal to the deputies to elect Havel by the end of the year. Havel had meanwhile arranged, with the help of his cameraman friend and fellow Civic Forum activist, Stanislav Milota, a series of top-secret meetings with Dubček, who was accompanied by his old friend and former Minister of Economic Planning in the 1968 government, František Vlasák. During the next few days, the foursome thrashed out an agreement, despite some mind-changing. The two opponents shook hands on taking turns to taste presidential power. Dubček initially would not agree to call off his candidacy, but in return for the double guarantee that he would be appointed as leader of the Federal Assembly, and that Havel would say publicly that he indeed supported Dubček's candidacy in the run-up to the forthcoming free elections, Dubček would happily support Havel's candidacy this time around.
The subsequent commitment of both men to keep silent about the deal worked against Dubček. Within the ranks of Civic Forum, Havel carefully planned a nebulously worded declaration of sympathy for the idea that, sometime in the future, a Slovak might become President. He then waited, until the day he enjoyed the advantage of incumbency. 'I feel a special obligation,' he said in a brief passage in his first presidential address to the country, 'to see that all the interests of the Slovak nation are respected and that no state office, including the highest one, will ever be barred to it in future.' Dubček meanwhile kept his part of the bargain to the letter. He spoke warmly of Havel, often standing by his side, all the while clinging publicly to his aim of becoming the next President of Czechoslovakia. That didn't happen — despite the free elections that were held shortly afterwards.
### **A Crowned Republic**
The reaction of the uniformed Castle staff who had been assembled in the First Courtyard to welcome the new President surprised everyone. As the tearful entourage passed through the lavish main gates, flanked by monograms of Marie Theresa and Joseph II, statues of battling giants, and symbols of the Bohemian Kingdom (a lion) and the Habsburg monarchy (an eagle), the heat of the revolution seemed to freeze. 'Unsmiling and defiant, they stared at us. Some glared, as if they resented our very presence and wanted us removed,' recalled Petr Pithart, who walked beside Havel on the last leg of what had seemed an endless journey.
The frosty welcome should not have surprised them. Although the Castle symbolized many good things to Czechs — even during the Communist period, from the time of Gottwald, it had often been considered a court of final appeal for commoners or citizens with complaints and requests — the President and his staff were an important source of patronage and, hence, equipped with the power to make and break the destinies of individuals. As Havel and his entourage entered the main western wing of the Castle, they had the feeling — lasting just for a few seconds — of entering a completely enclosed space bathed in sheer darkness. They felt lost. It was as if there was not the slightest chink of light. The air they breathed seemed dead. The dark felt deep, pure dark, darkness so deep that if they had imagined for an instant that they could see something bright before their eyes then it would be nothing but the nimbus of Kafka's castle.
The new President and his entourage were ushered to the second floor and the Emblem Hall, otherwise known as the Hall of the First Citizen of the State. There, around a rectangular table made of teak wood and a marble pedestal inscribed with the words 'Subordinate your personal troubles to those of the community' _(Obci starosti své osobni podrob),_ the denim-jeaned and jumpered new tenants gathered to hear Havel deliver a modest speech of thanks to his trusted friends. Champagne was drunk, after which Havel, accompanied by Olga, was first taken briefly to his office — the Office of the President — and then on a guided tour of the bits of the Castle formally closed to the public, escorted by the Castle guards.
Everybody felt bewildered. The building itself posed a problem that urgently needed to be solved: the symbolic shape of the new presidency. The difficulty, to combine the Castle with republican democracy, seemed insoluble. Here, up on the hill overlooking Prague, the pomposity of a massive structure encoded with a thousand years of power over others, a symbol of rulers swelling with ambition, vehement in their greed, sometimes uncontrollable in their lust, drinking their subjects' blood in long draughts. There, down below in the cobbled winding streets of the old city, a bubbling cauldron of dancing bodies and happy faces, renewed hopes, political merry-making, straightened spines, reborn social initiative, excited determination to put an end to hubris, to open up the world, to change it for the better. These were two different universes, as far apart, perhaps, as the humble subject cowering like an insignificant shadow at a remote distance before an emperor's sun. How possibly could the gap between them be bridged? Given the political impossibility of selling off the buildings or somehow bulldozing them down into the River Vltava below, was a new synthesis between the Castle and the democratic republic thinkable and practically possible? And given the constitutional impossibility of Havel refusing to use or acknowledge the Castle, what would the combination of Hradčany and popular power — expressed in the commonplace graffito, _'Havel je král'_ (Havel is King) — look like?
The strategy for which Havel intuitively opted was _not_ to cultivate the institutions of republican democracy, like parliament and a judiciary that upheld the rule of law. Instead, at first cautiously and then later expansively, Havel worked for the creation of a crowned republic. The oxymoron is unfamiliar in contemporary analyses of power. It is also unknown to previous typologies of states, which is odd considering that the first, and still best, schematic outline of a modern crowned republic was provided long ago by a poet and political thinker who was born not far from Prague. Friedrich von Hardenberg, better known by his pen-name Novalis, sketched plans at the end of the eighteenth century for a brand-new type of government that his contemporaries found utterly astonishing, even if many of them thought that such a state would prove in practice to be an impossible contradiction. In a number of writings, and especially in his set of aphorisms entitled _Glauben und Liebe, oder der König und die Königin,_ written to celebrate the accession to the throne of the reformist Friedrich Wilhelm III and his wife Luise in mid-November 1797, Novalis defended the French Revolution by denouncing all forms of despotism as corrupt and oppressive. He reckoned the Revolution to be an inevitable 'crisis of puberty' that humanity had to go through so that it could enjoy 'the delightful feeling of freedom, the desire for the new and young, the pride in the brotherhood of man, the joy in personal rights, and the powerful feeling of citizenship'. But against those radicals who assumed that the people _are_ by nature free and equal, and that therefore the main political task was to unchain their freedoms, if need be through violent rebellion, Novalis insisted that the people could only _become_ so by educating them into the ways of republican citizenship. 'First be human beings,' he urged in an unpublished note, 'and then the rights of human beings will come of their own accord.'
But through which kind of education could people best become citizens? Novalis answered: the ideal form of modern government is a synthesis of republicanism and monarchy. The vital ingredients of a republic — 'electoral assemblies, directorates, and liberty trees' — cannot be nurtured or sustained unless they are harnessed by a king or queen who serves as an inspiration to the people to press for the principles of liberty, equality, and fraternity. Novalis insisted, in an enigmatic passage, that in every genuine republic 'all people are capable of assuming the throne', by which he does not mean that monarchy should be an elected position or form of government. His point is rather that citizens should be uplifted by a virtuous monarch who moves closer to them, as it were, who brings the castle to the people, thereby giving them a sense of mission by appealing to their feelings, desires, and hopes. The monarch should be the instrument of republican _Bildung._ Individuals cannot and will not bind themselves to the state simply because it protects their property or rules in accordance with rational laws to which they have consented. The people will only obligate themselves to the state if they feel 'faith and love' _(Glauben und Liebe)_ for the monarch. Faith and love are not naturally occurring substances, however. The people can only learn to love and have faith in themselves as citizens by learning to love and have faith in a ruler whose wisdom and virtue and capacity for making decisions they trust and respect. Republics which nurture active citizenship cannot merely rely upon declarations of rights and the formulation and implementation of good laws; the capacity of their rulers to inspire admiration and respect for the republic is ultimately more important. 'What is the law,' Novalis asks, 'unless it is the expression of a lovable person who is worthy of respect?'
Novalis's proposals for cultivating monarchy within a republic openly acknowledged that the charismatic qualities of the ideal ruler could never stem from divine sources. Novalis detested divine-right theories. Remarkably, he also did not think that charisma flowed automatically from heredity. Although citizens' affection for the sovereign is likely to be enhanced by the fiction of their 'noble birth', Novalis insisted that heredity alone cannot guarantee faith and love, principally because no living person has the unique, infallible, extraordinary qualities that a good queen or king requires to do their job. Republics nurture citizens' capacities for thinking for themselves, asking critical questions, and publicly challenging power relationships that are considered illegitimate. So how then could the monarch develop charismatic qualities in an age of suspicion of power?
How indeed could royal power survive in an age of scepticism? Novalis replied: by surrounding the monarch with artists whose role is to fuse aesthetics and politics and thereby ensure that the monarch is seen by citizens as a lovable person of extraordinary intelligence, dignity, courage, and standing. The demanding task of the court artists — poets, painters, musicians — is to _invent_ a charismatic sovereign who is capable of lending 'the commonplace a higher meaning, the ordinary a mysterious appearance, and the finite the air of the infinite'. The power of the throne must be bathed in pomp. The figure of the ruler is to be (draped in such grandeur that the people will watch with warm hearts and open mouths. The job of the artists is to produce plays, operas, symphonies and other alluring works that transform the republic into a 'poetic state', a state that resembles a vast stage performance watched by the public and directed by the playwright monarch and a cast of citizen-actors.
### **Te Deum Laudamus**
Novalis's scheme suffered from the disadvantage that the monarch might be uninterested in art or that the King or Queen and the poets might not get along, thus bringing troubles to the poetic state, heaping disrepute upon the Crown and fomenting the suspicions of its citizens. Novalis's plans were stillborn, despite the fact that _Glauben und Liebe_ reportedly generated 'a sensation' in Berlin and elsewhere. King Friedrich Wilhelm III, who went so far as to declare himself to be a republican and friend of the revolution, but who confessed that he was not much interested in art, actually read the work. He nevertheless remained unimpressed. Besieged by the job of implementing wide-ranging reforms in Prussia, he was even ultimately angered by its recommendations. 'More is demanded of a king than he can possibly perform,' he reportedly said. 'It is forgotten that he is only a human being. One has only to bring a man who lectures the king about his duties away from his desk and to the throne; then he will see the difficulties that it is not possible to remove.'
The King's reaction revealed the difficulties in modern times of making power sparkle, but the weakness to which he pointed — the gap between the desk and the throne — most definitely did not apply to the poet-politician Havel. Those who talked at the time of Havel as a 'reluctant President', as a man who would rather be writing plays but who had been forced by events against his will into politics, missed the point: Havel had always been a political animal who knew well the art of directing others. And although Milan Šimečka and others were right to plead with Havel not to seek the presidency lest he lose his freedom to write and direct his own plays, they also underestimated the 'transferability' of his playwright's skills into the field of official politics. The point is that Havel had the advantage over most of his rivals of being an experienced political animal and a playwright who knew well the dramaturgical arts of directing others.
So it was not surprising that from the first day of assuming the presidency he began experimenting with his new role as King of the Castle. With mixed success, and always subject to the push and pull of revolutionary politics, the new sovereign tried to transform the Castle into a giant stage. From there, he tried to direct a new performance — the biggest so far in his life. The play served as the supreme expression of the revolution. It displayed the new-found sense of collective awareness and solidarity. There was a cast of thousands of people, some famous and others previously unknown, whose performances would for a time win the hearts of the country's citizenry and — this Novalis had not anticipated — attract the attention of the whole world.
The performance of Dvořak's _Te Deum_ in St Vitus's Cathedral on New Year's Eve was a sign of things to come. Olga was opposed to holding the ceremony — she thought that it would be too pompous and, hence, out of step with the levelling spirit of the revolution. The Havels' playwright friend Josef Topol eventually convinced her to attend the crowning of the new republic. So behind the scenes she set to work, beginning with a shopping expedition to buy her husband a second-hand suit. She came back with various bits and pieces. Contrary to the famous advice of Ibsen that best clothes should never be worn when fighting for freedom and truth, others pitched in. Prince Karel Schwarzenberg improved the wardrobe by bringing along to the embankment flat two suitcases of his own elegant clothing, prompting Havel to say, with a smile: 'I can't wear any of these! I'd look like a gigolo!' He eventually settled for a dark suit with trousers so obviously at half-mast that it was said by wits among the millions who watched the ceremony on television that the Communists had already set to work trimming the powers of the presidency.
Standing in the spot where Gottwald, and before him Beneš and Masaryk, had stood, Havel may not have realized just how much _pre-modern_ history was buried within the ceremony. This was admittedly not a repeat of Caesare Borgia's entry into Rome (1500) or the entry of Philip the Good into Bruges (1440) or Richard II's triumphal arrival in London (1392). And those who witnessed it, live or on television, would not have spotted that the vast theatrical ritual called the royal entry, which originated in Europe in the late fourteenth century, drew its ultimate inspiration from the Roman _adventus,_ and the medieval church's complex Advent liturgy, its dramatic celebration of the monarchs' inauguration into their reign by likening them to Christ's Palm Sunday entry into Jerusalem. Still there were some deeply rooted continuities. There was a feel of conversion about it all. Just as the coming of a king to a city was _like_ the Advent of Christ, so the reception by the supporters of the Velvet Revolution of their new political lord was _like_ the reception of their Saviour. Here too was the ritualized communal pageantry and drama of it all. The _Te Deum_ was like the public celebration of a new sovereign, himself treated as a Christ-like figure, who vowed before his people that together they should aspire towards a certain kind of polity. But it was more than that, for there was the sheer magic of it all. There was no consecration with balm, no wearing of crowns, no bearing of the orb and sceptre, certainly. But there were plenty of citizens who acted like Zacchaeus, who climbed a tree to witness the coming of Jesus to Jericho — tens of thousands of citizens euphoric at the formal entrance of the new Playwright-President of the free Czechoslovak Republic.
The _Te Deum_ was the first staged performance by the new President. The appointment of Petr Oslzlý as his cultural affairs adviser further confirmed Havel's wish for a theatrical state, for a refashioned Castle that ensured that citizens and sovereign performed their roles in a drama that aimed to express the truth of the world, to nudge existing conditions of life towards its high standards. During the 1980s, the wild-looking but gentle Oslzlý had worked as one of the most talented and popular actors at Brno's Theatre on a String. He enjoyed a reputation for integrity — he had worked as a 'dissident' organizer of the city's most successful underground university seminar and had acted within a theatre aptly named because it tottered constantly on the edge of nomenklatura — and secret-police harassment. Havel admired his work, and the two had become good friends by the time of _Largo Desolato._ During the summer before the revolution, Oslzlý had even staged anonymously a play by Havel called _Tomorrow the_ _Balloon Goes Up._ Oslzlý was active in Civic Forum from the beginning, but he was utterly surprised when Havel, who was at that very moment trying on the ill-fitting trousers that he would wear the following day for his inauguration, asked him to 'come and help me be President'. Oslzlý accepted, and the two set to work immediately to begin transforming the Castle into a work of art.
They agreed that the building needed a visual overhaul. It felt like an empty, dark and morbid dungeon, symbolized by the state of the original office that had been used by Masaryk, which was now blocked off, dusty and empty. Also symbolic was the state of Husák's office, which was long and sparsely furnished with oversized furniture. It had no clocks, and it was dominated by a long dark table cluttered with about twenty telephones, including a red-coloured one that was reportedly used either to call prostitutes and/or to serve as the hotline to Moscow. Lány Castle, the presidential weekend residence, was in no better shape. 'The fact that you are still living in your old apartment — is that a symbolic decision, or are you simply too lazy to move?' he was asked shortly after becoming President. 'I couldn't possibly live in that repulsive interior so absurdly decorated by Husák,' he replied drily, puffing a cigarette. 'It would be like throwing myself in prison. The presidency is a lot like a prison sentence — I'd rather not emphasize it.' Havel and Oslzlý initially concentrated on going around the Castle with the keeper of plans. On one voyage through the dark unknown, they discovered in the area of Husák's office a mismatch between the plans and what turned out to be a false wall concealing a beautiful door. Havel ordered that it be restored, to make the area feel friendlier. He did the same with the Castle gardens. He asked that a steel fence be torn down, and the graphic design artist Joska Skalník busied himself painting sky and clouds in select places around the courtyard fountain.
The dramaturgs also pushed ahead with smartening up the Castle staff by redesigning both their uniforms and the centrepiece ritual of the Changing of the Guard. 'Give the men new clothes,' Havel told Oslzlý. 'We cannot change history in a socialist uniform with a red star on its head.' Under Husák, the Changing of the Guard had been a routine military ritual performed by grim-faced soldiers dressed in baggy khakis. Under Havel, the Changing of the Guard was transformed into a fifteen-minute midday theatrical event costumed by Theodor Pištěk, who designed Miloš Forman's _Amadeus._ Each day, at the stroke of noon, a platoon of guards dressed in red, white and blue (the Czechoslovak colours) marched from their barracks in nearby Martinic Palace on Loretánská Street into the Castle's Courtyard of Honour, where they relieved their colleagues (from here on nobody used the word 'comrade') fatigued from twenty-four hours on duty. The arriving guards were greeted by six horn-players and a drummer, framed in upstairs windows and dressed like toy soldiers, playing resounding fanfares before camera-clicking crowds larger than those assembled under the Old Town Hall clock down the hill and across the river from the Castle.
Meanwhile Havel acquired a fleet of red, white and blue BMWs for use as the President's cavalcade. He was given a personal pedal scooter to speed up his movements, in style, along the impossibly long passageways of the building. Restoration and redecoration work on inner parts of the Castle got underway. Masaryk's library, which had gone to rack and ruin under Husák — it was filled with over 12,000 Party brochures and booklets, and had a tasteless mirrored ceiling to help his astigmatism — was cleared out and restored to its original wood-panelled, carpeted beauty. Under the supervision of Havel's friend Bořek Šípek, the President's office was freshened and brightened and made to feel opulent, but friendly. Aleš Lamr painted splashes of rainbow colour in the corners and on the walls. Havel's favourite paintings — by artists like David Němec and Jiří Sopko — were displayed. A joky fresco containing images of spies, clowns and his dog Dula was done by Vendula Císařovská. Olbram Zoubek's sculpture of an Egyptian woman with long golden hair was placed opposite an impressively large, elliptical black desk. Oriental rugs were thrown in all directions. And so that the new President could keep an eye on the nearby American Embassy, Petřín vineyards and other parts of Prague, a large mounted telescope was installed at the windows.
These were mostly just trimmings, of course. But Oslzlý and Havel were convinced that they were important first steps in transforming the Castle into the symbol and substance of free cultural expression. Each day, from all over the country, scores of letters arrived from groups and individuals full of ideas about what should be done in the field of culture. Convinced that the building should be made to symbolize the new-found freedom that needed badly to be nurtured, the two hatched a plan to turn the Castle into a giant stage for a day. In the summer of 1990, shortly after the first free parliamentary elections, Havel said to Oslzlý that something had to be done to celebrate 'the victory of the people'. He went on: 'You have a good feeling for how it should be done. The main aim should be to bring the Castle alive.' So a day-long Festival for Democracy was held on the Castle grounds. Under hot and sunny skies, thousands of people dropped in off the streets to witness performances by jugglers, musicians, mime artists. Trade unions and enterprises donated trucks, tables and chairs, and other equipment. Pilsener flowed freely from the taps of barrels donated by breweries. Bands thumped out rock 'n' roll numbers. Strangers chatted. Crowds danced. Lovers kissed. And the brand new President, dressed in blue jeans and a T-shirt, wandered through the throng, hugged by well-wishers, cameras clicking.
Such exercises in re-enchanting political power attracted international attention. During the next two years, offers of artistic help poured in from everywhere, and even foreign governments reciprocated. Novalis doubted that the struggle to transform the state into a work of art might take on an international dimension, but Havel proved him wrong. The earlier appointment of Shirley Temple Black as American Ambassador to Prague was a signal in this direction. So was the agreement of scores of big names to visit the Castle. Philip Roth came for dinner and complained about being stuck in London, and waxed eloquent about just how much rich 'material' was at the disposal of the Castle actors, including Havel. The English playwright Harold Pinter was invited by Havel in early 1990 for the opening of Pinter's _The Caretaker._ After the performance, the two playwrights had a drink and later went strolling across the Charles Bridge, only to be spotted by a group of young guitarists, who spontaneously played Beethoven's Ninth Symphony for their pleasure. Such was the unprompted affection for the new President, but also a mark of recognition of his early efforts to change the appearance of sovereign power. It seemed everybody who was somebody was there. Jane Fonda's arrival in the spring of 1990 made the Castle seem like a prospective film set. In the summer of 1991, Frank Zappa also agreed to come to the Castle, and to help publicly celebrate the withdrawal of Soviet troops from Czechoslovak territory by jamming at a concert — together with Havel's friend and aide Michael Kocáb, an unusual rock musician who had tirelessly involved himself in efforts to rid the country of the Soviets. On one visit, Zappa caused a big scene by arriving at Prague airport when the new US Ambassador, Shirley Temple Black, was also there. Much to her embarrassment, she hadn't heard of him, as all of Czechoslovakia saw hours later on television. Meanwhile, leather-jacketed, mean-looking Lou Reed flew in, perhaps to talk about Sweet Jane. Then came the Rolling Stones, who returned several times after striking up a good friendship with their groovy president mate from '68.
Amidst the efforts to give the Castle style, Havel didn't forget his own personal image. He arranged through his advisers for the State Education Publishing House to put out a charming sample volume of the thousands of children's letters and sketches sent to him during the first eighteen months of his presidency; each child who wrote to him received an informal letter of thanks, together with a xeroxed photograph of Mr President. He also urged his close friend and inner circle adviser, the author Eda Kriseová, to write his 'authorized' biography. She understandably hesitated. The form was unfamiliar to her and the timescale of the task — Havel wanted it to appear urgently — was daunting. She told him so. 'Stefan Zweig wrote biographies,' replied Havel, or words to that effect. 'But he's long dead,' the biographer retorted. 'Never mind,' said Havel. 'You should do it — to make me better known. The book should be personal. It should be _your_ picture of me.' Kriseová sketched his portrait in less than four months flat. Havel read through a draft, made some amendments before approving it, then — for some as yet unexplained reason — grew uneasy about the book when it was at press.
The biography appeared anyway, to be greeted by strong sales and cool reviews. Kriseová had intended to write a labour of love that provided ammunition for Havel's supporters. Dedicated to 'Vašek', it aimed to turn him into a positive hero, principally because Kriseová reasoned that, immediately after the revolution, with all of its muddling and uncertainty about the future, 'the people' needed a good 'fairy-tale' to help them through the necessary _catharsis —_ their cleansing in the flooding waters of filth thrown up by the _ancien régime,_ that is, to keep them going along the revolutionary path. Many readers and some reviewers objected to the political misuse of literature. The main fact-minded, empiricist attack came from the typewriter of Vilém Prečan, the country's best contemporary historian, who criticized the book for its 'interpretive chaos' and many factual errors and gaps. He concluded that it was one of those books that would have been better left unwritten. Then there were those who disliked the book's sycophancy. A _New York Times_ reviewer spotted that biography had been reduced to hagiography. Meandering 'like the kitchen reminiscences of a loving buddy through Mr Havel's remarkable life', wrote the reviewer Michael T. Kaufman, the book was best summarized as 'an official and genuinely adoring work that helped to introduce the heroic shepherd to his ecstatic flock'.
### **Fun and Games**
The symbolic redesign of the Castle compounded the daily tasks spawned by the revolutionary victory over Communism. Uneasy lies the head that wears the crown, observed King Henry IV, and so it was. Havel instantly had on his newly acquired black desk a mushrooming pile of tasks — new appointments, foreign-policy initiatives, receiving and replying to petitions from individual citizens and their organizations, dismantling the old nomenklatura system, handling the media. The problems seemed all-encompassing. Havel's tempo of life quickened. Gone were the days of sleeping late, drinking coffee and rum, writing a bit, going to the sauna, making love at odd times of the day. Scores, then hundreds and then thousands of letters began to pour each day into the Castle from congratulators and complainants, a growing number of them (Prince Karel Schwarzenberg later recalled) written in the form of petitions to the monarch. The reception was spectacular, sometimes wild. Gifts of all kinds flooded the Castle offices. There were even envelopes stuffed with money — a few with fat wads of greenbacks, which prompted the joke, among the Castle aides, that such gifts proved that the revolution was really a CIA plot after all.
New security structures had to be created. New Castle guards had to be trained to close the gates of the crowned republic at 11 p.m., to escort the security staff from the President's office, to check that all windows and doors were locked and that staff working late knew the night's password, then to patrol inside the grounds, Scorpion machine guns, infrared goggles and radio transmitters in hand. New office equipment had to be purchased from scarce funds to supplement the dusty old Czech and Russian typewriters that had been left behind. Scarce and unusable stationery made life more difficult. 'Someone should retype this,' Havel said to a colleague after spotting that a letter appointing an ambassador was written on a Communist job form. 'It's not your job,' added Havel apologetically, 'but you're the only secretary I can call... It's ridiculous. Could you please type it on Federal Republic stationery?'
Personnel had to be recruited — fast. An orgy of patronage went some way towards solving the problem. There were several typical methods used. Havel picked his own inner circle, whom he treated during the first year as a collective presidency. Other key people — Stanislav Milota, Prince Karel Schwarzenberg — were recommended and contacted by Havel personally. It was a time-consuming business and didn't always work (Havel and Milota went to see the writer Ludvík Vaculík, who decided firmly against coming to the Castle). Others who had been Havel's acquaintances before the revolution were contacted, and they in turn contacted others whom Havel did not know: it was state-building by nods and winks and word of mouth. A case in point was the appointment to the Castle of V. Valeš, who had been Minister of Foreign Trade in 1968, and who had done time in prison with Havel. Valeš called Komárek; Komárek called Václav Klaus; and Klaus spoke to Dlouhý. The tactic of nepotism sometimes produced bizarre combinations — wildly bearded cameraman Stanislav Milota rubbing shoulders with clean-cut bespectacled economist Václav Klaus, for instance — and matters were complicated by the fact that the procedures through which the co-ordination of the newly appointed staff was supposed to take place were initially undefined.
The architecture didn't help. Many newly appointed aides seemed to take ages to memorize the location of the in-house toilets, while most new staff seemed mesmerized by the labyrinthine structures of the Castle. But the most difficult adjustment that Havel and his inner circle of advisers had to make was getting used to the experience of exercising governmental power. Like John F. Kennedy, Havel had an unusually strong urge to govern, which made the adjustment easier. The heartfelt camaraderie, which sprang up around him instantly, also made everything worthwhile. Havel and his team had the feeling that they were at sea on the same tiny boat, and that they should do everything to avoid sinking it. The unconditional trust and loyalty resulted not only from the euphoria of being on the winning side in a revolution. Solidarity not only came from living in each other's pockets for eighteen hours each day, seven days each week. Fear also bred solidarity. The first few weeks and months in the Castle understandably felt dangerous. For the first six months, the Castle was partly policed by Ministry of the Interior guards, some of whom were literally hidden away in the woodwork. One day Havel demanded that Richard Sacher, the newly appointed Minister of the Interior, come to open up a keyless room situated near the President's proposed new office. Everybody was shocked when the concealed door was opened. There stood a fearsome-looking soldier on guard, armed with a Scorpion machine gun, listening to the sounds generated by various intercom devices planted in the surrounding rooms. Someone later asked Havel: 'Do you think that soldier knew who you were?' Said Havel cheekily: 'Probably so, because otherwise he would have shot me dead on the spot.'
Experiences like this were commonplace. Sometimes Havel responded by horsing around with his bodyguards — forcing them to work into the wee hours of the morning as he danced and drank at friends' parties — or by pushing the security system to its limits, just for the hell of it, without disrespect for its personnel. He seemed determined to prove the famous maxim of the eighteenth-century _philosophe_ Helvétius that men sometimes strive after power so that they can enjoy themselves. During a visit to a Czech village pub, Havel suddenly said to Joska Skalník: 'You wanna see something? Follow me!' Pretending to go to the toilet, the two escapees climbed out of an open back window and began strolling, hands in pockets, down a country road, belatedly followed by scrambling, nervous security men in their macs and on their walkie-talkies. Havel was also skilled at the night-time art of giving his bodyguards the slip — for instance, by pretending to go to bed, waiting for them to fall asleep, then tiptoeing out to a pub for a few drinks. Generally, security was no laughing matter. Guarded only by unarmed karate experts, the group members initially chose to work from one cramped room. They felt like conquerors in enemy territory. Even the straightforward experience of going to the toilet — down the long, red-carpeted corridors lined with Ministry of the Interior soldiers clutching sub-machine guns — was hemmed in with so much anxiety that the word relief assumed a new meaning. Fear made coping with the extraordinary work pressures that much more difficult. So did the lack of free time. It is commonly pointed out — using the obvious example of the imposition of clock time in early modern industrial factories — that those who exercise power over others always seek to determine their daily rhythms, their shared definition of the flows and constraints of time. But it is equally true that power over others extracts a price: the powerful have little or no free time as well.
From the first day, the Castle resembled a time-consuming machine. Havel and his team ran constantly, at high speed, feeling all the while that it was impossible to keep abreast of events. Consequently, everybody in the inner circle lost their private lives, and their sleep. Havel's average of three or four hours per night was typical. Nobody had any time for themselves, or for others outside their immediate circle. Tempers sometimes flared within the presidential group: sometimes those who exploded were simply allowed to exercise their right to explode so as to calm down naturally, or they were grabbed and physically shaken until they regained their senses, or they were ordered to go home to bed to rest. Everybody seemed to develop extra and thicker skins, to become more brusque, less patient, more prone to cause others to cry. Outside friendships became strained. Those with families at home found themselves so consumed and exhausted by their posts that they had little or no time to attend to their children or their partners. Children complained loudly and sometimes turned aggressive. Relationships suffered, partners found it hard to put up with their parvenu politicians, and at least one marriage became a casualty of prolonged absence.
So time-starved power bred mental and bodily stress, which was worsened by the sheer volume of situations and problems to be defined, judged and resolved. Lawyers sometimes sobbed uncontrollably. Secretarial staff couldn't cope. A good administrator was defined as someone who didn't break down sobbing until two in the afternoon. Everybody quickly recognized that some matters were insoluble. Life within the newly established Office of Amnesties and Complaints, for instance, threw up some extreme, but not atypical cases. A small example: embarrassed confusion descends on the Office of the President when an angry letter arrives, addressed to Havel and written by a man whose daughter had just been murdered by an individual personally amnestied several weeks earlier by the President. A bigger example: twenty-five former nomenklatura staff working within the Castle are fired, upon evidence that they have worked to obstruct justice and tarnish Havel's public image. And an example that is full of political danger: with 7,000 letters per month flooding into the Office of Amnesties and Complaints, it is decided to try to deal collectively with certain complaints by hosting open public meetings in the regions. In Bratislava, more than a thousand citizens crush into an auditorium to meet the President's aides. The venue is carefully chosen to provide an easy back-exit escape route leading to the railway-station shunting yards, where if necessary the presidential aides will sleep that night in empty wagons. The atmosphere is riotous. Many complainants are irate. Each of them expects that after more than four decades of publicly suppressed injustice grievances can and must be righted immediately. As soon as proceedings are opened, many citizens become hysterical, demanding that the omnipotent President pick up his magic telephone to solve problems personally. The wrathful citizens suddenly become calm at the moment one of the aides shouts: 'Listen! You are right! There is no justice in this world.'
Stories of moments like these were swapped among Havel and his advisers, often eliciting the wild laughter of relief. There was a shared sense, confirmed by the gloomy atmosphere in the Castle when they arrived, that totalitarian power was nervous, unsmiling, insecure, uptight. Humour seemed to be confidence-building, rebellious, democratic. Each joke was a tiny revolution. The memorable lighter moments came thick and fast, as when a camera found Havel at his Castle desk, under the gaze of two naked women striding across a wall-mounted canvas by Jiří Sopko. 'What did I sign?' he asks, frowning. 'Wait a minute... I was naming an ambassador, but I'm recalling him!' Havel laughed, adding: 'It's all so absurd.' Then there was the big cock-up over a precious letter that had been addressed to Havel at the Castle. Havel got wind of a man who so objected to his casual placatory remarks about the need for reconciliation with Germany that he began a hunger strike. Havel — aware that he might be said to be culpable for a death that would get widespread publicity — summoned the protester to his office to discuss the matter. The protester, Havel and his aides sat around in a circle to do business. The man explained that he had fought against the Nazis in Dukla Pass, that he therefore found repulsive Havel's remarks about the 'morally unacceptable' Czech expulsion of ethnic Germans at the end of World War II, and that he was now convinced that Havel was preparing to sell the country to the Germans.
After lengthy discussion, the man accepted Havel's appeal to abandon his hunger strike. He confirmed his decision a few minutes later to a Czechoslovak television crew in the President's office. After receiving a letter personally signed by Havel, the man left the Castle. Everybody felt relieved. But the following morning, Havel's aides received a telephone call from the same man, who was waiting downstairs with the security guards, at the stairway entrance to Havel's office. An aide went down to see what was the matter. The man was shaking and pale. He explained to the aide that he hadn't slept a wink because of the letter he had been given. 'But what is wrong with yesterday's letter?' asked the aide. 'It is a letter from Gorbachev to President Havel,' came the reply. Realizing that the petitioner had been given the wrong letter, the aide invited the man upstairs to pick up the correct letter. Havel spotted the two men. 'What's wrong?' he asked. 'Our friend was given the Gorbachev letter by mistake,' said the aide, who did not notice that at that moment the grey-suited Soviet Ambassador was sitting all ears on a nearby sofa.
Then there was the first state visit by Havel and his aides to Poland. It felt a bit like a re-run of the Charter 77 and Solidarnošć meetings a decade earlier, but with a difference or two. As Havel and his long-haired advisers descended the aircraft steps that led on to soft, red carpet, with a brass band playing the old Czechoslovak anthem, the Polish guards glared at the revolutionaries. 'They'd have made us into Siberian sausages if they'd had a chance,' recalled an aide. Sweet revenge came that evening, at a state dinner attended by everybody's old enemy, the Polish President General Jaruzelski, whose nickname was 'the crow'. Every effort was made to get him drunk. The revolutionaries succeeded. 'All things considered, you're not a bad guy,' slurred the famous writer and public intellectual, Adam Michnik, towards the end of the evening, Havel and the others chortling loudly. 'But you should give up and step down,' continued Michnik. At which moment President Jaruzelski lurched towards the floor, rescued from a nasty bump by several pairs of dissident hands.
### **The Manipulator**
Almost everybody who had contact with him — or had no contact at all — during the first period of his presidency noted his aloofness. Some pointed out that he'd always been coldly calculating when it came to keeping company. Others confessed their nostalgia for the old 'dissident' times when Havel seemed always to be available — and always willing to talk, drink and be merry. Stories began to circulate about how he had changed, and about how he seemed even to be embarrassed by the great Chinese walls of power that had come between him and his former friends and working colleagues.
A typical version ran something like this: During the first weeks of his presidency, Vašek is invited to a flat for drinks and political discussion. He arrives, dressed in blue jeans, looking crumpled and withdrawn, and is instantly greeted with hugs and kisses — and a barrage of laments about how nobody ever sees him any more, except on television. He seems to hang his head in embarrassment, reaches for a drink, wedges his tired body on to the arm of a chair or on to a bare patch on the crowded living-room floor, rolls a cigarette, and sits quietly as others speak, others looking on. Later the guests begin to mingle, laugh and dance. He receives another barrage of laments about how distant he has become. He again hangs his head and rolls another cigarette. And then another — as if rolling tobacco into paper is an involuntary defence reaction against guilt. Almost everybody then gets drunk with the President — partly because that's what always used to happen, partly because a revolution is taking place, and partly because everybody is thrilled to have a loved political actor back in their midst.
Then there were those who complained that his aloofness — the aloofness of the monarch of the crowned republic — hampered their job of trying to establish links between the emerging structures of government on the hill and the world beyond the Castle walls. This was a more serious objection, for it touched on the whole question of his accountability before the public, as well as his personal responsibility for the hundreds of decisions of consequence that he was now making on a daily basis. A strong version of this political type of objection came quickly, and almost spontaneously, from within the ranks of Civic Forum. The Forum had been his power base up until his election as President. It began to work hard to prepare and fertilize the soil out of which free parliamentary elections were to grow by the summer of 1990. Civic Forum thought of itself not as a party — the word was anathema to its many activists — but as a potentially country-wide para-political structure, run directly by citizens, whose aim was to institutionalize, as quickly as possible, the procedures and institutions of an electoral system that had been destroyed long ago by the _coup de Prague._ Civic Forum was a catalyst network geared to driving the revolution towards parliamentary democracy. Its activists were interested in the Polish and Hungarian examples of 'government by round table', but as an improvised citizens' initiative it was based on no political theory or thinker. It deliberately worked against the Machiavellian rules that state power should be sought after, that official politics was everything, that it was imperative, if only for the sake of survival, to fill power vacuums with strength wherever they existed. Civic Forum instead worked to change the rules of state politics from the outside. Wherever possible, subject to finding sources of funding, it tried to set up 'election centres' as well as teams of advisers supplied to local groups trying to form themselves into pressure groups or 'democratic' political parties. It was of course a tactic designed to benefit Civic Forum, but at this stage it was to be neither a social movement nor a political party — nor even a future government. 'Parties are for party members!' ran one of its posters for the forthcoming elections. 'Civic Forum is for all!'
Given Havel's stated commitment to free elections, it was indeed odd, his critics said, that from the outset he broke off virtually all contacts with Civic Forum. 'From the beginning there was a constant problem,' said Jan Urban, who later became chief spokesperson and convenor of Civic Forum. 'Havel and the rest of the Castle became totally separate, and very secretive. Their links with the outside world were uncoordinated. They contacted others only on their own terms.' Many within Civic Forum sensed that Havel's aloofness was politically undesirable — there were even occasions when the Castle seemed deliberately to be giving out contradictory information and advice, for the purpose of playing off the federal and two national governments, perhaps (so some within Civic Forum suspected) with the ultimate — unconstitutional — aim of creating a 'fourth government', a crowned republic rotating around President Havel.
The key players within Civic Forum were initially reluctant to blow the whistle publicly on Havel. The basic rule of 'dissident morality' — that individuals and groups refrained from screaming at each other publicly after sitting in prison with them — was observed, especially since everybody within Civic Forum remained scared of secret-police provocation and infiltration, and continued as well to treat the shadowy Communist Party as enemy number one. So there were efforts, from the last week of January 1990 onwards, to create a private 'pipeline' between Civic Forum and Havel. An informal, private meeting held regularly on Sunday evenings at Jan Urban's house was set up to exchange views and information — to act as a damage-limitation exercise. Havel's spokesman, Michael Žantovský, regularly attended and later so did others, like Ivan Gabal, Jan Ruml and Vladimír Mlynář. The pipeline meetings continued after the summer parliamentary elections, indeed they survived until the end of 1991, when a row with the Castle about its proposed constitutional amendments ended in acrimony.
The conviction that Havel had withdrawn into the Castle to become a power unto himself was quite at odds with his former self-image as a man who lived openly before others, in the truth. Although it shocked a good many former friends and political acquaintances, those who knew him well were less than surprised. Something like Havel's Law of Oligarchy was at work from the beginning. This was no 'iron law' of the kind outlined earlier this century by Robert Michels, for whom oligarchy springs up wherever there is organization. That so-called law rested upon faulty premises — including its supposition that 'the masses' are naturally docile and gullible, and its claim to be a universally applicable law. Havel's Law of Oligarchy was quite different. It grew out of a specific revolutionary context and nourished itself on the efforts to build a crowned republic.
To begin with, communication with anybody and everybody was generally difficult. There were few phones, no photocopiers, no fax machines. Even paper was in short supply. The presidential office also inherited from the _ancien régime_ an immensely large workload that simply had to be dealt with. _Raison d'état_ had to be followed, or so it was said. A new foreign policy had to be negotiated. Laws had to be reviewed and signed. New ministries had to be constructed. More staff had to be recruited, brought to the Castle and trained. New ambassadors had to present their credentials, and foreign delegations of government, business and civic organizations had to be received officially. The decision to switch over to the forms of protocol that operated during the Masaryk presidency of the First Republic was time-consuming, and also off-putting to would-be visitors to the Castle. Then there was the profoundly intimidating security system operating at the Castle. Not even Havel himself initially knew how it worked — at least not until the day that an alternative surveillance system provided by the American Embassy, and dubbed 'the refrigerator', was set up. Even that did not make it any easier for individuals and groups to make appointments, or (as some had hoped) to drop by for a quick chat and a coffee or brandy with the new President.
The absurd time pressures on Havel worked to prevent that in any case. Not only locals, but contacts from the four corners of the earth often had the experience — and do so still — of being squeezed out by a bureaucratic schedule which was strict and inflexible. After five or fifteen or thirty minutes, if the callers have been lucky, time is up. There is a firm knock at the door. 'Mr President', says the faintly smiling but businesslike assistant with a craning head, 'would you be so kind as to prepare for your next appointment, who is now waiting.' The distancing effects of such treatment were reinforced, from the outset, by the privileges affixed to the presidency. 'I find myself in the world of privileges, exceptions, perks, in the world of VIPs who gradually lose track of how much a streetcar ticket or butter costs, how to make a cup of coffee, how to drive a car and how to place a telephone call', he soon observed, adding: 'I find myself on the threshold of the very world of the Communist fat cats whom I have criticized all my life.' Havel's urge to have guaranteed access to the mass media inflated the privileges he enjoyed. The elbowing ratpack of newspaper and radio and television journalists began to take up valuable appointments. They in turn required minding, lest they said the wrong things, which in turn necessitated spokespersons, watchdogs who guarded the sovereign power carefully, at all times. Soon, it seemed as though hardly anybody, or that even nobody, could 'get' to the President.
No contemporary head of state can live without media coverage, it is true, but from early January 1990 it was obvious that a special dynamic, one traceable to his preferred role as a political _Ichspieler,_ provided crucial nourishment for Havel's Law of Oligarchy. Those from outside the Castle who tried to deal with him during this period found that he strongly preferred to operate outside institutional forms and procedures and to handle things personally. He no doubt found a certain freedom in presidential power. There were times when he found it a stimulant. 'I worry about him,' said his good friend, playwright Josef Topol, to Olga over coffee one morning, a year into his presidency. 'You shouldn't,' snapped Olga, rolling her eyes. 'He adores it! He'll never give it up!'
The role of _Ichspieler_ meant making decisions by personal wheeling and dealing, the art of which he had mastered from the time of the group of Thirty-Sixers. Especially before the revolution, in apartment meetings for instance, Havel had been admired for the way he would listen to many opposing or contradictory opinions, then take the floor for a few minutes to formulate a statement or a position that was acceptable to everybody present. Combined with his courageous struggle against imprisonment for two decades, it made him into a moral authority within the opposition. After the revolution, he continued to practise this art, but mainly within his immediate circle of trusted advisers. So when it came to dealing with outsiders, in encounters with members of the public for instance, Havel resorted to _ad hoc_ personal negotiations.
In Vojtěch Jasný and Miloš Forman's film _Why Havel?,_ he confessed that among the most enjoyable things about the presidency 'are these surprise visits, where I unexpectedly arrive at factories, offices, pubs, discos. All of a sudden, the President's there. It's unheard of. A woman sits in her office pretending to work while she munches on a roll. Someone knocks — 'Come in' — and in I walk. She's in shock. The roll feels like a rock in her throat. She starts babbling and the truth spurts out. Two minutes after I've left, she realizes she should have lied.' Exactly the same habit of acting as if he were the _deus ex machina,_ as a figure who personalized everything in order to resolve everything, was obvious to those who dealt with him daily through Civic Forum. 'Havel never understood the value of institutions, negotiations, and the need for compromise,' concluded Jan Urban, who found that negotiations were often fraught and frustrating, because for Havel Castle policy-making was 'always about making direct deals, personal compromises and, above all, manipulation. These tactics work perfectly well in small groups within a small opposition. But it would never have worked within a large opposition like that of Solidarność in Poland. And it most certainly never worked during the first months of his presidency, when power was seen simply as manipulation.'
Havel's propensity to manipulate others was nourished by his skill at playing the role of _Ichspieler_ before adoring audiences bubbling and throbbing with praise. During the first year of office, he joined the ranks of 'the world's great leaders'. Celebrity was a great aphrodisiac. He was blessed with a special kind of power — the power of charisma — whose mechanics were daily lubricated by his air of divinity before enthusiastic crowds devoted to his every move, his every word and gesture. Those individuals who want to believe should kneel, said Pascal, and kneel down they did. Projecting themselves outwards towards the Leader, individuals introjected him into their souls. He began to seem like a mortal endowed with immortality. Many were smitten by his theanthropic qualities. Public expectations of the extraordinary followed him everywhere. The humdrum routines of everyday life vanished in his presence. Like a prophet endowed with premonitions of a better world, he seemed to have the knack of inventing new ideas, of getting things done, of being in the right place at the right time. There were moments even when individuals felt _driven_ to be near him, to talk to him, even to touch his body. In the industrial town of Opava — the following story was typical — a young teacher dashed from her classroom at the end of the school day to try to catch a glimpse of him as he attended an official function at the municipal hall. Gripping a bunch of bright flowers, she nudged her way through an excited crowd. A policeman caught sight of her and kindly cleared a path for her to present the flowers to His Royal Highness — at exactly the moment that he was descending the steps of the municipal hall. The schoolteacher was ecstatic. There he stood, smiling at the teacher, who curtseyed before showering him with flowers. Her heart fluttered, head dizzied, and mind went completely blank. She later recalled that he was shorter than her — she had not expected to look down on him — that his nose was yellowed by pollen from a previous bunch of flowers — he looked like a happy clown — and that he smiled warmly and said in a hoarse statesman's voice, 'Thank you very much.'
'Charisma' is originally a theological term (from the Greek _kharis,_ favour or grace) meaning the gift of grace. It now refers to the apparently superhuman powers of a single individual to magnetize others like iron filings. The charismatic personality is as magical as it is unstable. For a time, charisma is blessed with the capacity to dignify the mundane, to glorify the obvious. Yet charismatic power usually doesn't last long. It fades with time and sometimes (as Shakespeare's character Antony discovers while lying in his tent, abandoned by the god Hercules) it can disappear overnight. Immediately following the Velvet Revolution, Havel seemed to be an exception to the rule of fading charisma. His habit of playing the role of charismatic _Ichspieler_ caused sensations, which made life hard for his critics. Whenever confronted with objections, concerning matters of style or policy, he would if necessary cut off the personal negotiations and go silent on his opponents. Several times he told his aides: 'Don't bring me messengers bearing bad news.' He could well have been uttering the words of a messenger in the company of the Queen of Egypt: 'Though it be honest, it is never good / To bring bad news / Give to a gracious message / An host of tongues; but let ill tidings tell /Themselves when they be felt.' So during the first months of his presidency — the habit continued throughout his political career — Havel worked hard to cultivate people who bore him good tidings. His appointment of Saša Brabcová as his personal translator was a case in point. Everybody working on the fringes of the Castle, and even some within, found her a puzzling woman in the Prague sense. Nobody really knew who she was and where she had come from — except that before the revolution she had been the personal aide of Miroslav Štěpán, the last First Secretary of the Communist Party of Czechoslovakia. Now working with Havel in the innermost circles of Castle power, she was party to the most confidential discussions and decisions. Some people within Civic Forum and within the Castle objected. Havel initially reacted with deaf ears. When pushed, his reaction was curt. 'She brings positive vibes to the Castle,' he said. And that was that.
## **_Decline_**
## **_(1990-1999)_**
### **Defections**
The republican monarch soon had his first taste of the maxim that elected political men who get mixed up in state politics are strongly pressured into playing by its rules, which means that they quickly learn the arts of manipulation, keeping matters secret, pulling strings, turning others' weaknesses into sources of strength, even turning themselves into devilish creatures who stop at nothing to get their ways — and, in so doing, creating adversaries ready to cause 'trouble'. Within the Castle, in accordance with this maxim, there was an immediate tendency for people around the elected Havel to act as if they themselves had been chosen by divine force. Not surprisingly, 'trouble' began immediately to come Havel's way.
There were aides, Stanislav Milota for example, who openly criticized the working practices of the Castle. The rugged, good-looking Milota was a former cameraman with a sharp eye for people. He was a good organizer and an articulate and down-to-earth working-class man from Žižkov, the rough district of Prague in which Olga had also been born. He had been a close friend of Havel's before and during the revolution and on 2 January 1990 he received a telephone call from the new President, inviting him to become Head of the Secretariat. 'Do you want an easy retirement with a big pension, or do you rather want to help me?' began Havel. According to Milota, the self-answering, either/or structure of the question was rather typical of how Havel manoeuvred people into making the decision he wanted. But Milota willingly agreed. Havel was pleased, and added, with a touch of irony. 'Good. I need someone to be my opponent in the Castle.'
Critical opposition he certainly got from his friend. Milota's instincts were proletarian, and he tried often to remind Havel that his own class background should not blind him to how most of the country lived. He was personally critical of Havel's attempts to crown the republic with works of contemporary pop art. 'I know you can't force this nation to like Beethoven and Shakespeare. But then can you do the same with Michael Jackson and the Rolling Stones?' Milota pointedly asked him one day. 'I have a different view from you of the wood from which this country has been hewn,' he continued. 'From your bourgeois background, you learned not to eat with your knife, and not to kiss the arses of comrade women. But I learned other things. Just as Olga did.'
These were rough and tough words. Milota was no friendlier towards what he dubbed the 'amoral behaviour' of senior officials during the first few months of the new regime. Havel's helpers were inclined to behave in ways familiar under the Communist _ancien régime._ The backscratching, toe-sucking and breast-fondling efforts that used to go into obtaining a visa to France, say, were now potentially in evidence around a new President actively committed to 'living in the truth'. It was not that Havel himself was becoming corrupted. It was rather that the Castle seemed to attract mindless profligates, said Milota. He was appalled by the heavy drinking on the first presidential flight to Moscow. 'Have you seen yourselves through the eyes of the flight attendants? Do you know how you're behaving?' he asked a group of them on board the plane. The earthy Milota was frank with Havel about the need for a more spartan approach to protocol. 'This is a nation that's demoralized. You should set an example. Don't take taxis and chauffeur-driven limos. Catch a tram up to the Castle. Have bread and a jug of water for lunch. You too need the occasional kick in the arse.'
Havel was normally a very precise person and would usually have kept excesses and amoral behaviour at bay, Milota later said. But during these early weeks, Havel was tired. He found it hard to keep control of the high-pressured dynamics of Castle life. Besides, he himself had an appetite for power and bohemian excess. He eventually told Milota to stop disrupting business with objections. 'I don't want to hear any more about all this,' he said. Relations between the two men worsened, especially during the preparations for the first presidential visit to the United States. According to Milota, Washington's fascination with Havel — 'the cleancut bourgeois guy who looked different from his rough-tongued Polish electrician counterpart' — served to overinflate the Castle's sense of its own power in the world. The planned delegation, the second biggest ever (after De Gaulle's) in the history of the United States, was too fat to fit into one aircraft. Milota told Havel that he was making the mistake of acting as if he were the President of a country like the People's Republic of China. 'Why do we need thirty bodyguards on this trip?' Milota asked. 'We're a country of only 15 million people. What is all this going to cost?' The reaction among Havel's advisers ranged from puzzlement to frosty suspicion that Milota was trying to get rid of them. He decided to get out first, to leave behind what he considered to be an orgy of powermongering. One afternoon in mid-May 1990, after sixteen weeks as Head of the Secretariat, he quietly plucked his jacket from the office coat rack, said to his secretaries that he was just stepping out for a moment for some fresh air, and never came back again to the Castle. Later that day, he sent a message to Havel, explaining (as the Communists used to do) that for health reasons he was 'taking early retirement'.
The message from Milota (he later heard) was received with stony silence. The notable exception was Olga, who not only liked and respected Milota, her fellow Žižkov radical, but also shared his feverish complaints, and said so loudly. She never found the Castle an especially hospitable place, and liked to dismiss it as 'the submarine'. Here were scores of people trapped eighteen hours a day inside an airless, dimly lit space, cut off from the real world, way out of their depths in treacherous waters, deeply uncertain of either their mission or their machine. Her husband's aides were mostly unqualified for the job, she told some of them to their face. Others were womanizers and drunkards. Still others were insecure narcissists who spent their time gazing at their own media images. Olga disliked fame. She was impatient with journalists who flattered her, or asked her such questions as what flowers or food she liked. She was not averse to telling them off, or interrupting them to say she had to empty her washing machine. She also disliked being trapped in the cage of Castle security. She often said to her bodyguards that she'd rather be playing bridge or walking in the countryside, and naturally got enormous pleasure from giving them the slip — as on the first American state visit, when unannounced she entered a lingerie shop, leaving her young male bodyguards standing pink-faced among bras and knickers and laced body gloves.
Olga had high but simple moral standards. She disliked snobbishness and despised prejudice, for instance against Romanies or the elderly. She insisted on frankness, simplicity, honesty, and no bullshit — and it is unsurprising that she clashed with some of the key Castle personnel. Mutual friends confirmed that she had a much better eye for people's character than did Havel. She could spot daggers in castlemen's smiles, and if she had her way, she told a friend during the first few weeks of the Castle under Havel's leadership, she would rid the place of some of them by 'hanging them with their own bloody neckties'. Some bit back at her for sentiments of that kind. Ladislav Kantor was among the targets of her criticism. She considered him a 'red-haired cretin', and several times tried to rap him over the knuckles — for instance when he queried, on security grounds, the proposed appointment of the great exiled Czech conductor Kubelík to the National Theatre. She said openly that Kantor was a flatterer of her husband, and that he was in danger of falling for it. Kantor responded by trying to draw Havel into such disputes, even on one occasion offering to get rid of the cuckoo in the nest. 'I can get you a divorce,' Kantor said.
Olga, as dignified and tough as polished old boots, was unmoved. At an early stage after the revolution, she made up her mind to turn her back on the Castle and instead of playing the hollow role of First Lady she devoted her energies to the fledgling civil society. She considered it a more meaningful option with credible precedents. As a young teenager, just before the _coup de Prague,_ she had been involved in running a Žižkov club-residence called Milíčův dům. Set up by a Christian pacifist, Přemysl Pitter, it functioned as an alternative community for young people whose family life had been shattered by poverty, war, bigotry. The club-cum-residence had sheltered Jewish children during the Reichsprotektorat, while during the years Olga was there many children came as refugees from the Sudetenland pogroms and concentration camps. The refuge offered tastes of other worlds. The children were encouraged to live as equals within a community; they were taught how to resolve their conflicts non-violently; and they were offered access to a big library, courses in art-appreciation and theatre, and generally to join in group activities like singing, gardening, sewing, knitting and ping-pong.
The director of the community centre fell out with the Communists, and in 1951 narrowly escaped to Switzerland after refusing to be drafted to the uranium mines at Jáchymov. Olga never forgot him or his bold initiative. Immediately after Havel went to the Castle, she began to wonder whether a similar kind of experiment could be made in defence of the fledgling civil society. She had had some thoughts of setting up an organization to protect animals or the environment, but her dream began to come true after making a state visit to Canada in February 1990. There she was approached by a rich Czech _émigré_ , a Montréal manufacturer of nuclear-reactor equipment named Karel Velan. He wanted to donate money to a Czech hospital, especially for the purpose of showing Czech doctors how things were done in the West. Olga soon spotted the advantages to be won from appealing to others to pool funds to help the disabled victims of Communism live in dignity. And so upon her return from Canada she set to work founding an organization called the Good Will Committee.
It was the first of its kind in post-Communist Czechoslovakia. Olga wanted it to be small, and to serve mainly as a clearing house for sponsors' and donors' money. Things turned out differently, in part because as each day passed the new organization attracted dozens then hundreds of letters seeking support. There were also hundreds of offers of financial support from post-'48 and post-'68 emigrants, Czech and Slovak businesses, and older citizens, especially poor women who sent 100-crown notes through the post. In its first phase, it was decided that the primary goal of the Committee was to re-equip and humanize the prison-like institutions of incarceration inherited from the _ancien régime_ — large institutions like borstals for children and centres of confinement for the disabled. Later, after a change of law covering the work of charities, the Good Will Committee — despite Olga's original desire to keep the initiative small — grew much larger and was renamed the Olga Havlová Foundation. She left the day-to-day management to her staff, instead concentrating on lobbying members of parliament and the social-welfare ministries, fund-raising, and — above all — visiting groups and individuals with the aim of deconstructing the old institutions and setting up new, smaller, civil-society institutions with a human face.
Václav Havel reacted supportively. Although at first he was 'a bit amused that his wife had found a hobby', he quickly grew proud of its intrinsic merits — so much so that he set up his own foundation, The Václav Havel Foundation, which until 1995 served to fund projects like the refurbishment of the Castle library and guided tours through the Castle for the blind. The desire for emulation was understandable, but the effects were different. The Good Will Committee proved that it was possible to pose a different — hopefully complementary, but potentially contradictory — understanding of politics, power and empowerment than that of the Castle. The President's big house on the hill: the seat of state power, wrapped in its imagery of flags, ornaments, guards, arms, courtiers. Its role: to draw upon tax revenues to issue orders, sanction laws, issue prepared statements, grant amnesties, provide symbolic and moral leadership, to bind the country to the outside world by means of diplomatic missions, meetings with heads of state, trade agreements, troop deployments, or (in the last instance) force of arms. By contrast, a charitable organization: a small and independently funded organ not of the state, but of civil society. Its role: to address the self-defined needs of its clients, to provide some stability and justice in their lives, to shield and protect them from the inconveniences resulting from state neglect, market forces, or social bigotry and discrimination — overall, to help the disempowered to feel stronger in the world by encouraging them to see and feel the importance of what the ancient Greeks called the _metaxu._ Through the charitable organization, in other words, the disempowered can come to sense the importance of nests in which they are warmed and nourished and gain self-confidence. They are encouraged to rely less on 'distant' and 'inflexible' governmental institutions. The powerless come to learn that power is not synonymous with large-scale organizations like states and corporations. They learn, on the contrary, that lines of power run through every nook and cranny of our lives, that large-scale organizations rest on these foundations of 'micro-power', with the implication that amendments and reversals of these same local relations of power — the empowering of the powerless — can be a counterweight to 'macro-power', and can have wider effects upon the overall structures of the state and civil society.
### **Parliament**
The active defence of civil society against the castled state, combined with criticism of the _Ichspieler,_ effectively called into question the practical vision of the crowned republic. So too did the active defence of parliamentary government during the first week of 1990. At the time, one of Havel's closest collaborators during the long years of Soviet-secured normalization recalled meeting him alone at the Castle for an hour on the day before his first major parliamentary speech. 'He was relaxed after lunch. He made himself comfortable, stretched out on a _chaise-longue,_ undid his tie, and talked quietly and frankly,' said the colleague. 'He told me that he had decided to be President for a year, after which he would make a public speech, perhaps before parliament, in which he would announce that he was standing down and that he had decided on a successor. He added,' continued the colleague, 'that there would not be a dry eye in the public during the speech.' The surprised colleague asked him whom he would nominate as the heir apparent. 'Havel refused to say, pointing out that the room in which they were sitting, the President's Office, was probably still bugged.' So the colleague wrote a well-known name on a piece of paper and passed it to him. Havel laughed, shook his head, then exclaimed: _'He's apolitical intriguer!_ ' Later the colleague learned that Havel instead had in mind Magdalena Vášáryová, a well-known beautiful star of Czechoslovak stage and screen.
The exchange between the new President and one of his most trusted friends was of no political consequence, except that it revealed something of Havel's rather cavalier attitude towards the parliament at the time. It also helps explain the political trouble that came his way next day. The hitherto unrevealed events went something like this. In the first few weeks after the revolution, public whisperings began about the future name of the Czechoslovak federation. Mistrust and bad feelings quickly developed. Various Czech politicians openly made fun of the Slovaks; some were even heard to say that a hyphen should be used between Czech and Slovak in Bratislava, but not abroad. Some Slovaks replied that their state should be mentioned first, as in Slovakoczechia, but this was treated in Prague as a good joke, then a bad joke.
Havel decided to act. On 23 January, driven by an instinct that it was time to move, he came to the Federal Assembly building, with the stated aim of addressing its members. Like Lycurgus or Solon — or Charles de Gaulle coming to the French National Assembly in 1958 — Havel would for a time occupy the four-storey, steel-beamed, ugly green glass structure, which was situated (Prague people often quipped) near Wenceslas Square, between a museum and a theatre. Havel would act as a popular sovereign battling against those trying to interpose themselves between the people and himself. Equipped with the full powers of a herald, he would urge the parliament to change the name of the country, alter its coat of arms, and rename its armed forces, and to do so by a disciplined parliamentary debate followed by a show of hands.
Before entering the Federal Assembly, Havel had coffee and a chat with the standing committee called the Presidium. Most of its members seemed afraid to speak against him. He was, after all, the ruler of the crowned republic, the unchallenged symbol and driving force of the revolutionary changes that had begun. And his reasoning was as precise as ever. He explained that he would say to the assembly that he was led by 'a responsibility to negotiate in accordance with the awakened will of the public'. Havel went on to reveal that he would present 'proposals for mutually implemented changes' that were 'expected by most people'. The proposals were inspired and called for by 'the public, to whom I feel my primary responsibility', he added. He then divulged that he would put a clear and concrete proposal for altering the name and key symbols of the country, dropping the word 'socialist'. The new name of the country was to be virtually the same as that used during the First Republic: The Czechoslovak Republic.
Not every member of the Presidium agreed with his tactics and intentions, as was explained on the spot by the country's leading constitutional lawyer, Zdeněk Jičinsky. The slim and short, grey-haired, goatee-chin-tufted, fox-faced, calm-mannered and highly intelligent Jičínskí was a seasoned politician, and he had no difficulty telling some bad news to the charismatic Havel, whom he had come to know during the early days of Civic Forum. 'It is simply impossible that you read out your proposals and then expect the members of the Assembly to raise their hands in acclamation,' Jíčínsky told Havel to his face. 'These are proposals of a special kind. Under the existing constitutional rules, they most certainly cannot be altered in this immediate way. In our federal system, state symbols cannot be changed by the Federal Assembly without the prior consultation and agreement of the republican parliaments: the Czech National Council and Slovak National Council.'
Havel, as headstrong as ever, went ahead with his plan. He even had the cheek to insist before the parliament that his proposals had to be treated as a package, that is, that in the interests of smooth passage they were not divisible. But Jičínský had correctly anticipated the mood of the assembled parliament. Havel's attempt to transform the parliament into a stage and to perform solo in front of its members — to cast himself in the role of _Ichspieler —_ failed. The deputies sent Havel packing; according to one eyewitness, his eyes were as glazed as a Greek statue. The Assembly refused to approve his package of proposals, and instead acted as catalyst of a wider public controversy about the themes that Havel had raised.
Naturally, the problem of the relative 'invisibility' of Slovakia instantly surfaced, and some Slovak deputies began to insist that the new name and symbols of the country should express the fact that Slovakia was also a republic. Their preferred solution was to insert a hyphen in the country's name — just as the country had first had after the Munich fiasco. Within the Czech lands plenty of angry voices began to make themselves heard — enabling a bizarre compromise to emerge. The Federal Assembly eventually passed legislation that enabled the country to have _two_ names: to be spelled without a hyphen in the Czech lands ('Czechoslovak Republic') and with a hyphen in Slovakia ('Czecho-Slovak Republic'). The new law was greeted with howls of protest at a big public rally in Bratislava on 30 March 1990. In the end, the law had to be amended to fulfil the requirements of 'making Slovakia visible'. As postage stamps from this period reveal, the country was from here on to be called the Czech and Slovak Federated Republic. The first battle in what would later be called 'the hyphen war' had been concluded.
Future historians will dispute whether or not Havel was culpable for his part in prematurely triggering off a bitter conflict that eventually soured Czech and Slovak relations for years to come. Beyond dispute is the little-known fact that prior to this conflict there was another: the issue of whether or not the new President really wanted to allow the development of a parliamentary democratic system of government. It sounds overdrawn to put it this way, but at the time, during the first weeks and months of the revolution, there were plenty of people inside and outside the Federal Assembly who worried that Václav Havel, the symbolic leader of the struggle to live in the truth under conditions of open government, was potentially a threat to the realization of exactly that goal. The feeling crystallized that there was a fundamental contradiction between Havel's desire for a strong and stable executive and the need in any democracy to control demagogy. The same feeling was strengthened by Havel's tendency to describe himself, in self-important terms, as the voice of Being, as 'an instrument of the time' who was being compelled 'to do what had to be done'. Some observers grew particularly nervous after his full-blooded attack on the status quo on the afternoon of the twenty-first anniversary of the military crushing of the Prague Spring. Standing on the balcony of the pollution-stained Civic Forum building, overlooking Wenceslas Square, flanked by aides and photographers and camera crews, Havel called for a 'second revolution' to get rid of the rubbish left over from the _ancien r_ é _gime. 370_
Such words served to confirm the suspicions of key players like Jičínský, who dug in their heels and so handed the President his first political defeat. Havel was a mite indignant. 'Experience has taught me that it is best to do the opposite of what Professor Jičínský advises,' he later said. 'Whenever I heeded his advice, whose common denominator was always the recommendation that I ought to postpone something, it had disastrous consequences.' Jičinsky later confirmed that he neither regarded Havel as a personal enemy nor really worried that he would turn out to be a Jacobin figure like Robespierre. 'Václav Havel was at the time a figure of absolute power. But, unlike Robespierre, he had no intention of acting in an absolutist way. Not only that, but Havel wanted disputes to be resolved peacefully. He didn't want people to settle scores in the streets. He was opposed to revolutionary violence.' But the allergic reaction of the Federal Assembly towards Havel — expressed most eloquently in the constitutionalist opinions of Jičínsky — reveals the grains of truth of the old maxim that all revolutions tend to breed professional revolutionists possessed of great initiative, organizational talent and elaborate doctrines. That old maxim implied that professional revolutionists initially appear to listen to their fellow citizens who are rebelling; later, they claim to be representatives of their supporters, who eventually become the objects of manipulation of the self-appointed revolutionaries, usually by violence.
Havel, who constantly appealed for non-violence and 'velvet' solutions, certainly did not fall victim to, let alone flirt with the second half of this maxim. Jičínský pointed out as well that Havel's anti-parliamentarian instincts were understandable. After all, it was a parliament dominated by unelected Communists whose next moves in the revolutionary power struggle were unknown. The parliament, Jičínský noted, had indeed elected Havel as President — it was among the sweetest ironies of the Velvet Revolution — but it might not have done so had voting been by secret ballot instead of by a show of cowed hands. Yet the trouble with Havel's position, Jičínský reasoned, was that he and his closest advisers knew little about constitutions and had little feel in particular for the actual and potential relationship between the presidency, the federal parliament and the constitution.
Havel and his aides set to work on the hunch that the constitution was a Communist device, and therefore rotten, and that the parliament ultimately consisted of a bunch of Communists who needed to be kept in check before being thrown out by a general election. Their presumption, argued Jičínský, ignored the basic point that the existing constitution, introduced in 1960 and amended in 1968, contained many clauses found elsewhere in parliamentary democratic constitutions. The first steps toward the 'democratization' of that constitution had been taken in the dying moments of the Husák presidency: the principles of the leading role of the Communist Party and the people's militia had been removed; the parliamentary procedure through which Havel was subsequently elected was introduced in the form of an amendment; and the wording of the oath of allegiance to be sworn by incoming presidents was changed so as to get rid of all references to 'socialism'. These various amendments Jíčinský welcomed. Their content was an improvement on what had existed before. They also helped to preserve and cultivate a spirit of constitutionalism and the commitment to the principle — vital in abnormal conditions like the Velvet Revolution — of what he called 'legal continuity'.
Jíčínský was especially critical of Havel's habit of playing the role of _Ichspieler._ 'Havel's personality was that of an artist, a dramatist,' said Jičínský later. 'He had no grasp of political science, no legal background, and only limited familiarity with the constitutional relationships in which he was acting.' Matters were exacerbated by his natural impatience. The insistence by a playwright that an instruction be carried out right away may be appropriate on the stage. But it was actually counterproductive in these early weeks of the revolution, when time was needed to get the new balance right among various branches of the constitution. 'Havel did not behave arrogantly,' he concluded. 'That was not his style. But when he realized he couldn't get his way immediately, his mood plummeted. He found strange the political terrain of parliament and constitutional change, and he did not know how to move about within their forms. Although he had absolute powers, he nevertheless should have had some respect for the institution of parliament.'
In the context, Jičínský's criticisms may have been judged as pedantic, as fun-spoiling, as curmudgeonly. But they were politically revealing, and although he didn't quite put it this way, they highlighted the precious role of parliaments as power-sharing and flexible power-taming devices, especially during the establishment and consolidation of democracy. During the first weeks of the revolution, Havel took the view that the current federal parliament was not only full of crooks and Commies, but that within the crowned republic that was being born, parliament functioned as an obstacle to living freely 'in the truth'. His hoary prejudice against parliament was worrying, especially in view of its rich history and — above all — its indispensability in democratic regimes. Parliaments are assemblies of decision-makers who consider themselves formally equal to one another in status, and whose authority as members of parliament rests on their claim to represent a wider political community. Parliaments in this sense superseded the traditional medieval assemblies (such as the German _Hoftage_ or English _witanegemots)_ , which had functioned — note the parallels here with Havel's attitude — mainly as loosely organized, _ad hoc_ consultative bodies summoned by the monarch for the purposes of seeking their counsel or opinion, or publicizing among the monarch's subjects special events, such as dynastic marriages, international treaties and new judicial and legislative measures.
In contrast to this medieval arrangement, parliaments in the modern sense first developed in the field of high tension between the public power of feudal monarchs and the cluster of private interests represented by the estates of nobility, clergy, peasantry and burghers. Bodies like the Spanish _cortes_ and the French _parlament_ (or _parlamentum)_ met more frequently and regularly, and also functioned as both consultative and deliberative bodies. Especially when the cohesion and influence of estates increased, and when at the same time government typically assumed the form of the _Ständestaat_ — a monarchy ruling over a society dominated by orders — parliaments became a vital intermediary between monarchic rulers and the (elected or appointed) representatives of the most privileged estates, who sought to define and defend matters of concern to the whole 'realm'.
These early European parliaments were by no means weak or intermittent. Not only the English parliament — often assumed to be the unique example of a powerful representative assembly — but nearly all Continental parliaments began to exercise considerable powers of granting taxes, participating in legislation and determining the justice of matters as diverse as succession and foreign policy. Here were the seeds of the more recent understanding of the necessity of parliaments to democracy. Although it is true that parliaments can play a variety of roles, two sometimes tensely interrelated functions of parliament are of special importance to democracy. First, parliaments are vital means of aggregating, co-ordinating and representing diverse social interests. This integrative capacity of parliament has often been misunderstood — by the Marxist tradition especially — as a mechanism of bourgeois class rule. Parliament _may_ become the political means of class domination — as Lenin put it, 'simply a machine for the suppression of one class by another'. But a cursory familiarity with the long history of European parliamentary assemblies suggests that there is no _essential_ relationship between parliament and bourgeois power. The effects of parliamentary forms are not necessarily produced by the forms themselves.
To express this first point differently: only when there is a supreme and _accountable_ political body — like a federal assembly — can _final_ decisions be taken which fairly and openly balance and transcend the particular, conflicting group relations of civil society. There is never a 'natural' harmony among social groups, and there is never a 'natural' equilibrium between society and the state. There is indeed a constant danger in a democratic system that party competition, freedom of association, the rule of law and other democratic procedures will be used to defeat democracy. Hence, parliament is an indispensable mechanism for anticipating and alleviating the constant pressure exerted by social groups upon each other, and upon the state itself. And, when faced with recalcitrant or power-hungry organizations or charismatic figures in crisis situations, parliament becomes vital for checking and ordering the suppression of those groups committed explicitly to destroying pluralism.
Parliaments have a second function: they are vital means of checking the secretive or unaccountable operations of state power, and hence, of dampening the desires of would-be dictators. Parliaments make it difficult or impossible for rulers to govern without open debate and organized opposition to state policies. The oppositional role of parliaments is based on the (originally medieval) premise that there is no necessary incompatibility between effective government and effective opposition. It is also based on the premise that opposition to state power can be effective only when the special privileges traditionally monopolized by those who rule — immunity from prosecution, rights freely to criticize and guaranteed pay and political status — are shared with their opponents. And the oppositional role of parliament rests on the perennial insight — ignored by Havel in the heat of the revolution, but outlined more than two centuries ago by a wise defender of power-sharing — that 'constant experience shows us that every person invested with power is apt to abuse it, and to carry that power as far as it will go'.
### **Lustration**
Freedom of speech is said to be the elixir of democratic life, a basic entitlement of citizens endowed with powers to act freely upon the world. Listen to Milan Kundera at the stormy Fourth Czechoslovak Writers' Congress in Prague in 1967, quoting Voltaire. 'In his letter to Helvétius, Voltaire wrote that beautiful phrase: "I disapprove of what you say, but I will defend to the death your right to say it." This formulates a fundamental ethical principle of modern culture,' said Kundera, to warm applause. He continued, more earnestly. 'Any suppression of views,' he said, 'even when the views that are being forcibly suppressed are erroneous, must lead, in the final analysis, away from the truth, for truth can be attained only through the interaction of views that are equal and free. Any interference with freedom of thought and words, no matter how discreet the technique or name given to such censorship, is a scandal in the twentieth century and a shackle on our emerging literature.'
Now consider the competing view that the vital principle of freedom of speech must have at least some limits, since freedom of expression, under certain conditions, can otherwise cripple freedom of expression. This view points out that standard free-speech arguments, like Kundera's, have all the earmarks of an ideology, essentially because they presume that counter-arguments are dangerous and must therefore be rejected by all right-thinking people. Free speech about free speech is frowned upon. The toleration of free speech is _in_ tolerant of those who doubt that freedom of expression is an absolute principle. The critics of free expression add another objection. There are times, they insist, when saying certain things publicly is insulting or defaming of others, which means that their capacity for action is damaged. Even the simple naming of another person — as in the court trial of someone who has been victimized, or is accused of victimizing another — can be damaging. Freedom of expression can be a refuge of scoundrels. And so, it is argued, defences of freedom of speech must be countered with legal restrictions upon what is said to others. The right to speak and the duty to be silent are like twins — the closest of relatives who dislike living apart, but who find it hard to live together without quarrelling.
The vexed relationship between speech and silence is a key dilemma of the modern condition. Within the first few months after Havel's election as President, it resurfaced with a vengeance — and sorely tested the principle, defended by Kundera, that words should be unmuzzled. The central political problem was this: What should be done about the 'crimes' committed by the Communists and their collaborators against citizens' rights? Should publicity about repression in the past be unlimited? Should the old nomenklatura be punished, initially by exposing their crimes before the public? Or should such publicity, which was bound to cause fear and ill-feeling, be restrained so that everybody could forgive and forget, and work together towards a more open and tolerant society?
Havel was aware during the revolution that such fraught questions were bound to stir up political trouble. The news reached him in early December 1989 that the shredding and burning of important StB files on a massive scale was underway. The first press reports appeared on 8 December, and within days the burnings were the butt of newspaper cartoons and street-level jokes. So during the roundtable talks with the Communists, a day before the announcement of the new Government of National Understanding, Havel moved to solve the problem by proposing Richard Sacher — a lawyer and senior functionary in the Czechoslovak People's Party — as the next Minister of the Interior. Sacher was a good man, he said. He was flexible, dynamic, and peace-loving. Others were less convinced, and Havel had to eat humble pie. The negotiators agreed in the end to entrust the whole police apparatus, including the StB and its files, to a triumvarate of Marián Calfa and his two first deputies, Valtr Komárek and Ján Čarnogurský. The decision made no impact on the mass destruction of files — 15,000 were reportedly weeded and shredded — so that one day after his election as President, on 30 December, Havel finally got his way by appointing Sacher as the new federal Minister of the Interior.
The appointment bred trouble. It produced a bitter political row that some Czechs soon came to call 'Sachergate'. The episode that broke out just before Easter in 1990 was arguably more of a political thriller than its American counterpart, and the only reason it did not bring down the President of the country was because, at the time, Havel's potential critics around the Castle held fast to the view that 'solidarity' with the Castle was vital if the _ancien régime_ was to be defeated. According to these critics, there was plenty of evidence that Sacher, immediately following his appointment, had set to work organizing his own personal collection of old security files, into the so-called 'Z-files'. His move was understandable — it was better to safeguard sensitive files in the inner vaults of the Ministry of the Interior than to trust others with them. But his critics were adamant that Sacher's tactic was both illegal and charged with blackmail potential. He was said to be refusing to co-operate with the newly established Office for the Protection of the Constitution and Democracy, directed by Zdeněk Formánek, who was now laying claim to the files, without success. Sacher had also secretly screened members of the cabinet and parliament. He was as well turning a blind eye to the ongoing removal of files by his StB agents.
This wasn't all. Some opponents of Sacher even suggested that Havel, who clearly knew about the whole business, and who was aware that there were scores of former dissidents with fat StB files, was being fed some of these (and perhaps other) files from Sacher's collection, and so was drawn into a cat's cradle of suspicion of others. Sacher's critics found puzzling his motives, which might have included his old loyalties to the Czechoslovak People's Party, which bore grudges against both the dissidents and the Communist Party. Sacher's links with Havel were also puzzling. It could not be ruled out that he was co-operating with Sacher, and learning to use the files, for the purpose of protecting his fledgling presidency against scandalous exposés. Whatever the case, Sacher's critics were convinced that there was mounting evidence that he was deliberately slowing down the reform of the Ministry of the Interior, that he was surrounding himself with Communist men and women from the 'old structures', and that he had just botched an attempt to sack some 800 StB officials. After signing their redundancy notices, which contained a right of appeal, Sacher was forced to reinstate them, and to pay them compensation, which cost Czechoslovak taxpayers millions of crowns.
Jan Urban, representing Civic Forum, dashed to the presidential country estate at Lány to confront Havel with the need to act decisively. At an opportune moment, when Havel was alone, Urban appealed to him. 'Václav,' he began quietly, looking him straight in the eye, 'I am playing a role in public life, but I don't presume that I should know everything about the inner workings of state. I understand that there may be matters of national security of which I should know nothing.' He hesitated, trying to get the emphasis right. 'But tell me, as President, is this Sacher affair of this type?' Urban added: 'I'll take you at your word. If you say "yes", then I'll not delve into it further. I promise I'll back off' Not wanting to lie, Havel winced, but gave no straight answer. 'Václav, we are in total opposition,' snapped Urban, who after some brief pleasantries scampered back to Prague to propose independent mediation of the dispute. Havel, knowing that he was cornered, consented. The respected moral philosopher Ladislav Hejdánek agreed to be the mediator and a stormy but closed six-hour meeting to consider his findings took place a week later at Civic Forum headquarters. Outside, pro-Havel demonstrators noisily protested that Civic Forum was preparing a _coup d'état._ Inside, Hejdánek vindicated the position of Civic Forum. Havel was thus forced to accept a deal that included the appointment of the seasoned Charter 77 activist Jan Ruml to the post of first Deputy Interior Minister, with special responsibility for the StB. A few days later, with rumours circulating that the security forces were mutinous, Ruml proved that political power sometimes needs gun barrels to get its way. He handed out a new set of legally watertight redundancy notices to the StB, flanked by mean-faced paratroopers armed with Scorpion sub-machine guns.
These were crazy times for Havel, who now went everywhere flanked by two female bodyguards. One was blonde, the other was brunette, so distinguishing him — he told friends — from Colonel Gaddafi, the only other head of state who used women to fend off assassins. The cool image was of little help in protecting him against the much more serious trouble, again to do with the StB, lurking around the corner. The taming of Sacher left unresolved the basic problem of what to do with the security files. For a while, Havel treated the matter as people's private business, as he did, with a look of amusement, when finding out the size of his own StB file. He soon became wiser, especially after February 1991, when the Federal Parliament appointed a commission to review the police files and to expose publicly parliamentarians who were listed therein as agents or collaborators. The commission ruled that elected politicians enjoyed immunity, and could therefore not be dismissed. It proposed instead that members of parliament listed in the StB files had two options: they could either resign quietly or be exposed publicly. A few weeks later, on 22 March 1991, a special televised session of parliament pointed fingers at ten elected MPs who were alleged to be StB collaborators, but who had refused to resign.
A Commie-hunt had begun. It soon led to the enactment of the most ethically dubious and politically controversial purging legislation in all of central and eastern Europe: the so-called lustration act, agreed by the Czech and Slovak National Assembly on 4 October 1991. The term 'lustration', derived originally from Latin _(lustrare,_ to purify through sacrifice), had older connotations in Czech and other European languages of moral purification through washing in holy water, and of going around, viewing or surveying or making a census of land or troops. The old meanings conveyed exactly what the new lustrators had in mind. Their chief aim was to bring into the public domain basic information about the extent of Communist misdoings, even to bring to justice those people who were up to their ears in the old system. Armed with truth, the lustrators insisted that freedom of expression was an unconditional right. Lustration involved not only exercising the basic right to expose state secrets. It also meant exercising the basic right of citizens to inform the wider public of the truth. The lustrators deplored the slow pace of revolutionary reforms. They insisted that unfulfilled expectations were rising, and that a new political census was urgently required. Some of the lustrators came close to saying that the Velvet Revolution had been too soft, and that the body politic now needed quick purification. Hence, weeding out collaborators — eliminating fear of the truth by widening the circle of fear and mutual recrimination against Communists — was a necessary price to pay for nurturing citizens' freedom of communication.
The lustrators acted with moral urgency, especially after the attempted _coup d'état_ in the Soviet Union during the summer of 1991. The lustrators loudly applauded the provisions of the new law, which passed by a very slim majority. It targeted at least a million people. These included former Communists who had held positions of power from the district level up, former secret-police agents, their collaborators (a term vaguely defined in the legislation), and anybody who received police training in Moscow. The law also applied to anybody who had belonged to Party-run groups, like the People's Militia, as well as to bodies such as the National Front Action that were used by the Party after 1948 to weed out undesirables from workplaces, sports clubs, schools and universities. The lustration law specified that all former members of these listed groups should for five years be banned from holding top-level administrative jobs in all branches of the state, including government ministries, the military, universities, the courts, broadcasting, and enterprises such as banks, railways and foreign-trade companies. The law also required that everybody in post, or seeking a post, in these sectors must from hereon present to their employer a document, issued by the federal Ministry of the Interior, to prove that they had been postively 'lustrated'.
The law triggered off country-wide howls of protest. Many grew nervous — understandably so, since Communism after 1948 and (especially) late-socialism after 1968 had been systems of power in which everybody, in one way or another, had been implicated. The critics of lustration pointed out that many of those seeking vengeance against the Communists — like Václav Klaus, the upwardly mobile Finance Minister — had political motives. The critics also pointed to the miserable irony that the architects of the law — 'right-wing Bolsheviks' Havel's friend Jiří Dienstbier dubbed them, sarcastically — had invested their trust and loyalty in the secret police. Their handwritten and computer records, containing at least 140,000 names, were presumed to be accurate, despite the well-known facts that the secret police used trickery, threats, bribes and lies to lure individuals into their nets of suspicion. The critics of lustration thus accused its defenders of ignoring the facts behind the facts. They charged the lustrators with allowing the secret police to rule — unquestioned — from their graves.
The lustration-law opponents also criticized its loopholes. Thousands of files of well-placed Communists had already been weeded, and probably destroyed. Top Communists who now worked in private business or those who had already retired with handsome pensions — like Miroslav Štěpán, the former Prague Party boss who now ponced around the country signing copies of his memoirs after serving only six months of a longer prison sentence for giving orders to use violence against demonstrators on the first day of the revolution — were also not covered by the law. Presumably, they were to get off, scot-free. Worst of all, said its critics, the lustration law, in the name of freedom of information, encouraged a climate of repressive incivility. Pelting each other with truth was destroying trust and loyalty to the public good. So, for instance, employers, anticipating trouble, were quickly getting on with the nasty business of 'lustrating' their staff, whether or not there was any reasonable suspicion of their culpability. Children of former Communists were suffering discrimination. Former Charter 77 supporters were discovering the names of informers in their ranks. Brothers and sisters were finding out that they had spied on each other. Many decent individuals who accepted the anonymous telephone caller's invitation to meet for coffee the following day now were being turned into guilted scapegoats. Truth was breeding hatred. Daily life was beginning to resemble an unpleasant scene from Hitchcock's _Rear Window._ Everybody was potentially the object of suspicion. Nobody was beyond victimization. The whole society could end up criminalizing itself.
Havel was caught in a squeeze. He reacted to the lustration controversy using the tactics of balanced diplomacy. When travelling outside the country, or speaking to foreign guests and hosts, he pointedly criticized the hysteria, name-calling and atmosphere of bitterness and suspicion produced by the lustration. In an interview with his friend Adam Michnik, he confessed his mounting anxiety about the 'lawless revenge and witch-hunts'. He told Jeri Laber of Helsinki Watch that the legislation was a recipe for injustice. 'We have not yet found a dignified and civilized way to reckon with our past,' he said. 'The lustration act affects the small fish. The big ones are laughing at us. They have become capitalists; the act does not affect them.' And he told an audience in New York that the legislation was anti-democratic. 'The problem is that the legislation is based on the principle of collective responsibility,' he said. 'It prohibits certain persons solely because they belonged to groups defined by their external characteristics. It does not allow their cases to be heard individually. This runs counter to the basic principles of democratic law.'
At home, in the local political scene, Havel was more circumspect. Chastened by Sachergate, he tried various ways of walking the tightrope stretched beween honest public appraisals of the Communist past and the current and future need to drain off the poisons of fear and revenge. He sided with those who feared the worst by confessing that his own blood had curdled after being handed a big, official-looking envelope, sealed and stamped, containing details of his candidacy for the Writers' Union in the mid-1960s. But he also sided with those who were unprepared to forgive and forget. He agreed that those who had committed clearly defined crimes should be brought to justice — and that (as the Czechs say) the only way to wash a staircase is from the top. He agreed as well that there needed to be public acknowledgement of the sufferings of the victims of Communism, especially of people killed or tortured. 'Parliament's desire to purge the public service is entirely legitimate,' he said. Lustration was 'a necessary law, an extraordinary law, a rigorous law'. So, he continued, he had no alternative but to sign the lustration bill into law. Otherwise the whole body politic would have suffered a convulsion following a head-on collision between the presidency and the parliament.
After confirming the lustration act, Havel submitted a letter to the parliament announcing that he would seek to amend the legislation, to ensure that every citizen should have the individual right to subpoena witnesses and cross-examine their accusers in an independent court. The letter pointed to the need to institutionalize free speech, but it was deliberately not worded in legalese. No parliamentary debate was required. The strategy of soft compromise with lustration was typical. Mostly, Havel stuck to generalized disapprovals of the whole business. He notably refused to discuss particular cases. Symptomatic was his calculated public silence about the extraordinary case of Jan Kavan, who had been accused — illegally, it turned out — of being an StB agent who had cleverly disguised himself at Palach Press, an opposition press agency in London. In December 1991, Havel met Jan Kavan and several of his old friends — Petr Uhl and Anna Šabatová — for drinks in a restaurant in central Prague to discuss Kavan's lustration. Havel made it clear to them that he had no doubt that the allegations about Kavan were false. Kavan was encouraged. But Havel went on to say that the whole case had become so politicized that it was impossible for him as President to take sides publicly. He was unable to pour water on a hot case that the ignorant said proved that where there is smoke there must be fire. Havel explained that it would put him on a confrontation course with the current government, especially because the matter was _sub judice,_ and would remain so until the courts handed down a decision. Kavan left the meeting with a good feeling of having been vindicated privately, although Havel — playing the role of prudent politician — had his agreement that the detailed contents of their discussion would not be divulged publicly to journalists.
Havel's tactic revealed a subtle but important change that had now descended upon his presidency. He had evidently bidden farewell to his old noble habit of drawing black-and-white distinctions between 'truth' and 'lies'. Before entering official politics, he had always insisted that the truth is always the truth. When asked what living in the truth actually meant, he always answered along the lines of Polonius: 'To thine own self be true / And it must follow, as the night the day / Thou canst not then be false to any man.' Truth is within ourselves, he told Antoine Spire shortly after his long spell in prison, it is a matter for our consciences, and its public expression is always justified, even in the face of threats and throttling. Once upon a time, even further back in his career, he liked to draw the corresponding distinction — famously outlined during the Prague Spring to Antonín Liehm — between truth-loving intellectuals and politicians who perforce are slaves to power. 'The reason intellectuals make such poor politicians,' he told Liehm, 'is that they are used to serving the interests of truth rather than using truth as a means of serving the needs of power.' Using truth cautiously, as a means of repairing and oiling the machinery of state power, and his seat within it, was now a much closer description of his actions. It turned out that the biblical injunction to seek the truth because truth sets us free is not always true. Lustration taught Havel that in official politics there is indeed no such thing as pure freedom of speech. He came to see that truths are sometimes out of season, that truth, like fruits, should only be plucked when ripe. Havel learned to watch his words. He learned the value of 'tact, the proper instincts, and good taste'. He understood that politics loves politesse — that presidential power is a friend of _measured_ truth.
### **Market Power**
Baroness Thatcher — bright-red lipstick, bouffant blue-rinsed hair, blue suit, matching bag — calls for Scotch on the rocks for two, in honour of her friend's swanky performance. Drinks promptly arrive in cut-crystal glasses, on a silver platter, courtesy of an unsmiling waiter wearing white gloves. The two friends engage in polite conversation, flanked by several hundred admirers attending a public lecture sponsored by London's Institute of Economic Affairs. At an opportune moment of silence, the unknown author of a forthcoming biography of Václav Havel butts in politely to ask the Iron Lady's friend, Dr Václav Klaus, what he thinks of his country's President. 'He is a half-socialist,' says Klaus, in a frank mood, pursing his lips. 'He has always been in favour of collective solutions. His speeches about so-called civil society are just the latest version of the same dogma. He is in love with state power.'
So few words, so much confidence. The public lecture that he had just delivered — in honour of the well-known Austrian economist Friedrich von Hayek, the darling of contemporary neo-liberalism — was equally strident. In a chandeliered ballroom setting — it was a full house of 300 invited guests — Dr Klaus had tried to convince his audience that he and his colleagues had begun to transform the Czech Republic into a free-market paradise. What was once among the most Stalinist states of the Warsaw Pact empire was now the most vibrant, bustling, and open society in the region, potentially an economy that could in future outpace the economic performance of its long-established Western democratic neighbours. It had taken great determination and fortitude to shift a whole nation of people from totalitarian servitude to a market system of liberty, but he and his government colleagues had managed it. The catastrophe of socialism was that it had turned an aquarium into fish soup. It had posed a massive challenge: to turn fish soup back into an aquarium. And it had been done, thanks to one of the most remarkable privatization plans in modern history.
Klaus went on to explain that elsewhere in the post-Communist bloc, in Poland and Hungary for instance, privatization had been carried out without clear legal rules. That had led many investors — both domestic and foreign — to discover with regret that they did not have clear legal title to their investments. So rather than lurch haphazardly into quasi-market reforms and 'spontaneous privatization', Klaus and his government had insisted upon the systematic re-creation of the foundations of an efficient market and a free society — the rule of law, clearly defined property rights, an efficient system of contract. The so-called voucher scheme was exemplary of this strategy. The starting point of the scheme, Klaus argued, was to take the ideologists of socialism at their word when they insisted that state properties and industries 'belonged to the people'. Vouchers were accordingly offered for sale at a nominal price to all citizens of Czechoslovakia. A system of auctions and bids had been created to enable the transfer of ownership of property into private hands. There it belonged, Klaus said. And the scheme had been enormously successful, he concluded. It had created widespread public support for privatization. It had proved to be an efficient way of transferring ownership rights from an irresponsible state to responsible private parties. And — since power and property are twins, as the seventeenth-century English political thinker James Harrington famously observed — the voucher system of privatization had laid the foundations for a political system capable of maximizing its citizens' freedom.
Throughout the lecture, and in the question period that followed, Klaus presented his case with great polish and dignity — and got roundly applauded for it. Those who know him well and who have worked around him often say that he is a shrewd political actor who in his dealings with others can be ruthlessly calculating. It might even be said, with a touch of exaggeration, that Klaus's political style in fact resembled that of a late twentieth-century Septimius Severus, the Roman emperor much admired by Machiavelli. The Czech Septimius Severus — tortoiseshell glasses, short grey hair, smart suits and ties — naturally had a late-modern look about him. But, like his Roman predecessor, the Czech Septimius had learned to combine the arts of manly charm and decency with the political qualities of a savage lion and a tricky fox. These qualities were first noted by others during Klaus's first dealings, on behalf of Civic Forum, with the Communists during the Velvet Revolution. Then an economist at the Institute of Forecasting of the Czechoslovak Academy of Sciences, he quickly proved himself to be a good organizer, a tough bargainer, and a brilliant spokesman for the neo-liberal alternative to late-socialism. He developed a reputation for resolution, professionalism, and a big ego — so big that it later spawned the commonplace joke that the only difference between God and Vaclav Klaus is that God doesn't think that He's Václav Klaus.
The Czech Septimius Severus played an active role in the co-ordinating committee of Civic Forum and, under the so-called Government of National Understanding led by Prime Minister Marián Čaifa, he had been rewarded with the post of Minister of Finance. He was not only a competent economist but also a talented political animal who had a sharp ear for what people were saying and thinking. He was unafraid of telling people about unpleasant realities or of taking risks. He proved that he was an ambitious fighter by deciding to run for office for Civic Forum in the June 1990 elections. He was convinced he could win anywhere, so he chose to stand in a coal-mining district of northern Moravia, in one of the inhospitable heartlands of the Communist Party — and won. Klaus soon after (13 October 1990) surprised many observers by winning 70 per cent of delegates' votes for the post of Chairman of Civic Forum at its Congress held in the Prague district of Hostivař. There should have been no surprise. For several months, he and his supporters had been very active, especially in the regional structures of Civic Forum. They had ambitions, as became evident in April 1991, when Civic Forum split and the breakaway Civic Democratic Party (ODS) was founded in Olomouc, in opposition to Jiří Dienstbier's Civic Movement (OH) party, which remained sympathetic to Havel.
Klaus, by now playing the political role of Septimius Severus with confidence, made publicly known his strong dislike of Civic Movement's undisciplined, left-wing laziness. Many within Civic Movement responded with the charge of careerism, which was true. Klaus worked hard to model his party on Mrs Thatcher's Conservative Party. The Civic Democratic Party was supposed to be a party of self-confident and enterprising individuals who together would accelerate the drive to post-Communism by legislating for the reintroduction of a market economy. Convinced that socialism was just a short and disastrous interlude between capitalism and capitalism, he was for the strong state and the free market. Despite claims to the contrary, Klaus always seemed less than interested in legal and political reforms for the sake of democracy. It was the mark of a man whose theories of free-market economics were formed during the period of late-socialism. Unlike the earlier advocates of democratic 'market socialism', Ota Šik for instance, Klaus worked during the 1970s and 1980s for the introduction of a free-market economy, if possible under the rubric of a powerful (late-socialist) state. With the outbreak of revolution, that Utopian vision of a free market suddenly became practical. Klaus lost no time in pushing the principles of free-market economics — using bossy political tactics and existing state structures wherever possible.
Both the aims and methods of the politics of the 'strong state, free market' contradicted the crowned republic, and put Klaus on a collision course with Havel. Their friendship got off to a bad start during the revolution, when at one point in an early meeting with the state authorities, Havel, effectively the leader of Civic Forum, introduced Klaus to the other side as 'Václav Wolf'. Klaus reportedly winced at the absent-minded — or unconsciously motivated — slip. The mutual respect thereafter dissolved in the emerging acids of party politics, so that by the summer of 1990, when Klaus was already an important force in both Civic Forum and the government (as Minister of Finance) Havel — still dreaming of a crowned republic — tried hard to get rid of him by offering him the post of Governor of the National Bank of Czechoslovakia. Septimius refused to take the poisoned bait. By now he was a seasoned political creature. He correctly sensed that Havel was mainly worried about threats to the presidency. Klaus responded by trying to clip Havel's political wings using every available sharp instrument. He built a new power base by campaigning for the founding of the new Civic Democratic Party, which he soon ruled, unchallenged. After becoming Czech Prime Minister in June 1992, Klaus also put the frighteners on Havel by proposing the idea that the then Prime Minister of the Federal Republic, Jan Stráský, be considered as the next serious candidate for the presidency of the country.
Then there was the ongoing political war of nerves that Klaus waged against Havel. Neutral observers frequently noted Klaus's pretended omnipotence: his political unwillingness to listen to anybody and his penchant for treating his opponents as children, or as morons. Another observer, sympathetic to Havel, noted the different political characters of the rivalling Václavs. In certain contexts, the President 'might think that he knows what's true and right, and that his opponent is an idiot. But he would never put it that way. Normally, he is reflective, tentative, and gives no simple answers'. Klaus, by contrast, always 'understood something of the psychology of winning power over others by aggression'. He always had 'a perfectly prepared strategy, which typically began with a punch in his opponent's stomach. He detested "wetness", even though, after conquering his opponent, he could pour on the charm.'
Behind the scenes, the different political styles produced considerable friction, as when the two men appeared on a nationwide television talk-show filmed in Brno, in December 1992. Before their appearance, which was hosted by the well-known presenter Antonín Přidal and featured several other guests, everyone gathered in a hotel lounge to have drinks. The mood was friendly — until Septimius arrived, late, hobbling along on crutches, nursing a leg recently injured while playing tennis. The atmosphere stiffened. It did not improve after the group moved to the dinner table. Everybody began to stare at their plates as Septimius rounded on each guest in turn. In a loud voice he told Přidal, who turned as pale as a ghost, that his programme was full of intellectual bullshit. Septimius then attacked another guest for his Europhilia. 'Brussels! A socialist nightmare that we must live without!' he snarled. Septimius then ticked off Havel, who ate his dinner in silence. Septimius went on to sermonize against intellectuals, whom he denounced as useless and sometimes dangerous meddlers in the world of power. After everybody had been told off, the party moved to the state television studios, where Václav Klaus was in fine — dynamic, buoyant — form. Like a bull at a gate baying for blood, Klaus charged at his opponents, including the shaken Havel, who spent the session defending himself with tentative statements and complicated formulae. After the filming was over, the whole group returned to the hotel for a parting drink. Suddenly, Septimius Severus became genial, charming even. He offered around the drinks, even though nobody felt like drinking with him. After a few minutes, sensing his absence to be imperative, Klaus left, with handshakes and smiles. The rest of the group, including Havel, slowly recovered, as if from a foiled encounter with a charming bully. They stayed on until half-past three in the morning, reminiscing, chatting and joking.
The Brno encounter was not atypical, for Havel often felt unnerved by the political abrasiveness of Klaus. Havel, never a morning person, found especially unpleasant his opponent's early-morning telephone calls, beginning with impossible statements like, 'I can't believe that you said what you did yesterday,' or unfriendly questions like, 'So can you tell me where we now stand?' Nearly every Wednesday morning, when the two met at the Castle for a briefing session, staff noted that the polite Havel would tense up beforehand, unsure of how today he would handle the 'attacking sarcasm' and other rough tactics of his unpredictable opponent. The tension was compounded by an ever-lengthening history of spats over one matter or another. Many of them were traceable ultimately to Klaus's hard-headed, savage-minded economism — and to his intense dislike of Havel's defensive resort to philosophical abstractions like 'the crisis of humanity' and the need for 'human decency'. Klaus had one — only one, but historically big — Idea, and he repeated it constantly to Havel's face. The Big Idea: no post-Communist society can become successful unless it quickly develops a dynamic and fully modern market-based system of commodity production and exchange. Compared with the unproductive stagnation of late-socialism, Klaus argued, economies driven by commodity production and exchange have the great advantage of enhancing their overall power by minimizing collective losses. Market forces ensure that factors of production that fail to perform according to the current (international) standards of efficiency are continuously and swiftly eliminated and forced to find alternative, more productive uses. Factors of production that are 'uncompetitive' go the wall. Klaus's Big Idea, in other words, was that markets mimic Abraham Lincoln's famous maxim that those who need a helping hand should look no further than the end of their right arm. In this way, markets invite the victims of competition to blame themselves — and to survive and then thrive by adapting to new standards of efficiency.
Ever since his teenage years, Havel had had difficulty with these arguments. He complained to his Thirty-Sixer friend Radim Kopecký about the supposed principle that life is 'an eternal struggle, tough, even cynical and merciless egoism'. The sixteen-year-old Havel tried to stake out the countervailing principle of 'soft humanism'. Sympathy for others was important, for no society could function without it, he insisted. Kopecký replied by accusing him of supposing that he somehow was living in the ancient world, in which the separation of markets from morality, politics and law went unrecognized. Modern times are different, Kopecký argued. Private property, market competition and its corresponding values of individualism tinged with nihilism are today unavoidable, whatever Communists and socialists and other moralists might think or say.
Many years later, thanks to the aggressive political rhetoric and manoeuvring of Klaus, Havel was forced in practice to live with a competitive party system and — a greater humiliation — to acknowledge the domestic and international imperative of developing the _non-state_ institution of legally guaranteed market forces. Klaus taught him, against his will, that the ideal of a crowned republic was just that, and that instead there must be _economic_ limits placed upon the scope and power of state institutions. Thanks to Klaus, the subjects of the crowned republic endured tremendous structural change: output from the private sector quickly eclipsed state production; the proportion of working people employed in agriculture dropped three times; most of Czechoslovak trade switched to OECD countries; while during 1991 alone, real wages fell by 30 per cent. It might even be said that Klaus's greatest political success against Havel was to force all Czechoslovaks to wake up suddenly to market realities — by giving each of them a taste of what it is like to return to medieval times, when (in matters such as military service, marriage and spiritual salvation) many more activities than now, paradoxically, were considered tradable items with a price tag attached.
There was a further irony produced by the tussle between Klaus and Havel. In attempting to counter the rise of Klaus, who threatened his sovereign power, Havel eventually latched on to two effective themes — democracy and civil society — that implied the need to draw stricter limits upon his own power. Not only did Havel come to accept the indispensable role of markets. He also came to call publicly for more democracy and to acknowledge the _non-state_ sources of social morality and co-operation that both democratic institutions and markets require to function as markets.
Havel's defence of democracy against his opponent's mean-spirited politics was evident in a widely reported speech before the chandeliered Czech Parliament in the spring of 1996. Arriving to the sounds of Smetana's _Fanfáry,_ standing before a forest of microphones, dressed in a smart black suit and a matching black-and-white-striped tie and pocket handerkerchief, sporting glasses, sipping water, a frog permanently in his throat, Václav Klaus looking on over his shoulder, Havel talked earnestly, in long sentences for over an hour, about the importance of democracy in the Czech Republic. He acknowledged the common-sense understanding of democracy as a form of rule that sub-divides the powers of making, implementing and adjudicating laws. Democracy is 'free competition among different political parties, the rule of law, the principle of civic equality', he added. But he went on to emphasize that democracy must not be treated merely as a technical mechanism _(soustava),_ or as a political machine _(soustroj_ í). Democracy, he proposed, is 'a certain attitude towards the world'.
What kind of attitude? Václav Klaus momentarily looked away and down as Havel began to speak of humility. 'Democracy is a way of being _[zp ůsob bytí],'_ he argued. It nurtures and thrives upon 'respect for others, honesty, creative work, good manners and taste, solidarity and respect for the cultures of different social groups and nations'. Democracy is the rule of humility. _Hubris_ is anathema to it, since democracy thrives on the humble willingness 'to behave as one expects others to behave'. Democracy demands humility towards the underdog. Respect for a minority by a majority is required in a democracy. So is 'humility towards the order and beauty of nature, as well as humility towards the beauty of things created by previous generations'. Democracy is a political system in which the exercise of power over people and power over matter, being inseparable, must be publicly controlled. Democracy cultivates a shared sense of the fallibility of human beings living in the natural world, which means, he concluded, that the quest for democracy must be 'a never-ending obligation' humbled by the awareness of its own fragility.
In the same speech on humility — it earned him long applause — Havel emphasized the need to cultivate a tolerant and open civil society. There were many sources of Havel's deep interest in the subject. Struggling to find a public language in which to do battle with the fox- and lion-like Klaus, Havel was forced to call into question his own earlier presumption that a crowned republic led by a charismatic _Ichspieler_ could serve effectively to replace the Communist order. In this and other speeches and writings, Havel began to develop a brilliant modern idea: that economic actors always and everywhere go about their business and do their work, and can only ever do so, insofar as they tap into, and cultivate, sources of 'social capital'. A market economy, he insisted, can only function as such if its members are 'embedded' in a wider civil society that harbours social interaction based on such norms as trust, reliability, punctuality, honesty, friendship, resolution, the capacity for group commitment, humility, and non-violent mutual recognition.
The point against Klaus was put with special force from the time of his 1992 New Year's Address to the Nation. 'Dear friends, I wish you success in your work in the New Year', he said. He added the kind of words that always irritated Klaus: 'I wish you health, peace, steady nerves, much patience, hope, and strength, and that you will all understand and help one another.' He went on: 'We must face difficulties and people of ill-will with a wise and united perseverance. In an atmosphere of decency, creativity, tolerance and a quiet resolution, we shall bear far more easily the trials we have yet to experience, and resolve all the large problems we must yet face.' The sentiments were arguably more than a principled reminder that markets require morality. Havel was taking political aim at what elsewhere he called the 'Wild West mentality' unleashed by post-Communist conditions. 'Spreading corruption, gold-fever, and the view that life is a jungle and so man must be a brute to man', he said, 'all these are simply the most familiar manifestations of that strange condition of a society in which the values of a totalitarian state have collapsed and the values of civil society have not yet come to fruition.' Havel here pointed, by implication, to the widespread looting of state assets in the name of privatization, for instance the practice of 'tunnelling' out of assets by majority shareholders taking advantage of inadequate protection by securities laws for minority shareholder rights. Havel was also in effect criticizing the Klausite uncivil effects of the obsession with state-backed privatization, especially for its blindness towards the way markets tend to 'fail', in the process weakening or destroying the structures of civil society upon which they otherwise depend for their survival and growth. Havel mentioned no examples, many of which however spring readily to mind. For instance: market forces tend to spread into all the nooks and crannies of social life, so violating the plurality of _non-market_ voices and identities — friendship, household life, religiosity, community life — that are otherwise crucial to the functioning of market forces. Market forces also suffer from a certain blindness towards losers: in market competition, certain groups and individuals, and sometimes whole regions and countries, necessarily lose, and yet such losses cannot be dealt with by markets, exactly because losses ('externalities', Klaus calls them) are easily translatable into 'price signals' and market criteria. Such 'market failures', Havel implied, demonstrate that market interaction cannot create the vital ingredients of social order upon which it otherwise depends. Klaus was blind to a basic 'law' of modern market economies: where there is no flourishing civil society, there can be no flourishing markets.
### **Velvet Divorce**
On the thundery summer's afternoon of 17 July 1992, members of the Slovak National Council — the Slovakian parliament — gathered at two o'clock in the old parliament building nestled under the Bratislava Castle on the banks of the Danube. A beautiful setting indeed for ugly business. Before the Council lay the job of deciding the future of the people, property and international standing of the Slovak lands. Members hushed as the Convenor began to read out the motion for the last time. The question was apparently straightforward: Did those members of the Council present in the chamber support or not the proposed Declaration of Sovereignty of the Slovak Nation?
Since the matter had been debated repeatedly during the past weeks, no discussion was allowed. Some dissenting members tried to disrupt the proceedings with shouted quips and questions. But the gag was vigorously applied, and the vote taken. By acclamation, out of 147 deputies, 113 voted for the motion, 10 abstained, and 24 deputies, most of them from Hungarian minority parties, bravely voted against. An hour later, upon hearing news of the vote relayed instantly by telephone to the Castle in Prague, a wrinkle-faced Havel announced to an agitated press pack his resignation as President of the Czech and Slovak Federated Republic. The country that had lasted seventy-five years had begun to end. Suddenly, and unexpectedly, the provincial city on the Danube was to become the capital city of a new state. The hope that post-1989 Czechoslovakia would prove to be a model multinational post-Communist democratic state, and that accordingly it would play a major stabilizing role in central Europe, was smashed to pieces. The leader of the crowned republic had already lost much ground to personal defections, parliamentary obstruction, a newborn party system, and the privatization of property. Now, with the loss of half his realm, the _Ichspieler_ had suffered a decisive blow. An important phase of Havel's political career — like many political careers — had ended in ruinous failure.
The evening headlines on television and radio, and in the next morning's press, were divided. In Prague, few welcomed his resignation and most were stunned into speechlessness, as if they had just received an unexpected electric shock from an unknown source. But there were also some who spoke of his departure from the Castle as an inevitable consequence of the deep-rooted enmity between the country's two predominant nations. According to this view, common among the hard-headed nationalist minds of the political elite of the republic, the ideal of a common Czechoslovak state had been doomed from the country's birth. The moment of birth of Czechoslovakia, a state populated primarily by Czechs and Slovaks, but also by Hungarians, Germans, Ukrainians and Poles, was also its moment of death. Czechoslovakia, on this view, was always an ill-conceived, artificial construction, which without external support and under external pressure would have disintegrated much earlier. So its moment of reckoning had finally arrived.
This nationalist view supposed that the history of Czechoslovakia resembled a ragged band of carriaged travellers bumping their way along a rocky path that led past the camouflaged hiding place of a man of decision called Procrustes, who at an opportune moment one midsummer's afternoon pounced unexpectedly on the carriage, dragged its occupants into his secluded stone cottage, flung them on a stretching rack, and tightened his ropes to the point where their state simply snapped in two. The view that there was a hidden logic of tragedy within Czechoslovakia, and that it triumphed finally in Bratislava in the Declaration of Sovereignty of the Slovak Nation, was a dangerous, if useful fiction. It was dangerous inasmuch as it fed the nationalist presumption that all nations are caught up in an animal struggle for survival, and that only the fittest survive. It was exactly this presumption that had fuelled the flames of the Yugoslav conflict going on at the same time. At the heart of the ideology of nationalism — and among the most peculiar features of its 'grammar' — is its simultaneous treatment of its opponents as everything and nothing. Nationalists, strictly defined, warn of the menace to their own way of life by those who are alien. The Other is viewed as a (potential) knife in the throat of the Nation, and nationalists are therefore driven by friend-foe calculations. Yet nationalists not only suffer from a judgement disorder that convinces them that Other nations live at their own expense. Nationalism is also arrogant, confidently portraying the Other as a worthless zero, as inferior rubbish. It follows that the Other is unworthy of respect or recognition, that it has few if any entitlements, not even when it constitutes a majority or minority of the surrounding population. Nationalists consequently suffer from a single-minded arrogance that leads them to label the Other as worthless, to taunt and spit at them or, in the extreme case, to press for their expulsion — or murder, even.
This image of the dangerous logic of nationalism is necessarily simplified, but within the Czechoslovak political class that emerged out of the Velvet Revolution there were certainly Czech and Slovak nationalists in this sense. They quickly found out that the rhetoric of nationalism was a politically useful fiction. It nourished the lives of two types of political animals: 'excretory' Czech nationalists, for whom the split-up of Czechoslovakia through the excretion of Slovakia represented a final triumph of 'pure' Czech statehood; and backward-looking Slovak nationalists, for whom the Declaration represented the final emancipation of the Slovaks as a captive nation — a positive contribution to the process of disintegration of old political boundaries triggered by the Versailles system formed after 1918.
The odd thing about these nationalist tensions is just how absent they were immediately after the revolution, that is, not much more than two years before the Slovak declaration of sovereignty. The point is important, since it suggests that the fiction that Czechoslovakia was a tragedy waiting to happen was groundless. It overlooked the most obvious three facts of all: that the difficulties between the Slovak and Czech lands were not somehow in the blood of their peoples; that the tensions that surfaced between the political elites of the two nations were mainly caused by Czech lethargy about Slovak grievances; and that the velvet divorce, as it was later to be called, was never popular with the citizens of either the Czech or Slovak lands of the country.
Havel himself quickly grasped the latter point. It was a paradox, because for many months before the announced carve-up of the country popular opinions about the past, present and future had become ever more agitated. For most people, post-Communism meant disorientation. Standards of living seemed to fall, jobs were insecure, services declined, existing political institutions and political leaders felt ever less competent, as Havel anxiously noted in an interview with Stanislava Dufková at Hrádeček in early November 1991. 'We are living in a time of peculiar — I would say — social and pyschological chaos,' he said in the conversation that was transmitted a day later on Czechoslovak Radio. 'People are unsettled by the fact that they cannot see firm order, structure of values, or orderly community life anywhere. Everything has been thrown into uncertainty. The whole legal system and the constitutional set-up are uncertain. Political parties are quarrelling among themselves. They attack each other. Everybody says something different. Everybody proposes something different. It is not known what the reform will bring or what social shocks it will cause.'
Given this climate of profound uncertainty bordering on chaos, it might have been expected that Czechoslovaks would have grasped for certainties. Appeals to the Nation might have been expected to work like a magic healing potion capable of restoring a sense of balance in their personal lives. But virtually the opposite happened. With daily life in a state of extreme flux, large numbers of people took shelter in the safe harbours of the given state. Czechoslovakia took on a new meaning as a bedrock of their existence. So in the autumn of 1991 Havel moved to harness this popular conservatism by calling for a state-wide referendum to decide the future of the country. The tactic — appealing over the heads of institutions to _il popolo,_ to preserve the state — was discussed at length with his close friend and adviser, Pavel Tigrid, who agreed to organize a petition for signatures in support of the status quo. It was to be called _Za spole čný stát_ (For a Common State),
The call for a referendum correctly read the aggregate public mood. By the summer of 1992, opinion polls showed more than eight out of ten respondents agreed that the future shape of the state should be determined not by politicians, but by citizens themselves. The petition collected nearly 2 million signatures, mostly in Bohemia and Moravia. Yet Havel's whole tactic of campaigning for a referendum failed for a variety of reasons. It pandered to the presumption, traceable to the eighteenth century, that every nation is entitled to its own chosen form of government, and in so doing, unwittingly, it highlighted the 'fictionality' of nations living together within a multinational state like Czechoslovakia. A properly conducted referendum might well have produced a clear majority of voters in favour of preserving the country — let us call them Czechoslovaks — but precisely that result would have highlighted the fact that at least a _minority_ did not think of itself as 'Czechoslovak', that 'the Czechoslovak nation' was not therefore a univocal entity, and indeed that it was a controversial and contradictory phenomenon, if only because it contained people who thought of themselves primarily as _Czechs_ or _Slovaks —_ which was precisely the opposite (divisive) effect that Havel had intended.
Exactly this irony surfaced during the early stages of the referendum campaign, which in Slovakia tended to be understood by growing numbers of people as a further example of arrogant Czech efforts to rule Slovakia from Prague. The irony was accentuated by Havel's implicit impatience with the tasks of bargaining and making compromises within a framework of existing constitutional rules and procedures in need of alteration. Immediately after the revolution, Havel (unlike Adolfo Suárez in Spain) made no effort to modify the constitution. In fact, nine months into his presidency he began actively to campaign for its retention. In a major speech to the Federal Assembly in September 1990, he declared himself in favour of the federation and the overwhelming number of 'federal people' who saw it as legitimate. The federation admittedly required some minor tinkering, he recommended; if that were done, the shining example of American federalism should be kept in mind. The speech backfired on him in Slovakia. Jozef Prokeš, the new leader of the Slovak National Party, struck back immediately, in a published open letter. 'Your reference to the American Constitution,' he wrote, 'has left the strong impression that you wish to continue with the ideology of Czechoslovakism, that is to say one nation in this state which, it seems, your statement about a federal people confirms. Until now this has not brought anything good in the relations between Czechs and Slovaks.'
Havel pounced on such criticism. On the first anniversary of the outbreak of the Velvet Revolution, he appeared on television before an audience of several million viewers. He dramatically called on the people to support him against their elected representatives. The _Ichspieler'_ s performance was dramatic, but revealing of the degree to which his strategy suffered from political nausea — from an active disregard for the flawed power of the given institutional procedures of the Czechoslovak state inherited from the Communists. Havel seemed to underestimate the severe irritation to the body politic caused by the Soviet-style federal constitution inherited from the '89 revolution. Although this constitution was not wholly a child of Soviet 'normalization', it nonetheless was stamped with the marks of that period. It resembled (as Havel's friend and Prime Minister from 1990 to 1992, Petr Pithart, noted) a two-member union of governments that made federation in the strict sense impossible, since there was in effect no way of voting to resolve differences between the two parties. The system was pseudo-federal. The system presupposed the existence of two separate constitutions which in truth did not exist, if only because _de facto_ power was exercised absolutely through the Party-state organs (the KSC or Czech Communist Party and, nominally, the KSS, or Slovak Communist Party). Each nation was excessively protected from the laws of its neighbour, for instance by strong rights of veto and, ultimately, by the right to secession that the law on the Czechoslovak federation of 1968 guaranteed to both republics.
Havel's impatience with negotiations and his resort to the referendum principle not only underestimated the burdens of the old constitution — and the urgent need to alter it. His antipolitical impatience also failed to foresee the ways in which that constitution produced bitter divisions about its future — so bitter in fact that the status quo, which Havel implicitly supported, became simply untenable. It is true that the Czech-Slovak struggle was conducted without threats of violence. The outbreak of war in the former Yugoslavia and the bloody birthpangs of the Russian Federation served as a warning to the political elites of every persuasion that _violent_ nationalism was to be avoided at all costs. Hence the _velvet_ nature of the dispute — the constant emphasis on the need to end the federation 'in an orderly manner', 'without hysteria', 'intelligently', and always with due respect for procedural rules. But still, from the outset, negotiations were marked by great bitterness, which raises the pertinent question of whether, or to what degree, Havel's own behaviour was salt to the festering wound.
There were some observers and participants who insisted that the Slovak withdrawal from the federation was in no small measure traceable to Havel's personal behaviour as President. An old Slovak adage that a nightingale must be judged by what it sings arguably applied well to Havel, whose popularity within Slovakia gradually diminished from the time of the revolution. Up to and during the revolution, many had loved him as a Czechoslovak patriot. He seemed to have no strong feelings of nationality and he certainly despised Czech and Slovak folklore, which the Communists had used as a cultural weapon to combat modernist and cosmopolitan cultural trends. His younger brother was married to a Slovak, and many Slovaks knew, by word of mouth, that he had received a rapturous reception in Bratislava during a public concert featuring Joan Baez. And immediately after assuming the presidency, Havel's immense popularity as the shining symbol of the country's hopes for the future had undoubtedly been fixed by his public appearances with Alexander Dubček, himself a Slovak who spoke Slovak, unlike others who went to Prague and spoke only Czech, a man who symbolized both the dramatic failure of the Prague Spring and a man with a sense of humour and a sense of justice who had suffered much under 'normalization'.
But Havel's reputation among the Slovaks was shakier than it seemed. Trouble brewed well before the revolution, indeed right back to the period of the launch of Charter 77, which eventually attracted a thousand Czech signatories, whereas only fifty Slovaks signed. There was at the time some feeling in Bratislava, where there were no embassies and, hence, none of the links to the outside world which the embassies provided the regime's opponents, that everything important involved going though Prague. And it seemed that people in Prague complemented this picture of themselves by talking of Slovakia as a poor and primitively beautiful place for walking through spring fields, swimming in summery lakes, crossing swelling autumn rivers, or skiing in wintery mountain snows. Immediately after the revolution, this Slovak suspicion of Czech indifference began to be trained on Havel himself.
During and immediately after the revolution, some recalled, leaders from Bratislava came to talk to Havel about the Civic Forum apparatus in Slovakia, only to be sent packing by him, with the advice that they should set up their own organization, later to be called the Public Against Violence. People noted as well how Havel's ears blocked out talk that the capital of the federation should be in Brno, which is halfway between Prague and Bratislava. It was noted too that no Slovak politician was close to Havel; that he never read Slovak newspapers, which were anyway unavailable in Prague; that he was unaware that there was a festering Slovak problem, even hints that he seemed to treat Slovaks as nice Catholic peasants who lived in the mountains, but whose education out of the old (fascist) ways would take time. Havel remained unmoved by the whispered criticisms, but his reputation suffered its first serious setback in Bratislava circles when he decided, under pressure from his advisers, to travel to Munich and Berlin to meet Chancellor Kohl in the first week of January 1990. It was his first foreign visit as the new head of state and, indeed, his first visit outside of Prague. The symbolism was obvious — the newly integrating, still powerful neighbour Germany was an obvious priority — but in Bratislava the visit was received as a slap in the face with a wet Czech carp.
Relations worsened during the preparations, in February 1990, for Havel's visit to Washington and other North American capital cities. Juraj Mihálik, a sculptor turned international relations 'specialist' on the twelve-member Co-ordinating Committee of the Revolution, reported that the delegation consisted of over 200 people. The new government rang from Prague, presumably with Havel's consent, to announce that the number of Slovaks in the delegation had to be reduced from eight to four. There were howls of protest from Bratislava, and the number was put back to eight. Slovaks in governing circles were even more astonished by the subsequent trip to Israel at the end of March 1990. The delegation included not a single Slovak politician; although there were two representatives of the Slovak Jewish community, the planned absence of Slovak politicians made it difficult to organize an official apology from the new Slovakia for the terrible crimes heaped upon Jews by the old Slovakia. It was as if Havel's men and women were bent on shoring up an old stereotype: Czechs were progressive, intelligent, liberal, whereas Slovaks were unreliable, anti-Semitic, unrepresentative of the newly freed Czechoslovakia. In the end, Milan Kňažko, a popular film, television and theatre actor, one of the leaders of the revolution in Bratislava and at the time Havel's single Slovak adviser at the Castle, went to Israel to make a speech of apology on behalf of the Slovakian population. Kňažko's political career never subsequently flourished. Although he accepted the post at the Castle on the understanding that he would later become a vice-president — a move that would have been warmly welcomed in Slovakia — the job never materialized. Kňažko instead found himself transformed into an ardent defender of Slovak interests. Open disagreement with Havel and his team ensued. After only several weeks in the Castle, Kňazko lost direct access to the President, who sometimes made his key adviser wait several days before agreeing to meet. Kňažko soon resigned.
The Slovak tensions with Havel thereafter publicly worsened, beginning with the outbreak of the so-called hyphen-war in the spring of 1990. Havel quickly developed a reputation for acting without consultation with the Slovaks — thanks to his (rebuffed) decision to instruct parliament to pass legislation about the country's name. Then there was Havel's announcement that Czechoslovakia was no longer going to produce arms for the world's armies, guerrillas, and gangs. He said publicly that he had given careful consideration to the ethics of the gargantuan arms trade, and had decided firmly against feeding it further. But somehow he seemed not to see either the importance of pre-negotiating the matter with a wide variety of the country's opinion-makers, including those resident in Slovakia, or that ethical principles can and often do collide, and that in this case the policy of disarmament, of a sudden shut-down of arms factories, would have a devastating effect on the economic and social life of Slovakia, where the arms industry was primarily based. The principle of opposing the production of guns in Slovakia overrode the principle of putting butter on its tables.
And so on, down the slippery slope of enmity. It wasn't long before Havel became the object of multiplying insults from Slovak secessionists. The President's clarion call for Czechoslovak unity 'faded into the voice of a Greek chorus'. In Bratislava, on 14 March 1991, during celebrations of the establishment of the Slovak state just prior to the outbreak of World War II, Havel was attacked by a small but noisy demonstration of between 2,000 and 3,000 people. Communists, fascists, anti-Semites, nationalists — all of them jeered, cursed and swore whenever Havel's name was mentioned. Events got out of hand when Havel, without informing the Slovak Minister of the Interior, began an impromptu walkabout in the heart of Bratislava while the demonstration was still taking place. The surprised demonstrators saw it as a provocation. Local observers added that there was an unusually large pack of foreign print and radio journalists and camera crews, and that that implied that the Castle had leaked news of the President's lightning visit to Bratislava. Whether Havel intended to attract a counter-demonstration or be martyred is unclear, but if local opinion in Bratislava is to be believed, then the President's office must have been delighted with the pictures and stories of the best-loved politician in the world being attacked by the primitive peasants of Slovakia. Havel was spat on, kicked, scratched, and told to fuck off home. It all seemed to confirm that the Slovaks were the troublemakers. A few months later, on 28 October 1991, during a rowdy celebration of the founding of Czechoslovakia, he was again attacked publicly, this time viciously. Havel's reputation in Slovakia was being ruined.
Symptomatic of these changes was the slow downturn in Havel's opinion-poll fortunes in Slovakia. Not much more than a year after the revolution, the person who had symbolically embodied the country's hopes for the future was suffering from popular mistrust. The proportion of Slovaks (60 per cent) willing to believe in him in January 1991 fell considerably below the corresponding levels of trust in the Slovak government (85 per cent). By August of that same year, less than half of Slovaks were willing to trust Havel compared to 84 per cent of Czechs. Although support for him rose somewhat in Slovakia towards the end of the year, and during early 1992, the corresponding level of popular trust remained far lower than in the Czech lands. Throughout this period, Mečiar and Dubček consistently remained the two most popular and trusted politicians in Slovakia, whereas Havel's rating at one point in the autumn of 1991 plummeted to a mere 9 per cent.
Havel's loss of popularity in Slovakia may be seen as the story of the public exposure of his unresolved ambivalence about his own national identity. Prior to the revolution he had always acted, written and spoken as a Czech, as a Czechoslovak, as a European, and as a cosmopolitan. From within this rather syncretic perspective, he took for granted the importance of the principle of national self-determination. On a doorway leading towards the study in his Prague flat there was a prominent red, white and blue sticker that read 'Free Czechoslovakia!'. But what is interesting about his Masaryk-like commitment to Czechoslovakia, especially when one looks carefully at his texts, is just how easily Havel wobbled between feisty declarations of support for the idea of Czechoslovakia and potentially contradictory, mawkish expressions of his underlying Czechness. 'My home is my Czechness, my nationality', he wrote before the break-up, 'and I see no reason whatsoever for not acknowledging this layer of my home; after all, it is as essentially self-evident for me as, for example, that layer of my home which I would call my male sex.' In moments such as these, Havel saw no necessary conflict between the principle of a multinational state and the principle of defending different people's national identity within that state. But when tempers began to flare in the Slovak lands after the revolution, Havel, like many other Czech politicians, was forced to choose between these two principles. They chose to act as the wronged partners of the crumbling federation.
Havel found himself an exponent of what might be called the subtle ideology of Czech clean hands. This ideology, like all ideologies that serve to rationalize particular interests through talk of generalities, ultimately blamed the Slovaks, with their hot-headed nationalism, for destroying the federation. Rather like the politely arrogant man who feels insulted and vindicated by a woman who grows furious at his uncomprehending arrogance and who, if he doesn't change his ways, is then left with no option but to leave or divorce him, many Czechs, Havel included, felt the Slovaks ultimately to be the failed partner of the federation. They were accused of backward-looking emotionalism, and from that accusation it was only a millimetre's jump to condescending talk of how the Czechs had never wanted to stifle the Slovaks' desire for freedom, that Czechs were now sad about the breakdown of the federation, even if in the end Czechs had been made to look like fools for having been so tolerant of their emotionally Volatile' partners.
In practice, although Havel had flirted with this ideology of Czech clean hands he had neither anticipated nor supported its perverse results. Although mostly unintended, the ideology of clean hands oiled Czech resentment and insult directed at the Slovaks which meant, paradoxically, that previous supporters of the federation could quickly be converted to the view that the Slovaks were a rotten tooth in the Czech body politic and had to be pulled to stop the toothache and to prevent further decay. Czech innocence quickly turned into talk of ridding the Czechs of the Slovak infection. Slovaks' worst fears about Czech prejudices materialized. Slovakia was said to have a weaker democratic tradition, to be politically less advanced, above all to be an 'economic burden' — despite the fact that at the time prospects for economic growth were generally much brighter in the Czech lands — and certainly an impediment in any future attempt successfully to convert the ramshackle Communist mode of production into a healthy, functioning capitalist economy. Too bad about respect for constitutional niceties or the democrats in Slovakia who would suffer isolation following the dissolution of the state. The choice was stark, as Václav Klaus and other spokesmen of the Civic Democratic Party (ODS) made perfectly clear after Havel's resignation: either radical economic reform or the regression into socialism in a common state.
It followed from this uncompromising attitude on the Czech side that all Slovak offers of a looser federal belt had to be rejected. The federation should be strangled. Like two armlocked wrestlers whose faces begin to look alike under strain, Czech separatists strengthened the hand of Slovak separatists. Pincered between them, Havel's position soon became unsustainable. The final humiliating blow against his reputation in Slovakia was hammered in by the least popular Slovak politician in the Czech-speaking regions of Bohemia and Moravia, Premier Mečiar. Just a fortnight before the Slovak declaration of sovereignty, on 3 July 1992, Mečiar, backed by the largest party in Slovakia, the HZDS (Movement for a Democratic Slovakia), successfully moved in the Federal Assembly to block the re-election of Havel as President, whose term was due to expire in October. Havel had at last been forced to pay the political price of his ambiguous role in the drama of the velvet divorce.
Nothing now stood in the way of the carve-up of the state without a referendum. The tempo of events quickened. In August, leaders of the two main parties (the HZDS and the ODS) from Slovakia and the Czech lands wrote the script for the smooth break-up of the state by agreeing to pass laws to end the federation, to divide up property in a ratio of 2:1 (according to population), to guarantee the powers of the successor republics and their recognition in international law, and to form a customs and monetary union. On 1 September 1992, the new Slovak constitution was ratified. The transfer of powers from the federation to the republics and the outright liquidation of federal institutions gathered momentum. In the last week of November, the Federal Assembly committed suicide by approving the break-up of the federation. Within a few weeks, the break-up of the state would become a reality.
The peaceful coexistence of two close nations living in one state ended with the sound of popping corks and clinking champagne glasses on New Year's Eve, 1992. Against Havel's wishes, and partly because of them, Czech negligence and Slovak grievance parted company. The country agreed to divorce itself. Friends reported that that evening Havel was melancholy. Communism was repressive; post-Communism now felt depressive. Whether he felt a touch of repentance for what he had — and had not done — is unknown, but whatever feelings he harboured were transformed into sadness upon hearing the news next day that his old rival and friend Alexander Dubček had been fatally injured in a car crash on his way to the Federal Assembly. The revelry and mourning that followed on New Year's Day, 1993 in Slovakia pretty much summed up the fate that had befallen the country. Some were jubilant, most were hesitant or nervous, but everybody now understood the new reality: Czechoslovakia was now the name of a country from the distant past.
### **Oh Europe!**
The story may be apocryphal. But those attending the David-like President during his inaugural state visit to Germany in January 1990 were reportedly left as breathless as Goliath-like Chancellor Helmut Kohl during the early seconds of their first-ever encounter. 'How would you react to this idea?' asked the crumpled Havel, less than diplomatically, mug of beer and cigarette in hand. 'Why don't we work together to dissolve all political parties? Why don't we set up just one big party: the Party of Europe?' Chancellor Kohl evidently glanced sideways and fell silent for a few seconds before recovering his footing. He reclaimed protocol by issuing the customary warm diplomatic congratulations to the new President of Czechoslovakia. He then asked his distinguished revolutionary guest whether he would care for something more to drink before formal talks got underway, as they promptly did, on matters other than the Party of Europe.
Something of the exuberance of political youth no doubt animated Havel's upstart question, but the theme of Europe — regardless of whether or not the story was true — quickly matured into one of the favourite and most effective weapons within his arsenal of political speeches and foreign-policy initiatives. His familiarity with the subject extended back to his teenage years, when for instance he and Radim Kopecký had made plans to develop a European-wide federation of youth along non-Communist lines. Havel had also done enough browsing in the family library to know by heart the oft-quoted and re-printed remark of Karel Čapek, first published when Havel was two years old: 'If you were to look for Czechoslovakia on the map it would suffice to place your finger precisely in the middle of Europe; it is there,' wrote Čapek. 'Just halfway between North and South, and between West and East, just in the middle between the four Seas whose shores outline the complicated contour of Europe. To be anchored in the very heart of Europe is not merely a geographical location, but it means the very fate of the land and of the nation that inhabits it.'
Following the triumph of totalitarianism in Russia and Germany, and the Munich agreement, this type of pro-European sentiment tended to become unfashionable, even embarrassed by finding itself in a verbal alliance with violent power. Europe tended to become a dirty or suspicious word, soiled by Mussolini's talk of 'European civilization' and Nazi propaganda against 'Asiatic and Jewish Bolshevism'. The subsequent defeat of German and Italian fascism, combined with the military advances of the Soviet Union into central Europe, meant not only the geopolitical subdivision of European territory. It also meant that the attempted symbolic revival of 'Europe' and the political quest for peaceful European integration — beginning with such experiments as the European Coal and Steel Community and the Treaty of Rome — necessarily excluded Czechoslovakia, confirming its consignment to the sphere of 'Eastern Europe' under Soviet domination. Havel himself never accepted the geopolitical arrangement, and tried repeatedly to challenge it publicly. The Charter 77 initiative was in this respect a turning point, because the whole underlying principle of the Charter was its bold attempt to act _as if_ European-wide agreement and co-operation on matters of human and civil rights actually existed in legal and political form. The revolutions on the western fringes of the Soviet empire in the autumn of 1989 dramatically confirmed this presumption. Suddenly, like the walls of Jericho, the barbed wire and concrete and guns dividing Europe lost their function. Europe was again free to negotiate its own peaceful reunification.
Havel's cheeky question to Chancellor Kohl pointed in this direction. Kohl may have retreated into his shell — according to the story — and vowed from there on to handle Václav Havel with a loud voice and powerful manner, and to restrict political arguments with him to _in camera_ sessions. For Havel, the outcome of his cheeky question was altogether different. Quick off the mark, and well ahead of most of the political spectrum in his own country, he chose to embark on the boldest move of his time in the office of the President. His foresight was to be rewarded with the greatest single achievement of his presidential career: to bring back international respect and recognition, even admiration, for his tiny country by beginning the slow and delicate and fraught process of negotiating the re-entry of the Czechs into the structures of European integration.
His campaigning for the Czechs' formal re-entry into Europe, using the Velvet Revolution as a springboard — 'bringing the Czech Republic into the European Union and into the twenty-first century', as he put it to a close friend, was undoubtedly helped along by the remarkable parallel resurgence of wider interest in European integration, stretching from the second half of the 1980s into the 1990s. During Havel's several presidencies, many observers and whole electorates welcomed various treaties, including the Single Europe (1992) Act, while most political leaders throughout the region willingly co-operated in such forums as the European Parliament and the annual meetings of the European Council. The spirit of European unity also appeared on the military front. Franco-German co-operation seemed nothing short of a miracle; the formation of a European Common Security and Foreign Policy was widely interpreted as a small (if incomplete) victory in Europe's struggle to control its own affairs; while for the first time ever — during the Gulf War — European countries acted in unison to defend their perceived interests outside of Europe. Even some part of the elites within the two countries that had traditionally felt least at home in Europe — Britain and Russia — seemed to be persuaded of its importance.
Picking up the threads of this trend, Havel began to sew using the same sharp principle that Jean Monnet, the most famous political architect of Europe, himself applied to the subject of European integration: if you want to change the world, find the most powerful point of leverage against the status quo instead of short-sightedly mucking around with present-day details. Havel did so in various different ways, each pursued simultaneously.
Intense efforts to repair and consolidate diplomatic relations with the various member states of the European Community (as it was still called in January 1990) was the most obvious step to be taken. During the first flying year of his presidency of Czechoslovakia, Havel made state visits to Berlin, Munich London, Paris, Rome, Lisbon, Strasbourg, Madrid and Barcelona, among other European cities. Meanwhile, he foresaw that his country's re-entry into the European mosaic of states required some co-ordination with the other newly independent central-eastern European states that had just emerged from under the Communist rubble. 'Good relations with our neighbours are in the fundamental interest of each of our countries as well as in the fundamental interest of Europe as a whole,' he said to a NATO summit in Brussels, called in early January 1994 to foster ties between itself and the four member states (the Czech Republic, Poland, Slovakia, Hungary) of the so-called Višegrád group. The speech was well received. It convinced enough domestic opinion that going into NATO — the American-dominated military alliance whose formation was spawned in part by the _coup de Prague_ a half-century earlier — would help to stabilize Czech democracy and make the Czech economy more attractive to foreign investors. The speech also evidently helped to consolidate agreement favouring the redefinition and acceptance of the Partnership for Peace, a scheme conceived in the previous October by NATO defence ministers as a way of fostering ties between central-eastern Europe and the alliance. 'Our countries have very similar views on the Partnership for Peace', said Havel following a handshake from President Bill Clinton after the Brussels meeting. 'I would be happy if today the city of Prague could emerge as a symbol of Europe standing in alliance.' Shortly afterwards, Czech entry into the military alliance that acts as policeman of the European region seemed a foregone conclusion — as it proved to be in March 1999 — with the NATO announcement of plans for joint training and the holding of military exercises on the soil of the Višegrád states. A few weeks later, as NATO bombs rained down on Serbia, Havel told delegates to the fiftieth-anniversary summit of NATO that the Czech Republic now formally belonged to 'the Western sphere of civilization. The same is true,' he added, 'of Slovakia, Slovenia, Romania, Lithuania, Latvia, Estonia, Bulgaria and other Balkan States.'
Then there was the need to tackle some difficult questions concerning relations with Germany. Just before the Velvet Revolution, Havel drafted and sent a private letter to President Richard von Weizsäcker. Anticipating controversial remarks made during a Czechoslovak Television interview a few weeks later, Havel apologized on behalf of the citizens of his country for the 'profoundly immoral' treatment of the ethnic German populations of the country immediately after the military defeat of Nazism. Havel confessed that no peaceful and good-willed _rapprochement_ between the new Germany and his own country — and no new relationship with the wider Europe — would be possible unless public recognition was given to the scale and brutality of the Czechs' treatment of their own ethnic German citizens. He noted that during the years 1945-1946 — Havel was speaking from experience as the owner of property at Hrádeček once owned by a victim — at least 2.5 million ethnic Germans were violently hunted out of the country, leaving behind perhaps only a scared minority of 200,000 survivors of the exodus. Such treatment was unacceptable, argued Havel. No good reasons could justify it. All Czechs and Slovaks should feel ashamed of what they or their distant relatives had done. The memory of it should for ever be preserved, and any future repetition of it could only be avoided, he implied, if a new treaty of understanding between the two countries was drafted, and signed. He concluded: 'Czechoslovak democrats owe German democrats something.'
Howls of protest greeted the proposal. But Havel was unflinching. There were many who pointed out that the exodus of ethnic Germans was just punishment for their support for Hitler's totalitarianism. While they claimed their right to a homeland, they had in fact renounced their home country of Czechoslovakia. They deserved everything they subsequently got. There were other critics who spotted that the apology to Germany was a prelude to negotiating entry into the European Community of states, in which Germany already exercised important powers. The reaction was something like: 'We've only barely begun to free ourselves as a country after more than fifty years, and now we're being asked to subordinate ourselves again, this time to the Germans and their Brussels agents.'
Havel aimed two barrels at such rhetoric. He singled out 'Czechocentrism' and 'provincial mistrust' towards the wider world as the rotten foundations on which anti-German xenophobia rested. Time and again — on television and especially during his weekly radio broadcast from the presidential estate at Lány — he attacked narrow-mindedness, ignorance of the wider world, and intolerance of others. He maintained that such attitudes were pointless, except to justify Czechs and Slovaks taking a political path that led nowhere except into a blind alley of isolation. Such attitudes also served secretly to reinforce the widespread unspoken assumption, to which Neville Chamberlain notoriously gave voice, that central Europe is another world, well off the main highways of world affairs, and really not worth a detour. Finally, he said, such attitudes had had murderous effects in the past, and they might well do so in the future, unless checked.
Havel tried to buttress his attack on anti-German xenophobia by standing on ramparts made from several different — not entirely compatible — arguments. He continued to remind his audiences that a cosmopolitan sense of responsibility for others is a citizen's duty — just as he had emphasized in the play _Redevelopment, or Slum Clearance (Asanace_ [1988]), when the character Zdeněk Bergman reacts to news of the death of the wise idealist Plekhanov: 'Confronted with his death, we realize that we must bear our portion of guilt for it, for we, too, are responsible for the sad state of this world.' Havel tried to add substance to his call for cosmopolitanism by repeating Čapek's theme of the Czech lands as the geopolitical crossroads of Europe. He tried as well to recast the same theme as a defence of _Mitteleuropa._ 'It was often in Vienna or Prague before anywhere else that potential threats to humanity appeared,' he told an Austrian audience. The long and often unhappy history of cultural and political contacts among the peoples of _Mitteleuropa_ — Havel's definition was fuzzy — now placed the region in 'the front line of the fight for democracy and stability in the whole of Europe'. Czechs and Slovaks should not gaze at their navels. They had the duty to think of themselves as members of a wider proto-political community that could serve as the hub of 'the West's ongoing efforts to live in peace and security'.
Havel's vague definition of _Mitteleuropa_ was perhaps deliberate, considering that in his hands it functioned as something resembling a future Utopia designed to stimulate the hopes and dreams of present-day citizens and governments. The idea of _Mitteleuropa_ evidently excluded 'Eastern' countries still haunted by the ghosts of Russian power and 'Western' countries like Britain, for whom the post-Communist lands were still regarded as far-away countries about which we know nothing (a prejudice voiced by Neville Chamberlain when Havel was still in nappies). But whether Havel intended to include in _Mitteleuropa_ countries as diverse as Sweden and Slovenia, Poland and Hungary and (parts of) Italy, was unclear. Presumably, his defence of the region included Germany, which is perhaps one reason why in his various efforts to demonstrate the need for cultural and political solidarity between Czechoslovaks and Germans he was strangely hare-lipped about the Holocaust. It was as if Havel made a political calculation not to stir up trouble with his country's neighbours. When the subject of the Holocaust did arise, Havel's vague argument — surely one of the most problematic in all of his political and artistic career — was as soothing to guilted Germans and quisling Czechs as it was objectionable to concerned Jewish ears in both countries. In the Holocaust, he said in a 1993 address at The George Washington University, 'the Chosen People were chosen by history to bear the brunt [of responsibility] for us all. The meaning of their sacrifice is to warn us against indifference to things we foolishly believe do not concern us.' Terms like 'history' and 'Fate' seemed designed to highlight the undeniable fact that the Holocaust is now part of our received historical tradition, so that any present and future efforts to look forward to a future freed from totalitarian power are _compelled_ to look backwards, to force us, again and again, to face up to what some human beings did to others for the first time ever. Yet the trouble with Havel's talk of 'Fate' and 'history' is that it so easily caused insult. Personal and group responsibility for the Holocaust was fudged, or dissolved into talk of abstract non-actors going under the name of forces with a will of their own.
No such depersonalized talk of 'history' infected his discussions of nationalist politics. With one eye on the Balkans war unleashed by the Milosevic regime in the early 1990s, Havel roundly-condemned nationalism, 'the hatred for anyone who seems to be playing the traitor to his roots or who claims different roots'. He pointed out that Communism and nationalism have a common mind-set. 'Both simplify the world,' he said, 'divide it into friends and enemies, the chosen and those condemned to contempt, into "us" as the better people and "them" as the worse. They do not examine individual merit or guilt, but prejudge, pigeonhole and, thus, divide society into the meritorious and the culprits.' And he went on to warn that the germs of nationalism are highly contagious. 'Czechocentrism' could ruinously conspire with Balkan nationalisms to succour little nationalists elsewhere in Europe. 'The fate of the so-called West', he concluded, 'is today being decided in the so-called East.'
These various arguments against 'Czechocentrism' were greeted with yet more howls of protest, at which Havel took aim with a second barrel. It was imperative, he argued, to move as quickly as possible towards a new treaty that resolved once and for all the bad feelings produced on both sides of the border by the cruel expulsion of ethnic Germans and the brutality of Nazism. A breakthrough along these lines came at the end of February 1992, when Havel met with Chancellor Kohl to sign a friendship treaty that included assurances of German support for Czechoslovakia's full membership in the European Community. In spite of a week of small but lively street protests — in Prague demonstrations of up to 5,000 people voiced concerns about the dangers of German territorial and economic domination — the atmosphere of the endorsement ceremony in the Castle's opulent Spanish Hall was festive. Havel, Kohl and their advisers raised champagne glasses in honour of the new 'spirit of commonality'. Havel was forthright. 'We are laying the foundations for good, friendly relations between our nations,' he said. 'We are shaping the future, setting the grounds for a fast way for Czechoslovakia into the family of European nations.' Kohl reciprocated the generosity. 'We have stood over too many graves in this century,' he said. 'We have shed too many tears. The time has come for us to learn from history. It is in this way that I understand our decision to help your country.'
After the break-up of Czechoslovakia, the friendship treaty in effect had to be renegotiated all over again. It was nonetheless a watershed agreement, and not only because it served as the written precedent for a pattern of inter-governmental negotiation that would lead ultimately to full membership within the European Union. The treaty — acting like a lance to a boil — also served to publicize the lingering grievances against such agreement. Few denied the material advantages offered by the treaty, which in addition to German support for Czechoslovak membership in the European Community also included provision for security measures, scientific collaboration, environmental protection and basic cultural, economic and governmental co-operation. The critics were vociferous about other matters, especially the reference in the treaty to the 'expulsion' of 2½ million ethnic Germans four decades earlier. A spokesman for Landsmannschaft, a pressure group representing them, told the business daily _Hospodá řské noviny_ that the pressing question of restitution had been left unresolved by the treaty. The Czech Septimius, who had by now worked his way up the political ladder to become federal Deputy Prime Minister, agreed. 'We are now signing a treaty that leaves unresolved the most dangerous issues,' Klaus said bitterly. He too objected — on free-market grounds, as ever — to the word 'expulsion', which 'could be a friendly gesture offering [Germany] certain moral satisfaction for the severity of this process carried out after the war'. But, he continued, 'the context in which this word is used in the treaty could germinate certain legal claims [by ethnic Germans] in the future'.
Czechoslovakia's privatization laws specifically precluded restitution claims by owners who lost their property before 1948 and, in any case, the negotiators of the treaty supposed, as Kohl himself openly admitted, that the European Community would serve as the future framework within which 'solutions for the settlement of foreign claims' would be found. Havel was more strident. He implied — it was not put quite so cynically — that the problem would wither away with the decline in the numbers of 'first generation' ethnic Germans. 'This issue, which seems to be controversial and dramatic at the moment, will gradually lose its controversial and dramatic nature,' he predicted. To which he added remarks about the basic principles of European integration. Those who continued to think in narrowly retributionist terms understated the co-operative spirit that Brussels was now trying to foster. The key point, Havel said, was that the European Community vision of a Europe without borders would make it 'possible for any European, including a Sudeten German, if he or she wants, to work, live, and invest in our country'.
The remark typified another move made by Havel in support of the Czechs' return to Europe: his efforts to provide a sophisticated moral-philosophical justification of the long-term process of European integration. Compared with other statesmen and stateswomen in the European region, Havel proved that he could himself write unaided the best — and the most thoughtful — speeches on the subject. His inaugural address to the European Parliament in Strasbourg in early March 1994 was typical. Havel acknowledged all that had been so far achieved through negotiation. Given how much 'unrest, chaos, and violence' Europe had suffered in the twentieth century, it was a near-miracle that so much common agreement and successful institution-building had been achieved in so little time, he said. He criticized those — he surely had in mind personalities like Margaret Thatcher and Václav Klaus — who misrepresented the European Union as a new Moloch with an insatiable appetite for otherwise freedom-loving individuals, groups, regions, nations, and states. He instead spoke of the Union as 'a space that allows the autonomous components of Europe to develop freely and in their own way in an environment of lasting security and mutually beneficial co-operation based on principles of democracy, respect for human rights, civil society, and an open market economy'.
Havel pointed to the nightmare alternative — genocidal war in the former Yugoslavia — before reiterating that the post-Communist countries of Europe had seen enough of such bloodshed this century. He stated bluntly what many of his fellow Czechs would not dare even to whisper. 'Yes,' he said, Czechs were ready to join the European Union 'because we know it will repay us many times over, as it will all Europeans'. He then praised the Maastricht Treaty of Union as a 'great administrative work', as 'a remarkable labour of the human spirit and its rational capacities' — in order to criticize its lack of 'a spiritual or moral or emotional dimension'. European integration could only succeed, he concluded, if it were given 'charisma'. Something like a new charter of European Union was required. It would give to 'millions of European souls an idea, a historical mission and a momentum'. The European charter would 'clearly articulate the values upon which it is founded and which it intends to defend and cultivate'. It would also 'take care to create emblems and symbols, visible bearers of its significance'.
Subsequent speeches tried to clarify and detail exactly what he meant by the European 'idea'. The efforts were unusually philosophical, the turn away from practical politics definite. It was as if the _Ichspieler_ had once again found his footing, a last remaining stage on which to perform to an audience — this time, significantly, one that stretched from Madeira to the Urals, from the frozen Arctic to sunny Cyprus, and even beyond, to interested audiences living in Tokyo, Beijing, Washington, Santiago, Canberra, New Delhi, Cairo, or Johannesburg. The stunning width of his audience matched the breathtaking height of his thoughts. The acrobatics involved talk of Schiller's 'Ode to Joy' and its insistence that freedom requires giving allegiance and commitment to 'the judge above the stars'. There were frequent mentions of the need for Europe to abandon its traditional quest 'to spread — violently or non-violently — its own religion, its own civilization, its own inventions, or its own power'. Havel even insisted that Europe should stop preaching 'the rule of law, democracy, human rights, or justice to the rest of the world'. Europe's key task, he said repeatedly, is 'to discover its conscience and its responsibility, in the deepest sense'.
The acrobatics were brilliantly executed and good to watch. And they certainly helped to consolidate his global reputation, and to win him prizes, gold medals, honorary doctorates, several shortlistings for the Nobel Prize, even the honour of being labelled 'the moral leader of Europe'. Yet the odd thing is that nobody spotted the tragic irony lurking within his efforts to become the moral leader of Europe with a global reputation. His campaigning for the Czech Republic's full entry into the European Union, if successful, would for ever prevent a repetition of the kind of unchallenged charismatic presidential power that he had once enjoyed, during the first months of the glorious Velvet Revolution. During his ten-year string of presidencies, on the domestic front, that charismatic power was subsequently tamed and permanently humbled, check by balance, push by pull, confrontation by confrontation. But on the international scene, in principle, Havel's power remained unchallenged. According to the Constitution of the Czech Republic (ratified on 16 December 1992), the President of the Republic 'shall be the head of the state' and 'shall not be answerable for the exercise of his function' (Article 54). Subject to the countersignature of the Prime Minister, or by a member of the government authorized by that minister, the President is sovereign in respect of such matters as representing the state in external affairs, negotiating and ratifying international treaties, acting as the supreme commander of the armed forces, appointing and promoting generals, appointing judges, and accrediting and receiving the heads of foreign diplomatic missions (Article 63).
Havel's statesman-like battle for Czech accession to the European Union effectively spelled the end of these sovereign powers, in substance if not in name. His daring rescue of a small, humiliated and insignificant country from the Soviet empire, his reinsertion of that country on the map of the world by pushing it towards the European region, had a political price. Full membership in the European Union actually required the creation of a _post-sovereign presidency,_ a sovereign leader who was no longer sovereign. European Union membership required a leader who ceased to be _primus inter pares_ within the upper echelons of the state, who instead is just one leader among three or four handfuls of leaders, who are themselves subject to the constraints and opportunities afforded by obedience to the so-called _acquis communautaire,_ the body of treaties, laws, and directives already agreed by the earlier political architects of European integration.
Future presidents of the Czech Republic may wish to thank — and some will want to curse — Havel for this spectacular change. But, whatever transpires and whatever is thought of the change, the Czech presidents who follow in his footsteps will feel the difference. They will of course sit beside the heads of large European member states; from time to time they will amend or veto their wills. But future Czech presidents will know that among the terms of their election is their acceptance of the fact that they can no longer engage in power politics in the early modern sense. Like the oxygen they breathe each few seconds, they shall have to operate within the kind of institutional framework anticipated in the Maastricht Treaty of Union. Thanks to that treaty, and Havel's efforts to extend it eastwards, all future heads of Czech state will not be heads of state. They will instead make politics within a three-pillared structure, comprising the original European Communities — the ESCE, EAEC and EC — plus the newly founded Common Foreign and Security Policy (CFSP) and co-operation in Home and Judicial Affairs (HJA). They will accept that the stated goal of 'creating an ever-closer union among the peoples of Europe' (Article A) requires not merely acceptance of the _acquis communautaire,_ but also a relative shift away from policy-making by consensus towards qualified majority voting, plus a quickening pace of Euro-legislation in all policy fields. All future heads of state will recognize that the Treaty of Union 'constitutionalizes' the principle of the 'Union Citizen'. They will understand that the combined effect of such changes, including the monetary union of existing and future member states, is to weaken and dissolve the principle of the sovereign territorial state. In other words — let us call this the European law of power-sharing — all heads of state will accept that they are subject to countervailing _supranational_ powers, even in such fundamental matters as representing the state in external affairs, negotiating and ratifying international treaties, acting as the supreme commander of the armed forces, and accrediting and receiving the heads of foreign diplomatic missions.
### **Metamorphosis**
'Dear Mr President.' The calm physician paused. 'I think it best that you have some tests, which we could begin this afternoon in nearby Innsbruck. They should not take long, and I emphasize that they are just routine. There is absolutely nothing to be worried about. I give you my word.' Minutes later, the Austrian staff in the local hamlet clinic in Reutt telephoned for an air ambulance, which promptly whisked the President of the Czech Republic to hospital for emergency surgery to remove 30 centimetres of heavily perforated intestine. So began his fourth hospitalization in a year. Despite fears, there were no signs of cancer and Havel, enmeshed in tubes and confined to hospital for several more weeks, was soon off the critical list, reportedly in a good mood, and even capable of a few post-operative jokes befitting a lucky head of state.
He was indeed lucky that bowels recognize no borders, and that he had had the good fortune to be out of his own country in mid-April 1998, on holiday in a small Austrian village in the Tyrolian Alps. 'The hospital is better than anything we have in Prague,' the President's brother Ivan remarked. 'And luckily Czech surgeons were not involved. It is not that they are less competent. It is that most of them might have hesitated or refused to do what had to be done, out of fear of failing and perhaps ruining their careers as a result.' The comment contained more than just a hint of concern about the imperfect state of the Czech health-care system, which can be so unresponsive (as the local joke has it) that the waiting list for pregnancy tests has been stretched to ten months. The comment pointed to some hard political facts: that despite the failures of the crowned republic, Havel's body and persona had in a way become royalized; that his illness was an instant media event; and that nobody around him dared put a foot wrong because a royal tragedy of epic proportions was now unfolding before everyone's eyes.
The sad public performance at the Prague Castle had begun seventeen months earlier. In early December 1996, a public scandal erupted during his first medical crisis, which pushed Havel towards the grave and left him permanently weakened. Some said that official secrecy, political incompetence and medical misjudgement had almost cost him his life. The facts were these. On 16 November 1996, Havel's personal physician, Michal Šerf, X-rayed his lungs. A spot was seen, but Serf considered that Havel's pneumonia first needed to be treated. Havel was so treated, but failed to respond. The symptoms — fever, shivering, double vision — worsened so his new girlfriend, the blonde actress Dagmar Veškrnová, sacked the physician, who had been a trusted friend from before the Velvet Revolution. At Prague's best hospital, Na Homolce, she made contact with other doctors, who administered sedatives and again X-rayed his lungs — anonymously.
Illness never strikes at an opportune moment, and Havel's was no exception. In the middle of crucial negotiations to effect Czech entry into NATO, his good health was both a practical necessity and a symbol of the Czech Republic's ability to see through high-powered negotiations at this level. So the doctors chose to keep the medical crisis a top secret, even from the rest of the medical profession. His lungs were X-rayed incognito, and the plates were circulated to other specialist doctors bearing the name of his chief bodyguard. It was evident that the right lung of the patient was marked by a black spot, so another opinion was sought, this time from one of Prague's leading medical professors, Dr Pavel Pafko. He wasted no time recommending surgery, which was carried out at his teaching hospital, the Third Surgical Clinic, located on Londýnská Street, just near where Havel had been born.
Minutes before the surgery began — as if facing his own execution — Havel and his Minister of Health lit up cigarettes under the glare of television lights, watched by a hundred reporters, jostling to get the last shot before the brave President disappeared into the operating theatre — perhaps into the grave. The procedure lasted four hours, during which Dr Pafko and his team located and promptly removed a malignant tumour more than half an inch long, together with the surrounding tissue. The President with only one-and-a-half lungs was then put into the intensive-care unit, separated by screens from the other patients.
From here on, opinions about what happened are divided, in no small measure because those closest to Havel began at that moment to disagree about what should be done. Shortly after the operation, Havel's left lung developed a new pneumonia. His pulse rate soared, and Dr Pafko, calling in another doctor, six nurses and a lung ventilator, carried out a tracheotomy — opening a hole in Havel's throat, so that he could breathe. No sooner had that been done than Havel developed heart trouble. A genuine crisis quickly followed. The lung ventilator stopped operating and were it not for Veškrnová, who walked into the intensive-care unit to find Havel asphyxiating, he would certainly have died.
That episode in the life-or-death drama rocked everybody's confidence. Veškrnová summoned a faith healer, who made three visits to Havel's bedside. His brother Ivan, convinced that the presidential staff were no longer on top of the situation, called in an independent doctor, whom he trusted. That prompted Veškrnová to get on the phone for international help. Eight days after the operation, as the patient's heart improved but overall condition worsened, a new infection developed. Although the laboratory-test results were inconclusive, and Havel was given a blood transfusion, splits developed within the team of twelve doctors led by Dr Pafko. Some wanted urgently to move Havel out of the Third Surgical Clinic. Others considered such a move unnecessary; still others were certain only that moving Havel was too dangerous. At exactly that moment Fortune — described by Machiavelli as 'mistress of one half our actions' — intervened to bring, on an overnight flight to Prague, a thirteenth doctor, a distinguished American named Robert J. Ginsberg. Head of thoracic surgery at the world-famous Memorial Sloan-Kettering Cancer Center in New York, Ginsberg had an instant stabilizing effect on the whole situation, despite some background grumbling about his medical credentials. He took one look at Havel before ordering the hospital staff to turn down the oxygen content of the ventilator. He personally cleaned the inside of Havel's airway, and then announced to the team of quarrelling doctors that the patient's fever would subside, and that he was on the road to a normal recovery. He was proved right.
As Ginsberg boarded his flight back to New York two days later, a rancorous public debate erupted in the Czech Republic. Why did Havel's X-rays bear the name of his chief bodyguard, some asked, and why was he allowed to smoke until a few seconds before he was wheeled into the operating theatre? Why on earth was a faith healer summoned to his bedside? And why, others asked, were events at Prague's reputedly best hospital allowed so obviously to slip out of control? Why did his surgeons quarrel themselves into doing nothing at the most critical point? The questions were not directly answered, and rumours circulated that Havel, who returned home to convalesce on 27 December, had slumped into deep despondency enforced by compulsory abstinence from cigarettes and alcohol.
Things didn't improve, politically speaking. On the eighth day after returning from hospital, Havel left his friends and the Czech public breathless by marrying Veškrnová in a private ceremony, to which not even his brother Ivan was invited. Some of his closest friends warned him not to go through with it. He told them, in reply, that he had reached the conclusion that Dáša had personally saved his life, and that he was besotted — since well before his operation, when they were already living together. There was apparently plenty of flowing libidinal energy. He initially loved the way she eyeballed him, he said, and she also found his bohemian-playwright side sexy. The day after the wedding — a twenty-minute ceremony held shortly before noon on 4 January 1997 at Prague's Žižkov Town Hall, where thirty-three years earlier he had married his first wife Olga — Havel addressed the country on his regular 'Talks from Lány' programme. 'I believe, or hope', he began, 'that we will be happy. And I believe in something else: that this new stage will help make me in some ways a better man than I have been.' Havel didn't elaborate his past shortcomings, but interestingly he did have much to say about Olga, who had died from cancer less than a year ago. 'Olga was my companion for almost forty-five years. She is and will always be an irreplaceable part of my soul. I married Dáša not to replace Olga, but simply because we love each other and want to live together.' Havel mentioned that a symbol of this continuity was the choice to get married in the same location. He then — inappropriately, thought some — went on to invoke Olga's support for the choice of his new forty-three-year-old wife. 'Before she died,' he said, 'Olga said I should remarry. At the time, I ruled it out categorically, and I was resolved to end my days alone. She was convinced that I can't live alone, and that I shouldn't. She was right, and life itself confirmed that when I was lucky enough to get to know Dáša.'
Press and television photographs from this period show the thin-looking Havel to be radiant. Yet whatever personal happiness he gained from the marriage seemed quickly to backfire upon him politically. 'Even if Dagmar Veškrnová had been an angel,' said one of Havel's trusted advisers later, 'the newlyweds would not likely have landed on their feet.' Public opinion indeed became restless, and even showed strange signs of vindictiveness. Havel began to resemble the kind-hearted king — in the well-known Czech nursery rhyme — who dabbed honey on his nose for his favourite bee to feed on, only to plummet into shock after the ungrateful insect grew restless and stung him. Just a few months into the marriage, his new wife told an invited audience of children and journalists at the Castle that her current favourite story-book character was the Golden Fish (released by fishermen after granting them three wishes) because she wanted to 'fulfil my husband's every wish'. Havel looked on, smiling. The state of sexual politics in the Czech Republic showed itself to be a few strides ahead of the performance, which was widely interpreted to border on bad taste. Some even said it resembled a tawdry scene out of one of Havel's absurdist plays. The observation highlighted the lingering public sympathy for Olga. It also underlined the fact that Havel's second marriage — 'our presidency' he subsequently called it in a Czech Television _faux pas —_ quickly became a political liability. Love is always a poor adviser, which is perhaps why during the year 1997 Havel acted like a besotted playwright swooning after a young actress rehearsing the part of Her Serene Highness. 'All her life, she had to play roles, to slip into them,' well-placed Prague observers remarked, or words to that effect. They added something like: 'She has no identity, and she is looking for a new role. It is quite probable that she is playing the role that he expects of her, especially considering that he has been ill and that from here on death is permanently on his mind.'
Havel had not had any practice in experimenting with these expectations. His first wife Olga had refused on principle to play the political role of First Lady; she preferred instead to busy herself with projects that aimed to empower the socially downtrodden. Dáša Veškrnová, by contrast, appeared to fancy a political role. Her discovery that, within the Castle, she had no automatic right to visit her new husband, upset her. So did her discovery, after drafting a reply letter to Madame Chirac, that she had no special rights, and that she was required to wait in a queue for her letter to be typed and forwarded to Paris. Veškrnová's disquiet fed her political aspirations, proof of which came during the last week of August 1997, when she told the Czech daily _Mladá fronta Dnes_ that she had been 'thrown into deep water' when she had married President Václav Havel, and that she now wanted a law to govern her functions, including a formal guarantee that she receive assistance from the President's staff. All hell broke loose. Pavel Rychetský, chairman of the Senate's important Commission on Constitutional and Legal Affairs, voiced typical criticism of Dáša's ambitions. 'The wife of the President is not a position,' he reminded her in the pages of _Lidové noviny,_ 'and it is definitely not a constitutional position'.He added that it was mistaken to think that the law had to be changed every time that family members of state officials had unsatisfied needs. There were rumbling noises from within the Castle and rumours began to reach the outside world that some staff were rather disgruntled, and even that one of Havel's most trusted aides had left after saying to her face something like: 'As you know, I have already handed in my resignation. You should know as well that, unlike other satrapies, this country is a parliamentary democracy with an elected president. You are only his wife.'
Havlová bit back. In a prepared statement, she told _Miada fronta Dnes_ that she was 'shocked by television and newspaper reports... which, without exception, accuse me of wanting to be a constitutional body, wanting to have my own law or even change the constitution'. She repeated that there were presently no legislative guarantees of her important position. How otherwise could she fulfil her duties? 'Almost every one of my decisions or letters,' she added, 'has some political significance and can, in one way or another, touch upon the interests or prestige of the head of state, and therefore the state itself Havel's spin doctor Špaček tried to make peace by reiterating in softer tones Dáša's key points. While the First Lady currently had two assistants, she honestly needed more help. 'She only wants a sentence in the existing law... that stipulates that the First Lady will receive as much help as is necessary.' This was hardly convincing, since the term necessity — a favourite of state-mongers, we learn from Machiavelli — was itself both the sore point and the unresolved issue.
Havel's political troubles were deepened by backing Dáša's perceived public indiscretions. There were quite a few of them, including a press conference outburst against journalists for failing to recognize her husband's 'right to free weekends, like every other employee'. Quips and vulgar jokes about her — and the corresponding state of her husband's health and political judgement — naturally began to circulate throughout Czech society. Dáša was quickly forced to learn that contemporary politics and high-profile media coverage are a married couple, and that the old distinction between on-stage and back-stage in politics is now obsolete. The more 'private' political stars try to be, the more 'publicity' they get. So tabloid journalists and image consultants rudely criticized her Versace wardrobe as too 'extravagant'. Unkindly, some said Dáša looked like a flight attendant, that she should lose a few kilos; or that she wore too much bright-red lipstick. Still others sneered that her nails were improperly manicured, or that her hair was a mess.
Havel meanwhile (perhaps unfairly) was made to look like the partner of a pin-up blonde featured in a down-market tabloid newspaper. 'Did you hear that Havel is planning to spend next Christmas with Olga?' ran one of the most cruel, popular jokes. 'But do you know who she is going to marry next?' ran a reply. 'Yeltsin!' Havel reacted defensively to such irreverence — he reportedly instructed his immediate staff at the Castle several times that they should like her — and in so doing began to act as if he were a politician cocooned in his own hubris. Things were not helped by the absence of Olga, who had always made efforts to check his indiscretions and to complain to him about the arselickers and skirtchasers within the ranks of his own staff. Neutral observers complained that the President seemed unusually ill-tempered and prone to mood-swings, possibly due to his prescribed medication.
Matters were worsened by Havel's loss of contact with acquaintances, friends and family — even his brother Ivan began to report to friends that he now regretted seeing him only once a year, whereas during his time in prison he used to see him the permitted four times a year. Machiavelli's comment that princes sometimes do things for the fame that outlives them seemed to rebound on him cruelly: fame brought him no friends, only attention. Havel's own predilection for playing the role of _Ichspieler_ consolidated this impression. On his wedding day, typically, he told reporters that he himself would decide how to handle the morality of what he had done, and what he would do in the future. 'Anyone who knows me a little,' he said, 'knows that when its comes to the important things in my life, I've always done what I consider to be right and that I've never taken into consideration how much people like or dislike my decisions.'
Some observers began to re-describe this self-justification for 'living in the truth' as pig-headedness. During 1997, all sorts of stories, some of them poisonous, began to circulate. Their veracity was uncertain, but they had the effect of stripping away the remaining layers of Havel's charisma. There were those who cited the Russian poet Joseph Brodsky, who had earlier warned Havel not 'to create illusions' by repeatedly using terms like 'global responsibilities', which 'are not much better at the core than the retrospective utopias of the latter-day nationalists or the entrepreneurial fantasies of the _nouveaux riches'_. Brodsky had implied that Havel was showing signs of clinging dogmatically to favourite philosophical tenets, perhaps because he had ever less time to read and to keep up with things, so that, naturally, he began to nourish himself on old literature and to parrot old intuitions. On a different note, foreign journalists treated to chain-smoking lunches in wine cellars at the foot of the Castle noted that he now talked more like a politician than a poet, a playwright, or philosophical critic of the modern world.Such perceptions, whatever their accuracy, fed deeper feelings that presidential power had cramped Havel's imaginative literary style, that political power had turned him into a maker of rote speeches defined by state duties. The possible implication was spelled out long ago by a wise philosopher: 'The possession of power unavoidably corrupts the free exercise of reason,' he wrote. Another philosopher harshened the point: 'Coming to power is a costly business,' he wrote, 'power _makes stupid..._ Politics devours all seriousness for really intellectual things'.
Havel's self-portrayals as a 'post-modern' president were a case in point. During his first term as President of the Czech Republic, his preaching 'post-modern' argument — that the modern technological age is ending, fortunately so because it has been defined above all by human arrogance towards both nature and other humans — was refreshing. It served as an important reminder that democracy thrives on humility. There were even moments when his public attacks on modernity exuded bravery. An example was his 4 July speech on the steps of Philadelphia's Independence Hall, when he told his American audience, some of them dressed in smart suits, others ambling by in cut-offs and T-shirts and licking ice-cream, that the 1776 revolution was founded on the mistaken 'anthropocentric' presumption that the doctrine of inalienable human rights, conferred on humanity by the Creator, subsequently encouraged Man to forget about the Creator and to act as 'the pinnacle of creation and lord of the world'.
Later repetition of this theme turned it into a stale cliché, and made it vulnerable to the common-sense objection that the content of Havel's 'post-modern' speeches was contradicted by the recognizably _modern_ spectacle of a head of state attempting to stave off political decline by reaching for abstractions and looking to the heavens. That suspicion of his motives was confirmed by other critics, who pointed to the need to rethink Havel's dissident period. The story circulated that those who once knew him well sometimes found him to be arrogant, and that some of his (former) acquaintances remember well a rowdy dispute he had had with Jan Vladislav about _Charta_ 77, shortly after its formation. According to the story, Vladislav objected to Havel doing things behind his and others' backs, for which Havel, when caught out, had the sense and good grace to apologize, adding with a strained face: 'You now know me. I am a manipulator.' That secret confession, observers began to say, revealed something of Havel's long-standing, deep-seated lust for being at the centre of things. Old friends began to mock his choice of Smetana's _Fanfáry_ as official muzak, and everybody — not merely those who had been politically booted upstairs or downstairs — complained about his aloofness. 'Several days ago,' recalled his loyal classmate from the King George School at Poděbrady, 'I was parking my car at Dejvice, when a presidential cavalcade suddenly came screaming down the main street. Václav was being driven home after returning from a state visit and the display of flashing lights and sirens was unbelievable. We used to laugh at such pompous displays of power in Communist times,' said his friend.'
Behind such complaints was the feeling, however vaguely expressed, that Václav Havel was now suffering from another illness: the kind that affects politicians who lose the art of knowing where to draw the limits and to bow gracefully out of politics, and who perforce fail to see that their political careers often end in tatters. After the break-up of Czechoslovakia, in the autumn of 1992, he clung to the role of the presidency, telling friends who visited him at Hrádeček that the Czech Republic needed a monarch-like symbol of continuity with the immediate past.Now, it was as if Havel was simply afraid of leaving politics, that his ego was now dependent on retaining office, that the advice of the banished Lord Belarius (in Shakespeare's _Cymbeline)_ applied well to him personally: 'The art o' the court / As hard to leave as keep, whose top to climb / Is certain falling, or so slipp'ry that / The fear's as bad as falling.' The impression that he was fearfully clinging to power — the perception that the once-beneficial _pharmakon_ of political power was now wearing off and producing pernicious effects — was certainly reinforced when Czech audiences watched with amazement as Havel did public battle over restituted family property with his sister-in-law, Ivan's wife, the mathematician Dagmar, who was the co-owner of the art deco extravaganza, Lucerna Palace, built by the President's grandfather earlier this century. The dispute quickly turned nasty, and the President decided to put the case in the hands of one of his advisers, former Communist Prime Minister Marián Čalfa. He turned out to be a legal consultant to a large firm with rumoured arms-trading connections, the Chemapol Group, which before going into liquidation in February 1999 then proceeded to buy out the President's share. The whole deal had a whiff of crony capitalism about it — and it felt to many that it was quite at odds with Havel's long-standing commitment to the ethical principle of living responsibly in the truth. The Lucerna dispute was compounded by the growing feeling, more or less vaguely expressed by growing numbers of journalists, politicians, office workers, young people, taxi drivers, that the Havel presidency was no longer (as is said in America) agenda-setting, that it was fast losing its sense of mission, dynamism, openness, its enthusiasm for the people.
More and more citizens began to conclude that it was a lame-duck presidency. The wise noted that Havel's career as a playwright was for ever destroyed. 'Is there no play,' he may have continued to muse, 'To ease the anguish of a torturing hour?'During a visit to Oxford in the mid-autumn of 1998, he said that he'd like to get back to drama, to write 'an absurdist play'. But the sad reality was that Havel, even if he still had the time and inclination, could not return to the world of theatre without being dogged by controversy. Other citizens began to say that his presidency displayed too much will power and too little won't power, that it no longer had much to do with the precept (emphasized in Oxford) that the politician 'should humbly look for the truth of this world without claiming to be its professional owner'. Others lamented the simple lack of courtesy of the presidency. A not untypical example, one that annoyed quite a few people, resulted from the promise by Havel's office that he would personally attend the fiftieth anniversary of the founding of his old school at Poděbrady. Although the organizers of the event arranged everything around Havel, and even though they hosted two visits beforehand by a squad of security agents, he let everybody down. At the very last minute, he sent an apology with a curt alibi that wasn't believed by anybody. Worst of all, growing numbers, in all walks of life, began to say that the presidency was publicly inaccessible — much more so and differently than during the early months after the revolution. Instead of the Castle coming closer to the people, Havel's critics said, it appeared to be drawing away into its own world, leaving the people behind and underneath, as if in a Kafka novel, where the Castle is permanently inaccessible. 'You cannot greatly influence the Castle's intentions any more,' commented one of his former trusted colleagues, choosing his metaphors with care. 'Havel's priorities are set so precisely and firmly that you cannot influence them. He is surrounded by courtiers _[dvo řané]:_ men and women who serve _auf dem Hof des Monarchs,_ courtiers whose job is to serve the King.'
Some of his harshest critics, speaking from experience, extended the point. Havel's courtiers, they said, were busy performing a variety of tasks. 'Good morning, sweet lord! How dost thou, good lord?' said the courtiers. They cooked his food, tailored and ironed his clothes, arranged his schedules, cut and blowdried his hair, put cushions behind his back, fitted slippers on his tired feet, as it were. But these same courtiers found that their utter dependence on the monarch was not negotiable. Naturally there was rivalry among them to get close to him. Eager to have him for themselves, they displayed the bad habit of boasting about how often they saw him. That bad habit had been noted during the first Havel presidency, but in the changed circumstances of this bad period, the habit had perversely image-damaging consequences: the more the courtiers struggled to have his ear, the more they became dependent upon the monarch — and the more he became dependent on lackeys as reality-definers and protectors. The courtiers' job was not to criticize him by flinging fresh ideas and opinions at him, for if they did that they risked confusing or irritating the monarch, for which they would then get the sack. No, Havel's critics said, the paltry job of the Castle courtiers was to confirm his intuitions and judgements. He consequently became cocooned in their words, smiles, nods, soundbites and press releases. The courtiers became mirrors to his reality, even to his vanity and — unfortunately for the monarch — they could not do differently. The mirrors became incapable of reflecting any other reality. Soon the King, who began to resemble a mirror of his mirrors, lived in a house of mirrors.
During this period of bodily illnesses and political decline, there were undoubtedly crowning moments Not all the water in the rough, rude sea of politics could wash the balm from the anointed King. Havel's success at playing the game of offering himself to the people for re-election — the reality was that he wanted the presidency at any price — and his subsequent re-election in late 1997 by the slimmest of parliamentary majorities to another term of office, despite brushes with death, was one example. Another was the skilful outmanoeuvring of his chief political enemy, Václav Klaus. Havel's splendid speech in defence of 'civil society' to the Czech parliament in early December 1997 also counted as an important highlight. And of greatest significance, and undoubtedly a big personal triumph, was the decision of the Czech parliament to back entry into NATO, despite rancorous criticism of his own long-standing support for that policy; and (in March 1999) the standing ovation given him by the French Senate after urging the creation of a federal Europe with a two-chamber parliament modelled along the lines of the American Congress.
Supporters and friends capitalized on these achievements. Acknowledging the political threats to his authority, they found time to regroup, to remind the world of the high stakes of his decline. 'Havel's one of the Czech Republic's best exports — along with Škoda cars, the Charles Bridge and pilsener beer,' said the wags. 'He is our best political asset,' said the more serious-minded lionizers. 'Whatever mistakes he's made, we have to support him. We'll otherwise not make it into the European Union — and end up with someone like Václav Klaus as our next president.' Such remarks, designed to touch up his fading image, made plain, at home, that Havel's authority was no longer naturally charismatic, and that it had to be fought for politically. For the bitter truth was that the events following his first illness, like dripping acid, had conspired to tarnish and corrode his political and moral authority. Havel-hunting had become a sport. It was almost as if Václav Havel were once again becoming a dissident.
The trend was anticipated by his old friend Adam Michnik, the distinguished Polish intellectual and publisher. 'A charismatic leader initially wields almost metaphysical power,' he said, mentioning Havel in the next breath. 'His entitlement to authority springs from the past: it is he who has worked the miracle, it is he who toppled dictatorship and brought about freedom. But this charisma is apt to fade under democratic conditions. No more miracles happen and the leader of an anti-Communist movement turns into a normal man marked by human weaknesses... At this stage,' Michnik added, 'the charismatic leader becomes a caricature of himself.' Shortly before Havel became first President of the Czech Republic, Michnik pursued the same point. 'Vašek,' he said, 'it's all very well riding high on applause and acclamation. But what will you do, how will you feel, when the clapping stops and the hissing and heckling begins?' That was a good question, to which Havel seemed no longer to have any good or surprising answers. Perhaps the only person suitably qualified to reply, if only he could, was the figure of death on the enchanting medieval clock in Prague's Old Town Square. Every hour, it shakes its head in disagreement with men's follies, for it knows that, come what may, time and the hour run through the roughest day.
So the Prague tragedy gradually unfolded. For the first time, voices here and there could be heard to whisper that the rule of the monarch-like Havel was perhaps coming to an end, and that the country would soon be on its own. 'Havel was the man who was able to stage this miracle play,' remarked his friend and Deputy Foreign Minister, Martin Palouš. 'The sacrifice was to cast himself in the lead role.' There were moments when Havel seemed to agree, as when he confessed that the Czechs' growing mood of despondency was perhaps inevitable, 'even if the country were ruled jointly by Pericles, Jesus Christ and Buddha'. Other voices suggested for the first time that his departure might be a positive challenge to Czech political thinking, political culture, and the political institutions themselves. A few even said openly that Havel had trapped the country's political class in a vicious circle: the longer he stayed, the more difficult it was for potential 'fresh blood' presidential candidates to surface. The probability seemed high that with the passing of time such whispers would grow into conversations, then into raised voices, even transformed into loud calls for his resignation. A small country in the heart of Europe was slowly learning that modern media coverage does not suffer either fools or heroes gladly... and that hubris gets rough treatment in a democracy.
### **The Gift of Death**
Death and dying: two nasty little words that send shivers down the spines of most people. The word dying means the declining capacity to make a mark on the world; it means growing isolation from others, pain, embarrassment, eventual extinction. The word death means the opposite of birth. It is the endpoint of dying, the moment at which the power of the living individual is finally extinguished — once and for ever. For most people, this endpoint of life is exactly as Thomas Hobbes described it more than three centuries ago — 'a perpetuall and restless desire of Power after Power, that ceaseth only in death.' Death — in the Christian world at least — is a blackened and lonely event filled with sobbing, brave speeches, dirge, mourning, loss. Death is exhaustion, melancholia, sadness, guilt. Death is no laughing matter; it is solemnity, for around the dying and the dead wit and laughter are unseemly, if only because death means nothingness. There are of course many ways of dying. But from this conventional standpoint there is only one end result: you are no more, you are no longer to be found anywhere, you are dead.
The popular understanding of death as the extreme borderline of power is not quite right. It correctly grasps that the lonely process of disappearing from the face of the earth ends in nothingness. But by treating dying and death as _a fact_ of life it overlooks their inescapably _political_ dimension. All individuals, presidents and other authority figures included, are confronted with the task of coping personally with their own effacement through death. Dead people have no troubles, but dying and death are inescapable problems for the living. Their resolution requires more than simply working through the gentle and painful sadness of disappearance from the company of others. That is the easy part. The task of coping with death — as Havel's friend Jan Patočka consistently taught — is much more and above all a matter of individuals cultivating _responsibility_ for their own death. This follows from the fact that everywhere, and at all times, death stalks life. 'Life as a self-respecting human being wouldn't be what it is unless it was constantly accompanied _[provázet]_ by death,' Havel told a television interviewer curious about his recent introduction to the Czech edition of _The Tibetan Book of the Dead (Bardo Thötröl)_. 'We know about death. We know that we all die, and that this [knowledge] distinguishes us from other beings,' he continued, before drawing his key conclusion: 'The individual must first of all think about if and why s/he either acts only within a given time on earth or tries to behave, as Masaryk said, _sub species aeternitatis,_ that is, reckon upon eternity when acting, as if everything is being recorded and evaluated _[zhodnocen_ í], and as if each one of our actions may or may not be an event that can for ever change the universe.'
Havel's remark was astute. Death is indeed the constant companion of life, and never more so than during the act of dying, when a certain measure of freedom can be exercised\by individuals. They may choose not to exercise this freedom, but in every case they are called upon to take it upon themselves _(auf sich nehmen_ as the philosopher Martin Heidegger puts it) to decide how they are to die and what their death means. Their death is always their own death — each is forced to speak in the first-person singular of 'my death' — which means that no one can step into their shoes and act out their role in the drama of dying. When individuals seek to do that — by passing on their powers to a doctor, for instance — they in effect refuse to explain themselves, to answer for their thoughts and actions before others. They act irresponsibly. They suppose or pretend that they cannot look death straight in the face. They stop 'practising for death' (as Socrates put it in Plato's _Phaedo)._ They give up wrestling with the basic problem of making judgements about how best to die. They do not receive the rich gift of death — the power to give life to the process of dying, to prove, in the face of impossibility and defeat, that it is possible to exercise vigilance over oneself in the presence of others.
From the time of his sixtieth birthday, when his health began rapidly to worsen, Havel found himself in the company of five of the country's past presidents, each of whom was squeezed between the imperative to act responsibly in the face of bodily death and the choice to carry on as President of the body politic. There were moments, for instance immediately after part of his lung was removed, when death was much on his mind — so much so that he secretly instructed a friend to prepare a tombstone for him, to be placed when the time came in the family crypt, located in the fourteenth arcade in Vinohradský cemetery. There were other moments when he confided that his body was too worn out for the presidency. His friend Jaroslav Šabata recalled accompanying him on a flight to Berlin to meet President Herzog and German ex-dissidents in November 1996, just before lung cancer struck. 'Havel was lying back one seat in front of us. He had a mild temperature,' Šabata noted. 'He thought it was flu — he didn't yet know what was going on. He was free and relaxed with his thoughts, both personal and political. At one point, like a bolt from the blue, he leaned over to us and whispered, "I've had enough of this presidency." He said it very expressively.'
A similar remark, using different words, slipped out into public eighteen months later, thanks to a tiny microphone hidden by journalists within a forest of large microphones and television cameras. In early June 1998, the ill-looking, ashen-faced Havel was recorded as saying that he was 'fed up with everything' — including his lazy office staff, journalists, and the political situation in general. The _faux pas_ caused him some public embarrassment. It even forced him to field questions on Czech television about whether he was giving consideration to his own 'abdication' _(abdikace)._ 'I can imagine that I would abdicate if my struggles against death, illnesses and operations went on indefinitely. But...' He paused, breathing heavily. 'I don't think I would abdicate because I became fed up... A characteristic of democracy is that governments are changed through elections, and that means that the president sometimes finds it easier to work with elected leaders than at other times.' Pressed by his television interviewers, he said that he had abdicated only once in his career — during the break-up of Czechoslovakia, when his role as the elected President sworn to uphold the country's federal constitution prevented him from signing legislation that would split the state. He went on to reiterate that he could not see any 'serious political reason' why he should now abandon his post. 'The only reason may possibly be my health,' he added. Sitting in a golden chair, dressed in a smart summer suit and tie, speaking often with his hands, the double-chinned President went on to confess that he was greatly bothered by his decline, that he understood that the absence of health is the same as the acute consciousness of having a mortal body: 'During the whole of my life, I've not been interested in my body,' he commented. 'I took it for granted that it was something like a natural carrier of my personality and spirit. It was in prison, when suffering from chronic pneumonia, that I noticed for the first time that I had a body. I was half-dead, and because of that they released me early. Since 1996, I've again had to realize that I have a body, and that I have to look after it. It's a novelty for me. I admit that it's hard to get used to.'
Public and private confessions of mortality were not especially typical. Something odd about the early winter life of President Havel is that he preferred to sing swan songs into the ears of death. Words like dying and death seemed to get smothered in elaborate denials, or to have no meaning at all. The more laden with illness he became during the course of the year 1998, the more he appeared officially to presume death to be a distant, quite unlikely event. Perhaps conceit always works strongest in the weakest bodies. Perhaps he was simply unused to not getting his way. Or perhaps his life had become such a habit that he no longer knew or cared what death was, or even that he had become unsuited for death. One afternoon, he paced nervously in circles around his seated physician, demanding an instant cure for all of his aches and pains, physical and spiritual. 'Would that I could change the weather, Mr President,' replied the physician respectfully, mocking his conceit. Havel's denials in public were equally forceful. When replying to journalists' questions about his deeply uncertain health and political future, the President consistently brushed aside the implication that he may have to 'abdicate'. In hospital, several times at the edge of the abyss, he reacted in exactly the same way. 'Václav Havel seems always to be above his illness,' remarked his Austrian surgeon, Professor Ernst Bodner. 'Václav Havel is probably the only patient who cannot wait to have his next operation,' he added. Less restrained before journalists than Czech doctors, the grey-haired, golf-loving Professor Bodner was unusually frank in describing Havel's hospital behaviour. 'Václav Havel has a very strong will, and that sometimes complicated life for us,' he said. The impatient Havel always got upset when something didn't happen at the right moment, but otherwise he acted like a man of iron fully prepared from within for everything. He insisted that stitches from his neck be removed without anaesthetic. Immediately after operations, after coming out from the narcosis, he always insisted on drinking wine, despite firm resistance and quiet protestations from the professor. Havel also clamoured several times against his confinement within the intensive-care unit. 'I feel as if I am in prison,' he grumbled. Professor Bodner balked. He explained that it was imperative that he stay in the unit. Bodner pleaded with Havel to help the team of doctors promote his full recovery. 'How long do I have to stay here?' snapped Havel. Bodner hesitated, then stated quietly, holding his breath, that it would probably be two days. 'Promise!' snapped Havel again. The professor didn't have a chance, and two days later, when he came to examine Havel, he was greeted instantly with the words: 'We're moving today.'
Havel was discharged from Prague's Central Military hospital on 28 August 1998, more than a month after undergoing yet more abdominal surgery, this time with numerous post-operational complications. After undergoing an operation on 26 July to remove a colostomy attached five months earlier to his lower intestine, he developed respiratory problems a week later while recuperating. Doctors performed a tracheotomy — the fourth in two years — that is, they inserted a tube into a hole made in the chain-smoking President's trachea to enable him to breathe. The next day, Havel's heart began to beat fast and irregularly. It took about two hours — using electrical shocks administered to his heart — to return his heartbeat and blood pressure to around normal. By then the beginnings of bronchial pneumonia had been spotted, and Havel was heavily sedated and forced to rest. Eventually, three weeks later, after slow but gradual improvement, the tube stuck in Havel's throat was removed, and the incision (reported Havel's personal doctor, Ilja Kotík) spontaneously closed. Everybody remained upbeat. Boris Štastný, one of the President's medical team, told the news agency ČTK that the surgery to remove a cancerous tumour from Havel's right lung in December 1996 had been completely successful, and that his lungs were now in 'perfect shape'. The odd reassurance resembled a scurvied ship's surgeon congratulating himself on sparing the whole crew from food poisoning. It was backed up with Professor Bodner's verdict that the ups and downs of surgery had drawn himself, the President and his wife together like a family. Then came the slicker words of the President's senior political adviser, Jiří Pehe. 'He's on top of things,' said Pehe, adding that in preparation for his planned trip to the United States on 15 September, the bed-ridden President Havel had carefully monitored Czech and world events — and had even commented publicly on the thirtieth anniversary of the Soviet invasion of Czechoslovakia.
Meanwhile, on the streets and around pub and kitchen tables, the spreading talk of Havel's bodily demise proved that many Czechs were wiser and more open than their President about the subject of death. Many familiarized themselves quickly with new words like bronchopneumonia and arrhythmia and kept track of the latest medical reports and complex details of procedures like tracheotomies and the removal of colostomies. Most of the big medical questions: 'Do his doctors know what they're doing?' and 'Is he dying?', and several large political questions: 'Should such a sick man carry on as President?' and 'Is anyone talking about a successor?' were repeatedly raised and dissected, answered and disputed before finding themselves relegated to a limbo of cautious indecision. Other citizens laced words with black humour that revealed the simple fact that nothing more than death was at stake. 'Do you know why Havel ran for President again last year?' went one of the most popular jokes. 'Because if he weren't at the Castle, he'd already be in Olšany cemetery!'
Dark humour often unnerves. It forcibly reminds individuals that they alone of all living beings _know_ that one day they shall not exist as individuals. Dark humour plays on their sense of the uncanny. It exposes the familiar way in which individuals process their strong childhood anxieties about dying by imagining themselves to be immortal. Dark humour reveals that death and dying are not subjects that the living like to contemplate, even in the healthiest moods. This golden rule applies especially to politicians and heads of state. They happen to be busy beings who can rarely, if ever, spare a moment's thought to the 'meaning' of anything that is basic, let alone to the process of dying. Always on the run, they often consider talk of their dying, or their need for urgent medical treatment, to be exaggerated, as Havel himself did when rejecting the advice of doctors to undergo further treatment. Politicians, and especially heads of state, are also prone to dismiss the subject of their own death because the considerable power they exercise over others seduces them into believing that they have full power over themselves. Like everybody else, they aspire to further life, to additional sums of being; but the thought that everything that individual human beings do and achieve ultimately turns against them seems far from their minds. Their lives are full of public attention and admiring glances. They swagger around their worlds; act self-confidently in the face of adversity; and often behave in defiant and domineering ways. Political success tricks them into presuming that the moment will never come when they will be unable to take a step in any direction, when literally nothing more will be possible.
That presumption is nourished by the certainty that simply by achieving the highest office they have achieved fame and therefore a certain form of immortality. They are treated as special beings endowed with god-like tendencies. Heads turn and bodies bow whichever way they walk. They reciprocate by playing the peacock to perfection. They bathe constantly in the halogen of televisual publicity. They appear on websites and — like Havel — have large and elaborate ones of their own. Print journalists write endlessly about them. Even the art of biography – one of whose many possible effects is to turn them into smouldering volcanoes, to lift them out of time and confer upon them a form of immortality by preserving their lives in words and pictures — helps them to forget that they live close to their skeletons. From time to time, famous political figures may wonder whether their fame resembles a gift of pearls that triggers self-doubts about their genuine or cultivated qualities. The wiser among them know that fame can be cruel by bringing loneliness, jealousy and dispute their way. But even those politicians whose fame proves short-lived feel their fame to be a glass that magnifies their power and rescues them from the oblivion of Vulgar death'. So they tend to become incapable of seeing themselves except from the inside. They think of themselves as necessary, even indispensable. They feel themselves to be an absolute reality, as a whole, as the whole... as therefore a being who _is_ God.
Enter the compulsory fact that each individual must learn to be the loser, and the corresponding question of whether or not the individual chooses to act responsibly in the face of death. The undeniable misfortune of an ageing and unwell head of state like Havel was that despite all appearances and denials to the contrary he was forced to observe at close range the slow but methodical degradation of his organs. Each extra day of his life saw him lose ground. His body gradually gave him the slip. One by one, sometimes obviously and otherwise discreetly, his organs took their revenge upon his power by detaching themselves from his body. It was as if they escaped from him and no longer belonged to him — that against his own orders his heart and lungs and bowels turned traitors, committed acts of indefinable treachery that were impossible to denounce or arrest, since they stopped at nothing and put themselves in no one's service. Such treachery threatened to turn him into a flesh-and-blood ghost and forced him in turn to reconsider his strong yearning to ignore death. Dying confronted Havel with the utterly personal problem of coming to terms with his own demise — with solving the insoluble problem of needing to reconcile the feeling of being everything with the evidence of becoming nothing.
The problem of how to square the power of dying sovereigns with the jagged fact of their own eventual powerlessness is especially pertinent in contemporary parliamentary democracies, including the unconsolidated Czech kind. Had Havel lived like a king in early modern times, the subject of death would have been much less troubling to him and his subjects. Once upon a time, say during the second half of the fourteenth century in Europe, sovereign monarchs like Edward VI and Queen Elizabeth I regarded themselves as immortal. According to the famous (originally medieval) formula of a _rex qui nunquam moritur,_ a 'king that never dies', every regal head of state is at the same time a flesh-and-blood mortal and the indestructible embodiment and head of the political community. Just like the body of Jesus Christ, the monarch has two bodies. One of them is visible, individual and mortal; the other is invisible, immortal and collective. Within the single body of the monarch, that is to say, two forms of power are melded: the power to make marks on the earthly world by means of government, and the power of the body politic, which although it cannot be seen or touched consists of all the mechanisms of law-making and government constituted, for the sake of the people and the public good, to compensate for the imperfections of the fragile human body and thus to withstand the ebb and flow of time.
This formula of the indestructible power of the monarch implied that the body politic always lives on unharmed when the body of the monarch becomes terminally ill, or suffers death by accident. Even the hands of an assassin cannot harm the body politic or the monarch. For that reason, contemporaries preferred to speak not of the _death_ of the monarch, but to use the word _demise_ to describe the process of transferring and relocating the body politic in the body of a new flesh-and-blood monarch. When the natural body of the monarch suffered demise, the body politic was reincarnated, at once and without controversy, in the mortal body of the successor monarch. Yet in a certain sense the deceased lived on too. The incarnation of the body politic in the body of the monarch did away with the problem of death; the deceased monarch never really died but — like King Henry VIII who survived for many years after the death of Henry Tudor — lived on as an immortal superbody.
Definite traces of this doctrine of the immortality of the monarch and monarchy reappeared in the totalitarian and late-socialist regimes under which Havel lived most of his life; whether called Stalin or Mao or Fidel or Gottwald, the bodily figure of the omniscient, omnipotent great leader — the Egocrat, to use Solzhenitsyn's term — towered over everybody and everything, like an invulnerable masculine body endowed with amazing strengths and talents, a mortal body which defied the laws of biological nature to attain immortality, precisely because it expressed and at the same time merged with, and drew sustenance from, the immortal body politic of the totalitarian system. So, for example, when President Klement Gottwald died in 1953, he was embalmed — like Stalin just before him — and put on display. Unfortunately, the Czechoslovak mortician, inexperienced in the techniques of embalming, bungled the job. The corpse began to rot, had to be replaced by a dummy, and eventually was moved from public view. Gottwald's fate pointed to more democratic times. For under democratic conditions, the immortality of the political body and its leader is not presumed. The body politic is split asunder permanently by the separation between the institutions of government and the myriad organizations of civil society. Within both domains, positions of power are not associated with bodies laying claim to immortality. Nobody sits on thrones. Nobody supposes themselves or others to be angelic. Nobody pretends that positions of power are properly 'merged' with the bodies of particular actors. Nothing is sacred. Everything is publicly questionable. Compared to absolute monarchies, relationships of power are disembodied and lose their sacred quality. There are no thrones. Power is not exercised by angels; often enough (it is presumed) power is wielded instead by potential or actual devils. And those who exercise power over others are considered mere mortals who occupy offices and positions temporarily, subject to good health, election and public controversy — and to removal from office.
As the twentieth century ended, the Czech Republic found itself caught up in the throes of a transition towards a disembodied presidency. Although a majority of its citizens — revealing their not-yet-democratic habits — still found it hard to distinguish between Václav Havel and the role of the Czech President, the republic and its citizens began to live in the subjunctive tense. No one quite knew what was going to happen and details of the events to come were still unknown. How long he would survive, whether he might recover, how he would die and who would succeed him couldn't be grasped. Yet one outcome was certain. The time of his state funeral was coming. A whole nation would fall silent, and so too would admirers within many other nations — from the United States of America and Canada to Russia, Japan and China. His corpse — its stubble still growing — would be expedited odourlessly and with technical perfection from his deathbed to the grave. But his death would be a global media event — on a scale much bigger than the state funeral of Masaryk.
Prague would double in size. As he lay in state in the old Castle of the Bohemian kings above the city, a queue some miles long would spring up. Mourners would wait all day, and all night, to see his body for the last time. The day of the funeral would be a public holiday. Hundreds of thousands of people, dressed in black and clutching flowers, would be seen lining the route taken by the cortège on the way to his final resting place. Huge black banners would fly from every office; his photograph, draped in black, would crowd every shop and news-stand and public place. Shared feelings of embarrassment would hold words back. Half-buried or forgotten anxieties about death would collectively resurface; fantasies of personal immortality would temporarily weaken. Around the graveside a forest of microphones, tripods, cameras, pads and pens would suddenly spring up. Obituaries, many of them written long ago and updated several times already, would appear in all four corners of the earth. Millions of words would be uttered. Many hundreds of different and conflicting points would be made. The words of the dead man (as Auden said) would be modified in the guts of the living. It would be said that he was a good man, a great man, a hero of the century. Harry S. Truman's remark that a statesman is a dead politician would be confirmed. Loud sounds of grinding axes would also be heard. His enemies would wish him good riddance. The wags would say that in democracies death is for some politicians a good career move. And through all the din of commentary and commentary upon the commentary, some wise voices would insist that one thing should be for ever remembered: that Václav Havel was a man who. had the misfortune of being born into the twentieth century, a man whose fate was politics, a man who achieved fame as the political figure who taught the world much more about power, the powerful and the powerless than most of his twentieth-century rivals.
## **Acknowledgements**
Acknowledgements — fond memories of the heart cast in words — are especially difficult to summarize in a project that stretches back nearly two decades, to the early 1980s, when I first made scholarly and political contact with the unhappy paradise called the Czechoslovak Socialist Republic. So I shall say only that I am most grateful to the many scores of people who have helped me to prepare and complete this book, especially during the past five years of intensive research and writing. For reasons of space, I cannot mention them all, although it would be wrong to let three groups of people suffer in silence the condescension of posterity.
Many individuals generously contributed their time and energy in interviews that I conducted in various countries around the world. A very few interviewees wished to remain anonymous because they personally feel too close to Václav Havel, and therefore do not wish to offend him, for instance by breaking a compact to remain silent about a certain phase of their lives together. There were others who asked for their anonymity because they felt, just prior to publication, that their political solidarity with him could be jeopardized by the book's uncompromisingly tough praise for Havel's achievements. I have naturally respected the wishes of the former small handful of people; the wishes of the latter group, consisting of only two individuals, I have accepted, with some puzzlement. Then there were those individuals who gave everything, sometimes more than once, always generously. I gratefully acknowledge the stimulating conversations with Václav Havel, to whom I explained at the outset of the project my intention to write an unauthorized biography with a difference, but without malice. His brother, Ivan Havel, understood from the beginning that the book was to be a serious work of scholarship, and accordingly gave his time and advice with great intelligence, wit, prudence, and patience. There were also many other interviewees whose comments and advice I have tried hard to incorporate in the book. They include: Rudolf Battěk; Václav Bělohradský; John Bok; Petr Brod; Karel Brynda; Barry Buzan; Ivan Chvatík; Penelope Connell; Viola Fischerová; Anna Freimanová; the late Ernest Gellner; Marketa Goetz-Stankiewicz; Vladimír Hanzel; Pierre Hassner; Dagmar Havlová; Milena Janišová; Zdeněk Jičínský; Jan Kavan; Václav Klaus; Radim Kopecký; Pavel Kosatík; Hana Ledecká; Tapani Lausti; Naděžda Macurová; Louise Mares; Adam Michnik; Stanislav Milota; František Novak; Martin Palouš; Jiří Pehe; Harold Pinter; Petr Pithart; Vilém Prečan; Adam Roberts; Richard Rose; Jacques Rupnik; Michal Schonberg; Prince Karel Schwarzenberg; Pavel Seifter; Michal Šerf; Jiřina Šiklová; Joska Skalník; H. Gordon Skilling; Josef Škvorecký; Andrej Stankovič; Olga Stankovičová; Max van der Stoel; Alois Strnad; Jiří Suk; Petruška Šustrová; Pavel Tigrid; Josef Topol; Jacqueline True; Oldřich Tůma; Jan Urban; Zdeněk Urbánek; Ludvík Vaculík; František Vlasák; Jitka Vodňanská; Phillip Whitehead; Paul Wilson; Václav Žak; and Milan Znoj.
Other individuals helped by providing invaluable materials and vital forms of technical assistance during the preparation of the book. My very special thanks are due to Derek Paton, a research assistant at the Centre for the Study of Democracy in London, and the Institute of Contemporary History in Prague. For nearly four years, he was a constant companion who tirelessly gathered documents, provided honest advice, arranged meetings and provided excellent translations, always with professional dedication, unending patience, outstanding intelligence, and lively humour. He should certainly not be implicated in any errors of judgement or public controversies spawned by the book. The British Academy's generous Fellowship is gratefully acknowledged. Gabriela Müllerová helped me improve my basic Czech and to analyse hundreds of stories and reports about Havel during a twelve-month period. Eva Skryová, Wendy Stokes, and Nancy Wood were partners in underground crime. Many staff and students at the Centre for the Study of Democracy provided indispensable help, especially Sara Amos, Patrick Burke, Bridget Cotter, Niels Jacob Harbitz, Simon Joss, Chantal Mouffe, John Owens, Richard Rose, and Richard Whitman. Many other colleagues at the University of Westminster provided invaluable support for my research work, including Professor Margaret Blunden, Professor Geoffrey Holt, Professor Keith Phillips, Professor Michael Trevan, and the Vice-Chancellor and Rector, Dr Geoffrey Copland. Some individuals generously supplied me with photographic illustrations, including Alexander Dobrovodský, Ivan Havel, Bohdan Holomíček, Martin Hykl, Jaroslav Krejčí, Tomki Němec, Magdalena Tichá, Jitka Vodňanská, Vladimir Weiss, Petr Zhoř, and the Czech News Agency. Still others have helped satisfy manifold requests, for instance by providing materials ranging from rare newspaper clippings to valuable primary source documents. They include: Timothy Garton Ash; Anthony Cantle; April Carter; Mita Castle; Vojtech Čelko; David Daniels; Marzia Ferrari; Klára Hůrková; Jan Kavan; Pavel Kosatík; Jiří Kuběna; Alan Levy; Paul Mier; Jana Nálevková; Petr Oslzlý; Jiřina Šiklová; Roger Scruton; H. Gordon Skilling; Eva Šormová; Alfred Stepan; Marketa Goetz-Stankiewicz; Viktor Stoilov; Jan Šulc; Helena Taylor; Oldřich Tůma; and Gerald Turner. For help during the past five years in translating and interpreting Havel, I should especially like to thank Paul Wilson and A.G. Brain, Derek Paton and Marzia Ferrari. In the world of publishing, I am especially grateful to Sara Fisher, Bill Hamilton, and Jim Gill at A.M. Heath; Petra Tobišková and Alexandra Panthel; and the fabulous group at Bloomsbury Publishers, especially my wise and skilled editors Liz Calder and Mary Tomlinson; and Penny Edwards, Jane Ellis, Nigel Newton; Matt Richell; and Will Webb.
The other members of my household enabled the book to reach press in numberless ways. There is no need to embarrass them by describing in detail their efforts to keep up my spirits and rescue me from gross obsessions. Rebecca Allison and Leo Lawson-O'Neil helped in more ways than they know. Big hugs and many kisses for George Keane and Alice Keane; and ditto for Kathy O'Neil, to whom I dedicate this book, with love.
## **Illustrations**
I gratefully acknowledge the generosity of those who furnished the photographs included in this book, and described below:
Following the contents page: the centre of attention, by Vladimir Weiss
Beginnings: during his first year, from the family archives
Folly: at the family gravesite, Košíře Cemetery, Prague, 1940, from the family archives.
Republicans: the Havel family strolling at Havlov, from the family archives
Devil's Playground: the javelin thrower, at Havlov, from the family archives
Zoology: 'My home, my castle!', at Havlov, from the family archives
Resistance: Miloš Havel, from the family archives
Cold Peace: Václav Havel with younger brother Ivan, on the first day he attended school, September 1944, from the family archives
Red Stars: With a Lenin hat, from the family archives
Coup de Prague: Dressed up as a musketeer, during summer holidays at Havlov, 1949, from the family archives
Flying Splinters: Božena Havlová, in the swimming pool at Havlov, from the family archives
Trials: Dressed as a Roman notable, with brother Ivan (left) and Jan Škoda (right), at Havlov, 1949, from the family archives
Thirty-Sixers: with the poet Jiří Paukert, from the family archives
Ashes on Ice: seated at a desk, with brother Ivan, in the embankment flat, Prague, September 1954, from the family archives
The Public Poet: with a cup of coffee, from the family archives
Stalin's Carcass: dressed like an eccentric family guest, at Havlov, pipe in hand, from the family archives
To Barracks: in uniform, as First Lieutenant Škrovánek, in the staged performance of Pavel Kohout's _September Nights,_ 1957-8, from the family archives
Socialist Realism: with Olga Šplíchalová, from the family archives
Garden Party: dressed for a performance at Hrádeček, 1976, by Bohdan Holomíček
The Crisis: at the Divadlo Na zábradlí, from the family archives
The Memorandum: with Arthur Miller, 1963, by Inge Morath
Summer Friendship: tie-dyed in a field of flowers, by Bohdan Holomíček
Mid-summer's Night: in London in 1968, by the _Guardian_
A Politician of Retreat: profile, in shades, from the family archives
Normalization: carrying a ladder in the orchard at Hrádeček, by Bohdan Holomíček
Late-Socialism: reading a book on the art of brewing, by Bohdan Holomíček
Beggars' Opera: the première of _Žebrácká opera,_ 1975, by Bohdan Holomíček
Charter 77: with Adam Michnik and Jacek Kuron (to Havel's left), at an illegal meeting with Solidarnošć, Krkonoše, from the Czechoslovak News Agency
Violence: reading, gramophone behind, from the family archives
Courage: as Caesar, about to die at Brutus's hand, from the family archives
The Powerless: gun-toting gangster, from Jitka Vodňanská and Alexander Dobrovodský
The Victim: clutching a bag of apples, after returning from prison, from my collection
Prison: dressed in black, smoking, from the family archives
Largo Desolato: 'All you need is love': with Olga at Hrádeček, by Tomki Němec
Temptation: 'You're Number One': with Jitka Vodňanská, on his fiftieth birthday, from Jitka Vodňanská
Cliff-Hanging: with whisky bottle, during an interview with Erica Blair, November 1986, by Gerald Turner
Revolution: at a Civic Forum meeting, by Jaroslav Krejčí
Velvet Power: Waving to a giant crowd from the balcony of the Melantrich building, Wenceslas Square, from the Czech News Agency
Machiavelli: facing Alexander Dubček, Ruzyně Airport, 1990, by Tomki Němec
A Crowned Republic: with tailors, Prague Castle, 1990, by Tomki Němec
Te Deum Laudamus: Olga and Václav on their knees in St Vitus's Cathedral, by Petr Zhoř
Fun and Games: with the Rolling Stones, Prague, 18 August 1990, by Tomki Němec
The Manipulator: watching himself on the BBC, Lány, 1990, by Tomki Němec
Defections: reversing his BMW at Lány, by Tomki Němec
Parliament: before a joint session of the US Congress, with Vice-President Dan Quayle and Speaker of the House of Representatives, Congressman Thomas S. Foley, 21 February 1990, by Tomki Němec
Lustration: in shades, guard in background, by Martin Hykl
Market Power: with Václav Klaus and Prince Karel Schwarzenberg, by Tomki Němec
Velvet Divorce: informing the Speaker of the Federal Assembly of his resignation, 17 July 1992, watched by Pavel Tigrid, by Tomki Němec
Oh Europe!: with Umberto Eco and Olga, on Capri, by Tomki Němec
Metamorphosis: with Dáša Havlová, by Tomki Němec
Death: on the beach at Cabo da Roca, in Portugal, 14 December 1990, by Tomki Němec
## **Guide to Czech Pronunciation**
Czech is a phonetic tongue, and that means that it is pronounced as it is written. The main stress of a word is always on the first syllable. The following brief guide to pronunciation should satisfy most demands of this book:
Vowels:
a | as in _pub_
---|---
á | as in _carp_
e | as in get
é | as in today
ě | as in yellow
i or y | as in sit
í or ý | as in peat
o | as in got
u | as in look
ů | as in cool
Consonants:
c | like the _ts_ in rats
---|---
č | like the _ch_ in chubby
ch | like the _ch_ in loch
g | like the _g_ in god
h | like the _h_ in had
j | like the y in yoke
r | like the _r_ in ripe, but rolled
ř | similar to the _rsh_ in Pershing, as in Dvořák
š | like the _sh_ in shop
ž | like the _s_ in pleasure
### Footnotes
Cited in _Vaclav Havel: A Czech Drama,_ a BBC documentary programme in the Bookmark series (London, 1987).
The postcard, dated 11 October 1936 and signed by Alice Moraweková and others, is reproduced in _Václav Havel 97_ (Prague, 1998), p. 7.
Václav Havel, _Letters to Olga._ June 1979-September 1982 (New York, 1988), p. 180.
The guide, written by an Honorary Foreign Member of the Masaryk Academy of Work, Gerald Druce, is entitled _In the Heart of Europe. Life in Czechoslovakia_ (London, 1936).
_In the Heart of Europe,_ op. cit., p. 166.
_In the Heart of Europe,_ op. cit., pp. 222–223.
M. de Vattel, _Le droit des gens, ou principes de la loi naturelle_ (Leiden, 1758), p. 6.
See 'The Hossbach Memorandum', in _Documents on German Foreign Policy 1918–45_ (London, 1949), series D, i, pp. 29–30.
Keith Feiling, _A Life of Neville Chamberlain_ (London, 1946), p. 367.
See Igor Lukes, _Czechoslovakia between Stalin and Hitler. The Diplomacy of Edvard Beneš in the 1930s_ (New York and Oxford, 1996), especially chapters 5–; and Boris Celovsky, _Das Münchener Abkommen 1938_ (Stuttgart, 1958).
Nevile Henderson, _Failure of a Mission, Berlin 1937-1939_ (New York, 1940), p. 163.
Compare the classic account of the earlier breakdown of the Weimar Republic — the ways in which it passed sequentially through the phases of loss of power, power vacuum, and the takeover of power — presented by Karl Dietrich Bracher, 'Auflösung einer Demokratie: Das Ende der Weimar Republik als Forschungsproblem', in _Faktoren der Machtbildung,_ ed., Arkadij Gurland (Berlin, 1952), pp. 39–98.
Cited in Vojtech Mastny, _The Czechs Under Nazi Rule. The Failure of National Resistance, 1939-1942_ (New York, 1971), p. 23 (translation altered). See also F. Lukeš, 'K volbě Emila Háchy presidentem tzv. druhé republiky', _Č asopis Národního musea,_ Social Science series, CXXXI (1962), pp. 114–120; and Hácha to Beneš, 10 December 1938, in Edvard Beneš, _Memoirs of Edvard Beneš: From Munich to New Year and New Victory_ (London, 1954), p. 97.
See 'Před nástupem mladých' (a speech in March 1933) and 'Barrandovská skupina' (minutes of a discussion group convened at Havlov, 24-28 May 1933) in V. M. Havel, _Mé vzpomínky_ (Prague, 1995), pp. 229–247 and 247-260.
_Mé vzpomínky,_ op. cit., p. 16.
Ibid.
_Mé vzpomínky,_ op. cit. especially parts 1,3.
From an interview with Václav Havel in the television programme, 'Pracovat a nezatrpknout', directed by Dita Fuchsová, Česká televize (21 February 1999).
Václav Havel in 'Pracovat a nezatrpknout', op. cit.
All quotations in the following passages are taken from Václav M. Havel, 'Barrandovská skupina', in _Mé vzpomínky,_ op. cit., pp. 247—260.
Wilhelm Keitel, _The Memoirs of Field-Marshall Keitel_ (New York, 1966), p. 79.
Karl Megerle, 'Deutschland und das Ende der Tschecho-Slowakei', _Monatshefte für auswärtige Politik,_ VI (1939), p. 770.
_Documents on German Foreign Policy, 1918-45,_ Series D, volume 4 (Washington, 1949-1958), p. 270.
Vít Vinas, _Jan Nepomucký, česká legenda_ (Prague, 1993), p. 69; and the fine study by Robert Pynsent, _Questions of Identity. Czech and Slovak Ideas of Nationality and Personality_ (Budapest, London and New York, 1994), pp. 190–196.
The following draws upon Vojtech Mastny, _The Czechs under Nazi Rule,_ op. cit., Detlef Brandes, _Die Tschechen unter deutschem Protektorat,_ volume 1: 1939-1942 (Munich, 1969); Sheila Grant Duff, _A German Protectorate: the Czechs under Nazi Rule_ (London, 1942); Callum MacDonald and Jan Kaplan, _Prague in the Shadow of the Swastika: A History of the German Occupation 1939-1945_ (Prague, 1995).
William Shakespeare, _Troilus and Cressida,_ Act 1, Scene 3.
Jean _Améry, Jenseits von Schuld und Sühne_ (Stuttgart, 1977), p. 67. Compare also the insightful work by Wolfgang Sofsky, _Die Ordnung des Terrors Das Konzentrationslager_ (Frankfurt am Main, 1993), especially part 1.
See Günther Deschner, _Heydrich: the pursuit of total power_ (London, 1981); and S. Aronson, _Reinhard Heydrich und die Frühgeschichte von Gestapo und SD_ (Stuttgart, 1971).
The description is provided by the Nazi jurist and SS member, R. Höhn, in an obituary printed in the _Deutsche Allgemeine Zeitung_ (13 June 1942) and quoted in Ernst Kohn-Bramstedt, _Dictatorship and Political Police. The technique of control by fear_ (London, 1945), p. 160.
Gerhard Ritter ed., _Hitlers Tischgespräche im Führerhauptquartier, 1941/1942_ (Bonn, 1951), p. 91; second edition (Stuttgart, 1963), p. 363.
Ibid., pp. 85, 91,176-177,288; second edition, pp. 349, 359, 363, 434-435. Heydrich's hardline speech of 2 October 1941 is reproduced in Václav Král, _Die Vergangenheit warnt. Dokumente über die Germanisierungs und Austilgungspolitik der Naziokkupanten in der Tschechoslowakei_ (Prague, 1960), pp. 121–132.
Ladislav Fuks, _The Cremator_ (London, 1984).
Emanuel Moravec published several booklets, including _Tatsachen und Irrtümer. Der Weg ins neue Europa_ (Prague, 1942). He committed suicide on 5 May 1945.
See Albin Eissner, 'Die tschechoslowakische Bevölkerung im Zweiten Weltkrieg', _Aussenpolitik,_ 13 (1962), pp. 328–334; Waller Wynne, Jr., _The Population of Czechoslovakia_ (Washington, 1953), p. 44, table 3; and Helena Krejčová and Jana Svobodová (eds.), _Postavení a osudy židouského obyvatelstva čechách a na Moravé v letech 1939-1945_ (Prague, 1998), p. 7.
These points are based respectively on _Mé vzpomínky,_ op. cit., and an interview with Jiřina Šiklová in Prague, 19 September 1996.
From a letter to his parents written during the Christmas period 1917, cited in _Mé vzpomínky,_ op. cit., p. 54.
Interview with František Novák, one of his oldest surviving friends, London (7 February 1997).
_Mé vzpomínky,_ op. cit., p. 53.
_Mé vzpomínky,_ op. cit., p. 64.
Leni Riefenstahl, _The Sieve of Time. The Memoirs of Leni Riefenstahl_ (London, 1992), p. 297.
Cited in _Prague in the Shadow of the Swastika,_ op. cit., p. 154. The article appeared in _Filmový kurýr_ (24 March 1939).
Quoted from the letter of Miloš Havel to the Minister of Information Václav Kopecký, 9 July 1945, reprinted in _Mé vypomínky,_ op. cit., pp. 93–94.
_Mé vzpomínky,_ op. cit., p. 92.
See the account of his attempt to rebuff the false information, ibid., pp. 90–91.
_Mé vzpomínky,_ op. cit., p. 65.
Miloš Havel to the Minister of Information Václav Kopecký, 9 July 1945, reprinted ibid., p. 94.
From an undated two-page report, written by Václav Havel and entitled, 'Konec války na Havlově', reprinted in _Václav Havel '97_ (Prague, 1998), pp. 124—125.
_Mé vzpomínky,_ op. cit., p. 65.
See the fragments from the years 301—60 B.C. by Diodorus Siculus, _The Historical Library_ (London, 1700), pp. 752-753, book XXV.
Kopecký's allegations are carefully listed in the letter of Miloš Havel to Václav Kopecký, 9 July 1945, reprinted in _Mé vzpomínky,_ op. cit. pp. 88–95. Kopecký told Miloš Havel (ibid., p. 93) that he had written a paper on the negotiations with the Nazis of 'those Havels'; unfortunately, its existence remains unproven, and its whereabouts are unknown.
See Miloš Havel's 'Report Dated 24 April 1946', reprinted in ibid., p. 100.
_Mé vzpomínky,_ op. cit., p. 66.
Interview with Radim Kopecký, Prague, 5 November 1998. Radim Kopecký, son of the former Czechoslovak Ambassador to Switzerland, was unrelated to Miloš Havel's enemy, Václav Kopecký.
_Mé vzpomínky,_ op. cit., p. 72.
Interview with František Novák, London, 7 February 1997.
See _Mé vzpomínky,_ op. cit., pp. 72–73: 'Miloš's escape cheered us, but it brought us hard times. By October 15th, we had to move out of our flat [on the Vltava embankment] where we had lived for forty-seven years. We found out as well that Havlov was sealed. The StB [secret police] in Brno wrongly presumed that Miloš was a co-owner of Havlov.' Until Havlov was reopened, Václav and his family had no option but to stay in Prague in the fourth-floor studio apartment previously owned by his maternal grandfather, who had died two months earlier.
The Czech National Socialists won 18 per cent, the People's (Catholic) Party 16 per cent, and the Social Democrats 13 per cent; and the Slovak Democrats, who won a clear majority (61 per cent) of the votes cast in Slovakia, gained an overall 14 per cent. But easily the lion's share of the aggregate vote was captured by the Communist Party, which won 38 per cent of the poll (40 per cent in Bohemia and Moravia and 30 per cent in Slovakia). See Hugh Seton-Watson, _The East European Revolution_ (New York, 1961), p. 182.
See the accounts provided by Karel Krátký, 'Czechs, the Soviet Union and the Marshall Plan', in O. A. Westad, _The Soviet Union in Eastern Europe 1945-1989_ (New York, 1994), pp. 9–25; Karel Kaplan and Vojtěch Mastný, 'Stalin, Czechoslovakia, and the Marshall Plan: New Documents from Czechoslovak Archives', _Bohemia,_ volume 32, 1 (1991), pp. 133–144.
Hubert Ripka, _Czechoslovakia Enslaved_ (London, 1950) provides a detailed account of the events from the losing insider's point of view.
_Foreign Relations of the United States,_ volume 4 (US Department of State, Washington, DC, 1948), pp. 741-742.
See Nina Pavelčíková, 'Pozoruhodná osobnost Hugo Vavrečky', _Lidové noviny,_ 6, 129 (6 June 1993); and Hugo Vavris, _Život je spís román_ (Ostrava, 1997), especially part 1.
Some background details are drawn from my several interviews with Václav Havel's brother, Ivan Havel, especially the one conducted in Prague, 23 April 1996. His brief account of the primary school is found in 'School for the Curious', in _Open Eyes and Raised Eyebrows,_ manuscript (Prague, 1997), part B, pp. 92–94.
_Story_ (Prague), 30 September 1998, p. 7.
Interview with Ivan Havel, Prague, 24 September 1997.
Václav Havel to his father, Havlov, 9 March 1947.
The following details are drawn from an interview with Havel's classmate at Poděbrady, Alois Strnad, Prague, 28 September 1997.
The scene is recalled in Paul (Pavel) Fierlinger's animated autobiography, _Drawn from Memory_ (Acme Filmworks, PBS American Playhouse, 1998), in which voice-over commentary by Havel himself is used.
Miloš Forman and Jan Novak, _Turnaround: A Memoir_ (London and Boston, 1994), pp. 55–56.
Ibid., p. 57.
_Lidové noviny,_ 1 April 1998, p. 4.
Interview with Viola Fischerová, Prague, 26 September 1997.
See the StB file mentioning 'the very damaging ideological activity' of Professor J. L. Fischer, in František Koudelka, _Státni bezpe čnost 1954—1968_ (Prague 1993), p. 146.
Cited in Josefa Slánská, _Report on My Husband_ (New York, 1969), pp. 4—6. The following account draws upon several works of varied quality, including Miriam Slingová, _Truth Will Prevail_ (London, 1968); Karel Kaplan, _Die politischen Prozesse in der Tschechoslowakei 1948-1954_ (Munich, 1986); Artur London, _The Confession_ (New York, 1971); and the two works by Eugen Loebl, _My Mind on Trial_ (New York, 1976) and _Die Revolution rehabilitiert ihre Kinder_ (Vienna, 1976). An important source, originally published in English, is Jiří Pelikán, _The Czechoslovak Political Trials, 1950-1954: The Suppressed Report of the Dub ček Government's Commission of Inquiry, 1968_ (Stanford, 1971). I have also consulted the transcript of Prague Radio broadcasts in the files of Radio Free Europe, _Trial of Rudolf Slánský_ (Munich, 1952).
Hannah Arendt, _Essays in Understanding, 1930-1954,_ ed., Jerome Kohn (New York, San Diego, London, 1994), p. 157.
National Security Council directive NSC 10/2 (May 1948).
See Roy A. Medvedev, 'New Pages from the Political Biography of Stalin', in Robert C. Tucker (ed.), _Stalinism. Essays in Historical Interpretation_ (New York, 1982), pp. 212–223.
H. Gordon Skilling, 'Stalinism and Czechoslovak Political Culture', ibid., p. 269.
Arthur Koestler, _Darkness at Noon_ (New York, 1961). On the Soviet trials see Hannah Arendt, _The Origins of Totalitarianism_ (New York, 1951); Roy Medvedev, _Let History Judge_ (New York, 1971).
George H. Hodos, _Show Trials. Stalinist Purges in Eastern Europe, 1948-1954_ (New York, 1987), p. 73.
Anne Louise Germaine de Staël-Holstein, _Considérations sur les principaux événemens de la Révolution française_ (London, 1818), book 2, chapter 15, p. 118: 'Because the various classes of society had almost no relations among themselves in France, their mutual antipathy was stronger... the irritability of a very sensitive nation inclined each person to jealousy towards his neighbour, towards his superior, towards his master; and all individuals not content to dominate humiliated one another.'
_Po roce socha řské práce_ (After a Year of Sculptural Work August, 1953], and dedicated to 'the Thirty-Sixers on the occasion of the first anniversary of their activity'), [p. 7. See also the interview with Havel in Antonín Liehm, _The Politics of Culture_ (New York, 1968), pp. 379–380.
_Po roce socha řské práce,_ op. cit., p. 14.
This and the following details of the relationship between Paukert and Havel are drawn from the radio broadcast written and presented by Paukert under his _nom d'emprunt_ Jiří Kuběna, _Z–mého orloje [From My Astronomical Clock]_ Czech Radio (Prague, 1997), programmes 5 (entitled 'Přítel z poštovní schránky' ['Friend from a Mail Box']; 6 (untitled), and 7 (entitled 'Havlov Revisited'); and Jiří Kuběna, _Krev ve víno. Výbor z díla (1953-1995)_ (Olomouc, 1995), pp. 583-584.
_Po roce socha řské práce_ op. cit., p. 4.
Václav Havel, _Do r ůzných stran,_ edited and introduced by Vilém Prečan, (Prague, 1986, 1990), pp. 274–76.
From _Z mého orloje,_ op. cit., programme 7 (entitled 'Havlov Revisited').
Ibid., programme 6 (untitled).
Interview with Viola Fischerová, Prague, 26 September 1997; Pavel Kosatík, _' Člověk má dělat to, načmá sílu'. Život Olgy Havlové_ (Prague, 1997), p. 58.
Václav Havel, _Po roce socha řské práce,_ op. cit.
Further evidence of the tension is found in the previously unrecorded correspondence between Radim Kopecký and Havel. See especially Kopecký to Havel (Prague, 16 December 1952); Havel's reply (Prague, 17 December 1952); and Kopecký to Havel (Prague, 28 December 1952).
Havel to Kopecký (Prague, 17 December 1952).
These and other functions of intermediary associations are discussed at greater length in my _Democracy and Civil Society_ (London and New York, 1988), and _Civil Society: Old Images, New Visions_ (Oxford and Palo Alto, 1999).
_Z mého orloje,_ op. cit., programme 6 (untitled); interview with Ivan Havel (Prague), 23 April 1996.
Václav Havel, _Disturbing the Peace_ (London and New York, 1990), p. 25.
_Turnaround,_ op. cit., p. 56.
Václav Havel, _1992 & 1993_ (Prague, 1994), p. 99.
_Disturbing the Peace,_ op. cit., p. 25.
_Disturbing the Peace,_ op. cit., p. 24.
Correspondence from Dr Louise Mares (née Marie-Luise Langrová), Sydney, Australia, 11 November 1998.
Interview with Viola Fischerová, Prague, 26 September 1997.
_The Czechoslovak Political Trials, 1950-1954,_ op. cit., p. 111.
Karel Kaplan, _Dans les archives du Comité Central_ (Paris, 1978), p. 212.
The proceedings are reported in four articles in _Literární noviny,_ number 48 (1956), p. 7. One of them, presumably based on his own contribution, is written by Václav Havel and entitled 'Program a jeho vyjádření' ('The Programme and its Expression'). Havel's later account of the Dob říš conference is found in _Disturbing the Peace,_ op. cit., pp. 28–33. A thorough search of the Czechoslovak Writers' Union record groups stored in the state archives in Staré Hrady, near Jičín, uncovered no new material, except traces of weeded files.
Compare the different views of the achievements and limitations of _Kv ěten,_ especially Zdeněk Pešat's mention of Havel, in Bohumil Svozil (ed.), _Č asopis Květen a jeho doba: Sborník materiálůz literárněvědné konference 36. Bezručovy Opavy 15-16. 9. 1993_ (Prague and Opava, 1994), pp. 13–16.
See Václav Havel, 'Pochyby o programu' and the reply by Miroslav Červenka, in _Kv ěten, 2_ (1956-1957), pp. 29–30.
Švec worked together with Jiří Štursa and his wife, Vlasta. The remark is cited in Marcela Kašpárková, 'Udělal Stalina, chtěl taky Masaryka', _Magazín Dnes + TV,_ 14 October 1993, p. 9.
'Udělal Stalina, chtěl taky Masaryka', op. cit., p. 8.
See the text of the speech, and other details of the unveiling, in _Rudé právo, 2_ May 1955, p. 3.
Cited in Zdeněk Hojda and Jiří Pokorný, _Pomníky a zapomníky_ (Litomyšl, 1996), p. 213.
Information provided by Milena Janišová, Institute for Contemporary History, Prague, 26 June 1998. Other useful background material includes Berthold Unfried, 'Denkmäler des Stalinismus and "Realsozialismus" zwischen Ikonoklasmus und Musealisierung', _Österreichische Zeitschrift für Geschichtswissenschaften,_ 5, 2 (1994), pp. 233–258; Marcela Kašpárková's interview with Jiří Štursa, one of the assistant architects of the monument, in 'Udělal Stalina, chtěl taky Masaryka', _Magazín Dnes + TV 4_ (4 October 1993), pp. 7–9; Josef Škvorecký, _Talkin' Moscow Blues_ (London and Boston, 1989), pp. 37–38; and 'Vykřičník století aneb "Čechy krásné"', _Reality Public Reportáž,_ 7-8 (1996), <http://www.capitol.cz/tisk/publicreality/1996 0708/page2.html>.
From Bohumil Hrabal's short story, 'Betrayal of the Mirrors', cited in _Pomníky a zapomníky,_ op cit., p. 205.
See Galia Golan, _The Czechoslovak Reform Movement. Communism in Crisis 1962-1968_ (Cambridge, 1971), part 1; H. Gordon Skilling, _Czechoslovakia's Interrupted Revolution_ (Princeton, NJ, 1976), pp. 30–42; Edward Taborsky, 'Czechoslovakia's March to Communism', _Problems of Communism,_ 10 (March—April 1961), pp. 34—41.
_Rudé právo_ (29 January 1957).
_Rudé právo,_ 17 April 1960.
Interview with Radim Kopecký, Prague, 5 November 1998.
Pavel Kosatík, _' člověk má ělat to_, nač _másílu',život Olgy Havlové_ (Prague, 1997), p. 53.
_Disturbing the Peace,_ op. cit., p. 37.
'On the Edge of Spring' (cycle of poems), published originally in samizdat form in Josef Hiršal and Jiří Kolář (eds.), Ž _ivot je všude_ (Prague, 1956). Translated by Derek Paton.
_' člověk má dělat to, načmá sílu', Život Olgy Havlové,_ op. cit., p. 26.
Telephone interview with Karel Brynda, Jihlava and Prague, 5 November 1998.
The authorities' reaction is described by Havel in _Václav Havel: A Czech Drama,_ op. cit.
Martin Esslin, in his introduction to _Three East European Plays_ (Harmondsworth, 1970), p. 16.
Václav Havel, _Vernisáž,_ in _Hry 1970-1976,_ op. cit., p. 276.
Klaus juncker, in the documentary film by Karel Prokop, 'Z Dramatika prezidentem', Česká televize (Prague, 1995).
_1992 & 1993,_ op. cit., p. 20.
Václav Havel, 'Politics and the Theatre', _Times Literary Supplement,_ 28 September 1967, p. 879.
Václav Havel, 'Light on a Landscape', in _Three Van ěk Plays_ (London and Boston, 1990), p. viii.
Václav Havel, 'Anatomie gagu', _Protokoly_ (Prague, 1966), pp. 126–127. Note that the English word 'estrangement' ( _Bertolt Brecht's 'Verfremdung')_ is a poor substitute for the Czech word used by Havel — _ozvláštn ění_ — which connotes 'distant', 'alien', and 'strange'.
From a conversation with Jan Grossman, filmed during 1965 at the Theatre on the Balustrade.
_Disturbing the Peace,_ op. cit., p. 40.
See Vladimír Justl, 'Po piatich rokoch', _Slovenské divadlo,_ 11 (1963), pp. 489–505; and Paul I. Trensky, _Czech Drama Since World War II_ (White Plains, 1978), _pp._ 104-106.
Ivan Vyskočil, 'Poznámky k Autostopu', in _Autostop_ (Prague, 1961), p. 1727.
Interview with Olga Havlová, in Eva Kantůrková, 'Olga Havlová', _Sešly jsme ν této knize_ (samizdat 1980 Prague, 1991]), [pp. 6–15.
Pavel Kosatík, _' člověk má dělat to, nač má sílu'. život Olgy Havlové,_ op. cit., pp. 71,91.
'Rozhovor s Janem Nedvědem o Tváři (Druhá část)', _St řední Europa, 9,_ 30 (May 1993), p. 92.
Paul I. Trensky, _Czech Drama Since World War II,_ op. cit., p. 108.
Václav Havel, _The Garden Party,_ in _Selected Plays 1963-83_ (London and Boston, 1992), pp. 11–12. The translation by Vera Blackwell loses something of the bureaucratic stiffness of the original. Compare the original version printed in the collection of Havel's plays, experimental poetry and essays, _Protokoly_ (Prague, 1966), p. 21.
_The Garden Party,_ op. cit., p. 10.
Andrej Krob, 'Pokus o aktuální přemýšlení o jednom zdánlivě neaktuálním dramatikovi', in _Milý Václave... Tv ůj. Přemýšlení o Václavu Havlovi_ (Prague, 1997), p. 83.
_The Garden Party,_ op. cit., p. 50.
The following accounts of the crisis-ridden process of liberalization before 1968 proved useful when preparing this vignette: _The Czechoslovak Reform Movement,_ op. cit; _Czechoslovakia's Interrupted Revolution,_ op. cit., part two; Kieran Williams, _The Prague Spring and its aftermath. Czechoslovak politics 1968-1970_ (Cambridge and New York, 1997), chapter 1.
See Karel Kaplan, _The Communist Party in Power: A Profile of Party Politics in Czechoslovakia_ (London, 1987), pp. 54–101; Archive of the ČSFR Government Commission for Analysis of the Events of 1967–1970, R131, cited in _The Prague Spring and its aftermath,_ op. cit., p. 14.
Good accounts of this trend include Jiří Kosta, _Abriss der sozialökonomischen Entwicklung der Tschechoslowakei, 1945-1977_ (Frankfurt, 1978); Martin Myant, _The Czechoslovak Economy, 1948—1988: The Battle for Economic Reform_ (Cambridge, 1989); and Judy Batt, _Economic Reform and Political Change in Eastern Europe: A Comparison of the Czechoslovak and Hungarian Experiences_ (London, 1988); and Karel Kaplan, _Sociální souvislosti krizí komunistického režimu ν letech 1953-1957 a 1968-1975_ (Prague, 1993).
Ference Fehér et al., _Dictatorship over Needs. An analysis of Soviet societies_ (Oxford, 1983), p. 25.
Jindřich Pecka, Josef Belda and Jiří Hoppe (eds), _Ob čanská společnost, 1967-1970. Emancipační hnutní Národní fronty, 1967-1970_ (Brno, 1995), p. 8.
Peter Hruby, _Fools and Heroes: The Changing Role of Communist Intellectuals in Czechoslovakia_ (Oxford, 1980), chapter 1.
Jacques Rupnik, 'The Roots of Czech Stalinism', in Raphael Samuel and Gareth Stedman-Jones (eds.), _Culture, Ideology, and Politics: Essays for Eric Hobsbawn_ (London, 1982), p. 312.
On the process of 'state-led liberalization from above', see Guillermo O'Donnell et. al., _Transitions from Authoritarian Rule_ (Baltimore and London, 1986); and _The Prague Spring and its aftermath,_ op. cit., especially part 1.
It is ironic that the new socialist understanding of power mirrored the new 'functionalist' understanding of power defended by Talcott Parsons, the high priest of American academic sociology, and a figure not known to be sympathetic to socialism. See Talcott Parsons, 'On the Concept of Political Power', _Proceedings of the American Philosophical Society,_ volume 107, 3 (June 1963), pp. 232–262, especially p. 243: 'The power of A over B is, in its legitimized form, the "right" of A, as a decision-making unit involved in collective process, to make decisions which take precedence over those of B, in the interest of the effectiveness of the collective operation as a whole.'
Alexander Dubček, with Jiří Hochman, _Hope Dies Last: The Autobiography of Alexander Dub ček_ (London, 1993), p. 112.
Josef škvorecký, 'Ten buržázní spratek', in _Milý _Václave_... _Tv_ ůj,_ op. cit., pp. 52–53.
See the graphic accounts provided in 'Rozhovor s Janem Nedvědem o Tváří', _St řední Europa,_ 8, 29 (1993), pp. 133–145, and 'Rozhovor s Janem Nedvědem o Tváří (Druhá část)', _St řední Europa,_ 9, 30 (May 1993), pp. 92–102. Nedvěd notes (p. 139) that he was informed at the time that Milan Kundera, a member of the top organ of the Writers' Union, voted in favour of the decision to liquidate the journal. According to Kaplan (p. 50), Kundera abstained. Either way, Havel must have not been pleased with Kundera, with whose literature and politics he subsequently did not see eye-to-eye.
'Rozhovor s Janem Nedvědem o Tváří', _St řední Europa,_ 8, 29 (1993), p.141.
_Trud_ (Moscow), 21 June 1968.
Václav Havel, 'Poznámky o polovzdélanost', _Tvá ř,_ 9-10 (December, 1964), pp. 23–29.
Interview with Andrej Stankovič, Prague, 10 November 1998.
_František Havlí ček, 'Nepřekročitelná hranice' Nονá mysl_ number 12 (1965), pp. 1374-82.
_Disturbing the Peace,_ op. cit., p. 83.
The Writers' Union conference had been convened to celebrate the twentieth anniversary of the 'liberation' of Czechoslovakia. The speech, entitled 'On Evasive Thinking', was delivered in Prague on 9 June 1965 — exactly twenty years after he wrote his account of the air raid on Havlov. It is reprinted in Václav Havel, _Open Letters. Selected Prose 1965-1990,_ ed. Paul Wilson (London and Boston, 1991), pp. 10–24.
_Disturbing the Peace,_ op. cit., pp. 87–88.
'Rozhovor s Janem Nedvědem o Tváři (Druhá čast)', _St ředníEuropa,_ _9,_ 30 (May 1993), p. 94.
Ibid., p. 101. 4
Interview with Andrej Stankovič, Prague, 10 November 1998.
'On Evasive Thinking', in _Open Letters,_ op. cit., pp. 10—11.
_Fools and Heroes',_ op. cit., p. xv.
See the account provided in Andreas Razumovsky, 'Der Mechanismus von Feigheit und Macht', _Frankfurter Allgemeine Zeitung,_ 5 August 1965.
The following material is drawn from my interview with Pavel Tigrid, Prague, 18 September 1996.
See 'KGB Report on the "Counterrevolutionary Underground" in Czechoslovakia, October 13, 1968', in Jaromír Navrátil, ed., _The Prague Spring 1968_ (Budapest, 1998), p. 515.
Aristotle, _Nicomachean Ethics,_ Book 8, Section 1.
The taped conversation, recorded in Peroutka's apartment in mid-summer 1968, was passed by Havel to Czechoslovak Radio, whose archivists subsequently lost or miscatalogued the material.
See the report by Stephen Klaidman, 'Czech Writer Here, Sees Opportunity for Liberals', _The New York Times,_ 5 May 1968.
Vaclav Havel — Czech Writer: An Interview with Joan Bakewell', _BBC Late Night Line Up_ (London), 26 June 1968.
The address is partly reprinted in _The Prague Spring 1968,_ op. cit., pp. 9–10.
Č _lov ěk má dělat to, načmá su ílu'. Život Olgy Havlové,_ op. cit., p. 53.
Cited by Jan Tříska in _Milý _V_ á _clave... Tv_ ůj,_ op. cit., pp. 68–69.
_Milý _Václave... Tv_ ůj,_ op. cit., p. 67.
'KGB Report on the "Counterrevolutionary Underground" in Czechoslovakia, October 13, 1968', in _The Prague Spring 1968,_ op. cit., p. 515.
Jan Tříska, in _Milý _Václave... Tv_ ůj,_ op. cit., pp. 65, 66.
See my 'Structural Transformations of the Public Sphere', _The Communication Review,_ volume 1, number 1 (1995), pp. 1–22.
_Rudéprávo_ (Prague), 2 May 1968.
_Disturbing the Peace,_ op. cit., p..94.
_Disturbing the Peace,_ op. cit., p. 96.
_Disturbing the Peace,_ op. cit., p. 95.
Václav Havel, 'On the Theme of an Opposition', _Literárnílisty,_ 4 April 1968, translated in _Open Letters,_ op. cit., pp. 25–35. The middle-of-the-road position staked out in Havel's argument is revealed in H. Gordon Skilling's good account of the debate about pluralism during this period, in _Czechoslovakia's Interrupted Revolution,_ op. cit., pp. 356–363.
The manifesto was issued on 13 May 1968 and later published as 'Manifest Klubu angažovaných nestraníků', _Svobodné slovo_ (Prague), 11 July 1968, p. 1.
The following account draws upon an interview with Josef škvorecký, Toronto, 17 November 1996,v and _Disturbing the Peace,_ op. cit., pp. 99–100. The scene is fictionalized in Josef škvorecký, _The Miracle Game_ (Toronto, 1990), pp. 149—156.
_Disturbing the Peace,_ op. cit., p. 100.
John Keane, 'The Politics of Retreat', _The Political Quarterly,_ volume 61, 3 (July-September 1990), pp. 340–352.
Edmund Burke, 'A Letter to a Member of the National Assembly, in Answer to Some Objections to His Book on French Affairs', in _The Works of The Right Honourable Edmund Burke_ (London, 1859), volume 4, p. 11.
Thomas Hobbes, _Leviathan, or The Matter, Forme, & Power of a Commonwealth Ecclesiasticall and Civill_ (London, 1651 1968]), part 1, [chapter 11.
_Transitions from Authoritarian Rule,_ op. cit.
Pavel Tigrid, _Why Dub ček Fell_ (London, 1971), p. 13.
Karl Philipp Gottlieb von Clausewitz, 'Vom Kriege', in _Hinterlassene Werke über Krieg und Kriegführung_ (Berlin, 1832-1834), Books 1-3.
Cited in _Why Dub ček Fell,_ op. cit., p. 94.
_Action Programme of the Communist Party of Czechoslovakia,_ printed as a special supplement of _Rudé právo_ (Prague), 10 April 1968, pp. 28–29.
_Why Dub ček Fell_, op. cit., p. 84.
Robert Rhodes James (ed.), _The Czechoslovak Crisis, 1968_ (London, 1969), p. 29; Philip Windsor and Adam Roberts, _Czechoslovakia, 1968: reform, repression and resistance_ (London, 1969), pp. 60–61.
Among the documents in my possession are 'Výzva spolobčanům!' (Liberec), 22 August 1968, and 'Všem občanům!' (Liberec), 26 August 1968.
' _Č lověk má dělat to, nač má sílu'. Život Olgy Havlové,_ op. cit., p. 104. Compare Havel's account of the occupation of Liberec in _Disturbing the Peace,_ op. cit., pp. 106–109. The direct quotations are from radio transcripts in my possession, dated from 23 August 1968.
Václav Havel's preface to _The Prague Spring 1968,_ op. cit., p. xvi.
_Disturbing the Peace,_ op. cit., p. 109.
Cited in _Why Dub ček Fell,_ op. cit., p. 102.
_Why Dub ček Fell,_ op. cit., p. 116.
This, and the following quotations, were kindly supplied in a letter from Professor Adam Roberts (Oxford), 25 May 1998. The StB transcript is available in Prague's Archive of the Ministry of the Interior of the Czechoslovak Socialist Republic, H 3-2, i.j. 46, č.j. N/Z-0079/69.
Václav Havel to Alexander Dubček, 9 August 1969, reprinted and translated in _Open Letters,_ op. cit., pp. 36–49.
In _Disturbing the Peace,_ op. cit., Havel later wrote about Dubček's non-decision: 'He disappeared rather quietly and inconspicuously from political life; he didn't betray his own cause by renouncing it, but he didn't bring his political career to a very vivid end either.'
Milan Kundera, 'Český úděl', _Listy,_ volume 1, numbers 7-8. (19 December 1968), pp. 1, 5. Havel's reply, 'Český úděl?' _Tvá ř, 2_ (1969), pp. 30–33, is printed in Vaclav Havel, _O lidskou identitu_ (London, 1984), pp. 195–196. Kundera's reply to Havel, 'Radikalismus a exihibicionismus', appeared in _Host do domu,_ volume 15 (1969), number 15, pp. 24–29, and was reprinted in _Sv ědectvtí,_ 74 (1985), pp. 343–349. The two writers subsequently made amends. See Kundera's homage to Havel, 'A Life Like a Work of Art', _The New Republic,_ 202 (29 January 1990), pp. 16–17, and Milan Kundera's letter to Havel, 24 October 1986.
See the interview conducted by Jiří Nožka, 'What He's Thinking About', _Sv ět ν obrazech,_ 48 (14 December 1968), reprinted in ibid., 1 (5 January 1990), pp. 4–5.
Václav Havel, 'Dovětek autora', _Hry 1970-1976_ (Toronto, 1977), p. 307.
Oldřich Tůma, 'Dubček and Legislative Measure No. 99', paper presented to the One Day Colloquium on Alexander Dubček, held at the Slovak Embassy, London, 7 November 1998.
The following details are drawn from Karel Kaplan, _Political Persecution in Czechoslovakia 1948-1972_ (Köln, 1983), especially pp. 27–40; Milan Šimečka, _Obnovení po řádku_ (samizdat, 1978, and Köln, 1979).
Gustáv Husák, 'May Day Speech', in _Information Bulletin of the Central Committee of the Communist Party of Czechoslovakia,_ 4 (Prague, 1984), p. 9.
Quoted from the documentary film by Olga Sommerová, _A_ _znovu Žebrácká opera (Beggar's Opera Revisited),_ Česká televize 1 (Prague, 1996).
Cited in _Divadlo na tahu: 1975-1995_ (Prague, 1996), pp. 16, 14.
Cited in Eda Kriseová, _Václav Havel: The Authorized Biography_ (New York, 1993), p. 93.
_Disturbing the Peace,_ op. cit., p. 125.
From the documentary film by Karel Prokop, _Z Dramatika prezidentem,_ Česká televize 2 (Prague, 1995).
_Disturbing the Peace,_ op. cit., p. 125.
Václav Havel, 'Dear Dr Husák', in _Open Letters,_ op. cit., pp. 50–83.
See 'Une centaine de personnalités se réclament la garantie des exercices des droits fondamentaux', _Le Monde_ (Paris), 7 January 1977, p. 3; _Frankfurter Allgemeine Zeitung_ (Frankfurt), 7 January 1977, p. 5, which refers to 'the non-Party playwright Václav Havel'; and 'Manifesto Challenge by Prague Dissidents', _The Times_ (London), 7 January 1977, pp. 1, 4.
_Charta 77: Za čátky_, part one of a two-part documentary produced by Česká televize 2 (Prague, 1996).
H. Gordon Skilling, _Charter 77 and Human Rights in Czechoslovakia_ (London, 1981), p. 4.
Vilém Prečan, _Kniha Charty_ (Köln, 1977), pp. 22–23.
Václav Havel, 'Breaking the ice barrier', an interview on BBC, first published in _Index on Censorship,_ volume 7, number 1 (January–February 1978), pp. 25—28.
The interview appears in _Kurier_ (Vienna), 31 March 1978. It was reprinted in _Listy,_ volume 8, number 5 (September 1978), pp. 63—65; and in _Infoch,_ number 5 (1978), pp. 5–7.
The Prague meeting was held on 28 January 1977, and is treated in _Charta 77:_ _Za čátky,_ op. cit., part one.
_Charta 77: Za čátky,_ op. cit., part one.
Václav Havel, 'Prohlášení' ('Declaration'), 21 May 1977, cited in _The Times_ (London), 23 May 1977.
Josef Frolík, _Špión vypovídá_ (Prague, 1990 1982]), [p. 273.
See for example _Práce_ (Prague), 11 March 1977; _Rudé právo,_ 12 January 1977; _Pravda_ (Bratislava), 12 January 1977; _Who is Václav Havel? (Kdo je Václav Havel?),_ originally broadcast on Czechoslovak Radio on 9 March 1977.
The theory of sovereign power is discussed in my 'Dictatorship and the Decline of Parliament', in _Democracy and Civil Society,_ op. cit., pp. 153–189; Harold J. Laski, _The Foundations of Sovereignty and Other Essays_ (London, 1921); and Carl Schmitt, _Political Theology, Four Chapters on the Concept of Sovereignty_ (Cambridge, Mass., 1985).
Jean Bodin, _Les Six Livres de la République_ (Paris, 1576), book 1, chapter 8.
'Poslední rozhovor', _O lidskou identitu,_ op. cit., pp. 152–155; the sentences cited here are slightly altered from the English translation, which appeared as 'Last Conversation', in _Charter 77 and Human Rights in Czechoslovakia,_ op. cit., pp. 242–244.
_Rudé právo,_ 21 May 1977.
Václav Havel, _'Prohlášení'_ ('Declaration'), 21 May 1977, cited in _The Times_ (London), 23 May 1977.
See his letter dated 1 June 1977 (O _lidskou identitu,_ op. cit., p. 278); and the interview conducted around the end of September 1977, later published in London, ibid., pp. 250–256.
See 'Last Word before the Court' (18 October 1977), ibid., pp. 327–330.
Ludvík Vaculík, 'Poznámky o statečnosti', dated 6 December 1978, circulated in typewritten samizdat form, and dedicated to the author Karel Pecka, on the occasion of his fiftieth birthday. See also Petr Pithart's reply dated 31 December 1978; Havel's reply to Vaculík dated 25 January 1979; and Havel's reply to Pithart dated 1 February 1979. Vaculík's early reaction to the controversy about courage is chronicled in _Č eský snář_ (samizdat and Prague, 1990), entry dated Thursday, 25 January 1979. I have also consulted Václav Havel's introduction to Ludvík Vaculík, _A Cup of Coffee with My Interrogator_ (London, 1987), pp. i—iv.
Interview with Ludvík Vaculík, Prague, 23 April 1996. See also his comments in _Č eský snář,_ op. cit.
Some examples include Marcus Tullius Cicero, _De Officiis_ (London, 1720), Book 1, chapter 2, section 5 and Book 1, chapter 19, section 62; Epictetus, _Discourses_ (Glasgow, 1766), Book 1, chapter 18, section 21; Plautus, _Amphitryon; or The two Socia's. A Comedy_ (London, 1690), 1. 646 (Act 1, scene 2),; and Plutarch, _The Lives of Aristeides and Marcus Cato_ (London, 1928), chapter 10, section 4.
Translated by Paul Wilson, the essay appeared in English in _The Power of the Powerless: Citizens Against the State in Central-Eastern Europe,_ edited by John Keane (London, 1985). This volume includes a selection of nine other essays addressed to Havel's thesis from an original collection of Czech and Slovak responses.
William Shakespeare, _Julius Caesar,_ Act 1, Scene 2.
Václav Havel, 'Dovětek autora', in _Hry 1970-1976_ (Toronto, 1977), p. 306.
See Peter Bachrach and Morton S. Baratz, 'Decisions and Nondecisions: An Analytical Framework', _American Political Science Review,_ volume 57 (1963), pp. 632-642.
Tomáš Garrigue Masaryk's notion of 'small-scale initiatives' _(drobná práce)_ referred to the importance of honest, responsible work in widely different areas of life, but contained within the existing social order. It emphasized the importance of cultivating morality and privileging enlightened education for the ultimate purpose of stimulating national self-confidence and national creativity. This notion of 'working for the good of the nation' not only supposed the availability of a framework of civil and political liberties within which citizens could get on with their work. It was also strongly wedded to a politics of _national_ reconstruction, that is to say, a project of developing and defending the right of nations to govern themselves through territorially sovereign states. 'The Power of the Powerless' was implicitly sympathetic to the same goal, but Havel's silence about 'the national question' was at this stage hard to interpret. He was forced later to come clean.
György Konrád, _Anti-Politics_ (London, 1984).
_The Power of the Powerless,_ op. cit., p. 205. Compare Václav Žák's original criticism of Havel and others for confusing 'the level of thinking about individual responsibility and the level of thinking about the operation of society', in 'Co je naše tradice' (samizdat, Prague, 1986).
This criticism of Havel is analysed in 'Co je naše tradice', op. cit.
Václav Černý, _Pam ěti 1945-1972_ (Brno, 1992 1983]), [p. 162. Černý reportedly added that Havel was 'utterly beside himself if a week went by without the world talking about him'.
Robert B. Pynsent, 'The Work of Václav Havel', _SEER,_ volume 73, 2 (April 1995), p. 271.
Václav Bělohradský, 'Jubileum', in _Milý Václave... Tv ůj,_ op. cit., p. 27.
Stanislaw Baranczak, _Breathing Under Water and Other East European Essays_ (Cambridge, Mass., and London, 1990), p. 54.
Cited in _Open Letters,_ op. cit., pp. 125–126.
_Der Spiegel,_ 23 (31 May 1976), pp. 193ff.
Václav Havel, _Letters to Olga,_ op. cit., pp. 23–24.
_Letters to Olga,_ op. cit., p. 138.
Ibid., p. 153.
Ibid., p. 145.
_Letters to Olga,_ op. cit., p. 147.
Havel here referred to Anna Kohoutová, with whom he was having an affair until the morning he was dragged from her bed, to begin this spell in prison. Stories of the affair are told by her daughter, Tereza Boučková, in her _Indiánský b ěh_ (Prague, 1992; first published in samizdat) and an interview published in _Magazín Dnes + TV_ (Prague), 10 September 1999, pp. 22–24. Boučková recalls that Havel, nicknamed 'Monolog', consummated the fantasy of sitting in a chair to watch Anna and her daughter strip naked; that Anna tried hard, without success, to get pregnant; and, after Havel was flung into Ruzyně, that his lover attempted to communicate with him by frequenting an adjoining children's playground, where she played waltzes at full blast on a cassette player _(Indiánský b ěh,_ op. cit., pp. 43, 122, 127).
_Letters to Olga,_ op. cit., p. 160.
Interview with Josef Topol (Prague), 6 March 1999.
_Disturbing the Peace,_ op. cit., p. 161.
_Letters to Olga,_ op. cit., p. 277.
Zdeněk Urbánek, 'Poděkování', _Ztracená zem ě_ (Prague, 1992), pp. 472–473.
_Disturbing the Peace,_ op. cit., p. 157.
Salman Rushdie (in an interview transmitted on National Public Radio [New York, 21 April 1999]) praised _Letters to Olga_ as among the small handful of his favourite books (which included James Joyce's _Ulysses)_ that he carried everywhere during his years of hiding from possible execution.
The impression is certainly reinforced by considering one letter _not_ included in either the English edition or the published Czech edition organized by Havel's friend, Jan Lopatka. It was a reply to Olga's earlier remark that Kamila Bendová, wife of Havel's prisonmate Václav Benda, had said that Havel never seemed to write such beautiful love letters to Olga as she received from her husband. So Havel tried to prove her wrong by writing just such a letter. 'We nicknamed it The Love Letter', said Ivan Havel later (in an interview, in Prague, on 24 September 1997). It turned out to be an essay on how to write love letters. It revealed how he seemed unable to write an open, warm, loving letter.
Interview with Pavel Kosatík (Prague), 30 September 1997; and with Anna Freimanová (Prague), 9 November 1998.
_Letters to Olga,_ op. cit., p. 27.
Eric Bailey, 'The First Lady of Prague. An Interview with Olga Havel', _Telegraph Weekend Magazine,_ September 1990, p. 18.
Marcela Pecháčková, Olga', _Magazín Dnes + TV,_ 8 February 1996, p. 10.
Anastázie Kudrnová, 'Šedesátiny Ferdinanda Vaňka', _Magazín Lidových novin,_ volume 1, number 1 (4-10 October 1996), p. 20.
Interview with her good friend and colleague Olga Stankovičová, Prague, 10 November 1998.
Hana Primusová and Milena Pekárková, _Olga_ (Prague, 1997), p. 49.
Ibid., pp. 20, 58.
_Olga,_ op. cit., p. 65.
Zdeněk Urbánek, 'Opora', ibid., p. 13.
_Olga,_ op. cit., pp. 36, 60.
Cited in Marcela Pecháčková, 'Olga', _Magaz_ í _n Dnes + TV,_ 8 February 1996, p. 8.
Ibid., p. 10. See also _Olga,_ op. cit., p. 29.
Josef Topol, cited in _Olga,_ op. cit., pp. 20–21.
I bid., p. 25.
Interview with Pavel Kosatík, Prague, 30 September 1997; and _' Člověk má dělat to, nač má sílu'. Život Olgy Havlové,_ op. cit., pp. 189–223.
Ibid., pp. 40, 41, 39.
Marcela Pecháčková, 'Olga', _Magazín Dnes + TV,_ 8 February 1996, pp. 11–12, where Landovský recalls: 'Olinka didn't like me much, and the worst thing that could happen to Vašek was to be caught with me. She was right in guessing that there were good times and girls around me and she wanted to have him only for herself. I think that Olinka was happiest when he was in prison and no one else was allowed to write to him. She could restrain Vašek best when he was under lock and key.'
Interview with Pavel Kosatík, Prague, 30 September 1997.
_Letters to Olga,_ op. cit., p. 184.
Interview with Jiřina Šiklová, Prague, 19 September 1996.
Václav Havel to Jitka Vodňanská, 17 November 1983.
Interview with Jitka Vodňanská, Prague, 9 November 1998.
Václav Havel to Jitka Vodňanská, 12 January 1988.
_Olga,_ op. cit., p. 49.
First published in samizdat in the Edice Petlice series as Václav Havel, _Largo desolato: hra o sedmi obrazech_ (Prague, 1984). I have also consulted the German edition translated by Joachim Bruss and edited by Siegfried Lenz, _Largo Desolato: Schauspiel in sieben Bildern_ (Reinbek bei Hamburg, 1985), and the English translation and adaptation by Tom Stoppard, _Largo Desolato: A Play in Seven Scenes_ (London and Boston, 1987). Dutch, French, and Italian translations also appeared during this period.
_Disturbing the Peace,_ op. cit., p. 66.
Cited in the documentary film by Karel Prokop, 'Z Dramatika prezidentem', Česká televize 2 (Prague, 1995).
Václav Havel, 'My temptation', _Index on Censorship,_ volume 15, number 10 (November/December 1986), p. 21.
'My temptation', op. cit., p. 19.
Aristotle, _Política,_ Book 5, chapter 2, section 8.
Václav Havel to Vilém Prečan, 5 November 1989 (Archives of the Czechoslovak Documentation Centre, Scheinfeld, number 1523/89).
Cited in _Svobodné slovo,_ 18 November 1989.
Cited in Todd Brewster, 'The People Rise', _Life_ (New York), February 1990, p. 32.
Interview with John Bok (Prague), 1 October 1997.
The text appeared as _Provolání_ (Prague, 19 November 1989). It is reproduced in John F. N. Bradley, _Czechoslovakia's Velvet Revolution. A Political Analysis_ (New York, 1992), annex 8.
See the second of the two-part documentary on _Charta_ 77, 'Changes', Česká televize (Prague, 1996), op. cit. 'It seems that we are living in thrilling, extraordinary, even dramatic times,' runs one soundbite. 'State power is on the one hand heightening its repression against citizens, arresting them, squirting them [ _st říkat ze stříkaček_ — much laughter in the crowd]. On the other hand, society is beginning to lose its fear, and more and more people are unafraid of publicly expressing their true opinions.'
Citedin _Czechoslovakia's Velvet Revolution,_ op. cit., p. 102. Other day-by-day accounts include Timothy Garton Ash, _The Magic Lantern: The Revolution of '89 Witnessed in Warsaw, Budapest, Berlin, and Prague_ (New York, 1990); and Bernard Wheaton and Zdeněk Kavan, _The Velvet Revolution: Czechoslovakia, 1988-1991_ (Boulder, Colorado, 1992).
Cited in Bernard Gwertzman and Michael T. Kaufman (eds.), _The Collapse of Communism by the Correspondents of 'The New York Times'_ (New York, 1990), p. vii.
See the various documents assembled in Jan Vladislav and Vilém Prečan (eds.), _Czechoslovakia: Heat in January 1989_ (Scheinfeld-Schwarzenberg, 1989).
Josef Škvorecký, 'Ten buržoazní spratek', in _Milý Václave_ ... _Tv ůj,_ op. cit., p. 54; the remark by Henry Kissinger is found in the documentary film, _Why Havel?,_ directed by Vojtěch Jasný, narrated by Miloš Forman (Los Angeles, 1990).
Cited in Kosatík, p. 251.
Interview with Petr Oslzlý (Brno), 7 November 1998.
'Ein Wort über das Wort,' _Frankfurter Allgemeine Zeitung_ (Frankfurt), 16 October 1989, p. 13.
The following details are drawn from the research note prepared by Blanka Císařovská (Institute for Contemporary History, Prague, 30 September 1997).
William Shakespeare, _Twelfth Night; Or, What You Will,_ Act 1, Scene 5.
From the interview with Ivan Lamper, 'Terén, na který nikdy nevstoupím', _Sport_ (Prague), 1, 3 (September 1989), pp. 6–11.
Václav Havel, 'An hour between a bankrupt and a politician', _Lidové noviny,_ 10 (October 1989), pp. 1–2.
The following account is taken from the gripping transcript of the meeting reproduced in Jiří Suk (ed.), _Ob čanské fórum_ (Prague, 1997), volume 2, pp. 80–90.
Speech to the Joint Session of the US Congress (Washington, D.C., 21 February 1990)', in _Toward a Civil Society. Selected Speeches and Writings 1990-1994_ (Prague 1995), p. 31.
The details of the meeting divulged here for the first time are drawn from my interview with Petr Pithart, Scheinfeld, 15 September 1996; my interview with Oldřich Tůma (London, 10 June 1997); the roundtable discussion between Petr Pithart, Jiří Kantůrek and others in _Prom ěny politického systému ν Československu na přelomu let 1989/1990_ (Prague, 1995), pp. 78–81; and the brief account provided in Jiří Suk (ed.), _Ob čanské fórum_ (Prague and Brno, 1997), volume 1, pp. 30–31.
According to Jaroslav Šabata, reporting the informed estimate provided by a 'worried-looking but resigned' Zdeněk Jičínský on the day before Havel announced his candidacy, 'there were about thirty supporters of the candidacy of Václav Havel, against whom there were about half a dozen supporters of Alexander Dubček.' See Jaroslav Šabata, _Sedmkrát sedm kruh ů_ (Olomouc, 1997), p. 103.
Interview with His Excellency Pavel Seifter, London, 15 March 1999.
Transcripts of nine rounds of talks that took place between 26 November and 9 December 1989 were printed after the revolution in Vladimír Hanzel, _Zrychlený tep d ějin_ (Prague, 1991). There were other meetings that went unrecorded, and it is unclear whether, for reasons of confidentiality or reputation, the invisible hand of Havel subsequently touched the manuscript. Further useful comments are to be found in Miloš Calda, 'The Roundtable Talks in Czechoslovakia', in Jon Elster (ed.), _The Roundtable Talks and the Breakdown of Communism_ (Chicago and London 1996), pp. 135–177.
Václav Havel and Milan Kňažko to Ladislav Adamec, 5 December 1989.
The proposal, which went unrecorded, is minuted in Jiří Suk (ed.), _Ob čanské fórum_ op. cit., volume 2, p. 90.
From the Czechoslovak Television address on 16 December 1989.
_Ob čanské fórum,_ op. cit., volume 1, p. 31.
The previously unrecorded account of the secret meeting is based on material provided in an interview with Stanislav Milota (Prague), 2 October 1997, and my correspondence (Prague, 24 November 1998) with František Vlasák, who wrote: 'I am very glad to confirm that in mid-December 1989 six brief meetings took place between Mr Havel and Mr Dubček, which I, at the request of both, arranged, and, together with Milota, organized at various places in Prague. The result of these complicated talks was the agreement that Mr Havel would be the candidate for office of President of the ČSSR and Mr Dubček for office of Leader of the National Assembly of the ČSSR. The last meeting took place after 15 December.'
See the transcripts reprinted in _Ob čanské fórum,_ op. cit., volume 2, pp. 263–272.
'New Year's Address to the Nation', in _Toward a Civil Society,_ op. cit., p. 19.
Interview with Petr Pithart, Scheinfeld, 15 September 1996.
Friedrich von Hardenberg was born on 2 May 1772 at the Castle of Oberwiedenthal in Thuringia, about 200 kilometres from Prague. His father belonged to the Moravians, and he was raised in Pietist circles. After attending school in Brunswick, he studied law at the universities of Jena, Wittenberg, and Leipzig, where he made contact with Romantics like Friedrich Schlegel. He also attended the mining academy at Freiberg and professionally his last years, which were marred by the deep sorrow of bereavement and unconsummated love, were spent in the department of mining of which his father was director. He became known as the region's most important Romantic poet. His principal works include the cycles _Hymnen an die Nacht_ and _Geistliche Lieder,_ prose tales like 'Die Lehrlinge zu Sais' and 'Heinrich von Ofterdingen', and philosophical and political works such as _Die Christenheit oder Europa_ (1799), _Die Enzyklopädie_ and _Glauben und Liebe oder der König und die Königin_ (1798). His politics were infused with qualified support for the principles of the French Revolution, while his poetry was steeped in the longing for death, of which night is the leading image. Von Hardenberg died of tuberculosis in Weissenfels, Thuringia, on 25 March 1801.
Novalis (Friedrich von Hardenberg), _Schriften_ (5 volumes; Stuttgart, 1977-1988), volume 2, p. 522.
Ibid., volume 3, p. 416, no. 762.
Ibid., volume 2, p. 489, no. 18.
_Schriften,_ op. cit., volume 2, p. 545, no. 105. See also ibid., p. 537, no. 55 and p. 534, no. 37,
Cited in Richard Samuel, 'Einleitung', in _Schriften,_ op. cit., volume 2, p. 479.
Milan Šimečka to Václav Havel, 11 December 1989.
Interview with Stanislav Milota, Prague, 2 October 1997.
On the late classical roots of the royal entry, see Ernst H. Kantorowicz, 'The "King's Advent" and the Enigmatic Panels in the Doors of Santa Sabina', _Art Bulletin,_ 26 (1944), pp. 207–231; Gordon Kipling, _Enter the King. Theatre, Liturgy, and Ritual in the Medieval Civic Triumph_ (Oxford, 1998); and Roy Strong, _Art and Power: Renaissance Festivals 1450-1650_ (Berkeley and Los Angeles, 1984).
Compare the different usages of a similar term by Roy Strong, _Splendor at Court: Renaissance Spectacle and the Theatre of Power_ (Boston, 1973) and Clifford Geert'z, _Negara: The Theatre State in Nineteenth-Century Bali_ (Princeton, 1980).
Interview with Petr Oslzlý, Brno, 7 November 1998.
From _Why Havel?,_ op. cit.
Interview with Andrej Stankovič, Masaryk Library, Prague Castle, 9 November 1998.
Interview with Andrej Stankovič, op. cit.
See Paul Berman, _A Tale of Two Utopias: The Political Journey of the Generation of 1968_ (New York, 1996), p. 197: 'Head turned away from camera. Face buried itself in hands. Televised mortification!... The ambassador from the United States volunteered that she did know something about Mr Zappa's daughter, Moon Unit. Czechoslovakia was aghast. People had no way to account for the United States ambassador's boorish airport behavior, except to mark her down as a cultural ignoramus who lacked the aplomb to boast to all of Central Europe about one of America's finest sons, the brilliant Zappa, a world figure in the field of popular music.' See also the transcript of the conversation between Havel and Reed in Hanif Kureishi and Jon Savage, _The Faber Book of Pop_ (London and Boston, 1995), pp. 696-709.
The book of letters and sketches, with an introduction by Havel's personal assistant, Vladimir Hanzel, was published as _Myli pane prezidente_ (Prague, 1992).
Eda Kriseová, _Václav Havel_. _Životopis_ (Prague, 1991).
Michael T. Kaufman, 'Once Upon a Time in Prague', _The New York Times Book Review,_ 24 October 1993, p. 33.
Interview with Prince Karel Schwarzenberg, Prague, 19 September 1997.
From _Why Havel?,_ op. cit.
Interview with Stanislav Milota, Prague, 2 October 1997.
_The New York Times_ (31 May 1990) reported that only at the end of May 1990 was the Castle cleared of listening devices ('bugs') planted by unknown persons. See also '"Free" Czechoslovakia? Shadows over the Transition', www.security—policy.org/papers/1990/90-55.html.
Jan Novak, _Commies, Crooks, Gypsies, Spooks and Poets_ (South Royalton, 1995), p. 113.
There were initially ten core aides clustered around Havel: the music adviser and organizer of public meetings and events, Ladislav Kantor; Eda Kriseová, who headed the newly established Office of Amnesties and Complaints; Jiří Křižan, a screen writer who shadowed the Ministry of Interior; Miroslav Kvašňák, who was in charge of Havel's bodyguards; Miroslav Masák, the Castle architect; the head of protocol, Stanislav Milota; Petr Oslzlý, who was in charge of promoting freedom of cultural expression; the visual artist Joska Skalník; the foreign-affairs adviser (and subsequently Ambassador to the United States) Alexandr Vondra; and Michael Žantovský, Havel's personal spokesman.
From _Why Havel?,_ op. cit.
Interview with Jan Urban, Prague, 3 November 1998. See also his important article, 'Bezmocnost mocných', _Listy,_ volume 23, 5 (1993), pp. 3–10.
The first edition of the book by Robert Michels was published in Germany, with the title _Zur Soziologie des Parteiwesens in der modernen Demokratie_ (Leipzig, 1911). A new edition, somewhat revised, with an added chapter on the war, was published in Italy in late 1914. The English edition, published in 1915, was based on the Italian version.
From a speech in acceptance of the Sonning Prize, Copenhagen, 28 May 1991, in _Toward a Civil Society,_ op. cit., p. 137.
Interview with Josef Topol, Prague, 6 March 1999.
Frorn _Why Havel?,_ op. cit.
Interview with Jan Urban, Prague, 3 November 1998.
Clive James, _Fame in the 20th Century_ (London, 1993), p. 243.
Interview with Gabriela Müllerová, London, September 1997.
William Shakespeare, _Antony and Cleopatra,_ Act 2, Scene 5.
The following material is drawn from an interview with Stanislav Milota, Prague, 2 October 1997.
Interview with Jiřina Šiklová, Prague, 19 September 1996.
The dispute with Kantor is confirmed in interviews with Olga Stankovičová, Prague, 10 November 1998; and with Stanislav Milota, Prague, 2 October 1997.
Interview with Olga Stankovičová, Prague, 10 November 1998.
Interview with Zdeněk Jičínský, Prague, 25 September 1996; see also his _Č eskoslovensk_ý _parlament ν polistopadovém vývoji_ (Prague 1993), pp. 106–111.
Václav Havel, _Summer Meditations on Politics, Morality and Civility in a Time of Transition._ (London and Boston, 1992), pp. xvi-xvii; Vaclav Havel, _Váženi ob čané_ (Prague, 1992), pp. 16–18
_Mladáfronta Dnes,_ 16 June 1992, p. 1.
One version of this old maxim about the unintended dynamic consequences of revolutionary politics was presented during the French Revolution by the greatest German liberal of the time, Georg Forster. See his _Kleine Schriften und Briefe,_ ed. Claus Träger (Leipzig, 1961), p. 344: 'The Revolution is a hurricane; who can harness it? Galvanized by its spirit, human beings find it possible to commit actions that posterity, out of sheer horror, will be unable to comprehend.'
See Juan J. Linz, 'The Perils of Presidentialism', _Journal of Democracy,_ volume 1, number 1 (Winter 1990), pp. 51–69.
The dualism between monarchs and estates — which developed nowhere else in the world, and was the forerunner of the polarity between state and civil society of the early modern era — is basic to understanding the origins of European parliamentary assemblies, as is pointed out in the classic essay by Otto Hintze, 'Weltgeschichtliche Bedingungen der Repräsentativverfassung 1931]', in _Staat und Verfassung_ (Göttingen, 1970), [pp. 140–185.
Charles Louis de Secondat, Baron de Montesquieu, _De l'esprit des lois_ (Paris 1979), volume 1, Book XI, chapter 4, p. 293.
Reprinted in _The Prague Spring 1968,_ op. cit., p. 8.
Stanley Fish, _There's No Such Thing as Free Speech and It's a Good Thing, Too_ (New York and Oxford 1994); John Keane, _The Media and Democracy_ (Oxford and New York, 1991).
Interview with Jan Urban (Prague), 3 November 1998. The Sacher affair first surfaced in the Czechoslovak press during mid-April 1990, for instance in _Lidové noviny_ (Prague), in the week beginning 18 April, and in _Respekt_ (Prague), 25 April — 1 May 1990.
Interview with Petruška Šustrová (Scheinfeld), 14 September 1996.
The following draws upon Herman Schwartz, 'Lustration in Eastern Europe', _Parker School Journal of East European Law,_ volume 1, number 2 (1994), pp. 141—171; Jiřina Šiklová, 'Lustration or the Czech Way of Screening', _East European Constitutional Review,_ volume 5, number 1 (Winter 1996), pp. 57–62; the interview with Petruška Šustrová, op. cit.; and detailed correspondence from Václav Žák (Prague), 14 March 1999.
Both quotations are from Jeri Laber, 'Witch Hunt in Prague', _The New York Review of Books_ (23 April 1992), p. 8.
From a speech in acceptance of an honorary doctorate awarded by New York University, 27 October 1991, reprinted in _Toward a Civil Society,_ op. cit., p. 158.
In an interview with Dana Emingerová and Luboš Beniak, 'Nejistota posiluje', _Mladýsv ět_ (Prague), 13 May 1991, p. 16.
An account of Kavan's case appears in Lawrence Weschler, _Calamities of Exile_ (Chicago, 1998), pp. 63–135.
Interview with Senator Jan Kavan, Prague, 23 September 1997.
William Shakespeare, _Hamlet, Prince of Denmark,_ Act 1, Scene 3; compare the almost identical formulation in the typewritten and hand-corrected samizdat interview, originally conducted by Antoine Spire in Prague, and finally dated 3 April 1983.
_The Politics of Culture,_ op. cit., p. 374.
Václav Havel, _Summer Meditations on Politics, Morality and Civility in a Time of Transition_ (London and Boston, 1992), p. 11.
From my conversation with Václav Klaus after he delivered the Hayek Memorial Lecture, London, 17 June 1997.
Niccoló Machiavelli, Il _principe,_ chapter 18.
Interview with Ivan Havel, Prague, 23 April 1996.
Interview with Jacques Rupnik, Paris, 29 April 1998.
From the essay on Klaus by Petr Nováček in _Týden_ (Prague), 8 December 1997, pp. 30–34. The same point was made in my interviews with Pavel Tigrid, Prague, 18 September 1996, and Prince Karel Schwarzenberg, Prague, 19 September 1997.
Havel to Kopecký (Prague, 17 December 1952).
Kopecký to Havel (Prague, 16 December 1952); Kopecký to Havel (Prague, 28 December 1952).
Česká televize 2 (Prague), 12 March 1996.
See the contributions by Havel and others to John Keane (ed.), _Civil Society and the State. New European Perspectives_ (London, 1988; reissued 1998). Compare his interesting comment, written in 1988, on the dustjacket of _Democracy and Civil Society,_ op. cit.: 'The various political shifts and upheavals within the communist world all have one thing in common: the undying urge to create a genuine civil society.'
'New Year's Address to the Nation' (Prague, 1 January 1992), in Václav Havel, _Toward a Civil Society. Selected Speeches and Writings 1990-1994_ (Prague, 1995), p. 174. Compare the tougher words against Klaus in 'A Crying Need for Intellectuals: an interview', _The New Presence_ (April 1999), p. 16: 'He sees things solely in terms of responsible individuals, the blind laws of the market and a centralized state: everything else he regards as nonsense. It is a very short-sighted, political attitude — if not actually suicidal.'
_1992 & 1993,_ op. cit., pp. 90, 53-54.
See my discussion of national identity and nationalism in _Civil Society: Old Images, New Visions,_ op. cit., pp. 79–113.
Stanislava Dufková, 'Hovory z Lán', an interview with President Vaclav Havel recorded at Hrádecek on 2 November 1991, broadcast on Československy Rozhlas Radio Network at 13.15 GMT on 3 November 1991.
Sharon Wolchik, 'The Politics of Ethnicity in Post-Communist Czechoslovakia', _East European Politics and Societies,_ 8, 1 (1994), p. 178.
Zdeněk Jičínský, 'Ke ztroskotání československého federalismu', in Rüdiger Kipke and Karel Vodička (eds.), _Rozlou čení s Československem_ (Prague, 1993), p. 77.
Václav Havel, 'Základ identity splečného státu', _Narodna obroda_ (Bratislava), 18 September 1990.
Jozef Prokeš, 'Otvorené list prezidentovi SFR', _Slovenská národ_ (Bratislava), 24 October 1990.
Karl-Peter Schwarz, _Tschechen und Slowaken: Der lange Weg zur friedlichen Trennung_ (Vienna, 1993), p. 222.
Interview with Petr Pithart (Scheinfeld), 15 September 1996. See also his 'The Break-Up of Czechoslovakia', _Scottish Affairs,_ 8 (Summer 1994), pp. 20–24.
Juraj Mihalík, from the manuscript _Vzpomínky na zlyhania,_ cited in Colm Tóibín, _The Sign of the Cross. Travels in Catholic Europe_ (London, 1994), p. 234.
_The Sign of the Cross,_ op. cit., p. 235.
Eric Stein, _Czecho/Slovakia. Ethnic Conflict, Constitutional Fissure, Negotiated Breakup_ (Ann Arbor, 1997), p. 2.
Sharon L. Wolchik, 'The Politics of Transition and the Break-Up of Czechoslovakia', in Jiří Musil (ed.), _The End of Czechoslovakia,_ op. cit., p. 229.
See 'Komu věří Slováci' ('Whom the Slovaks trust'), _Lidové noviny, 25_ October 1991, p. 2.
Václav Havel, _Letní p řemítaní_ (Prague, 1991), pp. 18–19.
An excellent account of the events is provided by Václav Zák, 'The Velvet Divorce — Institutional Foundations', in Jiří Musil (ed.), _The End of Czechoslovakia_ (Budapest, London and New York, 1995), pp. 244–268.
These are the opening words of Karel Čapek's 'Introduction', in Karel Čapek _et al, At the Cross-Roads of Europe. A Historical Outline of the Democratic Idea in Czechoslovakia_ (Prague, 1938), p. 3.
Interview with Paul Wilson, Toronto, 17 November 1996.
_The Prague Post,_ volume 4, 3 (19-25 January 1994), p. 1.
Václav Havel to President Richard von Weizsäcker, Prague, 5 November 1989.
Examples include the President's attack on 'provincial mistrust' and 'Czechocentrism' in the address from Lány on 14 January 1994.
_Asanace: hra o p ěti jednáních_ (Münich, 1988 first published the previous year in samizdat in Prague]), [p. 95. Compare the almost identical remarks in the interview, 'The struggle to be free needs support', _The Nation_ (Bangkok) 18 February 1994.
_1992 & 1993,_ op. cit., p. 83; see also his treatments of the _Mitteleuropa_ theme, ibid., pp. 124, 148, and his introduction, dated August 1996, to a small brochure about the Barrandov studios.
From the speech after receiving the President's Medal at The George Washington University, Washington, DC, 22 April 1993, reprinted in _Toward a Civil Society,_ op. cit., p. 228. The same argument that 'Fate' chose the Jews to make 'modern humanity face up to its responsibility' appears in Václav Havel, _Vážení ob čané_ (Prague, 1992), p. 108. Note the foul version of the understanding of the Holocaust as Destiny: Hitler's certainty, from 1936, that his actions were ordained by Providence. 'I go with the certainty of a sleepwalker along the path laid out for me by Providence', he told a jubilant crowd in Munich on 14 March 1936 (quoted in Ian Kershaw, _Hitler, 1889-1936: Hubris_ (Harmondsworth 1998), p. 527.
_1992 & 1993,_ op. cit., pp. 91, 80, 174.
All quotations concerning the signing of the treaty are from _The Prague Post_ (Prague), 3-9 March 1992, p. 1.
Speech delivered to the European Parliament, Strasbourg, 8 March 1994, in _Toward a Civil Society,_ op. cit., pp. 291–303.
An example of this (typical) kind of reasoned argument is 'The Hope for Europe', a public address delivered in Aachen, 15 May 1996, reprinted in _The New York Review of Books,_ 20 June 1996, pp. 38–41.
Timothy Garton Ash, 'The moral leader of Europe', _Independent_ (London), 21 October 1998, p. 5.
Telephone conversation with Ivan Havel, Prague and London, 16 April 1998. Compare the remarks of Karel Srp, in _News_ (Vienna) 23 April 1998, p. 74: 'Had it happened in Prague, he would have died. The Austrian doctors and his wife Dagmar saved him.'
The best-researched account is provided by Paul Berman, 'The Philosopher-King is Mortal', _The New York Times Magazine,_ 11 May 1997, pp. 32–59.
_II principe,_ op. cit., chapter 25.
_Hovory z Lán,_ Czech Radio (Prague), 5 January 1997.
Interview with Jiří Pehe, Prague, 5 March 1999.
Česká televizé 1 (Prague), 24 December 1997.
_Mladá fronta Dnes_ (25 August 1997). The ensuing controversy is documented in _Lidové noviny_ (26 August 1997) and _Mladá fronta Dnes_ (27 August 1997).
See the insightful remarks of Jindřich Ginter, 'Z herečky se první dáma nestala', _Slovo_ (Prague), 8 November 1997.
_Blesk_ (Prague), 30 October 1997. Worse was to come. In October 1998, Prague's TV Nova, the most talked-about private television station in central-eastern Europe, reported that the marriage of the presidential couple was in crisis. The claim was based on a then-unpublished book co-authored by Přemysl Svora, _Sedm týdn ů, které otřásly Hradem [Seven Days that Shook the Castle]_ (Prague, 1998). Following the programme, the Havels vigorously denied the allegations and filed a libel suit against TV Nova. Dáša accused its mogul, Vladimir Železny (whose name means 'iron' in Czech) of trying to blackmail the President into pardoning Zelezny's son David, a convicted rapist. Železny replied that the President's wife made him nauseous. 'I consider the statement by the First Lady, I stress 'lady', of this country, to be a fishwife's argument.' He went on to express surprise that Havel co-initiated the libel suit. 'Well,' the smooth-tongued Železný added, 'husbands don't always have it easy.' A few months later, after an out-of-court settlement for an undisclosed sum was reached, TV Nova apologized to the Havels on its evening news programme.
Interview with Olga Stankovicová, Prague, 10 November 1998.
'Politologům se nelíbi Havlovo příliš emotivní vystupování', _MF Dnes_ (Prague), 9 December 1997, p. 3. Later evidence of his continuing depression is found in the leaked memorandum, 'Mym podřízeným' ('To my subordinates'), reprinted in _Lidové noviny_ (Prague), 10 October 1998, p. 27. The memorandum outlines a media strategy ('I want to be seen less and heard less'), and begins with a confession: 'This weekend I was in one of the deepest depressions in a long time. It was probably evident at our meeting, or in my introduction. If I put anyone in a bad mood, I apologize for that. On the other hand, I tell myself that it doesn't do any harm if my colleagues occasionally have a peek at the sombre spirit of their boss.'
Cited in _The Prague Post_ (Prague), 8-14 January 1997, p. 1.
The Brno newspaper _Moravsko slezský den_ (21 November 1997) reported that, although 65.7 per cent of Czechs still 'trusted' Havel, his popularity had dropped 20 per cent during 1997 alone.
Joseph Brodsky to Václav Havel, printed in the _New York Review of Books,_ 41, 4 (1994), p. 30
Christopher Hitchens, 'Havel in the Castle', _The Nation_ (Washington, DC), 16 December 1996, p. 8.
Immanuel Kant, _Zum ewigen Frieden. Ein philosophischer Entwurf_ (Berlin, 1795), second supplement, in _Immanuel Kants Werke,_ ed. Ernst Cassirer, volume 6 (Berlin, 1914); Friedrich Nietzsche, _Götzen-Dämmerung, oder Wie man mit dem Hammer philosophirt_ (Leipzig, 1889), p. 59.
Speech in acceptance of the Philadelphia Liberty Medal, Philadelphia, 4 July 1994.
Interview with Alois Strnad, Prague, 28 September 1997.
Interview with Paul Wilson, Toronto, 1 June 1998. According to Wilson, Havel rejected any suggestions that he might in future play the kind of public role carved out by the former Canadian Prime Minister, Pierre Trudeau. 'I can't see that I would have as much, or more, influence as a writer than as a president,' said Havel.
William Shakespeare, _A Midsummer Night's Dream,_ Act 5, Scene 1.
Address in acceptance of an Honorary Degree from Oxford University, Oxford, 22 October 1998, posted at <http://www.hrad.cz/president/Havel/speeches/1998/2210_uk.html>.
Adam Michnik, in a speech to the Friedrich Naumann Foundation (Berlin, 1995).
Cited in Jonathan Steele, 'Crushed-velvet revolutionary', _Guardian_ (London), 13 March 1999. A similar remark was made in my interview with Palouš, (Prague) 24 September 1997.
'A Crying Need for Intellectuals', _The New Presence,_ op. cit., p. 18.
_Leviathan,_ op. cit., Part 1, chapter 11.
Jan Patočka, _Heretical Essays in the Philosophy of History,_ translated by Erazim Kohák (Chicago and La Salle, Illinois, 1996), p. 105.
Interview with Antonín Pridal, 'Z očí do očí', Česká televize 2, Prague, 1996.
Of the eight former presidents of Czechoslovakia, six either stepped down for health reasons (Masaryk [1918-1935]; Beneš [1935-1938; 1941-1946; 1946-1948]; Svoboda [1968-1973; 1973-1975]); or died when in office (Gottwald [1948-1953]; Zápotocký [1953-1957]); or died in prison shortly after being arrested (Hácha [1938-1945]). See Vladimír Kadlec, _Podivné konce našich prezident ů_ (first published in samizdat, Prague, 1989 [1991].
Jaroslav Šabata, _Sedmkrát Sedm Kruh ů_ (Olomouc, 1997), p. 107.
All quotations are from the pre-recorded interview with Havel conducted by Bohumil Klepetko and Jolana Voldánová and transmitted on ČTV 2, 13 June 1998.
Interview with Michal Serf, Prague, 2 November 1998.
The following quotations are drawn from the interview with Professor Bodner conducted by Marek Wollner, _Týden,_ 31 (27 July 1998), pp. 18, 20.
_The Prague Post_ (2-8 September 1998), p. 2.
_Rytmus ž ivota,_ 31 (29 July 1998), p. 5; cf. _Lidové noviny,_ 27 July 1998, p. 3. Compare the remark of Miroslav Čerbák, head of the Doctors' Concilium responsible for treating Havel during this period: 'He is the type of person who, when he feels a task and duty, comes alive' _(MF Dnes_ [Prague], 4 December 1997).
Homer, _Iliad,_ Book XI, 1, 394.
Ernst H. Kantorowicz, _The King's Two Bodies. A Study in Medieval Political Theology_ (Princeton, NJ, 1957), especially pp. 3–23, 314-450.
_Lidové noviny,_ 21 November 1997, p. 3. In a readers' poll, the same newspaper reported that there were some Czechs who liked what Havel had done for their country, but who were emphatic that 'the atmosphere of irreplaceability' enveloping the Castle ( _atmosféra nenahraditelnosti)_ was bad for the role of the presidency.
See the first-hand account by H. Gordon Skilling, 'Letters from Prague 1937', _Kosmas, Journal of Czechoslovak and Central European Affairs_ (London, 1982), p. 71.
## **A Note on the Author**
John Keane is Director of the Centre for the Study of Democracy, and Professor of Politics at the University of Westminster. Born in Australia, he completed his education at the universities of Adelaide, Toronto and Cambridge. He has written many books, including the acclaimed biography of Tom Paine and _The Media and Democracy_ (which has been translated into nineteen languages), and is a frequent contributor to radio, television, newspapers, and magazines.
## By the Same Author
Public Life and Late Capitalism
Democracy and Civil Society
The Media and Democracy
Tom Paine: A Political Life
Reflections on Violence
Civil Society: Old Images, New Visions
First published 1999
This electronic edition published in 2012 by Bloomsbury Publishing Plc
Copyright © 1999 by John Keane
The moral right of the author has been asserted
Bloomsbury Publishing Plc,
50 Bedford Square
London WC1B 3DB
A CIP catalogue record for this book
is available from the British Library
ISBN: 978 1 4088 3208 0
All rights reserved. You may not copy, distribute, transmit, reproduce or otherwise make available this publication (or any part of it) in any form, or by any means (including without limitation electronic, digital, optical, mechanical, photocopying, printing, recording or otherwise), without the prior written permission of the publisher. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages.
Visit www.bloomsbury.com to find out more about our authors and their books You will find extracts, author interviews, author events and you can sign up for newsletters to be the first to hear about our latest releases and special offers
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Finale bezeichnet einen beschließenden Abschnitt der Dramaturgie eines musiktheatralischen Werkes. In der Konfiguration der "Nummern" innerhalb eines musikdramatischen Werkes hat das Finale eine Sonderstellung inne: In der Regel beginnt es nicht gleichsam voraussetzungslos, wie oft andere "offene" Formen im musikdramatischen Genre, etwa eine Introduktion oder ein Ensemblestück inmitten eines Aktes. Vielmehr ist in der Regel davon auszugehen, dass nach einer Peripetie in der Handlung das Finale mit einem Eklat beginnt, der durch eine außergewöhnlich konfliktreiche Personen- oder Handlungskonstellation motiviert ist. Diese Situation kann bereits zuvor herbeigeführt worden sein und im "Schluss"-Abschnitt eines Aktes oder eines ganzen Werkes auch nur zu einem wie auch immer gearteten vorläufigen Ende oder Abschluss gebracht werden.
Zweierlei Arten des Finalensembles sind in der Oper möglich und kommen gerade auch in der sogenannten "großen" Oper des späten 18. bis 19. Jahrhunderts vor: das Finale eines Aktes, mit dem die Oper noch nicht schließt, und das Werk-Finale. Zwar kann jede dieser Finalarten noch Perspektiven für Künftiges eröffnen, doch weicht die dramaturgische Situation in beiden Fällen beträchtlich voneinander ab. In der Ausgangssituation aber unterscheidet sich das vorläufige Finale naturgemäß kaum von dem endgültigen, es ist nur die Frage, ob die dramatische Situation noch genügend Zündstoff birgt, weitere "Handlungen" zu motivieren.
Eine häufig gewählte und oft effektvolle dramaturgische Konstellation besteht darin, dass die bereits in der Exposition und dem weiteren Verlauf der Handlung schwelenden Privatkonflikte der Protagonisten im Finale unversehens an die Bühnen-Öffentlichkeit gezerrt werden. Dies bietet dann auch die Möglichkeit, das bereits in Duetten oder anderen "kleinen" Ensemble-Formen Verhandelte im großen Rahmen coram publico noch einmal in gesteigerter Form zu wiederholen, es somit auch noch einmal völlig neu zu beleuchten.
In der Regel kann man davon ausgehen, dass es sich bei den Finali um vielgliedrige "Nummern" handelt, in denen die Protagonisten und ihre Vertrauten oder Chöre in mehreren verschiedenen Situationen mit- und nacheinander konfrontiert werden, und dass sich im Idealfall die Handlung aufgrund überraschender Effekte und Neuigkeiten unvorhergesehenermaßen weiterentwickelt. Eine besondere musikalische Form stellt dagegen das sogenannte "Kettenfinale" dar, das die Komponisten der Opera buffa entwickelten. Wie bei einem Rondo werden einzelne musikalische Themen im Wechsel aneinandergereiht, teils kehren aber auch einzelne Themen unmittelbar, oder nach einem gewissen zeitlichen Abstand, wieder.
In manchen Opern, insbesondere den "Zauberopern" nach Art der Zauberflöte, sind die musikalischen Abschnitte eines Finales stark voneinander getrennt; es finden hier dann sogar mehrfach Wechsel der Kulissen statt.
Eine einheitliche Gestalt ist bei Finalnummern nicht gegeben, und dennoch gibt es in fast allen Opern des späten 18. und des 19. Jahrhunderts musikalisch-dramatische (Groß-)Abschnitte, die als Finale bezeichnet werden.
Literatur
Gerd Rienäcker: Finali in Opern von E. T. A. Hoffmann, Louis Spohr, Heinrich Marschner und Carl Maria von Weber. Gedanken zur Theorie und Geschichte des Opernfinales. Habilitationsschrift Humboldt-Universität Berlin 1984.
Paul Joseph Horsley: Dittersdorf and the finale in late-eighteenth-century German comic opera. Diss. Cornell University 1988.
Till Gerrit Waidelich: "Falsch" positioniert? Anmerkungen zu Finali und finalartigen Szenen in Schuberts Opern, in: "Dialekt ohne Erde". Franz Schubert und das 20. Jahrhundert (= Studien zur Wertungsforschung Bd. 34, hg. Otto Kolleritsch), Wien–Graz 1998, S. 187–199.
Claire Badiou: Carl Dahlhaus und die zeitliche Diskontinuität der Oper. Einige Überlegungen zu Zeitstrukturen im Finale von "Le nozze di Figaro". In: Hermann Danuser, Peter Gülke und Norbert Miller in Verbindung mit Tobias Plebuch (Hrsg.): Carl Dahlhaus und die Musikwissenschaft. Werk, Wirkung, Aktualität. Ed. Argus, Schliengen 2011, ISBN 3-931264-76-9, ISBN 978-3-931264-76-5, S. 125–131.
Teil einer musikalischen Form
Teil einer Oper | {
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{"url":"https:\/\/ai.stackexchange.com\/questions\/18269\/monte-carlo-updates-on-policy-gradient-with-no-terminal-state","text":"Consider some MDP with no terminal state. We can apply bootstrapping methods (like TD(0)) to learn in these cases no problem, but in policy gradient algorithms that have only a simple monte carlo update, it requires us to supply a complete trajectory (which is impossible with no terminal state).\n\nNaturally, one might let the MDP run for 1000 periods, and then terminate as an approximation. If we feed these trajectories into a monte carlo update, I imagine that samples for time period t=1,2,...,100 would give very good estimates for the value function due to the discount factor. However, the time periods 997, 998, 999, 1000, we'd have an expected value for those trajectories far different than V(s) due to their proximity to the cutoff of 1000.\n\nThe question is this:\n\n1. Should we even include these later-occurring data points when we update our function approximation?\n\nOR\n\n1. Is the assumption that these points become really sparse in our updates, so they won't have much effect in our training?\n\nOR\n\n1. Is it usually implied that the final data reward in the trajectory is bootstrapped in these cases (i.e., we have some TD(0)-like behavior in this case)?\n\nOR\n\n1. Are monte carlo updates for policy gradient algorithms even appropriate for non-terminating MDPs due to this issue?\n\u2022 It'd be better to only have one question; you can have follow-ups in separate posts. \u2013\u00a0Oliver Mason Feb 27 at 9:49\n\u2022 @OliverMason It isn't really four different questions; it's 4 hypothetical explanations that the OP has come up with to explain his own confusion, and he's asking which of them are on point. So I vote to leave it open \u2013\u00a0Dennis Soemers Mar 6 at 20:25\n\nNaturally, one might let the MDP run for 1000 periods, and then terminate as an approximation. If we feed these trajectories into a monte carlo update, I imagine that samples for time period t=1,2,...,100 would give very good estimates for the value function due to the discount factor. However, the time periods 997, 998, 999, 1000, we'd have an expected value for those trajectories far different than V(s) due to their proximity to the cutoff of 1000.\n\nI think your intuition is... partially right here, but not entirely precise. Recall that a value function $$V(S)$$ is generally defined as something like (omitting some unimportant details like specifying the policy):\n\n$$V(S_i) = \\mathbb{E} \\left[ \\sum_{t=0}^{\\infty} \\gamma^t R_{i+t} \\right].$$\n\nThe \"samples for time period $$t = 1, 2, \\dots, 100$$ that you mention are not estimates for this full value function. They're estimates for the corresponding individual terms $$R_{i+t}$$. Indeed, in general, your intuition is right that the closer they are to the \"starting point\" $$i$$, the more likely they'll be to be accurate estimators. This is because larger $$t$$ are typically associated with larger numbers of stochastic state-transitions and stochastic decision-making, and therefore often exhibit higher variance.\n\n1. Should we even include these later-occurring data points when we update our function approximation?\n\nTheoretically, you absolutely should. Suppose you have an environment where almost every reward is equal to $$0$$, and only after 1000 steps do you actually observe a non-zero reward. If you don't include this, you'll learn nothing! In practice, it can often be a good idea to give them less importance though. This already happens automatically by picking a discount factor $$\\gamma < 1$$.\n\n1. Is it usually implied that the final data reward in the trajectory is bootstrapped in these cases (i.e., we have some TD(0)-like behavior in this case)?\n\nOR\n\n1. Are monte carlo updates for policy gradient algorithms even appropriate for non-terminating MDPs due to this issue?\n\nIt would be possible to do some form of bootstrapping at the end yeah, cut off and then have a trained value function predicting what the remainder of the rewards would be. TD($$\\lambda$$) with $$\\lambda$$ close to $$1$$ would be much closer in behaviour to true MC updates than TD($$0$$) though. Either way, it would be technically incorrect to still call it Monte-Carlo then, it would no longer be pure Monte-Carlo. 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Q: DataTables using PHP with MySQL: How to modify the mysql query? So I'm trying to populate a html table using a table in my database. Lets call it 'business' and one of the columns is called 'id'.
I am trying to use WHERE. I
For example something like..
SELECT * all FROM business WHERE id=4.
Do I need to modify $sWhere?
Here is the code that I am using for server side processing.
/*
* Script: DataTables server-side script for PHP and MySQL
* Copyright: 2010 - Allan Jardine, 2012 - Chris Wright
* License: GPL v2 or BSD (3-point)
*/
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* Easy set variables
*/
/* Array of database columns which should be read and sent back to DataTables. Use a space where
* you want to insert a non-database field (for example a counter or static image)
*/
$aColumns = array('bus_num', 'bus_phone', 'category_name', 'bus_status');
/* Indexed column (used for fast and accurate table cardinality) */
$sIndexColumn = "id";
/* DB table to use */
$sTable = "business";
/* Database connection information */
$gaSql['user'] = "dev";
$gaSql['password'] = "dev";
$gaSql['db'] = "dev";
$gaSql['server'] = "localhost";
/* REMOVE THIS LINE (it just includes my SQL connection user/pass) */
$db = mysql_connect('localhost', 'dev', 'dev');
if (!$db){
die ("Could not connect to database" . mysql_error());
exit();
}
$db_selected = mysql_select_db('dev', $db);
if(!$db_selected) {
die ('Can\'t use:' . mysql_error());
}
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* If you just want to use the basic configuration for DataTables with PHP server-side, there is
* no need to edit below this line
*/
/*
* Local functions
*/
function fatal_error ( $sErrorMessage = '' )
{
header( $_SERVER['SERVER_PROTOCOL'] .' 500 Internal Server Error' );
die( $sErrorMessage );
}
/*
* MySQL connection
*/
if ( ! $gaSql['link'] = mysql_pconnect( $gaSql['server'], $gaSql['user'], $gaSql['password'] ) )
{
fatal_error( 'Could not open connection to server' );
}
if ( ! mysql_select_db( $gaSql['db'], $gaSql['link'] ) )
{
fatal_error( 'Could not select database ' );
}
/*
* Paging
*/
$sLimit = "";
if ( isset( $_GET['iDisplayStart'] ) && $_GET['iDisplayLength'] != '-1' )
{
$sLimit = "LIMIT ".intval( $_GET['iDisplayStart'] ).", ".
intval( $_GET['iDisplayLength'] );
}
/*
* Ordering
*/
$sOrder = "";
if ( isset( $_GET['iSortCol_0'] ) )
{
$sOrder = "ORDER BY ";
for ( $i=0 ; $i<intval( $_GET['iSortingCols'] ) ; $i++ )
{
if ( $_GET[ 'bSortable_'.intval($_GET['iSortCol_'.$i]) ] == "true" )
{
$sOrder .= $aColumns[ intval( $_GET['iSortCol_'.$i] ) ]."
".($_GET['sSortDir_'.$i]==='asc' ? 'asc' : 'desc') .", ";
}
}
$sOrder = substr_replace( $sOrder, "", -2 );
if ( $sOrder == "ORDER BY" )
{
$sOrder = "";
}
}
/*
* Filtering
* NOTE this does not match the built-in DataTables filtering which does it
* word by word on any field. It's possible to do here, but concerned about efficiency
* on very large tables, and MySQL's regex functionality is very limited
*/
$sWhere = "";
if ( isset($_GET['sSearch']) && $_GET['sSearch'] != "" )
{
$sWhere = "WHERE (";
for ( $i=0 ; $i<count($aColumns) ; $i++ )
{
if ( isset($_GET['bSearchable_'.$i]) && $_GET['bSearchable_'.$i] == "true" )
{
$sWhere .= $aColumns[$i]." LIKE '%".mysql_real_escape_string( $_GET['sSearch'] )."%' OR ";
}
}
$sWhere = substr_replace( $sWhere, "", -3 );
$sWhere .= ')';
}
/* Individual column filtering */
for ( $i=0 ; $i<count($aColumns) ; $i++ )
{
if ( isset($_GET['bSearchable_'.$i]) && $_GET['bSearchable_'.$i] == "true" && $_GET['sSearch_'.$i] != '' )
{
if ( $sWhere == "" )
{
$sWhere = "WHERE ";
}
else
{
$sWhere .= " AND ";
}
$sWhere .= $aColumns[$i]." LIKE '%".mysql_real_escape_string($_GET['sSearch_'.$i])."%' ";
}
}
/*
* SQL queries
* Get data to display
*/
$sQuery = "
SELECT SQL_CALC_FOUND_ROWS ".str_replace(" , ", " ", implode(", ", $aColumns))."
FROM $sTable
$sWhere
$sOrder
$sLimit
";
$rResult = mysql_query( $sQuery, $gaSql['link'] ) or fatal_error( 'MySQL Error: ' . mysql_errno() );
/* Data set length after filtering */
$sQuery = "
SELECT FOUND_ROWS()
";
$rResultFilterTotal = mysql_query( $sQuery, $gaSql['link'] ) or fatal_error( 'MySQL Error: ' . mysql_errno() );
$aResultFilterTotal = mysql_fetch_array($rResultFilterTotal);
$iFilteredTotal = $aResultFilterTotal[0];
/* Total data set length */
$sQuery = "
SELECT COUNT(".$sIndexColumn.")
FROM $sTable
";
$rResultTotal = mysql_query( $sQuery, $gaSql['link'] ) or fatal_error( 'MySQL Error: ' . mysql_errno() );
$aResultTotal = mysql_fetch_array($rResultTotal);
$iTotal = $aResultTotal[0];
/*
* Output
*/
$output = array(
"sEcho" => intval($_GET['sEcho']),
"iTotalRecords" => $iTotal,
"iTotalDisplayRecords" => $iFilteredTotal,
"aaData" => array()
);
while ( $aRow = mysql_fetch_array( $rResult ) )
{
$row = array();
for ( $i=0 ; $i<count($aColumns) ; $i++ )
{
if ( $aColumns[$i] == "version" )
{
/* Special output formatting for 'version' column */
$row[] = ($aRow[ $aColumns[$i] ]=="0") ? '-' : $aRow[ $aColumns[$i] ];
}
else if ( $aColumns[$i] != ' ' )
{
/* General output */
$row[] = $aRow[ $aColumns[$i] ];
}
}
$output['aaData'][] = $row;
}
echo json_encode( $output );
A: /*
* Filtering
* NOTE this does not match the built-in DataTables filtering which does it
* word by word on any field. It's possible to do here, but concerned about efficiency
* on very large tables, and MySQL's regex functionality is very limited
*/
//$sWhere = "";
if ( isset($_GET['sSearch']) && $_GET['sSearch'] != "" )
{
$sWhere = "WHERE id='4' AND (";
for ( $i=0 ; $i<count($aColumns) ; $i++ )
{
if ( isset($_GET['bSearchable_'.$i]) && $_GET['bSearchable_'.$i] == "true" )
{
$sWhere .= $aColumns[$i]." LIKE '%".mysql_real_escape_string( $_GET['sSearch'] )."%' OR ";
}
}
$sWhere = substr_replace( $sWhere, "", -3 );
$sWhere .= ')';
} else {
$sWhere = "WHERE id = '4' ";
}
A:
DataTables is a plug-in for the jQuery Javascript library. It is a
highly flexible tool, based upon the foundations of progressive
enhancement, which will add advanced interaction controls to any HTML
table.
you might want to use:
Server-side processing | PHP with MySQL This script serves as the
basis for the testing and development that happens with DataTables, so
it is always right up to date, and will always implement all of the
features that are supported in DataTables with server-side processing
(with the exception of regex filtering - for database access speed
reasons).
To use the code on your own server, simply change the $aColumns array
to list the columns you wish to include from your database, set
$sIndexColumn to a column which is indexed (for speed), $sTable to the
table name, and finally fill in your database connection parameters to
$gaSql. Please note that this script uses json_encode which requires
PHP 5.2 or newer. For a version of this script which is compatible
with older versions please see the PHP 4 compatible
http://datatables.net/development/server-side/php_mysql
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 965 |
package org.meteogroup.jbrotli.jni;
import org.testng.annotations.Test;
import java.net.URL;
public class LoadLibraryTest {
@Test
public void the_library_can_be_loaded() throws Exception {
URL resource = this.getClass().getResource("/lib/linux-x86-amd64/libbrotli.so");
Runtime.getRuntime().load(resource.getFile());
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,341 |
Q: I get this error "Unhandled exception at 0x009437bd in Hash functions.exe: 0xC0000005: Access violation reading location 0x00000001" I get this error over and over again when I run my project. Don't know where is the problem. I know it's about some free memory I used again, or a null pointer or access to a non exist memory but actually I checked all the pointers and they are declared as what they should to be.
Here's the code:
#include <iostream>
using namespace std ;
typedef struct ND {
int ID;
char* Name;
char* Address;
int Age;
double GPA;
ND * next;
} NODE;
class HF {
private :
int count;
int size ;
int prime;
int a ,b;
NODE ** HT;
public:
HF ();
HF ( int n , int p , int a, int b);
~ HF ();
int findindex(int key);
bool insert (int ID,char* Name,char* Address,int Age,double GPA);
bool retrieve (int & ID,char* & Name,char* & Address,int & Age,double & GPA);
bool remove(int key);
double GetLoadFactor ();
};
HF :: HF ()
{
size = 100;
prime = 997;
a = 23 ;
b = 88;
count =0;
HT = new NODE* [size];
for (int i=0; i< size ; i++)
HT[i] = NULL;
}
HF :: HF ( int n , int p , int a, int b)
{
size = n;
prime = p;
a = a;
b = b;
count = 0;
HT = new NODE* [size];
for (int i=0; i< size ; i++)
HT[i] = NULL;
}
HF :: ~ HF ()
{
NODE *p;
for (int i=0 ; i<size ; i++)
{
while (HT[i] != NULL)
{
p = HT[i];
HT[i] = HT[i] -> next ;
delete p;
}
}
delete [] HT ;
}
int HF :: findindex(int key)
{
int index ;
index = (((a*(key)+b) % prime) % size) ;
index = index % size ;
return index;
}
bool HF :: insert (int ID,char* Name,char* Address,int Age,double GPA)
{
int i ;
NODE * n;
n = new NODE;
n -> ID = ID;
n -> Address = Address;
n -> Name = Name;
n -> Age = Age;
n -> GPA = GPA;
n -> next = NULL;
i = findindex(ID);
if ( HT[i] == NULL)
{
HT[i] = n;
}
else
{
n -> next = HT[i];
HT[i] = n;
}
count ++ ;
return true;
}
bool HF ::retrieve (int & key,char* & Name,char * &Address,int & Age,double & GPA)
{
int i ;
NODE *p;
i = findindex(key);
if ( HT[i] == NULL)
{
return false;
}
else
{
p = HT[i];
if ( HT[i] -> ID == key)// here is the break point
{
key = p-> ID ;
Name = p-> Name ;
Address = p-> Address ;
Age = p-> Age;
GPA = p-> GPA ;
return true ;
}
while ( p != NULL)
{
if ( p-> ID == key)
{
key = p-> ID ;
Name = p-> Name ;
Address = p-> Address ;
Age = p-> Age;
GPA = p-> GPA ;
return true ;
}
else
p = p-> next ;
}
}
return false;
}
bool HF :: remove (int key)
{
int i ;
NODE *p1 , *p2;
i = findindex(key);
if ( HT[i] == NULL)
{
return false;
}
else
{
p1 =p2 = HT[i];
if(HT[i] -> ID == key)
{
HT[i] = HT[i] -> next;
delete p2;
return true;
}
while ( p2 != NULL)
{
if ( p2 -> ID == key)
{
p1 -> next = p2 -> next ;
delete p2;
count --;
return true;
}
else
{
p1 =p2;
p2 = p2 -> next;
}
}
}
return false;
}
double HF :: GetLoadFactor()
{
double L;
L = (double) count/size ;
return L;
}
int main ()
{
double L;
int x,age;
char * name , *address;
double GPA;
HF UHashFunc1;
HF UHashFunc2( 11 , 7 , 3 , 0);
UHashFunc1.insert( 6 , "Ahmed" , "Jenin" , 20 , 3.5);
UHashFunc1.insert( 1 , "Sarah" , "Jenin" , 18 , 3.2);
UHashFunc1.insert(40 , "Mohammad" , "Tolkrem", 19 , 3.0);
UHashFunc1.insert(2 , "Ala'a" , "Jerusalem", 19 , 2.6);
UHashFunc1.insert(41 , "Raghad" , "Tolkrem", 19 , 1.6);
UHashFunc1.insert(80 , "Mohammad" , "Jenin", 22 , 2.7);
UHashFunc1.insert(83 , "Murad" , "Nablus", 18 , 3.7);
UHashFunc1.insert(44 , "Reem" , "Hebron", 19 , 2.9);
UHashFunc1.insert(50 , "Wajde" , "Qalqelya", 20, 1.7);
UHashFunc1.insert(42 , "Belal" , "Hebron", 20 , 3.4);
UHashFunc1.insert(3 , "Ahmed" , "Nablus", 21 , 1.9);
UHashFunc1.insert(84 , "Haitham" , "Nablus", 21 , 3.1);
cout <<"enter the ID you want to retrieve"<<endl;
cin>>x;
if(UHashFunc1.retrieve(x,name,address,age,GPA))
{
cout << "ID:"<<x<<endl;
cout << "Name:"<<name<<endl;
cout << "Address:"<<address<<endl;
cout << "Age:"<<age<<endl;
cout << "GPA:"<<GPA<<endl;
}
else
cout<<"NOT FOUND"<<endl;
cout <<"enter the ID you want to retrieve"<<endl;
cin>>x;
if(UHashFunc1.retrieve(x,name,address,age,GPA))
{
cout << "ID:"<<x<<endl;
cout << "Name:"<<name<<endl;
cout << "Address:"<<address<<endl;
cout << "Age:"<<age<<endl;
cout << "GPA:"<<GPA<<endl;
}
else
cout<<"NOT FOUND"<<endl;
L=UHashFunc1.GetLoadFactor();
cout << "The current load factor is : " << L <<endl;
UHashFunc1.remove(42);
L=UHashFunc1.GetLoadFactor();
cout << "The current load factor is : " << L <<endl;
x=84;
UHashFunc1.retrieve(x,name,address,age,GPA);
cout << "ID:"<<x<<endl;
cout << "Name:"<<name<<endl;
cout << "Address:"<<address<<endl;
cout << "Age:"<<age<<endl;
cout << "GPA:"<<GPA<<endl;
x=1;
UHashFunc1.retrieve(x,name,address,age,GPA);
cout << "ID:"<<x<<endl;
cout << "Name:"<<name<<endl;
cout << "Address:"<<address<<endl;
cout << "Age:"<<age<<endl;
cout << "GPA:"<<GPA<<endl;
x=50;
UHashFunc1.retrieve(x,name,address,age,GPA);
cout << "ID:"<<x<<endl;
cout << "Name:"<<name<<endl;
cout << "Address:"<<address<<endl;
cout << "Age:"<<age<<endl;
cout << "GPA:"<<GPA<<endl;
cout << "Enter The ID you want to remove"<<endl;
cin>>x;
if(UHashFunc1.remove(x))
{
L=UHashFunc1.GetLoadFactor();
cout << "The current load factor after removing a record is : " << L <<endl;
}
else
{ cout << "NOT Exist"<<endl;}
if(UHashFunc1.remove(2))
{
L=UHashFunc1.GetLoadFactor();
cout << "The current load factor after removing a record is : " << L <<endl;
}
else
{ cout << "NOT Exist"<<endl;}
UHashFunc1.insert( 45 , "Amjad" , "Nablus" , 19 , 2.0);
L=UHashFunc1.GetLoadFactor();
cout << "The current load factor after adding a record is : " << L <<endl;
if(UHashFunc1.remove(80))
{
L=UHashFunc1.GetLoadFactor();
cout << "The current load factor after removing the record is : " << L <<endl;
}
else
{ cout << "NOT Exist"<<endl;}
if(UHashFunc1.remove(50))
{
L=UHashFunc1.GetLoadFactor();
cout << "The current load factor after removing the record is : " << L <<endl;
}
else
{ cout << "NOT Exist"<<endl;}
UHashFunc2.insert( 5 , "Ahmed" , "Jenin" , 20 , 3.5);
UHashFunc2.insert( 1 , "Sarah" , "Jenin" , 18 , 3.2);
UHashFunc2.insert(9 , "Mohammad" , "Tolkrem", 19 , 3.0);
UHashFunc2.insert(2 , "Ala'a" , "Jerusalem", 19 , 2.6);
UHashFunc2.insert(8 , "Raghad" , "Tolkrem", 19 , 1.6);
UHashFunc2.insert(100 , "Mohammad" , "Jenin", 22 , 2.7);
UHashFunc2.insert(50 , "Murad" , "Nablus", 18 , 3.7);
UHashFunc2.insert(23 , "Reem" , "Hebron", 19 , 2.9);
UHashFunc2.insert(40 , "Wajde" , "Qalqelya", 20, 1.7);
UHashFunc2.insert(17 , "Belal" , "Hebron", 20 , 3.4);
UHashFunc2.insert(3 , "Ahmed" , "Nablus", 21 , 1.9);
UHashFunc2.insert(7 , "Haitham" , "Nablus", 21 , 3.1);
cout <<"enter the ID you want to retrieve from the 2nd Func"<<endl;
cin>>x;
if(UHashFunc2.retrieve(x,name,address,age,GPA))
{
cout << "ID:"<<x<<endl;
cout << "Name:"<<name<<endl;
cout << "Address:"<<address<<endl;
cout << "Age:"<<age<<endl;
cout << "GPA:"<<GPA<<endl;
}
else
cout<<"NOT FOUND"<<endl;
cout <<"enter the ID you want to retrieve from the 2nd Func"<<endl;
cin>>x;
if(UHashFunc2.retrieve(x,name,address,age,GPA))
{
cout << "ID:"<<x<<endl;
cout << "Name:"<<name<<endl;
cout << "Address:"<<address<<endl;
cout << "Age:"<<age<<endl;
cout << "GPA:"<<GPA<<endl;
}
else
cout<<"NOT FOUND"<<endl;
L=UHashFunc2.GetLoadFactor();
cout << "The current load factor is : " << L <<endl;
UHashFunc2.remove(2);
L=UHashFunc2.GetLoadFactor();
cout << "The current load factor is : " << L <<endl;
x=5;
UHashFunc2.retrieve(x,name,address,age,GPA);
cout << "ID:"<<x<<endl;
cout << "Name:"<<name<<endl;
cout << "Address:"<<address<<endl;
cout << "Age:"<<age<<endl;
cout << "GPA:"<<GPA<<endl;
x=1;
UHashFunc2.retrieve(x,name,address,age,GPA);
cout << "ID:"<<x<<endl;
cout << "Name:"<<name<<endl;
cout << "Address:"<<address<<endl;
cout << "Age:"<<age<<endl;
cout << "GPA:"<<GPA<<endl;
x=50;
UHashFunc2.retrieve(x,name,address,age,GPA);
cout << "ID:"<<x<<endl;
cout << "Name:"<<name<<endl;
cout << "Address:"<<address<<endl;
cout << "Age:"<<age<<endl;
cout << "GPA:"<<GPA<<endl;
cout << "Enter The ID you want to remove from the 2nd Func"<<endl;
cin>>x;
if(UHashFunc2.remove(x))
{
L=UHashFunc2.GetLoadFactor();
cout << "The current load factor after removing a record is : " << L <<endl;
}
else
{ cout << "NOT Exist"<<endl;}
if(UHashFunc2.remove(2))
{
L=UHashFunc2.GetLoadFactor();
cout << "The current load factor after removing a record is : " << L <<endl;
}
else
{ cout << "NOT Exist"<<endl;}
UHashFunc2.insert( 45 , "Amjad" , "Nablus" , 19 , 2.0);
L=UHashFunc2.GetLoadFactor();
cout << "The current load factor after adding a record is : " << L <<endl;
if(UHashFunc2.remove(100))
{
L=UHashFunc2.GetLoadFactor();
cout << "The current load factor after removing the record is : " << L <<endl;
}
else
{ cout << "NOT Exist"<<endl;}
if(UHashFunc2.remove(9))
{
L=UHashFunc2.GetLoadFactor();
cout << "The current load factor after removing the record is : " << L <<endl;
}
else
{ cout << "NOT Exist"<<endl;}
cin>>x;
return 0;
}
There are no building errors just these ones when break point
First-chance exception at 0x009437bd in Hash functions.exe:
0xC0000005: Access violation reading location 0x00000001. Unhandled
exception at 0x009437bd in Hash functions.exe: 0xC0000005: Access
violation reading location 0x00000001. First-chance exception at
0x009437bd in Hash functions.exe: 0xC0000005: Access violation reading
location 0x00000001. The thread 'Win32 Thread' (0x1e40) has exited
with code -1073741510 (0xc000013a). The program '[788] Hash
functions.exe: Native' has exited with code -1073741510 (0xc000013a).
A: I was able to easily reproduce the error you ran into.
You have a constructor for HF that takes parameters like this:
HF :: HF ( int n , int p , int a, int b)
{
size = n;
prime = p;
a = a;
b = b;
As you can see the parameter names a and b are exactly the same as the member variable names. Hence HF::a and HF::b are never assigned values. Hence they are always uninitialized and contain garbage. Hence you get nothing but random values, and all the hashing stuff you are trying to do doesn't work as a result.
You should change the parameter names to something different. Say with capital letters perhaps:
HF :: HF ( int n , int p , int A, int B)
{
size = n;
prime = p;
a = A;
b = B;
Once I do that, it solves all the memory corruption errors, and it runs to completion just fine.
A: Learn to use, and then apply, std::vector<T>, std::string, std::shared_ptr<T>, std::unique_ptr<T>. Then come back if problem persists.
A: This is most certainly a NULL pointer. You are accessing memory location 1 (0x00000001), which is 1 byte offset from NULL (aka 0x00000000). The code you posted is verbose and a bit of a mess, and without a line number where you are accessing the pointer, it's hard to say where exactly you are accessing a NULL pointer.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,931 |
\section{Introduction}\label{Sec:intro}}
\IEEEPARstart{S}{tandard} machine learning assumes that training and test data are drawn from the same underlying distribution. As such, uniform convergence bounds guarantee the generalization of models learned on training data for the use of testing \cite{MLFoudatation2014}. Although standard machine learning has achieved great success in various tasks \cite{alexnet, girshick2014rich,jia2019orthogonal}, even with few training data \cite{vinyals2016matching,zhang2019part} or training data of multiple modalities \cite{jia2019deep}, in many practical scenarios, one may encounter situations where annotated training data can only be collected easily from one or several distributions that are related to the testing distribution. In other words, the target data of interest follow a distribution differing from the training source data.
A typical example in deep learning-based image analysis is that one may annotate as many synthetic images as possible, but often fails to annotate even a single real image. Thus it is expected to adapt the models learned from synthetic images for testing on real images. This problem setting falls in the realm of transfer learning or domain adaptation \cite{transfer_survey}. In this work, we focus particularly on unsupervised domain adaptation (UDA), in which target data are completely unlabeled.
In the literature, theoretical studies on domain adaptation characterize the conditions under which classifiers trained on labeled source data can be adapted for use on the target domain \cite{ben2007analysis,ben2010theory,mansour2009domain,courty2016optimal}. For example, Ben-David \emph{et al.} \cite{ben2010theory} propose the notion of distribution divergence induced by the hypothesis space of binary classifiers, based on which a bound of the expected error on the target domain is thus developed. Mansour \emph{et al.} \cite{mansour2009domain} extend the zero-one loss used in \cite{ben2010theory} to arbitrary loss functions of binary classification. These theoretical results motivate many of existing UDA algorithms, including the recently popular ones based on the domain-adversarial training of deep networks \cite{dann,adda,cada,mcd,symnets}. A common motivation of these algorithms is to design adversarial objectives concerned with minimax optimization, in order to reduce the hypothesis-induced domain divergence via the learning of domain-invariant feature representations.
While theoretical adaptation conditions are strictly derived under the setting of binary classification with analysis-amenable loss functions, practical algorithms easier to be optimized are often expected to be applied to the cases of multiple classes. In other words, the learning objectives in many of the recent algorithms are only inspired by, rather than strictly derived from the domain adaptation bounds in \cite{ben2010theory,mansour2009domain}. This gap between theories and algorithms is recently studied in \cite{mdd}, where the notion of margin disparity discrepancy (MDD) induced by pairs of multi-class scoring hypotheses is introduced to measure the divergence between domain distributions. This thus extends theories in \cite{ben2010theory,mansour2009domain} and connects with the multi-class setting of practical algorithms.
The MDD introduced in \cite{mdd} is constructed using a scalar-valued function of \emph{relative margin}. It characterizes a disagreement between any pair of multi-class scoring hypotheses. This disagreement, however, does not take relationships among all of the multiple classes into account. As a result, the theory developed in \cite{mdd} cannot properly explain the effectiveness of a series of recent UDA algorithms \cite{mcd,symnets,adr,swd,Cicek_2019_ICCV}. In this work, we are motivated to follow \cite{mdd} and develop a theory for unsupervised multi-class domain adaptation (multi-class UDA) that connects more closely with recent algorithms. Inspired by the MDD of \cite{mdd} and the multi-class classification framework of Dogan \emph{et al.} \cite{dogan2016unified}, which aggregates violations of class-wise \emph{absolute margins} as a single loss, we technically propose a notion of matrix-formed, \emph{Multi-Class Scoring Disagreement (MCSD)}, which takes a full account of the element-wise disagreements between any pair of multi-class scoring hypotheses.
MCSDs defined over domain distributions induce a novel \emph{MCSD divergence}, measuring distribution distance between the source and target domains. Based on MCSD divergence, we develop a new adaptation bound for multi-class UDA. A data-dependent, probably approximately correct (PAC) bound is also developed using the notion of Rademacher complexity. We connect our results with existing theories of either binary \cite{ben2010theory} or multi-class UDA \cite{mdd} by introducing their absolute margin-based equivalent or variant of domain divergence, as well as the corresponding domain adaptation bounds. We show the advantages of MCSD divergence over these absolute margin-based equivalent/variant (and also their corresponding ones in \cite{ben2010theory} and \cite{mdd}).
The bounds derived in our theory of multi-class UDA based on either MCSD divergence or
the absolute margin-based versions of \cite{ben2010theory} and \cite{mdd}
naturally suggest adversarial objectives of minimax optimization, which promote the learning of feature distributions invariant across source and target domains. We term such an algorithmic framework as \emph{Multi-class Domain-adversarial learning Networks (McDalNets)}, as illustrated in Figure \ref{FigMcDalNets}. While it is difficult to optimize the objectives of McDalNets directly, we show that a few optimization-friendly surrogate objectives instantiate the recently popular methods \cite{mcd,mdd}, thus (partially) explaining the underlying mechanisms of their effectiveness. In addition to McDalNets, we introduce a new algorithm of \emph{Domain-Symmetric Networks (SymmNets)}, which is motivated from our same theory of multi-class UDA. Figure \ref{FigSymmNet} is an illustration of this. The proposed SymmNets is featured by a domain confusion and discrimination strategy that ideally achieves the same theoretically derived learning objective.
While most of the theories and algorithms presented in the paper are concerned with \emph{closed set UDA}, where the two domains share the same label space, one might also be interested in other variant settings, such as \emph{partial} \cite{san,mada,pada,iwanpda,transfer_example_partial} or \emph{open set} \cite{open_set_math,open_set_bp} UDA. In this work, we present simple extensions of SymmNets that are able to achieve partial or open set UDA as well. We conduct careful ablation studies to compare different algorithms of McDalNets,
including those based on the absolute margin-based versions of \cite{ben2010theory} and \cite{mdd}, as well as our newly introduced SymmNets. As shown in Table \ref{Tab:different_implementation}, experiments on six commonly used benchmarks show that algorithms of McDalNets based on MCSD divergence consistently improve over those based on the absolute margin-based versions of \cite{ben2010theory} and \cite{mdd},
certifying the usefulness of fully characterizing disagreements between pairs of scoring hypotheses in multi-class UDA. Experiments under the settings of the closed set, partial, and open set UDA also empirically verify the effectiveness of our proposed SymmNets.
\subsection{Relations with Existing Works}
\subsubsection{Domain Adaptation Theories}
In the literature, these exist theoretical domain adaptation results concerning mostly with the classification problem and also with regression \cite{cortes2014domain,cortes2015adaptation,mansour2009domain}. For classification, these results consider either a setting where target data are partially labeled \cite{mohri2012new,zhang2012generalization}, or the standard unsupervised setting from the perspectives of optimal transportation \cite{courty2016optimal,courty2017joint} or hypothesis-induced domain divergence \cite{ben2007analysis,ben2010theory,mansour2009domain,kuroki2019unsupervised,mdd}. We focus on the latter line of theories, which are closely related to the one we contribute.
The seminal domain adaptation theories \cite{ben2007analysis,ben2010theory,mansour2009domain} bound the expected target error for binary classification with terms characterizing the expected source error, the domain distance under certain metrics of distribution divergence, and constant ones that depend on the capacity of the hypothesis space; the term of domain distance differentiates these theoretical bounds. For example, Ben-David \emph{et al.} \cite{ben2007analysis,ben2010theory} propose for binary classification the zero-one loss-based ${\mathcal{H}\Delta\mathcal{H}}$-divergence by characterizing the disagreement between any pair of labeling hypotheses; Mansour \emph{et al.} \cite{mansour2009domain} introduce a notion of discrepancy distance by extending the zero-one loss used in \cite{ben2007analysis} to general loss functions of binary classification; by fixing one hypothesis of \cite{mansour2009domain} to the ideal source minimizer, Kuroki \emph{et al.} \cite{kuroki2019unsupervised} propose a more tractable source-guided discrepancy. Although many of the recent algorithms \cite{dann, adda, mcd, symnets} are motivated from seminal theories \cite{ben2007analysis,ben2010theory}, the gap between theories of binary classification and practical algorithms of multi-class classification remains.
To reduce this gap, Zhang \emph{et al.} \cite{mdd} make a first attempt to extend the theories of \cite{mansour2009domain,ben2010theory} to the case of multiple classes by introducing a novel notion of margin disparity discrepancy (MDD); MDD is a measure of domain distance built upon a scalar-valued function of margin disparity (MD), which can to some extent characterize the difference of multi-class scoring hypotheses.
While both our MCSD and those of \cite{ben2010theory,mansour2009domain,mdd} are based on the characterization of disagreements between any pair of labeling/scoring hypotheses, our MCSD is capable of characterizing them at a finer level, especially in the multi-class setting (cf. Figure \ref{Fig:f-f-disp}). Technically, our MCSD characterizes element-wise disagreements of multi-class scoring hypotheses by aggregating violations of class-wise absolute margins. By contrast, the zero-one loss-based counterpart of \cite{ben2010theory} only characterizes the labeling disagreement, and the margin disparity (MD) of \cite{mdd} improves over \cite{ben2010theory} with a scoring disagreement that is based on a scalar-valued, relative margin.
Consequently, the domain divergence induced by our MCSD can better explain the effectiveness of a series of recent UDA algorithms \cite{mcd,symnets,adr,swd,Cicek_2019_ICCV}, whose designs take the relations of scores of all the multiple classes into account.
\subsubsection{Algorithms of Multi-Class Domain Adaptation}
Existing algorithms of multi-class UDA are mainly motivated by learning domain-invariant feature representations \cite{dan,jan,dann,adda,mcd,symnets,adr,swd,Cicek_2019_ICCV,zhu2017unpaired,rozantsev2018beyond,dwt,dada}, or by minimizing the domain discrepancy in the image space via image generation \cite{pixel_level,isola2017image}. We briefly review the former line of algorithms, focusing on those based on the strategy of adversarial training.
Motivated to minimize the domain divergence measured by ${\mathcal{H}\Delta\mathcal{H}}$-divergence of \cite{ben2010theory}, Ganin \emph{et al.} \cite{dann} introduce the first strategy of the domain-adversarial training of neural networks (DANN), where a binary classifier is adopted as the domain discriminator, and the domain distance is minimized by learning features of the two domains in a manner adversarial to the domain discriminator. Tzeng \emph{et al.} \cite{adda} summarize three implementation manners of adversarial objective, including minimax \cite{dann}, confusion \cite{domain_confusion}, and GAN \cite{gan}. The domain discriminator of the binary classifier enables the learning of the alignment of marginal feature distributions across domains, but it is ineffective for the alignment of conditional feature distributions, which is necessary for practical UDA problems in a multi-class setting. Recent methods \cite{mcd,symnets,mdd,adr,swd,Cicek_2019_ICCV} strive to overcome this limitation by playing adversarial games between two classifiers.
More specifically, Saito \emph{et al.} \cite{mcd} adopt the maximum $L_1$ distance of output probabilities of two symmetric classifiers as a surrogate domain discrepancy; Lee \emph{et al.} \cite{swd} replace the $L_1$ distance in \cite{mcd} with the Wasserstein distance \cite{villani2008optimal}, taking advantage of its geometrical characterization; in \cite{mdd}, two classifiers are used asymmetrically to estimate conditional feature distributions with margin loss; in \cite{adr}, two task classifiers are introduced implicitly by applying two random dropouts to the same task classifier; a classifier concatenated by two task classifiers is adopted to implement the adversarial training objective in \cite{symnets,Cicek_2019_ICCV}.
Motivated by the domain adaptation bounds to be presented in Section \ref{Sec:theory_motivation}, we propose an algorithmic framework of McDalNets, whose optimization-friendly surrogate objectives instantiate these recently popular methods \cite{dann,mdd,mcd} (cf. Section \ref{SecMcDalNetAlgms}), thus (partially) explaining the underlying mechanisms of their effectiveness. We also introduce a new algorithm of SymmNets, whose learning objective aligns with our developed theoretical bound as well (cf. Section \ref{SecSymmNets}).
\subsubsection{Variants of Problem Settings}
The theories and algorithms discussed so far apply to the problem setting of closed set UDA, where a shared label space across domains is assumed. There exist other variant settings, e.g., partial \cite{san} or open set \cite{open_set_math} UDA. We discuss these settings and the corresponding methods as follows.
The setting of partial UDA assumes that classes of the target domain constitute an unknown subset of those of the source domain. To address the challenge brought by partial class coverage, a typical strategy is to weight source instances using the collective prediction evidence of target instances \cite{san,pada,iwanpda,transfer_example_partial}. Simply extending our SymmNets with a weighting scheme gives excellent results.
The setting of open set UDA assumes that both the source and target domains contain certain classes that are exclusive to each other, where for simplicity all the unshared classes in each domain are aggregated as a single (super-) unknown class. A key issue to extend methods of closed set UDA for the use in the open set setting is to design appropriate criteria that reject the target instances of unshared classes. To this end, Busto \emph{et al.} \cite{open_set_math} adopt a predefined distance threshold, and Saito \emph{et al.} \cite{open_set_bp} learn rejection automatically via the adversarial training. Our algorithm of SymmNets is flexible enough to be applied to open set UDA simply by adding an additional output neuron to the task classifier that is responsible for the aggregated super-class, while keeping other algorithmic ingredients fixed.
\subsection{Contributions}
Many recent algorithms for multi-class UDA \cite{mcd,adr,swd,Cicek_2019_ICCV}, including our preliminary work of SymmNets \cite{symnets}, rely on an adversarial strategy that learns to align conditional feature distributions across domains via a full account of the relationships among the hypotheses of classifiers. While these algorithms are inspired by classical domain adaptation theories \cite{ben2010theory,mansour2009domain,ben2007analysis}, their learning objectives are largely designed empirically; as such, the connections between theories and algorithms remain loose. The present paper aims to improve over the recent theory of multi-class UDA \cite{mdd}, and to connect with these algorithms more closely by formalizing a new theory of multi-class UDA, which underlies these algorithms with a framework that also inspires new algorithms. We summarize our technical contributions as follows.
\begin{itemize}
\item We propose to aggregate violations of absolute margin functions to define a notion of matrix-formed, \emph{Multi-Class Scoring Disagreement (MCSD)}, which enables a full characterization of the relations between any pair of scoring hypotheses. Based on the induced \emph{MCSD divergence} as a measure of domain distance, we develop a new adaptation bound for multi-class UDA; a data-dependent PAC bound is also developed using the notion of Rademacher complexity. We connect our results with existing theories of either binary or multi-class UDA, by introducing
their absolute margin-based equivalent or variant of domain divergence, and the corresponding adaptation bounds.
\item Our developed theories naturally suggest adversarial objectives to learn aligned conditional feature distributions across domains; we term such an algorithmic framework based on deep networks as \emph{Multi-class Domain-adversarial learning Networks (McDalNets)}. We show that different instantiations of McDalNets via surrogate learning objectives either coincide with or resemble a few recently popular methods, thus (partially) underscoring their practical efficacy. We also introduce a new algorithm of \emph{Domain-Symmetric Networks (SymmNets-V2)} based on our same theory of multi-class UDA, which improves over \emph{SymmNets-V1} proposed in our preliminary work.
\item While theories and algorithms presented in the paper are mostly concerned with the problem setting of closed set UDA, we also present simple extensions of SymmNets that work equally well under the settings of partial or open set UDA. We conduct careful ablation studies to compare different algorithms of McDalNets,
including those based on the absolute margin-based versions of \cite{ben2010theory} and \cite{mdd},
as well as our newly introduced SymmNets. Experiments on commonly used benchmarks show the advantages of McDalNets and SymmNets, certifying the effectiveness of fully characterizing disagreements between pairs of scoring hypotheses in multi-class UDA. We have made our code available at \url{https://github.com/YBZh/MultiClassDA}.
\end{itemize}
\color {black}
\section{A Theory of Unsupervised Multi-Class Domain Adaptation}
\label{Sec:theory_motivation}
We present in this section a theory of unsupervised multi-class domain adaptation (multi-class UDA). Our theoretical derivations follow \cite{ben2010theory,mansour2009domain,mdd}, but with a key novelty of measuring the distance between domain distributions using a divergence that fully characterizes the relations between different hypotheses of multi-class classification. We also present variants of the proposed divergence to connect with theoretical results developed in the literature. We start with a learning setup of multi-class UDA. Table \ref{tab-notations} gives a summary of our used math notations. All proofs are given in the appendices.
\begin{table}[t]
\centering
\caption{A summary of the used math notations.}\label{tab-notations}
\begin{tabular}{lp{5cm}}
\hline
Notations & Meaning \\ \hline
$K$ & Number of classes \\
$\mathbb{R}$ & The space of real numbers \\
$\mathbb{R}^K$ & The space of $K$-dimensional real vectors \\
$\mathcal{X}$ & Instance space \\
$\mathcal{Y}$ & Label space \\
$\mathcal{H}, \mathcal{F}$ & Hypothesis spaces of labeling or scoring functions \\
\textcolor{black}{$\vect{x},\vect{x}^s_i, \vect{x}^t_i$} & \textcolor{black}{A general instance, an $i^{th}$ source instance, or an $i^{th}$ target instance in the space $\mathcal{X}$} \\
\textcolor{black}{$D$} & \textcolor{black}{A distribution over a domain (e.g., $\mathcal{X}\times \mathcal{Y}$)} \\
\textcolor{black}{$D_x$} & \textcolor{black}{A marginal distribution over $\mathcal{X}$ when $D$ is over $\mathcal{X}\times \mathcal{Y}$} \\
\textcolor{black}{$P, Q$} & \textcolor{black}{Source or target distributions over $\mathcal{X}\times \mathcal{Y}$} \\
\textcolor{black}{$P_x, Q_x$} & \textcolor{black}{Source or target marginal distributions over $\mathcal{X}$} \\
\textcolor{black}{$h: \mathcal{X}\rightarrow \mathcal{Y}$} & \textcolor{black}{A function in a hypothesis space $\mathcal{H}$} \\
\textcolor{black}{$f, f', f'': \mathcal{X}\rightarrow \mathbb{R}^K$} & \textcolor{black}{Functions in a scoring space $\mathcal{F}$} \\
\textcolor{black}{$f_k, f'_k, f''_k: \mathcal{X}\rightarrow \mathbb{R}$} & \textcolor{black}{The $k^{th}$ components of $f, f'$, or $f''$} \\
\textcolor{black}{$\mu: \mathbb{R}^K \times \mathcal{Y} \rightarrow \mathbb{R}^K$} & \textcolor{black}{Absolute margin function of Definition 1} \\
\textcolor{black}{$\mu_k: \mathbb{R}^K \times \mathcal{Y} \rightarrow \mathbb{R}$} & \textcolor{black}{The $k^{th}$ component of $\mu$} \\
\textcolor{black}{$\Phi_\rho: \mathbb{R}\rightarrow [0,1]$} & \textcolor{black}{Ramp loss (5) with margin $\rho$} \\
\textcolor{black}{$\mathbb{E}$} & \textcolor{black}{Expectation of a random variable} \\
\textcolor{black}{$\mathbb{I}$ [Boolean expression]} & \textcolor{black}{Indicator function, which returns 1 when the expression is true, and 0 otherwise } \\
\hline
\end{tabular}
\end{table}
\subsection{Learning Setup}
Multi-class UDA assumes two different but related distributions over $\mathcal{X\times Y}$, namely the source one $P$ and target one $Q$. Learners receive $n_s$ labeled examples $\{(\vect{x}_i^s,y_i^s)\}_{i=1}^{n_s}$ drawn i.i.d. from $P$ and $n_t$ unlabeled examples $\{\vect{x}_j^t\}_{j=1}^{n_t}$ drawn i.i.d. from $Q_x$. The goal of multi-class UDA is to identify a labeling hypothesis $h: \mathcal{X}\rightarrow \mathcal{Y}$ from a space $\mathcal{H}$ such that the following \emph{expected error} over the target distribution is minimized
\begin{equation}\label{EqnExpectTargetErr}
\mathcal{E}_Q(h) := \mathbb{E}_{(\vect{x},y)\sim Q} L(h(\vect{x}), y) ,
\end{equation}
where $L$ is a properly defined loss function. For ease of theoretical analysis, Ben-David \emph{et al.} \cite{ben2007analysis,ben2010theory} assume $L$ as a zero-one loss of the form $\mathbb{I}[h(\vect{x})\neq y]$, where $\mathbb{I}$ is the indicator function, which is extended in \cite{mansour2009domain} as general loss functions of binary classification. Domain adaptation theories \cite{ben2010theory,mansour2009domain,mdd} typically bound the expected target error (\ref{EqnExpectTargetErr}) using derived meaningful terms.
Consider a space $\mathcal{F}$ that contains the scoring function $f: \mathcal{X} \rightarrow \mathbb{R}^{|\mathcal{Y}|} = \mathbb{R}^K$, which induces a labeling function $h_{f}(\vect{x}) = \arg \max_{k\in \mathcal{Y}} f_k(\vect{x})$, where $f_k$ denotes the $k^{th}$ component of the vector-valued function $f$. Adding the same function $g: \mathcal{X}\rightarrow \mathbb{R}$ to all components $f_k$ of $f$ does not change the classification decision, since $\arg\max_{k\in \mathcal{Y}}f_k(\vect{x}) = \arg\max_{k\in \mathcal{Y}}(f_k(\vect{x}) + g(\vect{x}))$; this could be problematic for obtaining unique solutions of scoring functions. Similar to \cite{dogan2016unified}, we fix this issue by enforcing the sum-to-zero constraint $\sum_{k=1}^K f_k(\vect{x}) = 0$ to the scoring functions.
\subsection{Domain Distribution Divergence and Adaptation Bounds based on Multi-Class Scoring Disagreement}\label{subsec:multi-class-loss}
Unsupervised domain adaptation is made possible by assuming the closeness between the distributions $P$ and $Q$; otherwise classifiers learned from the labeled source data would be less relevant for the classification of target data. The measures of distribution distances thus become crucial factors in developing either UDA theories or the corresponding algorithms.
{\color{black}
\subsubsection{Existing Measures of Domain Divergence}
In the seminal work \cite{ben2010theory}, a key innovation is the introduction of a distribution distance induced by a hypothesis space $\mathcal{H}^{\{0, 1\}}$ of binary classification
\begin{equation}\label{equ:HDeltaHDivergence}
d_{0\text{\rm -}1} (P_x, Q_x) := \sup\limits_{h,h' \in \mathcal{H}^{\{0, 1\}}} \left| \mathbb{E}_{Q_x} \mathbb{I}[h\neq h'] - \mathbb{E}_{P_x} \mathbb{I}[h\neq h'] \right| ,
\end{equation}
\textcolor{black}{where $\mathbb{E}_{Q_x} \mathbb{I}[h\neq h'] = \mathbb{E}_{\vect{x}\sim Q_x} \mathbb{I}[h(\vect{x})\neq h'(\vect{x})]$, i.e., the zero-one loss-based expectation of the hypothesis disagreement, which we term as \emph{hypothesis disagreement (HD)} to facilitate the subsequent discussion, and similarly for $\mathbb{E}_{P_x} \mathbb{I}[h\neq h']$; the disagreement between $h$ and $h'$ in fact specifies a measurable subset $\{\vect{x} \in \mathcal{X} | h(\vect{x})\neq h'(\vect{x}) \}$, and the distribution distance (termed $\mathcal{H}\Delta\mathcal{H}$-divergence in \cite{ben2010theory}) between $P_x$ and $Q_x$ is measured on the subsets by taking the supremum over all pairs of $h, h' \in \mathcal{H}^{\{0, 1\}}$.}
Compared with the simple $\ell_1$ distribution divergence, the distance (\ref{equ:HDeltaHDivergence}) is more relevant to the problem of domain adaptation and can be estimated from finite samples for an $\mathcal{H}^{\{0, 1\}}$ of fixed VC dimension \cite{ben2010theory}. Based on the same idea of characterizing the hypothesis disagreement, Mansour \emph{et al.} \cite{mansour2009domain} extend the zero-one loss-based distance (\ref{equ:HDeltaHDivergence}) to general loss functions $L$, giving rise to the distance (termed \emph{discrepancy distance} in \cite{mansour2009domain})
\begin{equation}\label{equ:DiscDivergence}
d_L (P_x, Q_x) := \sup\limits_{h,h' \in \mathcal{H}} \left| \mathbb{E}_{Q_x} L(h, h') - \mathbb{E}_{P_x} L(h, h') \right| .
\end{equation}
Note that (\ref{equ:DiscDivergence}) is symmetric and satisfies triangle inequality, but it does not strictly define a distance since it is possible that $d_L (P_x, Q_x) = 0$ for $P_x \neq Q_x$.
{\color{black}
In spite of being more general, the distance (\ref{equ:DiscDivergence}) applies only to UDA problems of binary classification. To develop multi-class UDA, disagreement of multi-class hypotheses should be taken into account. The key issue here is to extend binary loss functions $L$, especially \emph{margin-based ones}, to the case of multiple classes \cite{VapnikBook}. In literature, there exists no a canonical formulation of multi-class classification; various formulation variants have been proposed depending on different notions of multi-class margins and margin-based losses \cite{koltchinskii2002empirical,lee2004multicategory,liu2011reinforced,szedmak2005learning}, where margins are usually defined either by comparing components $\{f_k\}_{k=1}^K$ of a $K$-class scoring function $f$ (i.e., \emph{relative margins}), or directly on the components $\{f_k\}_{k=1}^K$ themselves (i.e., \emph{absolute margins}). Based on this idea, Zhang \emph{et al.} \cite{mdd} first investigate multi-class UDA by measuring the disagreement of multi-class hypotheses with a relative margin function \cite{koltchinskii2002empirical}. Given a fixed $f$, a \emph{margin disparity discrepancy (MDD)} is proposed in \cite{mdd} that defines the distribution divergence as
\begin{equation}\label{equ:MarginDisparityDiscrepancy}
d_{MD}^{(\rho)} (P_x, Q_x) := \sup\limits_{f' \in \mathcal{F}} [\mathbb{E}_{Q_x} \Phi_\rho(\rho_{f'}(\cdot, h_{f})) - \mathbb{E}_{P_x} \Phi_\rho(\rho_{f'}(\cdot, h_{f}))],
\end{equation}
where $\mathbb{E}_{Q_x}\Phi_\rho(\rho_{f'}(\cdot, h_{f})) = \mathbb{E}_{\vect{x}\sim Q_x}\Phi_\rho(\rho_{f'}(\vect{x}, h_{f}{(\vect{x})}))$ is termed as the \emph{margin disparity (MD)} in \cite{mdd}, which is induced by $f$ and $f'$ w.r.t. the distribution $Q_x$, the MD $\mathbb{E}_{P_x}\Phi_\rho(\rho_{f'}(\cdot, h_{f}))$ is similarly defined, $\Phi_\rho$ is a ramp loss defined as
\begin{equation} \label{equ-ramp_loss}
\Phi_\rho(x) :=
\begin{cases}
0, & \rho \leq x \\
1 - x/{\rho}, & 0 < x < \rho \\
1, & x \leq 0
\end{cases},
\end{equation}
and $\rho_{f}(\vect{x}, y) = \frac{1}{2} \left(f_y(\vect{x}) - \max_{y' \neq y} f_{y'}(\vect{x}) \right)$ is the relative margin function. The MDD (\ref{equ:MarginDisparityDiscrepancy}) improves over (\ref{equ:HDeltaHDivergence}) and (\ref{equ:DiscDivergence}) by using the hypothesis $h_{f}$ of a given $f$ to induce a relative margin of the scoring function $f'$, thus successfully measuring a disagreement between the multi-class $f$ and $f'$. We note that the induced relative margin depends only on the component of $f$ that has the maximum value (i.e., the hypothesis $h_{f}$); it does not fully characterize the disagreements between $f$ and $f'$. It is in fact this deficiency of MDD that motivates the present paper. By proposing a new divergence that can fully characterize the disagreements between pairs of multi-class scoring functions, we expect to develop the corresponding theory of multi-class UDA that helps underscore the effectiveness of a series of recent UDA algorithms \cite{mcd,symnets,adr,swd,Cicek_2019_ICCV}.
}
\subsubsection{The Proposed Domain Divergence and Adaptation Bound based on Multi-Class Scoring Disagreement}
The multi-class classification framework of Dogan \emph{et al.} \cite{dogan2016unified} decomposes a multi-class loss function into class-wise margins and margin violations (i.e., large-margin losses), and then aggregates these violations as a single loss value. Inspired by this framework, we propose in this paper a matrix-formed, \emph{multi-class scoring disagreement (MCSD)} to fully characterize the difference between any pair of scoring functions $f', f'' \in \mathcal{F}$, which is later used to define a distribution distance tailored to multi-class UDA. We first present the necessary definition of the absolute margin function.
\begin{definition}[Absolute margin function]\label{AbsMarginFuncDefinition}
The absolute margin function $\mu: \mathbb{R}^K \times \mathcal{Y} \rightarrow \mathbb{R}^K$, with $\mu = [\mu_1, \dots, \mu_K]^{\top}$, is defined on a multi-class scoring function $f(\vect{x}) \in \mathbb{R}^K$ and a label $y \in \mathcal{Y}$ as
\begin{equation}
\mu_k(f(\vect{x}),y) =
\begin{cases}
+f_k(\vect{x}), & k = y \\
-f_k(\vect{x}), & k \in \mathcal{Y} \setminus \{y\}
\end{cases}.
\end{equation}
\end{definition}
Given the sum-to-zero constraint $\sum_{k=1}^K f_k(\vect{x}) = 0$, the defined margin function enjoys the following properties \cite{dogan2016unified}.
\begin{itemize}
\item $\mu_y(f(\vect{x}),y)$ is non-decreasing w.r.t. $f_y(\vect{x})$ ,
\item $\mu_k(f(\vect{x}),y)$ is non-increasing w.r.t. $f_k(\vect{x})$ $\forall \ k \in \mathcal{Y} \setminus \{y\}$
\item When $\mu_k(f(\vect{x}),y) \geq 0 \ \forall \ k\in \mathcal{Y}$ and $\exists k\in\mathcal{Y}$ such that $\mu_k(f(\vect{x}),y) > 0$, we have $\arg\max_{k\in\mathcal{Y}}f_k(\vect{x}) = y$ .
\end{itemize}
The third property characterizes the correct classification by checking non-negativeness/positiveness of absolute margins. To develop MCSD, we consider the ramp loss (\ref{equ-ramp_loss}) to penalize margin violations.
For $\rho > 0$ and a distribution $D$ over $\mathbb{R}$, ramp loss has the nice property of $\mathbb{E}_{x\sim D}\Phi_\rho(x) \geq \mathbb{E}_{x\sim D}\mathbb{I}[x\leq 0]$, which is important to bound the target error $\mathcal{E}_Q(h_{f})$ using margin-based loss functions defined over the scoring function $f$.
}
\begin{definition}[Multi-class scoring disagreement]
For a pair of scoring functions $f', f'' \in \mathcal{F}$, the multi-class scoring disagreement (MCSD) is defined with respect to a distribution $D$ over the domain $\mathcal{X}$ as
\begin{equation}\label{EqnMCSD}
\text{\rm MCSD}_D^{(\rho)}(f', f'') := \frac{1}{K}\mathbb{E}_{\vect{x}\sim D} \|\mat{M}^{(\rho)}(f'(\vect{x})) - \mat{M}^{(\rho)}(f''(\vect{x}))\|_1,
\end{equation}
where $\|\cdot\|_1$ is the $L_1$ norm and $\mat{M}^{(\rho)}(f(\vect{x}))\in [0,1]^{K\times K}$ is the matrix of absolute margin violations defined as
\begin{equation} \label{equ:Martix-M}
\mat{M}^{(\rho)}_{i,j}(f(\vect{x})) = \Phi_\rho(\mu_i(f(\vect{x}),j)).
\end{equation}
\end{definition}
Each column $\mat{M}_{:, k}^{(\rho)}$ of the matrix $\mat{M}^{(\rho)}$ computes violations of the absolute margin function $\mu(f(\cdot), k)$ w.r.t. a class $k\in \mathcal{Y}$, and the corresponding $\|\mat{M}_{:, k}^{(\rho)}(f') - \mat{M}_{:, k}^{(\rho)}(f'')\|_1$ measures the difference of margin violations between the scoring functions $f'$ and $f''$. The proposed MCSD (\ref{EqnMCSD}) is based on the absolute value aggregation of these disagreements.
To have an intuitive understanding of the behaviors of $f'$, $f''$, and the $\text{\rm MCSD}_D^{(\rho)}(f', f'')$, we plot in Figure \ref{Fig:f-f-disp-MCSD} the value of $\text{\rm MCSD}_D^{(\rho)}(f', f'')$ (firing on a single instance $\vect{x}$) in the case of $K = 3$ and $\rho = 5$, by fixing either $f'(\vect{x})$ or $f''(\vect{x})$ and using the other as the argument.
\begin{figure*}[t]
\subfigure[]{
\hspace{0.8cm}
\begin{minipage}[t]{0.3\linewidth}
\centering
\includegraphics[width=0.95\linewidth] {images/MCSD_V1_ff-eps-converted-to.pdf}\hfill
\includegraphics[width=0.95\linewidth] {images/MCSD_V1_f-eps-converted-to.pdf}
\end{minipage}}
\hfill
\subfigure[]{
\begin{minipage}[t]{0.3\linewidth}
\centering
\includegraphics[width=0.95\linewidth] {images/MCSD_V2_ff-eps-converted-to.pdf}\hfill
\includegraphics[width=0.95\linewidth] {images/MCSD_V2_f-eps-converted-to.pdf}
\end{minipage}}
\hfill
\subfigure[]{\label{Fig:f-f-disp-MCSD}
\hspace{0.3cm}
\begin{minipage}[t]{0.3\linewidth}
\centering
\includegraphics[width=0.95\linewidth] {images/MCSD_ff-eps-converted-to.pdf}\hfill
\includegraphics[width=0.95\linewidth] {images/MCSD_f-eps-converted-to.pdf}
\end{minipage}}
\caption{Plots of various disagreements between two scoring functions $f'$ and $f''$ firing on a single instance $\vect{x}$ in a case of $K=3$ and $\rho=5$, where the scoring functions satisfy the sum-to-zero constraint. Top row: fix $f'(\vect{x})$ to be $[10;-5;-5]$ and use $f''(\vect{x}) = [f''_1;f''_2;-(f''_1 + f''_2)]$ as the argument; Bottom row: fix $f''(\vect{x})$ to be $[10;-5;-5]$ and use $f'(\vect{x}) = [f'_1;f'_2;-(f'_1 + f'_2)]$ as the argument. \textcolor{black}{(a) The $\widetilde{\text{\rm MCSD}}$ (\ref{EqnMCSDDegen2MDD}), which can be considered as an absolute margin-based variant of the margin disparity (MD) \cite{mdd} (cf. terms in (\ref{equ:MarginDisparityDiscrepancy})); (b) the $\widehat{\text{\rm MCSD}}$ (\ref{EqnMCSDDegen2HDH}), which is an absolute margin-based equivalent of the hypothesis disagreement (HD) \cite{ben2010theory} (cf. terms in (\ref{equ:HDeltaHDivergence})); (c) our proposed $\text{\rm MCSD}$ (\ref{EqnMCSD}). } }\label{Fig:f-f-disp}
\end{figure*}
We have the following definition of distribution distance based on the proposed MCSD.
\begin{definition}[MCSD divergence] \label{DefMCSDDist}
Given the definition of MCSD, we define the divergence between distributions $P_x$ and $Q_x$ over the domain $\mathcal{X}$ with respect to the space $\mathcal{F}$ as
\begin{multline}\label{EqnMCSDDist}
d^{(\rho)}_{MCSD}(P_x, Q_x) := \\ \sup\limits_{f',f''\in \mathcal{F}}[\text{\rm MCSD}_{Q_x}^{(\rho)}(f', f'') - \text{\rm MCSD}_{P_x}^{(\rho)}(f', f'')] .
\end{multline}
\end{definition}
The proposed MCSD divergence (\ref{EqnMCSDDist}) satisfies the properties of non-negativity and triangle inequality, but it is not symmetric w.r.t. $P_x$ and $Q_x$. Nevertheless, we show its usefulness for multi-class UDA by developing the following bound.
\begin{theorem}\label{TheoremMCSDUDAGenBound}
Fix $\rho>0$. For any scoring function $f \in \mathcal{F}$, the following holds over the source and target distributions $P$ and $Q$,
\begin{equation}\label{EqnMCSDUDAGenBound}
\mathcal{E}_Q(h_{f}) \leq \mathcal{E}^{(\rho)}_P(f) + d^{(\rho)}_{MCSD}(P_x, Q_x) + \lambda,
\end{equation}
where the constant $\lambda = \mathcal{E}^{(\rho)}_P(f^*) + \mathcal{E}^{(\rho)}_Q(f^*)$ with $f^* = \arg\min\limits_{f\in \mathcal{F}}\mathcal{E}^{(\rho)}_P(f) + \mathcal{E}^{(\rho)}_Q(f)$, and
\begin{equation}
\mathcal{E}_Q(h_{f}) := \mathbb{E}_{(\vect{x},y)\sim Q} \mathbb{I}[h_{f}(\vect{x})\neq y] ,
\end{equation}
\begin{equation}
\mathcal{E}^{(\rho)}_P(f) := \mathbb{E}_{(\vect{x},y)\sim P} \sum_{k=1}^K \Phi_{\rho}( \mu_k(f(\vect{x}),y) ) .
\end{equation}
\end{theorem}
\textcolor{black}{Theorem \ref{TheoremMCSDUDAGenBound} has a form similar to the domain adaptation bounds proposed by Ben-David \emph{et al.} \cite{ben2010theory} and Zhang \emph{et al.} \cite{mdd}; differently, it relies on the absolute margin-based loss function and MCSD divergence to achieve a full characterization of the difference between scoring functions of multi-class UDA.} As the bound (\ref{EqnMCSDUDAGenBound}) suggests, given the fixed $\lambda$, the expected target error $\mathcal{E}_Q(h_{f})$ is determined by the distance $d^{(\rho)}_{MCSD}(P_x, Q_x)$ (and the expected loss $\mathcal{E}^{(\rho)}_P(f)$ over the source domain); smaller $d^{(\rho)}_{MCSD}(P_x, Q_x)$ indicates better adaptation of multi-class UDA.
\textcolor{black}{To connect with domain adaptation bounds developed in the literature, notably those proposed in \cite{mdd,ben2010theory}, we first present the following absolute margin-based variant of MD \cite{mdd} (cf. terms in (\ref{equ:MarginDisparityDiscrepancy})) and the absolute margin-based equivalent of HD \cite{ben2010theory} (cf. terms in (\ref{equ:HDeltaHDivergence})), for a pair of scoring functions $f', f''\in \mathcal{F}$ w.r.t. a distribution $D$}
\begin{equation} \label{EqnMCSDDegen2MDD}
\widetilde{\text{\rm MCSD}}_D^{(\rho)}(f', f'') := \mathbb{E}_{\vect{x}\sim D}\Phi_{\rho/2}[\mu_{h_{f''}(\vect{x})}(f''(\vect{x}),h_{f'}(\vect{x}))] ,
\end{equation}
\begin{equation}\label{EqnMCSDDegen2HDH}
\widehat{\text{\rm MCSD}}_D^{(\rho)}(f', f'') := \mathbb{E}_{\vect{x}\sim D}\mathbb{I}[\Phi_{\rho}[\mu_{h_{f''}(\vect{x})}(f''(\vect{x}),h_{f'}(\vect{x}))] = 1] .
\end{equation}
\textcolor{black}{The terms (\ref{EqnMCSDDegen2MDD}) and (\ref{EqnMCSDDegen2HDH}) also measure the multi-class scoring disagreements to some extent, and give the corresponding distribution divergence $d^{(\rho)}_{\widetilde{MCSD}}$ as the absolute margin-based variant of MDD \cite{mdd}, and $d^{(\rho)}_{\widehat{MCSD}}$ as the absolute margin-based equivalent of $\frac{1}{2}\mathcal{H}\Delta\mathcal{H}$-divergence \cite{ben2010theory}, respectively. We have the following propositions for $\widetilde{\text{\rm MCSD}}$ and $\widehat{\text{\rm MCSD}}$. }
\begin{prop}
\label{TheoremMCSDDegen2MDDUDAGenBound}
Fix $\rho>0$. For any scoring function $f \in \mathcal{F}$,
\begin{equation}\label{EqnMCSDDegen2MDDUDAGenBound}
\mathcal{E}_Q(h_{f}) \leq \mathcal{E}^{(\rho)}_P(f) + d^{(\rho)}_{\widetilde{MCSD}}(P_x, Q_x) + \lambda,
\end{equation}
\end{prop}
\begin{prop}
\label{TheoremMCSDDegen2HDHUDAGenBound}
Fix $\rho>0$. For any scoring function $f \in \mathcal{F}$,
\begin{equation}\label{EqnMCSDDegen2HDHUDAGenBound}
\mathcal{E}_Q(h_{f}) \leq \mathcal{E}^{(\rho)}_P(f) + d^{(\rho)}_{\widehat{MCSD}}(P_x, Q_x) + \lambda.
\end{equation}
\end{prop}
\textcolor{black}{Note that $\mathcal{E}_Q(h_{f})$, $\mathcal{E}^{(\rho)}_P(f)$, and $\lambda$ are defined as the same as these in Theorem \ref{TheoremMCSDUDAGenBound}, and $d^{(\rho)}_{\widetilde{MCSD}}$ and $d^{(\rho)}_{\widehat{MCSD}}$ are defined following the definition of $d^{(\rho)}_{MCSD}$ (cf. Definition \ref{DefMCSDDist}) by replacing the term $\text{\rm MCSD}$ (\ref{EqnMCSD}) with $\widetilde{\text{\rm MCSD}}$ (\ref{EqnMCSDDegen2MDD}) and $\widehat{\text{\rm MCSD}}$ (\ref{EqnMCSDDegen2HDH}) respectively.}
Compared with the scalar-valued, absolute margin-based versions (\ref{EqnMCSDDegen2MDD}) and (\ref{EqnMCSDDegen2HDH}) (and also their corresponding ones in \cite{mdd} and \cite{ben2010theory}), our matrix-formed MCSD (\ref{EqnMCSD}) is able to characterize finer details of the scoring disagreements, as illustrated in Figure \ref{Fig:f-f-disp}. Consequently, the domain adaptation bound developed on the induced MCSD divergence would be beneficial to characterizing multi-class UDA in a finer manner, which possibly inspires better UDA algorithms.
\subsection{A Data-Dependent Multi-class Domain Adaptation Bound}
In this section, we extend the multi-class UDA bound in Theorem \ref{TheoremMCSDUDAGenBound} to a PAC bound, by showing that both terms of $\mathcal{E}^{(\rho)}_P(f)$ and $d^{(\rho)}_{MCSD}(P_x, Q_x)$ can be estimated from finite samples. Our extension is based on the following notion of Rademacher complexity.
\begin{definition}[Rademacher complexity]
Let $\mathcal{G}$ be a space of functions mapping from $\mathcal{Z}$ to $[a, b]$ and $\mathcal{S} = \left\{z_1,...,z_m\right\}$ be a fixed sample of size $m$ draw from the distribution $D$ over $\mathcal{Z}$. Then, the empirical Rademacher complexity of $\mathcal{G}$ with respect to the sample $\mathcal{S}$ is defined as
\begin{equation}
\widehat{\mathfrak{R}}_{\mathcal{S}}(\mathcal{G}) := \frac{1}{m} \mathbb{E}_\sigma \sup\limits_{g\in \mathcal{G}}\sum_{i=1}^{m}\sigma_i g(z_i),
\end{equation}
where $\{\sigma_i\}_{i=1}^m$ are independent uniform random variables taking values in $\left\{-1, +1\right\}$. The Rademacher complexity of $\mathcal{G}$ is defined as the expectation of $\widehat{\mathfrak{R}}_{\mathcal{S}}(\mathcal{G})$ over all samples of size $m$
\begin{equation}
\mathfrak{R}_{m,D}(\mathcal{G}) := \mathbb{E}_{\mathcal{S}\sim D^m} \widehat{\mathfrak{R}}_{\mathcal{S}}(\mathcal{G}).
\end{equation}
\end{definition}
The Rademacher complexity captures the richness of a function space by measuring the degree to which it can fit random noise. The empirical version has the additional advantage that it is data-dependent and can be estimated from finite samples. We have the following definition from \cite{mohri2012foundations}, before introducing our Rademacher complexity-based adaptation bound.
\begin{definition}
For a space $\mathcal{F}$ of scoring functions mapping from $\mathcal{X}$ to $\mathbb{R}^{|\mathcal{Y}|}$, we define
\begin{equation}
\Pi_1(\mathcal{F}) := \{ \vect{x} \rightarrow f_k(\vect{x}) | k \in \mathcal{Y}, f\in \mathcal{F}\}.
\end{equation}
\end{definition}
The defined space $\Pi_1(\mathcal{F})$ can be seen as the union of projections of $\mathcal{F}$ onto each output dimension.
\begin{theorem}\label{theorem-overall}
Let $\mathcal{F}$ be the space of scoring functions mapping from $\mathcal{X}$ to $\mathbb{R}^K$. Let $P$ and $Q$ be the source and target distributions over $\mathcal{X\times Y}$, and $P_x$ and $Q_x$ be the corresponding marginal distributions over $\mathcal{X}$. Let $\widehat{P}$ and $\widehat{Q}_x$ denote the corresponding empirical distributions for a sample $\mathcal{S} = \{(\vect{x}_i^s,y_i^s)\}_{i=1}^{n_s}$ and a sample $\mathcal{T} = \{\vect{x}_j^t\}_{j=1}^{n_t}$. Fix $\rho>0$. Then, for any $\delta > 0$, with probability at least $1 - 3\delta$, the following holds for all $f\in \mathcal{F}$
\begin{equation}\label{equ-theorem1}
\begin{aligned}
\mathcal{E}_Q(h_{f}) \leq & \mathcal{E}^{(\rho)}_{\widehat{P}}(f) + d^{(\rho)}_{MCSD}(\widehat{P}_x, \widehat{Q}_x) \\
& + (\frac{2K^2}{\rho} + \frac{4K}{\rho})\widehat{\mathfrak{R}}_\mathcal{S}(\Pi_1(\mathcal{F}))
+ \frac{4K}{\rho}\widehat{\mathfrak{R}}_\mathcal{T}(\Pi_1(\mathcal{F})) \\
& + 6K\sqrt{\frac{\log\frac{4}{\delta}}{2n_s}} + 3K\sqrt{\frac{\log\frac{4}{\delta}}{2n_t}} + \lambda,
\end{aligned}
\end{equation}
where the constant $\lambda = \min\limits_{f\in \mathcal{F}}\mathcal{E}^{(\rho)}_P(f) + \mathcal{E}^{(\rho)}_Q(f)$, and
\begin{equation}
\mathcal{E}^{(\rho)}_{\widehat{P}}(f) := \frac{1}{n_s}\sum_{i=1}^{n_s} \sum_{k=1}^K \Phi_{\rho}( \mu_k(f(\vect{x}^s_i),y^s_i) ) .
\end{equation}
\end{theorem}
\section{Connecting Theory with Algorithms}
\label{Sec:SymNet}
In the derived bound (\ref{equ-theorem1}) of multi-class UDA, the constant $\lambda$ and complexity terms are assumed to be fixed given the hypothesis space $\mathcal{F}$. To minimize the expected target error $\mathcal{E}_Q(h_{f})$, one is tempted to minimize the first two terms of $\mathcal{E}^{(\rho)}_{\widehat{P}}(f)$ and $d^{(\rho)}_{MCSD}(\widehat{P}_x, \widehat{Q}_x)$. In practice, a function $\psi$ of the feature extractor is typically used to lift the input space $\mathcal{X}$ to a feature space $\mathcal{X}^{\psi} = \{ \psi(\vect{x}) | x \in \mathcal{X} \}$, where with a slight abuse of notation, the space $\mathcal{F}$ of the scoring function $f: \mathcal{X}^{\psi}\rightarrow \mathbb{R}^{|\mathcal{Y}|} = \mathbb{R}^K$ and the induced labeling function $h_{f}: \psi(\vect{x})\rightarrow \arg\max_{k\in \mathcal{Y}}f_k(\psi(\vect{x}))$ are again well defined. We correspondingly write as $P^{\psi}$ and $Q^{\psi}$ for the source and target distributions over the lifted domain $\mathcal{X}^{\psi}\times \mathcal{Y}$, and their empirical (or marginal) versions as $\widehat{P}^{\psi}$ and $\widehat{Q}^{\psi}$ (or $P_x^{\psi}$ and $Q_x^{\psi}$). The function $\psi$ is typically implemented as a learnable deep network.
Given the learnable $\psi$, minimizing the right hand side of the bound (\ref{equ-theorem1}) can be achieved by identifying $\psi^{*}$ that minimizes $d^{(\rho)}_{MCSD}(\widehat{P}_x^{\psi}, \widehat{Q}_x^{\psi})$, and additionally identifying $f^{*}$ with $\psi^{*}$ that minimizes $\mathcal{E}^{(\rho)}_{ \widehat{P}^{\psi} }(f)$. Recall that the MCSD divergence (\ref{EqnMCSDDist}) is defined by taking the supremum over all pairs of $f', f'' \in \mathcal{F}$. Spelling $d^{(\rho)}_{MCSD}(\widehat{P}_x^{\psi}, \widehat{Q}_x^{\psi})$ out gives the following general objective of minimax optimization for multi-class UDA
\begin{equation}
\begin{gathered} \label{equ-opt1}
\min\limits_{f,\psi}\ \mathcal{E}^{(\rho)}_{\widehat{P}^{\psi}}(f) + [\text{\rm MCSD}_{\widehat{Q}_x^{\psi}}^{(\rho)}(f', f'') - \text{\rm MCSD}_{\widehat{P}_x^{\psi}}^{(\rho)}(f', f'') ], \\
\max\limits_{f',f''}\ [\text{\rm MCSD}_{\widehat{Q}_x^{\psi}}^{(\rho)}(f', f'') - \text{\rm MCSD}_{\widehat{P}_x^{\psi}}^{(\rho)}(f', f'')] ,
\end{gathered}
\end{equation}
which suggests an adversarial learning strategy to promote domain-invariant conditional feature distributions via the learned $\psi$, thus extending \cite{dann} to account for multi-class UDA. We term the general algorithm (\ref{equ-opt1}) via the adversarial learning strategy as \emph{Multi-class Domain-adversarial learning Networks (McDalNets)}. Figure \ref{FigMcDalNets} gives an architectural illustration, where the scoring function $f$ is for the multi-class classification task of interest, and $f'$ and $f''$ are auxiliary functions for the learning of $\psi$. Since $f$, $f'$, and $f''$ contain all the parameters of classifiers, we also use them to respectively refer to the task and auxiliary classifiers.
\begin{figure}[htb]
\includegraphics[width=1.0\linewidth] {images/McDalNets.pdf}
\caption{An architectural illustration of Multi-class Domain-adversarial learning Networks (McDalNets), which is motivated from the theoretically derived objective (\ref{equ-opt1}). The gradient reversal layer is adopted here to implement the adversarial objective; we note that other implementations (e.g., those discussed in \cite{adda}) would apply as well.}
\label{FigMcDalNets}
\end{figure}
\subsection{Different Algorithms of Multi-class Domain-adversarial learning Networks}
\label{SecMcDalNetAlgms}
The proposed MCSD divergence is amenable to the theoretical analysis of multi-class UDA. However, it is difficult to directly optimize the MCSD based problem (\ref{equ-opt1}) via stochastic gradient descent (SGD), due to the use of ramp loss $\Phi_\rho$ in MCSD (\ref{EqnMCSD}) that causes an issue of vanishing gradients. \footnote{We have tried to train the McDalNets (illustrated in Figure \ref{FigMcDalNets}) with the exact objective (\ref{equ-opt1}). However, it turns out that the optimization stagnates after a few iterations, since absolute values of the outputs of scoring functions increase over the predefined $\rho$, and the gradients thus vanish.} To develop specific algorithms of McDalNets that are optimization-friendly, we consider surrogate functions of MCSD (\ref{EqnMCSD}), which are easier to be trained by SGD and also able to characterize the disagreements of all $K$ pairs of the corresponding elements in scoring functions $f', f'' \in \mathcal{F}$. These surrogates give the following objectives of specific algorithms
\begin{equation}
\begin{gathered} \label{equ-opt2}
\min\limits_{f,\psi}\ \mathcal{L}_{\widehat{P}^{\psi}}(f) + [\text{\rm SurMCSD}_{\widehat{Q}_x^{\psi}}(f', f'') - \text{\rm SurMCSD}_{\widehat{P}_x^{\psi}}(f', f'') ], \\
\max\limits_{f',f''}\ [\text{\rm SurMCSD}_{\widehat{Q}_x^{\psi}}(f', f'') - \text{\rm SurMCSD}_{\widehat{P}_x^{\psi}}(f', f'')] ,
\end{gathered}
\end{equation}
\noindent \emph{respectively} with $\text{\rm SurMCSD}_{D^{\psi}}(f', f'')$ over a distribution $D^{\psi}$ as
\begin{equation}\label{equ-mcd}
\begin{aligned}
& (L_1/\text{\rm MCD \cite{mcd}} ): \mathbb{E}_{\vect{x}\sim D}\frac{1}{K}\|\phi(f'(\psi(\vect{x})))-\phi(f''(\psi(\vect{x})))\|_1,
\end{aligned}
\end{equation}
\begin{equation}\label{equ-kl}
\begin{aligned}
& (\text{\rm KL}): \mathbb{E}_{\vect{x}\sim D} \frac{1}{2}[\text{\rm KL}(\phi(f'(\psi(\vect{x}))), \phi(f''(\psi(\vect{x})))) \\
& \qquad\qquad + \text{\rm KL}(\phi(f''(\psi(\vect{x}))), \phi(f'(\psi(\vect{x}))))],
\end{aligned}
\end{equation}
\begin{equation}\label{equ-cross-entropy}
\begin{aligned}
& (\text{\rm CE}): \mathbb{E}_{\vect{x}\sim D} \frac{1}{2}[\text{\rm CE}(\phi(f'(\psi(\vect{x}))), \phi(f''(\psi(\vect{x})))) \\
& \qquad\qquad + \text{\rm CE}(\phi(f''(\psi(\vect{x}))), \phi(f'(\psi(\vect{x}))))],
\end{aligned}
\end{equation}
where $\phi(\cdot)$ is the softmax operator, $\text{\rm KL}(\cdot,\cdot)$ is the Kullback-Leibler divergence, and $\text{\rm CE}(\cdot,\cdot)$ is the cross-entropy function, and due to the same issue from the ramp loss, we have used a standard log loss
\begin{equation}\label{logloss}
\mathcal{L}_{\widehat{P}^{\psi}}(f) = \mathbb{E}_{(\vect{x},y)\sim \widehat{P}} -\log[\phi_{y}(f(\psi(x)))],
\end{equation}
to replace the term $\mathcal{E}^{(\rho)}_{\widehat{P}^{\psi}}(f)$ of empirical source error in (\ref{equ-opt1}). While MCSD (\ref{EqnMCSD}) takes a matrix-formed difference, the optimization-friendly surrogates (\ref{equ-mcd}), (\ref{equ-kl}), and (\ref{equ-cross-entropy}) generally take vector forms that characterize scoring disagreements between $K$ entry pairs of $f'$ and $f''$. In fact, we have the following proposition to show the equivalance of the matrix-formed MCSD to an aggregation of $K$ disagreements between any entry pair of $f'$ and $f''$.
\begin{prop}\label{PropMCDRelateMCSD}
Given the ramp loss $\Phi_\rho$ defined as (\ref{equ-ramp_loss}), there exists a distance measure $\varphi: \mathbb{R}\times \mathbb{R} \rightarrow \mathbb{R}_+$ defined as
\begin{equation}
\varphi(a,b) = (K-1)|\Phi_\rho(-a)-\Phi_\rho(-b)|+|\Phi_\rho(a)-\Phi_\rho(b)|, \nonumber
\end{equation}
such that the matrix-formed $\| \mat{M}^{(\rho)}(f'(\vect{x})) - \mat{M}^{(\rho)}(f''(\vect{x})) \|_1$ in MCSD (\ref{EqnMCSD}) can be calculated as the sum of $\varphi$-distance values of $K$ entry pairs between $f'_k(\vect{x})$ and $f''_k(\vect{x})$, i.e.,
\begin{equation}
\| \mat{M}^{(\rho)}(f'(\vect{x})) - \mat{M}^{(\rho)}(f''(\vect{x})) \|_1 = \sum_{k=1}^K \varphi(f'_k(\vect{x}), f''_k(\vect{x})). \nonumber
\end{equation}
\end{prop}
We also consider an algorithm that replaces the MCSD terms of (\ref{equ-opt1}) with
\textcolor{black}{a surrogate function of the scalar-valued, absolute margin-based version (\ref{EqnMCSDDegen2MDD}), giving rise to}
\begin{equation}
\begin{gathered} \label{equ-opt2-degen}
\min\limits_{f,\psi}\ \mathcal{L}_{\widehat{P}^{\psi}}(f) + [\widetilde{\text{\rm SurMCSD}}_{\widehat{Q}_x^{\psi}}(f', f'') - \widetilde{\text{\rm SurMCSD}}_{\widehat{P}_x^{\psi}}(f', f'') ], \\
\max\limits_{f',f''}\ [\widetilde{\text{\rm SurMCSD}}_{\widehat{Q}_x^{\psi}}(f', f'') - \widetilde{\text{\rm SurMCSD}}_{\widehat{P}_x^{\psi}}(f', f'')] ,
\end{gathered}
\end{equation}
\noindent with $\widetilde{\text{\rm SurMCSD}}_{D^{\psi}}(f', f'')$ over a distribution $D^{\psi}$ as \footnote{For better optimization, we follow \cite{gan,mdd} and practically implement the surrogate disagreement terms in (\ref{equ-opt2-degen}) as
\begin{equation} \label{equ-mdd-form-long}
\begin{gathered}
\widetilde{\text{\rm SurMCSD}}_{\widehat{Q}_x^{\psi}}(f', f'') = \mathbb{E}_{\vect{x}\sim \widehat{Q}}\log[1-\phi_{h_{f'}(\psi(\vect{x}))}(f''(\psi(\vect{x})))], \\
\widetilde{\text{\rm SurMCSD}}_{\widehat{P}_x^{\psi}}(f', f'') = \mathbb{E}_{\vect{x}\sim \widehat{P}}-\log[\phi_{h_{f'}(\psi(\vect{x}))}(f''(\psi(\vect{x})))].
\end{gathered}
\end{equation}
}
\begin{equation}\label{equ-mdd-form-ori}
\begin{aligned}
& (\text{\rm MDD \cite{mdd} variant}): \mathbb{E}_{\vect{x}\sim D}-\log[\phi_{h_{f'}(\psi(\vect{x}))}(f''(\psi(\vect{x})))] .
\end{aligned}
\end{equation}
\textcolor{black}{Similarly, an algorithm based on the scalar-valued, absolute margin-based version (\ref{EqnMCSDDegen2HDH}) can be considered as an equivalent of the DANN algorithm \cite{dann} }
\noindent with $\widehat{\text{\rm SurMCSD}}_{D^{\psi}}(f', f'')$ over a distribution $D^{\psi}$ as \footnote{For better optimization, we follow \cite{dann} and practically implement the surrogate disagreement terms in (\ref{equ-dann-form-ori}) as
\begin{equation} \label{equ-dann-form-dann}
\begin{gathered}
\widehat{\text{\rm SurMCSD}}_{\widehat{Q}_x^{\psi}}(f', f'') = \mathbb{E}_{\vect{x}\sim \widehat{Q}}\log[1- {\rm sigmoid}(d(\psi(\vect{x})))], \\
\widehat{\text{\rm SurMCSD}}_{\widehat{P}_x^{\psi}}(f', f'') = \mathbb{E}_{\vect{x}\sim \widehat{P}}-\log[{\rm sigmoid}(d(\psi(\vect{x})))].
\end{gathered}
\end{equation}
}
\begin{equation}\label{equ-dann-form-ori}
\begin{aligned}
& (\text{\rm DANN \cite{dann}}): \mathbb{E}_{\vect{x}\sim D}-\log[{\rm sigmoid}(d(\psi(\vect{x})))],
\end{aligned}
\end{equation}
where $d: D^{\psi} \to \mathbb{R}$ is a mapping function, and $\mathbb{I}[d(\psi(\vect{x})) > 0] = \mathbb{I}[h_{f'}(\psi(\vect{x})) = h_{f''}(\psi(\vect{x}))]$.
We note that algorithms discussed above resemble some recently proposed ones in the literature of UDA. For example, the objective (\ref{equ-opt2}) with the surrogate (\ref{equ-mcd}) is equivalent to the MCD algorithm \cite{mcd};
\textcolor{black}{the objective (\ref{equ-opt2-degen}) with the surrogate (\ref{equ-mdd-form-ori}) can be considered as a variant of MDD \cite{mdd}. }
In Section \ref{SecExps}, we conduct ablation studies to investigate the efficacy of these algorithms, and compare them with a new one to be presented shortly, which is motivated from the same theoretically derived objective (\ref{equ-opt1}).
\subsection{A New Algorithm of Domain-Symmetric Networks}\label{SecSymmNets}
\begin{figure*}
\begin{center}
\includegraphics[width=0.8\linewidth] {framework_long.pdf}
\end{center}
\caption{The architecture of our proposed SymmNets, which includes a feature extractor $\psi$ and three classifiers of $\mathbf{f}^s, \mathbf{f}^t$, and $\mathbf{f}^{st}$. Note that the classifier $\mathbf{f}^{st}$ shares its layer neurons with those of $\mathbf{f}^s$ and $\mathbf{f}^t$. Parameters of the classifiers (i.e., $\mathbf{f}^s, \mathbf{f}^t$, and $\mathbf{f}^{st}$) and those of the feature extractor $\psi$ are respectively updated by gradients from loss terms in green and yellow boxes. Please refer to the main text for how the objectives are defined.}
\label{FigSymmNet}
\end{figure*}
Apart from the task classifier $f$, algorithms of McDalNets presented above use two auxiliary classifiers $f'$ and $f''$ only for learning $\psi$, which is less efficient in the use of parameters. To improve the efficiency, we propose an integrated scheme that concatenates $f'$ and $f''$ as $[f'; f''] \in \mathbb{R}^{2K}$, and lets them be respectively responsible for the classification of the source and target instances, as shown in Figure \ref{FigSymmNet}. We correspondingly use the notations of $f^s$ and $f^t$ to replace $f'$ and $f''$, and denote the concatenated classifier as $f^{st}$, which \emph{shares parameters with} $f^s$ and $f^t$. We term such a network as Domain-Symmetric Networks (SymmNets) due to the symmetry of class-wise neuron distributions in $f^s$ and $f^t$.
To achieve the theoretically motivated learning objective (\ref{equ-opt1}), we have the following two designs to train SymmNets.
\begin{itemize}
\item Since target data $\{ \vect{x}_j^t \}_{j=1}^{n_t}$ are unlabeled, to enforce symmetric predictions between the respective $K$ neurons of $f^s$ and $f^t$, we use a \emph{cross-domain training scheme} that trains the target classifier $f^t$ using labeled source data $\{ (\vect{x}_i^s, y_i^s) \}_{i=1}^{n_s}$.
\item While different algorithms presented in Section \ref{SecMcDalNetAlgms} take the adversarial training strategy (e.g., a manner of reverse gradients \cite{dann}) to learn domain-invariant conditional feature distributions, for SymmNets, we instead use a \emph{domain confusion (and discrimination) training scheme} on the concatenated classifier $f^{st}$ to achieve the same goal.
\end{itemize}
We introduce the following notations before presenting the algorithm of SymmNets. For an input $\vect{x}$, $f^s(\psi(\vect{x})) \in \mathbb{R}^K$ and $f^t(\psi(\vect{x})) \in \mathbb{R}^K$ are the output vectors before the softmax operator $\phi$, and we denote $\vect{p}^s(\vect{x}) = \phi(f^s(\psi(\vect{x}))) \in [0, 1]^K$ and $\vect{p}^t(\vect{x}) = \phi(f^t(\psi(\vect{x}))) \in [0, 1]^K$. We also apply softmax to the output of the concatenated classifier $f^{st}$, resulting in $\vect{p}^{st}(\vect{x}) = \phi([f^s(\psi(\vect{x}));f^t(\psi(\vect{x}))]) \in [0, 1]^{2K}$. For ease of subsequent notations, we also write $p^s_k(\vect{x})$ (\emph{resp.} $p^t_k(\vect{x})$ or $p^{st}_k(\vect{x})$), $k \in \{1, \dots, K\}$, for the $k^{th}$ element of the probability vector $\vect{p}^s(\vect{x})$ (\emph{resp.} $\vect{p}^t(\vect{x})$ or $\vect{p}^{st}(\vect{x})$) predicted by $f^s$ (\emph{resp.} $f^t$ or $f^{st}$).
\vspace{0.1cm}
\noindent\textbf{Learning of the Source and Target Task Classifiers} We train the task classifier $f^s$ using a standard log loss over the labeled source data as follows
\begin{equation} \label{Loss_task_sc}
\min_{f^s} {\cal{L}}_{\widehat{P}^{\psi}}^s (f^s) = - \frac{1}{n_s} \sum_{i=1}^{n_s} \omega_{y_i^s} \mathrm{log}(p^s_{y_i^s}(\vect{x}_i^s)),
\end{equation}
where $\omega_{y_i^s} \in [0,1]$ is fixed as the value of $1$ for closed set and open set UDA, and will be turned active in Section \ref{SecExt2PartialOpenSet} for the extension of SymmNets to the setting of partial UDA.
To account for element-wise disagreements between predictions of $f^s$ and $f^t$, it is necessary to establish neuron-wise correspondence between them. To this end, we propose a cross-domain training scheme that trains the target classifier $f^t$ again using the labeled source data
\begin{equation} \label{Loss_task_tc}
\min_{f^t} {\cal{L}}_{\widehat{P}^{\psi}}^t (f^t) = - \frac{1}{n_s} \sum_{i=1}^{n_s} \omega_{y_i^s} \mathrm{log}(p^t_{y_i^s}(\vect{x}_i^s)) .
\end{equation}
At a first glance, it seems that training $f^t$ on $\{ (\vect{x}_i^s, y_i^s) \}_{i=1}^{n_s}$ only makes it a duplicate classifier of $f^s$. However, its effect on establishing neuron-wise correspondence between $f^s$ and $f^t$ is very essential to achieve learning of domain-invariant features via the objectives of domain confusion and discrimination, as presented shortly. We also present ablation studies in Section \ref{SecExps} that verify the efficacy of the scheme (\ref{Loss_task_tc}).
\vspace{0.1cm}
\noindent\textbf{Adversarial Feature Learning via Domain Confusion and Discrimination} Algorithms in Section \ref{SecMcDalNetAlgms} use surrogate MCSD functions and minimize the induced MCSD divergence to learn $\psi$, in order to align conditional feature distributions across source and target domains. Instead of using surrogate MCSD functions in SymmNets, we propose domain confusion objectives to directly reduce the domain divergence, by learning $\psi$ such that it produces features whose scoring disagreements between $f^s$ and $f^t$ (\emph{via their parameter-sharing $f^{st}$}) on both the source and target domains are \emph{equally small (and ideally null)}. Our confusion objectives are as follows
\begin{align}
\notag\min_{\psi} \text{\rm ConFUSE}_{\widehat{P}^{\psi}}^{st} (f^{s},f^t) = & - \frac{1}{2n_s} \sum_{i=1}^{n_s} \omega_{y_i^s} \mathrm{log}(p^{st}_{y_i^s}(\vect{x}_i^s)) \\ & - \frac{1}{2n_s} \sum_{i=1}^{n_s} \omega_{y_i^s} \mathrm{log}(p^{st}_{y_i^s+K}(\vect{x}_i^s)) , \label{Loss:cate_conf_s} \\
\notag\min_{\psi} \text{\rm ConFUSE}_{\widehat{Q}_x^{\psi}}^{st} (f^{s},f^t) = & - \frac{1}{2n_t} \sum_{j=1}^{n_t} \sum_{k=1}^{K} p^{st}_{k+K}(\vect{x}_j^t) \mathrm{log}(p^{st}_k(\vect{x}_j^t)) \\ & - \frac{1}{2n_t} \sum_{j=1}^{n_t} \sum_{k=1}^{K} p^{st}_k(\vect{x}_j^t) \mathrm{log}( p^{st}_{k+K}(\vect{x}_j^t)) , \label{Loss:do_conf_t}
\end{align}
where for a source example $(\vect{x}^s, y^s)$ with the label $y^s = k$, we identify its corresponding pair of the $k^{th}$ and $(k+K)^{th}$ neurons in $f^{st}$, and use a cross-entropy between the (two-way) uniform distribution and probabilities on this neuron pair; for a target example $\vect{x}^t$, we simply use a cross-entropy between probabilities respectively on the first and second half sets of neurons in $f^{st}$. We again fix $\omega_{y_i^s} = 1$ for closed set and open set UDA.
To provide an adversarial objective to the confusion ones (\ref{Loss:cate_conf_s}) and (\ref{Loss:do_conf_t}), we use the following domain discrimination loss
\begin{align} \label{Loss_domain_stc}
\notag \min_{f^{s},f^t} \text{\rm DisCRIM}_{\widehat{P}^{\psi}, \widehat{Q}_x^{\psi}}^{st} (f^{s},f^t) = & - \frac{1}{n_s} \sum_{i=1}^{n_s} \omega_{y_i^s} \mathrm{log}(p^{st}_{y_i^s}(\vect{x}_i^s)) \\ & - \frac{1}{n_t} \sum_{j=1}^{n_t} \mathrm{log}(\sum_{k=1}^{K} p^{st}_{k+K}(\vect{x}_j^t)) ,
\end{align}
where $\omega_{y_i^s} = 1$ for closed set and open set UDA, and $p^{st}_k(\vect{x})$ and $p^{st}_{k+K}(\vect{x})$ can be viewed as the probabilities of classifying an example $\vect{x}$ of class $k$ as the source and target domains respectively.
\vspace{0.1cm}
\noindent\textbf{Overall Learning Objective} Combining (\ref{Loss:cate_conf_s}) and (\ref{Loss:do_conf_t}), and (\ref{Loss_task_sc}), (\ref{Loss_task_tc}), and (\ref{Loss_domain_stc}) gives the following objective to train SymmNets
\begin{align} \label{Loss:overall}
\notag & \min_{\psi} \text{\rm ConFUSE}_{\widehat{P}^{\psi}}^{st} (f^{s},f^t) + \lambda \text{\rm ConFUSE}_{\widehat{Q}_x^{\psi}}^{st} (f^{s},f^t), \\
& \min_{f^s, f^t} {\cal{L}}_{\widehat{P}^{\psi}}^s (f^s) + {\cal{L}}_{\widehat{P}^{\psi}}^t (f^t) + \text{\rm DisCRIM}_{\widehat{P}^{\psi}, \widehat{Q}_x^{\psi}}^{st} (f^{s},f^t) ,
\end{align}
where $\lambda \in [0,1]$ is a trade-off parameter to suppress less stable signals of $\text{\rm ConFUSE}_{\widehat{Q}_x^{\psi}}^{st} (f^{s},f^t)$ at early stages of training, since signals of $\text{\rm ConFUSE}_{\widehat{P}^{\psi}}^{st} (f^{s},f^t)$ from labeled source data are authentic and thus more stable. We note that the objective (\ref{Loss:overall}) of SymmNets is different from that in our preliminary work \cite{symnets}: in (\ref{Loss:overall}), the scoring disagreements between $f^{s}$ and $f^{t}$ are minimized \textit{explicitly} on target data, the entropy objective is achieved \textit{implicitly} in the target confusion objective (\ref{Loss:do_conf_t}), and both the class and domain supervision of source data is adopted in the domain discrimination objective (\ref{Loss_domain_stc}); in our preliminary work \cite{symnets}, the scoring disagreements between $f^{s}$ and $f^{t}$ are minimized \textit{implicitly} on target data, the entropy objective is adopted \textit{explicitly}, and only the domain supervision of source data is adopted in the domain discrimination objective.
we use \textbf{SymmNets-V1} and \textbf{SymmNets-V2} to report the results respectively from these two versions of our algorithms.
\vspace{0.1cm}
\noindent\textbf{Theoretical Connection} We discuss the conditions on which the objective (\ref{Loss:overall}) of SymmNets connects with the theoretically derived objective (\ref{equ-opt1}). We first show with the following proposition that the objective (\ref{Loss:overall}) minimizes the term in (\ref{equ-opt1}) of empirical source error defined on both the $f^s$ and $f^t$.
\begin{prop}
\label{PropSymmNetConnectMcDalNet-SrcErr}
Let $\mathcal{F}$ be a rich enough space of continuous and bounded scoring functions, with the sum-to-zero constraint $\sum_{k=1}^K f_k =0$. For $f^s, f^t \in \mathcal{F}$ and a fixed function $\psi$ that satisfies $\psi(\vect{x}_1)\neq \psi(\vect{x}_2)$ when $y_1\neq y_2$, $\exists \ \rho > 0$ such that, the minimizer $f^{s*}$ of ${\cal{L}}_{\widehat{P}^{\psi}}^s (f^s)$ in (\ref{Loss:overall}) also minimizes the term $\mathcal{E}^{(\rho)}_{\widehat{P}^{\psi}}(f^s)$ in (\ref{equ-opt1}) of empirical source error defined on $f^s$, and the minimizer $f^{t*}$ of ${\cal{L}}_{\widehat{P}^{\psi}}^t (f^t)$ in (\ref{Loss:overall}) also minimizes the term $\mathcal{E}^{(\rho)}_{\widehat{P}^{\psi}}(f^t)$ in (\ref{equ-opt1}) of empirical source error defined on $f^t$.
\end{prop}
We note that the assumption of continuous and bounded scoring functions in Proposition \ref{PropSymmNetConnectMcDalNet-SrcErr} could be \emph{practically} met with the function implementation of the fully-connected network layer; the assumption of $\psi(\vect{x}_1)\neq \psi(\vect{x}_2)$ when $y_1\neq y_2$ is also reasonable with properly initialized and learned $\psi$. The objective (\ref{equ-opt1}) promotes the alignment of conditional feature distributions across the two domains, by learning $\psi$ that reduces MCSD divergence. We show with the following proposition that the objective (\ref{Loss:overall}) has the same effect.
\begin{prop}
\label{PropSymmNetConnectMcDalNet-FeaAligh}
For $\psi$ of a function space of enough capacity and fixed functions $f^s$ and $f^t$ with the same range, the minimizer $\psi^{*}$ of $\text{\rm ConFUSE}_{\widehat{P}^{\psi}}^{st} (f^{s},f^t) + \lambda \text{\rm ConFUSE}_{\widehat{Q}_x^{\psi}}^{st} (f^{s},f^t)$ with the parameter $\lambda > 0$ in (\ref{Loss:overall}) zeroizes $\text{\rm MCSD}_{\widehat{Q}_x^{\psi}}^{(\rho)}(f^s, f^t) - \text{\rm MCSD}_{\widehat{P}_x^{\psi}}^{(\rho)}(f^s, f^t)$ in (\ref{equ-opt1}) of empirical \text{\rm MCSD} divergence defined on $f^s$ and $f^t$.
\end{prop}
We finally note that given the fixed $\psi$, minimizing the domain discrimination term $\text{\rm DisCRIM}_{\widehat{P}^{\psi}, \widehat{Q}_x^{\psi}}^{st} (f^{s},f^t)$ in (\ref{Loss:overall}) over $f^s$ and $f^t$ (together with the minimization of ${\cal{L}}_{\widehat{P}^{\psi}}^s (f^s)$ and ${\cal{L}}_{\widehat{P}^{\psi}}^t (f^t)$) will increase the measured divergence between $\widehat{P}_x^{\psi}$ and $\widehat{Q}_x^{\psi}$, thus providing an adversarial feature learning signal similar to the one provided by maximizing the MCSD divergence in (\ref{equ-opt1}).
Specifically, $\text{\rm MCSD}_{\widehat{P}_x^{\psi}}^{(\rho)}(f^s, f^t)$ is minimized by minimizing ${\cal{L}}_{\widehat{P}^{\psi}}^s (f^s) + {\cal{L}}_{\widehat{P}^{\psi}}^t (f^t)$ based on the Lemma \textcolor{red}{A.2} in the appendices (i.e., $\text{\rm MCSD}_{\widehat{P}_x^{\psi}}^{(\rho)}(f^s, f^t) \leq \mathcal{E}^{(\rho)}_{{\widehat{P}}^{\psi}}(f^s) + \mathcal{E}^{(\rho)}_{\widehat{P}^{\psi}}(f^t)$) and the Proposition \ref{PropSymmNetConnectMcDalNet-SrcErr}. On the other hand, minimizing $\text{\rm DisCRIM}_{\hat{P}^{\psi}, \hat{Q}_x^{\psi}}^{st} (f^{s},f^t)$ maximizes the output diversity of $f^s$ and $f^t$, thus resulting in the maximization of $\text{\rm MCSD}_{\hat{Q}_x^{\psi}}^{(\rho)}(f^s, f^t)$.
\section{Extensions for Partial and Open Set Domain Adaptation}
\label{SecExt2PartialOpenSet}
The theories and algorithms discussed so far apply to the \emph{closed set} setting of multi-class UDA, where a shared label space between the source and target domains is assumed. In this section, we show that simple extensions of our proposed algorithm of SymmNets can be used for either the \emph{partial} \cite{san,pada,iwanpda,transfer_example_partial} or the \emph{open set} \cite{open_set_math,open_set_bp} multi-class UDA.
\vspace{0.1cm}
\noindent\textbf{Partial Domain Adaptation} The partial setting of multi-class UDA assumes that classes of the target domain constitutes an \emph{unknown subset} of that of the source domain. As the setting suggests, a key challenge here is to identify the source instances that share the same classes with the target domain. To this end, we leverage the class-wise symmetry of neuron predictions between $f^s$ and $f^t$ in SymmNets, and propose a soft class weighting scheme that simply weights source instances using collective prediction evidence of target instances from $f^t$. Specifically, we compute the following class-wise averages of prediction probabilities for target instances, and use these averaged probabilities $\{ \omega_{y_i^s}\}_{i=1}^{n_s}$ as weights for terms in the objectives (\ref{Loss_task_sc}), (\ref{Loss_task_tc}), (\ref{Loss:cate_conf_s}), and (\ref{Loss_domain_stc}) that involve labeled source data $\{(\vect{x}_i, y_i)\}_{i=1}^{n_s}$
\begin{align}
\omega_k = \frac{1}{n_t}\sum_{j=1}^{n_t} p_k^t(\vect{x}_j^t) , \ k \in \{1, \dots, K\} .
\end{align}
Such a scheme has the effect that source instances that are potentially of the classes exclusive to the target domain would be weighted down in the instance-reweighting version of the learning objective (\ref{Loss:overall}), thus promoting partial adaptation. In practice, we use more balanced class-wise weights in the early stages of training via
\begin{align}
\omega_k \leftarrow \xi \frac{\omega_k}{\max_{k\in \mathcal{Y}}\omega_k} + (1-\xi) , \ k \in \{1, \dots, K\} .
\end{align}
where $\xi$ is a parameter set to be smaller in the early stages of training. We note that similar soft weighting schemes are also used in \cite{san,pada}.
\vspace{0.1cm}
\noindent\textbf{Open Set Domain Adaptation} The open set setting of multi-class UDA takes a step further to assume that the target domain contains certain classes exclusive to the source domain as well. Let $K^s$ and $K^t$ respectively denote the numbers of classes in the source and target domains, and $\widetilde{K}$ be the number of classes common to them, which is assumed known in \cite{open_set_math,open_set_bp}. We have $\widetilde{K} \leq K^s$ and $\widetilde{K} \leq K^t$. Extending SymmNets for the open set setting can be simply achieved by adapting its $f^s$ and $f^t$ to respectively have $\widetilde{K} + 1$ output neurons, where the final neuron of $f^s$ is responsible for an aggregated prediction of the domain-specific $K^s - \widetilde{K}$ classes, and the same applies to the adapted $f^t$. Although domain-specific classes in the source domain are treated as a single, super class, to achieve effective training of the adapted SymmNets via SGD, we still respect their overall population by sampling a $\nu \geq 1$ factor of more source examples from the super class than those from each of the $\widetilde{K}$ shared classes, when constituting training source batches. We investigate different values of $\nu$ in Section \ref{SecExps}; setting $\nu = 6$ consistently gives good results. Since target instances are unlabeled, we simply sample them randomly to constitute training target batches.
\color {black}
\section{Experiments}
\label{SecExps}
In this section, we conduct experiments to investigate the practice of our introduced theory and algorithms. We compare different algorithms or implementations of McDalNets, including these based on the absolute margin-based equivalent of \cite{ben2010theory} and variant of \cite{mdd},
and our proposed SymmNets-V1 \cite{symnets} and SymmNets-V2 under the closed set setting of multi-class UDA. We also evaluate the efficacy of our SymmNets for partial and open set settings. These experiments are conducted on seven benchmark datasets by implementing algorithms on three backbone networks, which are specified shortly. Additional experiments, results, and analyses are provided in the appendices.
\begin{table}[htb]
\begin{center}
\caption{Summary of datasets. ``C'', ``P'', and ``O'' indicate the respective settings of the closed set, partial, and open set domain adaptation.}
\label{Tab:datasets}
\begin{tabular}{l|cccc}
\hline
\multirow{2}{*}{Dataset} & Involved & No. of & No. of & No. of \\
& Tasks & Domains & Classes & Samples \\
\hline
ImageCLEF-DA \cite{ImageCLEFDA} & C & 3 & 12 & 1,800 \\
Office-31 \cite{office_31} & C+P+O & 3 & 31 & 4,110 \\
Office-Home \cite{office_home} & C+P & 4 & 65 & 15,500 \\
Digits \cite{mnist,usps,svhn} & C & 3 & 10 & 172.5K \\
Syn2Real\cite{syn2real} & O & 2 & 13 & 248K \\
VisDA-2017 \cite{visda,syn2real} & C & 2 & 12 & 280K \\
DomainNet \cite{peng2018moment} & C & 6 & 345 & 586.6K \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{table*}[htb]
\centering
\caption{\textcolor{black}{Accuracy (\%) of different instantiations of McDalNets on the datasets of Office-31 \cite{office_31}, ImageCLEF-DA \cite{ImageCLEFDA}, Office-Home \cite{office_home}, Digits \cite{mnist,svhn,usps}, VisDA-2017 \cite{visda}, and DomainNet \cite{peng2018moment} under the setting of closed set UDA. Each accuracy reported here is a \textit{result averaged over individual tasks of a specific dataset}. All the results of individual tasks for the respective datasets are given in the appendices.}}
\label{Tab:different_implementation}
\begin{tabular}{l|c|c|c|c|c|c}
\hline
Methods & {\scriptsize Office-31} & {\scriptsize ImageCLEF} & {\scriptsize Office-Home} & {\scriptsize Digits} & {\scriptsize VisDA-2017} & {\scriptsize \textcolor{black}{DomainNet}} \\
\hline
Source Only & 81.8 & 82.7 & 58.9 & 70.5 & 41.8 & \textcolor{black}{24.4} \\
\hline
{\scriptsize McDalNets based on the following surrogates of $\widehat{\text{\rm MCSD}}$ (\ref{EqnMCSDDegen2HDH}) and $\widetilde{\text{\rm MCSD}}$ (\ref{EqnMCSDDegen2MDD})} & & & & & & \\
\quad DANN \cite{reverse_grad,dann} (\ref{equ-dann-form-dann}) & 82.8 & 84.2& 60.0 & 72.5 & 58.4 & \textcolor{black}{27.1} \\
\quad MDD \cite{mdd} variant (\ref{equ-mdd-form-long}) & 84.5 &86.7 & 61.1 & not converge & not converge & \textcolor{black}{26.5} \\
\hline
{\scriptsize McDalNets based on the following surrogates of MCSD (\ref{EqnMCSD})} & & & & & \\
\quad $L_1/\text{\rm MCD}$\cite{mcd} (\ref{equ-mcd}) &84.7 &87.0& 62.0 & 90.6 & 70.4 & \textcolor{black}{27.7} \\
\quad KL (\ref{equ-kl}) &84.6 &87.6& 63.3 & 82.9 & 69.0 & \textcolor{black}{27.6} \\
\quad CE (\ref{equ-cross-entropy}) &85.3 & 87.8&64.0 & 94.9 & 70.5 & \textbf{\textcolor{black}{27.9}} \\
\hline
SymmNets-V2 (\ref{Loss:overall}) & \textbf{89.1} & \textbf{89.7}& \textbf{68.1} & \textbf{96.0} & \textbf{71.3} & \textbf{\textcolor{black}{27.9}} \\
\hline
\end{tabular}
\end{table*}
\vspace{0.1cm}
\noindent\textbf{Datasets} We use the benchmark datasets summarized in Table \ref{Tab:datasets} for our evaluation. In the closed set UDA, we follow standard protocols \cite{reverse_grad, dan} for the datasets of Office-31 \cite{office_31}, Office-Home \cite{office_home}, ImageCLEF-DA \cite{ImageCLEFDA}, and VisDA-2017 \cite{visda}: all labeled source and target samples are used for training; for the Digits datasets of \cite{mnist,svhn,usps}, we follow the protocols in \cite{adr}; we follow the standard split for the DomainNet dataset \cite{peng2018moment}. In partial UDA, all labeled source samples construct the source domain, and the target domain is constructed following the protocols of \cite{san,pada}: for Office-31 \cite{office_31}, the samples of ten classes shared by Office-31 \cite{office_31} and Caltech-256 \cite{caltech} are selected as the target domain; for Office-Home \cite{office_home}, we choose (in alphabetic order) the first 25 classes as target classes and select all samples of these 25 classes as the target domain. In open set UDA, the samples of ten classes shared by Office-31 \cite{office_31} and Caltech-256 \cite{caltech} are selected as shared classes across domains. In alphabetical order, samples of Class 21$\sim$Class 31 and Class 11$\sim$Class 20 are used as unknown samples in the target and source domains, respectively; we follow the standard split for the benchmark dataset of Syn2Real \cite{syn2real}.
\noindent\textbf{Implementations Details} All our methods are implemented using the PyTorch library. For the close set and partial settings of UDA, we adopt a ResNet pre-trained on ImageNet \cite{imagenet}, after removing the last fully connected (FC) layer, as the feature extractor $\psi$. We fine-tune the feature extractor $\psi$ and train a classifier $\mathbf{f}^{st}$ from scratch with the backpropagation algorithm. The learning rate for the newly added layers is set as $10$ times of that of the pre-trained layers. All parameters are updated by SGD with a momentum of $0.9$. We follow \cite{reverse_grad} to employ the annealing strategy of learning rate and the progressive strategy of $\lambda$: the learning rate is adjusted by $\eta_p = \frac{\eta_0}{(1+\alpha p)^{\beta}}$, where $p$ is the progress of training epochs linearly changing from $0$ to $1$, $\eta_0 = 0.01$, $\alpha = 10$, and $\beta = 0.75$, which are optimized to promote convergence and low errors on source samples; $\lambda$ is gradually changed from $0$ to $1$ by $\lambda_p = \frac{2}{1+\mathrm{exp}(-\gamma \cdot p)} - 1$, where $\gamma$ is set to $10$ in all experiments. We empirically set $\xi = \lambda$ in all experiments. Our classification results are obtained from the target task classifier $\mathbf{f}^{t}$ unless otherwise specified, and the comparison between the performance of the source and target task classifiers is illustrated in Figure \ref{fig:convergence}.
For the open set UDA, we follow \cite{syn2real} to replace the very top FC layer of an ImageNet pre-trained ResNet with three FC layers powered by the batch normalization \cite{bn} and Leaky ReLU activation; the feature extractor $\psi$ is defined by pre-trained layers together with first two of the three added FC layers, and the last FC layer is the classifier $\mathbf{f}^{st}$. We freeze parameters of pre-trained layers and update those of the added FC layers with a learning rate of $0.001$, following \cite{open_set_bp}. We also follow \cite{open_set_math, open_set_bp} to report OS as the accuracy averaged over all classes and OS$^*$ as that averaged over the domain shared classes only. We additionally implement our methods based on the AlexNet \cite{alexnet} and modified LeNet \cite{lecun1998gradient,adda} to testify its generalization to different architectures. Please refer to the appendices for more details.
For a fair comparison, results of other methods are either directly reported from their original papers if available or quoted from \cite{cada}, \cite{pada} and \cite{open_set_bp,syn2real} for the closed set, partial and open set settings of UDA, respectively.
\subsection{Analysis on Different Instantiations of McDalNets}
In this section, we investigate different instantiations of McDalNets that are achieved by using surrogate functions (\ref{equ-mcd}), (\ref{equ-kl}), or (\ref{equ-cross-entropy}) to replace the MCSD terms in the general objective (\ref{equ-opt1}), by comparing with the counterparts based on surrogate functions (\ref{equ-dann-form-dann}) or (\ref{equ-mdd-form-long}) of scalar-valued versions of (\ref{EqnMCSDDegen2HDH}) or (\ref{EqnMCSDDegen2MDD}).
These experiments are conducted on the datasets of Office-31 \cite{office_31}, ImageCLEF-DA \cite{ImageCLEFDA}, Office-Home \cite{office_home}, Digits \cite{mnist,svhn,usps}, VisDA-2017 \cite{visda}, and DomainNet \cite{peng2018moment} under the setting of closed set UDA. In practice, we downweight the MCSD divergence in (\ref{equ-opt1}) with respect to the feature extractor $\psi$ at early stages of training, resulting in the following objective
\begin{equation}
\begin{gathered} \label{equ-opt1-parctical}
\min\limits_{f,\psi}\ \mathcal{E}^{(\rho)}_{\widehat{P}^{\psi}}(f) + \zeta [\text{\rm MCSD}_{\widehat{Q}_x^{\psi}}^{(\rho)}(f', f'') - \text{\rm MCSD}_{\widehat{P}_x^{\psi}}^{(\rho)}(f', f'') ], \\
\max\limits_{f',f''}\ [\text{\rm MCSD}_{\widehat{Q}_x^{\psi}}^{(\rho)}(f', f'') - \text{\rm MCSD}_{\widehat{P}_x^{\psi}}^{(\rho)}(f', f'')] ,
\end{gathered}
\end{equation}
where we empirically set $\zeta = \lambda$, which is described in the beginning of Section \ref{SecExps}. The weight $\zeta$ is similarly applied to objectives based on surrogate MCSD functions. We adopt the gradient reversal layer to implement the adversarial objective.
Therefore, the instantiation of McDalNets with the surrogate function (\ref{equ-dann-form-dann}) of the scalar-valued $\widehat{\text{\rm MCSD}}$ (\ref{EqnMCSDDegen2HDH}) coincides with that of DANN \cite{reverse_grad,dann}.
The implementation details of other settings are the same as these described in the beginning of Section \ref{SecExps}, except that we train three classifiers $\mathbf{f}$, $\mathbf{f}'$, and $\mathbf{f}''$ from scratch and the classification results are obtained from the task classifier $\mathbf{f}$. For ease of optimization, we also train auxiliary classifiers $\mathbf{f}'$ and $\mathbf{f}''$ using a standard log loss over labeled source data. The ``Source Only'' indeed gives a lower bound, where we fine-tune a model on the source data only.
Results in Table \ref{Tab:different_implementation} show that all instantiations of McDalNets improve over the baseline of ``Source Only'', certifying the efficacy of the MCSD divergence in the domain discrepancy minimization. The McDalNets based on MCSD surrogates (\ref{equ-mcd}), (\ref{equ-kl}), and (\ref{equ-cross-entropy}) generally achieve better results than those based on surrogates (\ref{equ-dann-form-dann}) and (\ref{equ-mdd-form-long}) of
the scalar-valued $\widehat{\text{\rm MCSD}}$ (\ref{EqnMCSDDegen2HDH}) and $\widetilde{\text{\rm MCSD}}$ (\ref{EqnMCSDDegen2MDD}),
testifying the advantages of characterizing finer details of the scoring disagreement in multi-class UDA. McDalNets based on the MCSD surrogate of CE (\ref{equ-cross-entropy}) generally achieves better results than those based on the MCSD surrogates of $L_1/\text{\rm MCD \cite{mcd}}$ (\ref{equ-mcd}) and KL (\ref{equ-kl}), probably due to the mechanism where the CE-based surrogate (\ref{equ-cross-entropy}) also makes predictions of lower entropy; further explanation via illustration is given in the appendices. Among all algorithms, SymmNets-V2 proposed in the present paper achieves the best results across all tasks, confirming its efficacy in multi-class UDA.
\begin{table*}[htb]
\centering
\caption{Ablation experiments on components of SymmNets-V2 using the datasets of Office-31 \cite{office_31} and VisDA-2017 \cite{visda} under the setting of closed set UDA. All methods are based on models adapted from a 50-layer ResNet. Please refer to the main text for specifics of these methods.
}
\label{Tab:ablation_study}
\begin{tabular}{lcccc|c}
\hline
Methods & A $\to$ W & A $\to$ D & D $\to$ A & W $\to$ A & Synthetic $\to$ Real \\
\hline
SymmNets-V2 (w/o ${\cal{L}}_{\widehat{P}^{\psi}}^t$) & 71.0$\pm$0.8 & 74.5$\pm$0.9 & 63.3$\pm$0.2 & 62.8$\pm$0.1 & 41.9 \\
SymmNets-V2 (w/o adversarial training) & 78.3$\pm$0.3 & 83.3$\pm$0.2 & 64.6$\pm$0.5 & 66.6$\pm$0.1 & 41.6 \\
SymmNets-V2 & \textbf{94.2}$\pm$0.1 & \textbf{93.5}$\pm$0.3 & \textbf{74.4}$\pm$0.1 & \textbf{73.4}$\pm$0.2 & \textbf{71.3} \\
\hline
\end{tabular}
\end{table*}
We also plot convergence curves for different instantiations of McDalNets in Figure \ref{fig:convergence}, where we observe that those based on MCSD surrogates of $L_1/\text{\rm MCD \cite{mcd}}$ (\ref{equ-mcd}), KL (\ref{equ-kl}), and CE (\ref{equ-cross-entropy}) converge generally smoother than those based on surrogates (\ref{equ-dann-form-dann}) and (\ref{equ-mdd-form-long}) of the scalar-valued $\widehat{\text{\rm MCSD}}$ and $\widetilde{\text{\rm MCSD}}$.
It could be attributed to the in-built function property of MCSD (\ref{EqnMCSD}), as illustrated in Figure \ref{Fig:f-f-disp}. We particularly note that McDalNets based on the scalar-valued $\widetilde{\text{\rm MCSD}}$ surrogate (\ref{equ-mdd-form-long})
does not converge on the datasets of Digits and VisDA-2017. In comparison, SymmNets-V2 achieves the lowest classification error and the smoothest convergence.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.0\linewidth] {images/convergence_comp.pdf}
\end{center}
\caption{ Convergence plottings on the adaptation task \textbf{W} $\to$ \textbf{A} of the Office-31 \cite{office_31} by the Source Only, McDalNets based on the $\widehat{\text{\rm MCSD}}$ surrogate (\ref{equ-mdd-form-long}) (variant of MDD \cite{mdd}) and $\widetilde{\text{\rm MCSD}}$ surrogate (\ref{equ-dann-form-dann}) (DANN \cite{reverse_grad,dann}), McDalNets based on the MCSD surrogates $L_1$ (\ref{equ-mcd}) (MCD \cite{mcd}), KL (\ref{equ-kl}), and CE (\ref{equ-cross-entropy}), and SymmNets-V2. SymmNets-V2-$\mathbf{f}^s$ and SymmNets-V2-$\mathbf{f}^t$ represent the results obtained from the source classifier $\mathbf{f}^s$ and target classifier $\mathbf{f}^t$, respectively.}
\label{fig:convergence}
\end{figure}
In this section, we investigate the effects of different components in our proposed SymmNets-V2 by conducting ablation experiments on the datasets of Office-31 \cite{office_31} and VisDA-2017 \cite{visda} under the setting of closed set UDA, where networks are adapted from a 50-layer ResNet. To investigate how the cross-domain training term ${\cal{L}}_{\widehat{P}^{\psi}}^t$ (\ref{Loss_task_tc}) contributes to a better adaptation in our overall adversarial learning objective (\ref{Loss:overall}), we remove it from (\ref{Loss:overall}) and denote the method as ``SymmNets-V2 (w/o ${\cal{L}}_{\widehat{P}^{\psi}}^t$)''. To evaluate the efficacy of our adversarial training, we remove the domain discrimination loss $\text{\rm DisCRIM}_{\widehat{P}^{\psi}, \widehat{Q}_x^{\psi}}^{st}$ (\ref{Loss_domain_stc}) and the domain confusion loss of target data $\text{\rm ConFUSE}_{\widehat{Q}_x^{\psi}}^{st}$ (\ref{Loss:do_conf_t}) from the overall objective (\ref{Loss:overall}), and use the following degenerate form to replace the domain confusion loss of source data $\text{\rm ConFUSE}_{\widehat{P}^{\psi}}^{st}$ (\ref{Loss:cate_conf_s})
\begin{align}
\min_{\mathnormal{\psi}} - \frac{1}{2n_s} \sum_{i=1}^{n_s} \omega_{y_i^s} \mathrm{log}(p^{st}_{y_i^s}(\vect{x}_i^s)) - \frac{1}{2n_s} \sum_{i=1}^{n_s} \omega_{y_i^s} \mathrm{log}(p^{st}_{y_i^s+K}(\vect{x}_i^s)) ;
\end{align}
we denote this method as ``SymmNets-V2 (w/o adversarial training) ''.
Note that classification results for SymmNets (w/o ${\cal{L}}_{\widehat{P}^{\psi}}^t$) are obtained from the source task classifier $\mathbf{f}^{s}$ due to the inexistence of the direct supervision signals for the target task classifier $\mathbf{f}^{t}$. Results in Table \ref{Tab:ablation_study} show that SymmNets-V2 outperforms ``SymmNets-V2 (w/o adversarial training)'' by a large margin, verifying the efficacy of the discrepancy minimization via our proposed adversarial training. The performance slump of ``SymmNets-V2 (w/o ${\cal{L}}_{\widehat{P}^{\psi}}^t$)'' manifests the importance of the cross-domain training term ${\cal{L}}_{\widehat{P}^{\psi}}^t$ (\ref{Loss_task_tc}) for learning a well-performed target task classifier in adversarial training.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.9\linewidth] {images/partial_weight_distribution.pdf}
\end{center}
\caption{Histograms of class weight $\omega_k$ learned by SymmNets-V2 (with active $\omega_k$) on the task of \textbf{A} $\to$ \textbf{W} under the setting of partial UDA. Model is adapted from a 50-layer ResNet.}
\label{fig:partial_weight_distribution}
\end{figure}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.9\linewidth] {images/eta_change.pdf}
\end{center}
\caption{Curve plottings for test accuracy of the unknown class (Unknown) and the mean accuracy over all classes (OS) and domain-shared classes (OS$^*$), when setting different values of $\nu$ in open set UDA. The results are reported on the \textbf{A} $\to$ \textbf{W} task of Office-31 dataset \cite{office_31} based on the SymmNets-V2 adapted from a 50-layer ResNet.}
\label{fig:open_set_eta_change}
\end{figure}
\subsection{Ablation Studies of SymmNets}
\begin{figure*}[h!]
\begin{minipage}[t]{0.13\linewidth}
\vspace*{-2cm}
DANN \cite{reverse_grad,dann}
\end{minipage}
\hfill
\subfigure[Close Set UDA]{
\begin{minipage}[t]{0.28\linewidth}
\centering
\includegraphics[width=0.77\linewidth] {images/closed_dann_domain_a2w.pdf}
\end{minipage}}
\hfill
\subfigure[Partial UDA]{
\begin{minipage}[t]{0.28\linewidth}
\centering
\includegraphics[width=0.77\linewidth] {images/partial_dann_domain_a2w.pdf}
\end{minipage}}
\hfill
\subfigure[Open Set UDA]{
\begin{minipage}[t]{0.28\linewidth}
\centering
\includegraphics[width=0.77\linewidth] {images/open_dann_domain_a2w.pdf}
\end{minipage}}
\\
\begin{minipage}[t]{0.13\linewidth}
\vspace*{-2cm}
SymmNets-V2
\end{minipage}
\hfill
\subfigure[Close Set UDA]{
\begin{minipage}[t]{0.28\linewidth}
\centering
\includegraphics[width=0.77\linewidth] {images/closed_symnets-v2_domain_a2w.pdf}
\end{minipage}}
\hfill
\subfigure[Partial UDA]{
\begin{minipage}[t]{0.28\linewidth}
\centering
\includegraphics[width=0.77\linewidth] {images/partial_symnets-v2_domain_a2w.pdf}
\end{minipage}}
\hfill
\subfigure[Open Set UDA]{
\begin{minipage}[t]{0.28\linewidth}
\centering
\includegraphics[width=0.77\linewidth] {images/open_symnets-v2_domain_a2w.pdf}
\end{minipage}}
\caption{The t-SNE visualization of feature representations learned by DANN (top row) and SymmNets-V2 (bottom row) under settings of the closed set, partial, and open set UDA. Blue and red points are the respective samples from the source domain \textbf{A} and target domain \textbf{W}. For partial UDA, we illustrate the feature representations learned by SymmNets-V2 (With active $\omega_k$), where we focus on domain-shared classes, and leave the source classes exclusive to the target domain as an indistinguishable cluster via the soft class weighting scheme, as discussed in Section \ref{SecExt2PartialOpenSet}. A visualization with class label information is given in the appendices.}
\label{Fig:sne}
\end{figure*}
\vspace{0.1cm}
\noindent \textbf{Soft Class Weighting Scheme in Partial UDA}
To investigate the efficacy of the soft class weighting scheme, we activate it with the strategy described in Section \ref{SecExt2PartialOpenSet}, giving rise to the method of ``SymmNets-V2 (with active $\omega_k$)''. Tables \ref{Tab:partial_office31} and \ref{Tab:partial_Office-Home} show that results of SymmNets-V2 (with active $\omega_k$) improve over those of SymmNets-V2, empirically verifying its effectiveness.
To have an intuitive understanding of what has happened, we illustrate in Figure \ref{fig:partial_weight_distribution} the learned weight of each source class on the adaptation task of $\textbf{A}$ $\to \textbf{W}$. SymmNets-V2 (with active $\omega_k$) assigns much larger weights to domain-shared classes than the classes exclusive to the source domain, thus suppressing misalignment across the two domains.
\begin{table}[htp]
\centering
\caption{Accuracy (\%) on the VisDA-2017 dataset \cite{visda} for closed set UDA. All comparative methods are based on a 101-layer ResNet except the MDD and CDAN+E, which are based on a 50-layer ResNet }
\label{Tab:visda}
\begin{tabular}{lc}
\hline
Methods & Synthetic $\to$ Real \\
\hline
Source Only \cite{resnet} & 52.4 \\
DANN \cite{dann} & 57.4 \\
CDAN+E \cite{cada}& 70.0 \\
MCD \cite{mcd} & 71.9 \\
ADR \cite{adr} & 73.5 \\
MDD \cite{mdd} & 74.6 \\
SWD \cite{swd} & 76.4 \\
\hline
\textbf{SymmNets-V1} \cite{symnets} & 72.1 \\
\textbf{SymmNets-V2} & \textbf{76.8} \\
\hline
\hline
TPN \cite{tpn} & 80.4 \\
CAN \cite{can} & \textbf{87.2} \\
\hline
\textbf{SymmNets-V2-SC} & 86.0 \\
\hline
\hline
\end{tabular}
\end{table}
\begin{table*}[htb]
\centering
\caption{Accuracy (\%) on the Office-31 dataset \cite{office_31} for closed set UDA. Results are based on models adapted from a 50-layer ResNet.}
\label{Tab:office31}
\begin{tabular}{lccccccc}
\hline
Methods & A $\to$ W & D $\to$ W & W $\to$ D & A $\to$ D & D $\to$ A & W $\to$ A & Avg \\
\hline
Source Only\cite{resnet} & 68.4$\pm$0.2 & 96.7$\pm$0.1 & 99.3$\pm$0.1 & 68.9$\pm$0.2 & 62.5$\pm$0.3 & 60.7$\pm$0.3 & 76.1 \\
DAN \cite{dan} & 80.5$\pm$0.4 & 97.1$\pm$0.2 & 99.6$\pm$0.1 & 78.6$\pm$0.2 & 63.6$\pm$0.3 & 62.8$\pm$0.2 & 80.4 \\
RTN \cite{rtn} & 84.5$\pm$0.2 & 96.8$\pm$0.1 & 99.4$\pm$0.1 & 77.5$\pm$0.3 & 66.2$\pm$0.2 & 64.8$\pm$0.3 & 81.6 \\
DANN \cite{reverse_grad,dann} & 82.0$\pm$0.4 & 96.9$\pm$0.2 & 99.1$\pm$0.1 & 79.7$\pm$0.4 & 68.2$\pm$0.4 & 67.4$\pm$0.5 & 82.2 \\
ADDA \cite{adda} & 86.2$\pm$0.5 & 96.2$\pm$0.3 & 98.4$\pm$0.3 & 77.8$\pm$0.3 & 69.5$\pm$0.4 & 68.9$\pm$0.5 & 82.9 \\
JAN-A\cite{jan} & 86.0$\pm$0.4 & 96.7$\pm$0.3 & 99.7$\pm$0.1 & 85.1$\pm$0.4 & 69.2$\pm$0.3 & 70.7$\pm$0.5 & 84.6 \\
MADA \cite{mada} & 90.0$\pm$0.1 & 97.4$\pm$0.1 & 99.6$\pm$0.1 & 87.8$\pm$0.2 & 70.3$\pm$0.3 & 66.4$\pm$0.3 & 85.2 \\
SimNet \cite{SimNet} & 88.6$\pm$0.5 & 98.2$\pm$0.2 & 99.7$\pm$0.2 & 85.3$\pm$0.3 & 73.4$\pm$0.8 & 71.8$\pm$0.6 & 86.2 \\
MCD \cite{mcd} & 89.6$\pm$0.2 & 98.5$\pm$0.1 & 100.0$\pm$.0 & 91.3$\pm$0.2 & 69.6$\pm$0.1 & 70.8$\pm$0.3 & 86.6 \\
CDAN+E \cite{cada} & 94.1$\pm$0.1 & 98.6$\pm$0.1 & \textbf{100.0}$\pm$.0 & 92.9$\pm$0.2 & 71.0$\pm$0.3 & 69.3$\pm$0.3 & 87.7 \\
MDD \cite{mdd} & \textbf{94.5}$\pm$0.3 & 98.4$\pm$0.1 & \textbf{100.0}$\pm$.0 & 93.5$\pm$0.2 & \textbf{74.6}$\pm$0.3 & 72.2$\pm$0.1 & 88.9 \\
\hline
\textbf{SymmNets-V1 \cite{symnets}} & 90.8$\pm$0.1 & \textbf{98.8}$\pm$0.3 & \textbf{100.0}$\pm$.0 & \textbf{93.9}$\pm$0.5 & \textbf{74.6}$\pm$0.6 & 72.5$\pm$0.5 & 88.4 \\
\textbf{SymmNets-V2} & 94.2$\pm$0.1 & \textbf{98.8}$\pm$0.0 & \textbf{100.0}$\pm$.0 & 93.5$\pm$0.3 & 74.4$\pm$0.1 & \textbf{73.4}$\pm$0.2 & \textbf{89.1} \\
\hline
\hline
Kang \emph{et al.} \cite{attention_alignment} & 86.8$\pm$0.2 & \textbf{99.3}$\pm$0.1 & \textbf{100.0}$\pm$.0 & 88.8$\pm$0.4 & 74.3$\pm$0.2 & 73.9$\pm$0.2 & 87.2 \\
TADA \cite{tada} & 94.3$\pm$0.3 & 98.7$\pm$0.1 & 99.8$\pm$0.2 & 91.6$\pm$0.3 & 72.9$\pm$0.2 & 73.0$\pm$0.3 & 88.4 \\
CADA-P \cite{Kurmi_2019_CVPR} & \textbf{97.0}$\pm$0.2 & 99.3$\pm$0.1 & \textbf{100.0}$\pm$.0 & \textbf{95.6}$\pm$0.1 & 71.5$\pm$0.2 & 73.1$\pm$0.3 & 89.5 \\
CAN \cite{can} & 94.5$\pm$0.3 & 99.1$\pm$0.2 & 99.8$\pm$0.2 &95.0$\pm$0.3 &\textbf{78.0}$\pm$0.3 & \textbf{77.0}$\pm$0.3 & 90.6 \\
\hline
\textbf{SymmNets-V2-SC} & 94.9$\pm$0.3 & 99.1$\pm$0.1 & \textbf{100.0}$\pm$.0 & \textbf{95.6}$\pm$0.3 & 77.6$\pm$0.4 & \textbf{77.0}$\pm$0.3 & \textbf{90.7} \\
\hline
\end{tabular}
\end{table*}
\begin{table*}[htb]
\centering
\caption{Accuracy (\%) on the ImageCLEF-DA dataset \cite{ImageCLEFDA} for closed set UDA. Results are based on models adapted from a 50-layer ResNet.}
\label{Tab:ImageCLEF}
\begin{tabular}{lccccccc}
\hline
Methods & I $\to$ P & P $\to$ I & I $\to$ C & C $\to$ I & C $\to$ P & P $\to$ C & Avg \\
\hline
Source Only\cite{resnet} & 74.8$\pm$0.3 & 83.9$\pm$0.1 & 91.5$\pm$0.3 & 78.0$\pm$0.2 & 65.5$\pm$0.3 & 91.2$\pm$0.3 & 80.7 \\
DAN \cite{dan} & 74.5$\pm$0.4 & 82.2$\pm$0.2 & 92.8$\pm$0.2 & 86.3$\pm$0.4 & 69.2$\pm$0.4 & 89.8$\pm$0.4 & 82.5 \\
DANN \cite{reverse_grad,dann} & 75.0$\pm$0.6 & 86.0$\pm$0.3 & 96.2$\pm$0.4 & 87.0$\pm$0.5 & 74.3$\pm$0.5 & 91.5$\pm$0.6 & 85.0 \\
JAN \cite{jan} & 76.8$\pm$0.4 & 88.0$\pm$0.2 & 94.7$\pm$0.2 & 89.5$\pm$0.3 & 74.2$\pm$0.3 & 91.7$\pm$0.3 & 85.8 \\
MADA \cite{mada} & 75.0$\pm$0.3 & 87.9$\pm$0.2 & 96.0$\pm$0.3 & 88.8$\pm$0.3 & 75.2$\pm$0.2 & 92.2$\pm$0.3 & 85.8 \\
CDAN+E \cite{cada} & 77.7$\pm$0.3 & 90.7$\pm$0.2 & \textbf{97.7}$\pm$0.3 & 91.3$\pm$0.3 & 74.2$\pm$0.2 & 94.3$\pm$0.3 & 87.7 \\
\hline
\textbf{SymmNets-V1 \cite{symnets}} & \textbf{80.2}$\pm$0.3 & \textbf{93.6}$\pm$0.2 & 97.0$\pm$0.3 & \textbf{93.4}$\pm$0.3 & 78.7$\pm$0.3 & \textbf{96.4}$\pm$0.1 &\textbf{89.9} \\
\textbf{SymmNets-V2} & 79.0$\pm$0.3 & 93.5$\pm$0.2 & 96.9$\pm$0.2 & \textbf{93.4}$\pm$0.3 & \textbf{79.2}$\pm$0.3 & 96.2$\pm$0.1 & 89.7 \\
\hline
\hline
CADA-P \cite{Kurmi_2019_CVPR} & 78.0 & 90.5 & 96.7 & 92.0 & 77.2 & 95.5 & 88.3 \\
\hline
\textbf{SymmNets-V2-SC} & \textbf{79.2}$\pm$0.2 & \textbf{96.2}$\pm$0.3 & \textbf{96.8}$\pm$0.1 & \textbf{93.8}$\pm$0.2 & \textbf{77.8}$\pm$0.4 & \textbf{96.2}$\pm$0. & \textbf{90.0} \\
\hline
\end{tabular}
\end{table*}
\begin{table*}[h]
\begin{center}
\caption{Accuracy (\%) on the Office-Home dataset \cite{office_home} for closed set UDA. Results are based on models adapted from a 50-layer ResNet.}
\label{Tab:Office-Home}
\begin{tabular}{L{26.2mm}C{7.7mm}C{7.7mm}C{7.9mm}C{7.7mm}C{7.7mm}C{7.9mm}C{7.7mm}C{7.7mm}C{7.7mm}C{7.9mm}C{7.9mm}C{7.9mm}C{7.9mm}C{9mm}}
\hline
Methods &A$\to$C &A$\to$P &A$\to$R &C$\to$A &C$\to$P &C$\to$R &P$\to$A &P$\to$C &P$\to$R &R$\to$A &R$\to$C &R$\to$P & Avg \\
\hline
Source Only\cite{resnet} &34.9 & 50.0 & 58.0 & 37.4 & 41.9 & 46.2 & 38.5 & 31.2 & 60.4 & 53.9 & 41.2 & 59.9 &46.1 \\
DAN \cite{dan} & 43.6 & 57.0 & 67.9 & 45.8 & 56.5 & 60.4 & 44.0 & 43.6 & 67.7 & 63.1 & 51.5 &74.3 &56.3 \\
DANN \cite{reverse_grad,dann}& 45.6 & 59.3 & 70.1 & 47.0 & 58.5 & 60.9 & 46.1 & 43.7 & 68.5 & 63.2 &51.8 & 76.8 &57.6 \\
JAN \cite{jan} & 45.9 & 61.2 & 68.9 & 50.4 & 59.7 & 61.0 & 45.8 & 43.4 & 70.3 & 63.9 &52.4 & 76.8 &58.3 \\
CDAN+E \cite{cada} & 50.7 & 70.6 & 76.0 & 57.6 & 70.0 & 70.0 & 57.4 & 50.9 & 77.3 &70.9 & 56.7 &81.6 &65.8 \\
MDD \cite{mdd} & \textbf{54.9} & 73.7 &77.8 & 60.0 & 71.4 & 71.8 &61.2 & \textbf{53.6} & 78.1 & 72.5 & \textbf{60.2} & 82.3 & \textbf{68.1} \\
\hline
\textbf{SymmNets-V1 \cite{symnets}} & 47.7 & 72.9 & 78.5 & 64.2 &71.3 &\textbf{74.2} &64.2 &48.8 &79.5 &\textbf{74.5} &52.6 &82.7 & 67.6 \\
\textbf{SymmNets-V2} & 48.1 & \textbf{74.3} & \textbf{78.7} & \textbf{64.6} &\textbf{71.8} & 74.1 & \textbf{64.4} & 50.0& \textbf{80.2} & 74.3 & 53.1& \textbf{83.2} & \textbf{68.1} \\
\hline
\hline
DWT-MEC \cite{dwt} & 50.3 & 72.1 & 77.0 & 59.6 & 69.3 & 70.2 & 58.3 & 48.1 & 77.3 & 69.3 &53.6 &82.0 & 65.6 \\
TADA \cite{tada} & 53.1 & 72.3 & 77.2 & 59.1 & 71.2 &72.1 & 59.7 & 53.1 & 78.4 &72.4 &60.0 & 82.9 & 67.6 \\
CADA-P \cite{Kurmi_2019_CVPR} & \textbf{56.9} &76.4 &\textbf{80.7} & 61.3 & \textbf{75.2} & 75.2 &63.2 & \textbf{54.5} & 80.7 & \textbf{73.9} & \textbf{61.5} & \textbf{84.1} & \textbf{70.2} \\
\hline
\textbf{SymmNets-V2-SC} & 51.6 & \textbf{76.9} & 80.3 & \textbf{68.6} &71.8 &\textbf{78.3} &\textbf{65.8} &50.5 &\textbf{81.2} &73.1 &54.2 &82.4 & 69.6 \\
\hline
\end{tabular}
\end{center}
\end{table*}
\vspace{0.1cm}
\noindent \textbf{Investigation of the Values of $\nu$ in Open Set UDA}
We conduct experiments on the Office-31 dataset to investigate the effects of different values of $\nu$ for open set UDA. We plot in Figure \ref{fig:open_set_eta_change} the accuracy of the unknown class, and mean accuracy over domain-shared classes (OS$^*$) and all classes (OS) with different values of $\nu$. As $\nu$ increases, the accuracy of the unknown class improves significantly whereas the mean accuracy of domain-shared classes drops slightly. We empirically set $\nu=6$ in all experiments, which consistently gives good results.
\vspace{0.1cm}
\noindent\textbf{Feature Visualization} To have an intuitive understanding of what features comparative methods have learned, we visualize via t-SNE \cite{sne} in Figure \ref{Fig:sne} the network activations respectively from the feature extractors of DANN \cite{reverse_grad,dann} and SymmNets-V2 on the adaptation task of \textbf{A} $\to$ \textbf{W}. Compared with features learned by DANN, those by SymmNets-V2 are better aligned across the two domains for shared classes under all the settings of the closed set, partial, and open set UDA, and they are well distinguished for domain-specific classes under the settings of partial and open set UDA; the visualization confirms the fineness of SymmNets-V2 in characterizing multi-class UDA.
\begin{table*}[htb]
\centering
\caption{Accuracy (\%) on the Office-31 dataset \cite{office_31} for partial UDA. Results are based on models adapted from a 50-layer ResNet.}
\label{Tab:partial_office31}
\begin{tabular}{lccccccc}
\hline
Methods & A $\to$ W & D $\to$ W & W $\to$ D & A $\to$ D & D $\to$ A & W $\to$ A & Avg \\
\hline
Source Only\cite{resnet} & 54.52 & 94.57 & 94.27 & 65.61 & 73.17 & 71.71 & 75.64 \\
DAN \cite{dan} & 46.44 & 53.56 & 58.60 & 42.68 & 65.66 & 65.34 & 55.38 \\
DANN \cite{reverse_grad,dann} & 41.35 & 46.78 & 38.85 & 41.36 & 41.34 & 44.68 & 42.39 \\
ADDA \cite{adda} & 43.65 & 46.48 & 40.12 & 43.66 & 42.76 & 45.95 & 43.77 \\
RTN \cite{rtn} & 75.25 & 97.12 & 98.32 & 66.88 & 85.59 & 85.70 & 84.81 \\
JAN\cite{jan} & 43.39 & 53.56 & 41.40 & 35.67 & 51.04 & 51.57 & 46.11 \\
PADA \cite{pada} & 86.54 & 99.32 & \textbf{100.00} & 82.17 & 92.69 & 95.41 & 92.69 \\
ETN \cite{transfer_example_partial}& 94.52 & \textbf{100.00} & \textbf{100.00} & 95.03 & \textbf{96.21} & 94.64 & 96.73 \\
\hline
\textbf{SymmNets-V2} & 83.10 & 92.91 & 94.27 & 77.71 & 74.42 & 73.49 & 82.61 \\
\textbf{SymmNets-V2} (With active $\omega_k$) & \textbf{99.83} & 98.64 & \textbf{100.00} & \textbf{97.85} & 93.25 & \textbf{96.00} & \textbf{97.60} \\
\hline
\end{tabular}
\end{table*}
\begin{table*}[htb]
\begin{center}
\caption{Accuracy (\%) on the Office-Home dataset \cite{office_home} for partial UDA. Results are based on models adapted from a 50-layer ResNet.}
\label{Tab:partial_Office-Home}
\begin{tabular}{L{26.9mm}C{7.7mm}C{7.7mm}C{7.9mm}C{7.7mm}C{7.7mm}C{7.9mm}C{7.7mm}C{7.7mm}C{7.7mm}C{7.9mm}C{7.9mm}C{7.9mm}C{7.9mm}C{9mm}}
\hline
Methods &A$\to$C &A$\to$P &A$\to$R &C$\to$A &C$\to$P &C$\to$R &P$\to$A &P$\to$C &P$\to$R &R$\to$A &R$\to$C &R$\to$P & Avg \\
\hline
Source Only\cite{resnet} &38.57 & 60.78 & 75.21 & 39.94 &48.12 &52.90 &49.68 &30.91 &70.79 &65.38 &41.79 &70.42 &53.71 \\
DAN \cite{dan} &44.36 &61.79 &74.49 &41.78 &45.21 &54.11 &46.92 &38.14 &68.42 &64.37 &45.37 &68.85 &54.48 \\
DANN \cite{reverse_grad,dann} &44.89 &54.06 &68.97 &36.27 &34.34 &45.22 &44.08 &38.03 &68.69 &52.98 &34.68 &46.50 &47.39 \\
PADA \cite{pada} &51.95 &67.00 &78.74 &52.16 &53.78 &59.03 &52.61 &43.22 &78.79 &73.73 &56.60 &77.09 &62.06 \\
ETN \cite{transfer_example_partial} & \textbf{59.24} &77.03 & 79.54 &62.92 & 65.73 &75.01 &68.29 &55.37 &84.37 &75.72 &\textbf{57.66} &\textbf{84.54} &70.45 \\
\hline
\textbf{SymmNets-V2} & 53.12 & 67.87 &73.57 &62.43 & 56.73 &64.08 &\textbf{56.26} &59.61 &69.36 &66.64 &52.30 &69.56 &62.63 \\
\textbf{SymmNets-V2} & \multirow{2}{*}{55.46} &\multirow{2}{*}{\textbf{78.71}} &\multirow{2}{*}{\textbf{84.59}} &\multirow{2}{*}{\textbf{70.98}} & \multirow{2}{*}{\textbf{67.39}} &\multirow{2}{*}{\textbf{77.91}} &\multirow{2}{*}{\textbf{76.22}} &\multirow{2}{*}{54.45} &\multirow{2}{*}{\textbf{88.46}} &\multirow{2}{*}{\textbf{77.23}} &\multirow{2}{*}{57.07} &\multirow{2}{*}{83.75} &\multirow{2}{*}{\textbf{72.69}} \\
(With active $\omega_k$) &&&&&&&&&&&&& \\
\hline
\end{tabular}
\end{center}
\end{table*}
\begin{table*}[h!]
\begin{center}
\caption{Accuracy (\%) on the Office-31 dataset \cite{office_31} for open set UDA. Results of all methods are based on models adapted from a 50-layer ResNet.}
\label{Tab:open_Office31}
\begin{tabular}{lllllllllllllll}
\cline{1-15}
\multirow{2}{*}{Methods} & \multicolumn{2}{|c|}{A$\to$D} & \multicolumn{2}{c|}{A$\to$W} & \multicolumn{2}{c|}{D$\to$A} & \multicolumn{2}{c|}{D$\to$W} & \multicolumn{2}{c|}{W$\to$A} & \multicolumn{2}{c|}{W$\to$D} & \multicolumn{2}{c}{AVG} \\ \cline{2-15}
& \multicolumn{1}{|c}{OS} & \multicolumn{1}{c|}{OS$^*$} & \multicolumn{1}{c}{OS} & \multicolumn{1}{c|}{OS$^*$} & \multicolumn{1}{c}{OS} & \multicolumn{1}{c|}{OS$^*$} & \multicolumn{1}{c}{OS} & \multicolumn{1}{c|}{OS$^*$} & \multicolumn{1}{c}{OS} & \multicolumn{1}{c|}{OS$^*$} & \multicolumn{1}{c}{OS} & \multicolumn{1}{c|}{OS$^*$} & \multicolumn{1}{c}{OS} & \multicolumn{1}{c}{OS$^*$} \\ \hline
\hline
\multicolumn{1}{l|}{Source Only \cite{resnet}} & 85.2 & \multicolumn{1}{l|}{85.5} & 82.5 & \multicolumn{1}{l|}{82.7} & 71.6 & \multicolumn{1}{l|}{71.5} & 94.1 & \multicolumn{1}{l|}{94.3} & 75.5 & \multicolumn{1}{l|}{75.2} & 96.6 & \multicolumn{1}{l|}{97.0} & 84.2 & 84.4 \\
\multicolumn{1}{l|}{DANN \cite{dann}} & 86.5 & \multicolumn{1}{l|}{87.7} & 85.3 & \multicolumn{1}{l|}{87.7} & 75.7 & \multicolumn{1}{l|}{76.2} & 97.5 & \multicolumn{1}{l|}{\textbf{98.3}} & 74.9 & \multicolumn{1}{l|}{75.6} & \textbf{99.5} & \multicolumn{1}{l|}{\textbf{100.0}} & 86.6 & 87.6 \\
\multicolumn{1}{l|}{ATI-$\lambda$\cite{open_set_math}} & 84.3 & \multicolumn{1}{l|}{86.6} & 87.4 & \multicolumn{1}{l|}{88.9} & 78.0 & \multicolumn{1}{l|}{79.6} & 93.6 & \multicolumn{1}{l|}{95.3} & 80.4 & \multicolumn{1}{l|}{81.4} & 96.5 & \multicolumn{1}{l|}{98.7} & 86.7 & 88.4 \\
\multicolumn{1}{l|}{AODA\cite{open_set_bp}} & 88.6 & \multicolumn{1}{l|}{89.2} & 86.5 & \multicolumn{1}{l|}{87.6} & 88.9 & \multicolumn{1}{l|}{90.6} & 97.0 & \multicolumn{1}{l|}{96.5} & 85.8 & \multicolumn{1}{l|}{84.9} & 97.9 & \multicolumn{1}{l|}{98.7} & 90.8 & 91.3 \\
\multicolumn{1}{l|}{STA \cite{liu2019separate}} & 93.7 & \multicolumn{1}{l|}{96.1} & 89.5 & \multicolumn{1}{l|}{92.1} & 89.1 & \multicolumn{1}{l|}{\textbf{93.5}} & 97.5 & \multicolumn{1}{l|}{96.5} & 87.9 & \multicolumn{1}{l|}{87.4} & \textbf{99.5} & \multicolumn{1}{l|}{99.6} & 92.9 & 94.1 \\
\hline
\multicolumn{1}{l|}{\textbf{SymmNets-V2} ($\nu=6$)} & \textbf{96.3} & \multicolumn{1}{l|}{\textbf{97.5}} & \textbf{95.7} & \multicolumn{1}{l|}{\textbf{96.1}} & \textbf{91.6} & \multicolumn{1}{l|}{91.7} & \textbf{97.8} & \multicolumn{1}{l|}{\textbf{98.3}} & \textbf{92.3} & \multicolumn{1}{l|}{\textbf{92.9}} & 99.2 & \multicolumn{1}{l|}{\textbf{\textbf{100.0}}} & \textbf{95.5} & \textbf{96.1} \\
\hline
\hline
\end{tabular}
\end{center}
\end{table*}
\begin{table*}[h!]
\begin{center}
\caption{Accuracy (\%) on Syn2Real dataset \cite{syn2real} for open set UDA. Results of all methods are based on models adapted from a 152-layer ResNet.}
\label{Tab:open_visda}
\begin{tabular}{l|C{3.7mm}C{3.7mm}C{3.7mm}C{3.7mm}C{3.7mm}C{3.7mm}C{3.7mm}C{3.7mm}C{3.7mm}C{3.7mm}C{3.7mm}C{3.7mm}C{3.7mm}|C{3.7mm}C{3.7mm}}
\hline
Methods & \rotatebox{45}{plane} & \rotatebox{45}{bcycle} &\rotatebox{45}{bus} & \rotatebox{45}{car} & \rotatebox{45}{horse} & \rotatebox{45}{knife} & \rotatebox{45}{mcycl} & \rotatebox{45}{person} & \rotatebox{45}{plant} & \rotatebox{45}{sktbrd} & \rotatebox{45}{train} & \rotatebox{45}{trunk} & \rotatebox{45}{unk} & \rotatebox{45}{OS$^*$} & \rotatebox{45}{OS}\\
\hline
\multicolumn{14}{l}{\textbf{Known-to-Unknown Ratio = 1:1}} & & \\
\hline
Source Only \cite{resnet} & 36 & 27 & 21 & 49 & 66 & 0 & 69 & 1 & 42 & 8 & 59 & 0 & 81 & 31 & 35 \\
DANN \cite{dann} & 53 & 5 & 31 & 61 & 75 & 3 & 81 & 11 & 63 & 29 & 68 & 5 & 76 & 43 & 40 \\
AODA \cite{open_set_bp} & 85 & 71 & 65 & 53 & 83 & \textbf{10} & 79 & 36 & 73 & 56 & 79 & \textbf{32} & \textbf{87} & 60 & 62 \\
\textbf{SymmNets-V2} ($\nu=6$) & \textbf{93} & \textbf{79} & \textbf{85} & \textbf{75} & \textbf{92} & 3 & \textbf{91} & \textbf{80} & \textbf{84} & \textbf{69} & \textbf{75} & 2 & 57 & \textbf{69} & \textbf{68} \\
\hline
\hline
\multicolumn{14}{l}{\textbf{Known-to-Unknown Ratio = 1:10}} & & \\
\hline
Source Only \cite{resnet} & 23 & 24 & 43 & 40 & 44 & 0 & 56 & 2 & 24 & 8 & 47 & 1 & \textbf{93} & 26 & 31 \\
AODA \cite{open_set_bp} & 80 & 63 & 59 & 63 & 83 & 12 & 89 & 5 & \textbf{61} & 14 & 79 & 0 & 69 & 51 & 52 \\
\textbf{SymmNets-V2} ($\nu=6$) &\textbf{90}& \textbf{72} & \textbf{76} & \textbf{68} & \textbf{90} & \textbf{14} & \textbf{94} & \textbf{18} & 59 & \textbf{20} & \textbf{83} & \textbf{5} & 70 & \textbf{59} & \textbf{59} \\
\hline
\end{tabular}
\end{center}
\end{table*}
\subsection{Comparisons with the State of the Art} \label{SecResults}
\noindent\textbf{Closed Set UDA} We report in Table \ref{Tab:visda}, Table \ref{Tab:office31}, Table \ref{Tab:ImageCLEF}, and Table \ref{Tab:Office-Home} the classification results respectively on the popular closed set UDA datasets of VisDA-2017 \cite{visda}, Office-31 \cite{office_31}, ImageCLEF-DA \cite{ImageCLEFDA}, and Office-Home \cite{office_home}. Compared with existing adversarial learning-based methods, including the seminal one of DANN \cite{dann} and the recent ones of MCD \cite{mcd}, CDAN \cite{cada}, MDD \cite{mdd}, and SWD \cite{swd}, our SymmNets-V2 achieves better performance on most of these benchmarks, demonstrating the efficacy and fineness of SymmNets-V2 in characterizing multi-class UDA. We note that there exist a few recent methods that focus on other strategies, such as the feature attention strategy \cite{tada,cada}, prototypical network \cite{tpn}, prediction consistency w.r.t input perturbation \cite{dwt}, and intra- and inter-class discrepancies \cite{can}, all of which are orthogonal to the strategy of adversarial training studied in the present work. To compare with these methods more fairly, we consider a few strategies of these methods amenable to adversarial training, including the class-aware sampling \cite{can} empowered by alternative optimization \cite{can}, use of pseudo labels of target data as in the prototypical network \cite{tpn}, and the min-entropy consensus \cite{dwt}, resulting in a variant of our method termed as ``SymmNets-V2 Strengthened for Closed Set UDA (SymmNets-V2-SC)''. SymmNets-V2-SC boosts the performance of SymmNets-V2 on the closed set UDA, especially on the VisDA-2017 dataset \cite{visda}, indicating a promising direction of combining multiple strategies for the setting of closed set UDA.
\noindent\textbf{Partial UDA} We report in Table \ref{Tab:partial_office31} and Table \ref{Tab:partial_Office-Home} the classification results respectively on the popular partial UDA datasets of Office-31 \cite{office_31} and Office-Home \cite{office_home}. The seminal methods \cite{dan, dann} achieve worse results than the Source Only baseline; in contrast, our SymmNets-V2 improves over the Source Only baseline by a large margin, confirming the effectiveness of our method in characterizing the domain distance at a finer level. Our SymmNets-V2 (with active $\omega_k$) outperforms all state-of-the-art methods on the two benchmark datasets, again confirming the effectiveness of our method.
\noindent \textbf{Open Set UDA} We report in Table \ref{Tab:open_Office31} and Table \ref{Tab:open_visda} the classification results respectively on the popular open set UDA datasets of Office-31 \cite{office_31} and Syn2Real \cite{syn2real}. Our SymmNets-V2 ($\nu=6$) outperforms all state-of-the-art methods on the two benchmarks, confirming the effectiveness of our method in aligning both the domain-shared classes and the unknown class across source and target domains.
\section{Conclusion}
In this paper, we study the formalism of unsupervised multi-class domain adaptation. We contribute a new bound for multi-class UDA based on a novel notion of Multi-Class Scoring Disagreement (MCSD); a corresponding data-dependent PAC bound is also developed based on the notion of Rademacher complexity. The proposed MCSD is able to fully characterize the relations between any pair of multi-class scoring hypotheses, which is finer compared with those in existing domain adaptation bounds. Our derived bounds naturally suggest the Multi-class Domain-adversarial learning Networks (McDalNets), which promotes the alignment of conditional feature distributions across source and target domains. We show that different instantiations of McDalNets via surrogate learning objectives either coincide with or resemble a few recently popular methods, thus (partially) underscoring their practical effectiveness. Based on our same theory of multi-class UDA, we also introduce a new algorithm of Domain-Symmetric Networks (SymmNets), which is featured by a novel adversarial strategy of domain confusion and discrimination. SymmNets affords simple extensions that work equally well under the problem settings of either closed set, partial, or open set UDA. Careful empirical studies show that algorithms of McDalNets based on the MCSD surrogates consistently improve over these based on the scalar-valued versions.
Experiments under the settings of closed set, partial, and open set UDA also confirm the effectiveness of our proposed SymmNets empirically. The contributed theory and algorithms connect better with the practice in multi-class UDA. We expect they could provide useful principles for algorithmic design in future research.
\ifCLASSOPTIONcompsoc
\section*{Acknowledgments}
\else
\section*{Acknowledgment}
\fi
This work is supported in part by the National Natural Science Foundation of China (Grant No.: 61771201), the Program for Guangdong Introducing Innovative and Enterpreneurial Teams (Grant No.: 2017ZT07X183), and the Guangdong R\&D key project of China (Grant No.: 2019B010155001).
\ifCLASSOPTIONcaptionsoff
\newpage
\fi
\bibliographystyle{IEEEtran_bst}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,297 |
//
// YGAllDetailCategoryController.m
// WangYe
//
// Created by 阳光 on 2017/2/19.
// Copyright © 2017年 YG. All rights reserved.
//
#import "YGAllDetailCategoryController.h"
#import "YGAllDetailPicCell.h"
#import "YGAllDetailTextCell.h"
#import "YGAllDetailMovieCell.h"
#import "YGAllDetailCategoryItem.h"
#import "YGAllDetailPhotoBrowerController.h"
#import "YGListDetailMovieController.h"
#import "YGEssenceWebController.h"
#import "YGListDetailMovieController.h"
@interface YGAllDetailCategoryController ()<UITableViewDelegate, UITableViewDataSource>
/** 图片视图 */
@property(nonatomic, strong) UIImageView *iconIV;
/** 背景图片 */
@property(nonatomic, strong) UIView *TopNavView;
/** 表头标题 */
@property(nonatomic, strong) UILabel *headLabel;
/** 表头视图 */
@property(nonatomic, strong) UIView *headView;
/** 表视图 */
@property(nonatomic, strong) UITableView *tableView;
/** 返回按钮 */
@property(nonatomic, strong) UIButton *backBtn;
/** 列表数组 */
@property(nonatomic, strong) NSMutableArray *detailCategoryArr;
/** 页数 */
@property(nonatomic, assign) NSInteger pageNum;
/** 是否能够加载更过 */
@property(nonatomic, strong) NSString *canLoadMore;
@end
@implementation YGAllDetailCategoryController
#pragma mark - 构造方法
- (instancetype)initWithImageName:(NSString *)imageName labelName:(NSString *)labelName ID:(NSString *)ID
{
self = [super init];
if (self) {
self.imageName = imageName;
self.labelName = labelName;
self.ID = ID;
}
return self;
}
- (void)viewDidLoad {
[super viewDidLoad];
self.view.backgroundColor = [UIColor whiteColor];
[self configUI];
[self configNetManager];
//注册TableViewCell
[self.tableView registerClass:[YGAllDetailPicCell class] forCellReuseIdentifier:@"YGAllDetailPicCell"];
[self.tableView registerClass:[YGAllDetailTextCell class] forCellReuseIdentifier:@"YGAllDetailTextCell"];
[self.tableView registerClass:[YGAllDetailMovieCell class] forCellReuseIdentifier:@"YGAllDetailMovieCell"];
}
#pragma mark - 网络请求
- (void)configNetManager
{
__weak typeof(self) weakSelf = self;
[NetManager GETAllDetailCategory:1 ID:self.ID completionHandler:^(YGAllDetailCategoryItem *allDetailCategoryItem, NSError *error) {
if (error) {
[self.view showMessage:@"网络有误..."];
} else {
[self.tableView endHeaderRefresh];
self.pageNum = 1;
self.canLoadMore = allDetailCategoryItem.canLoadMore;
[self.detailCategoryArr addObjectsFromArray:allDetailCategoryItem.articleList];
[self.tableView reloadData];
if ([allDetailCategoryItem.canLoadMore isEqualToString:@"0"]) {
[self.tableView endFooterWithNoMore];
}
}
}];
self.tableView.mj_footer = [MJRefreshAutoNormalFooter footerWithRefreshingBlock:^{
[NetManager GETAllDetailCategory:self.pageNum + 1 ID:weakSelf.ID completionHandler:^(YGAllDetailCategoryItem *allDetailCategoryItem, NSError *error) {
[self.tableView endFooterRefresh];
if (error) {
[weakSelf.view showMessage:@"网络有误..."];
} else
{
weakSelf.pageNum += 1;
weakSelf.canLoadMore = allDetailCategoryItem.canLoadMore;
[weakSelf.detailCategoryArr addObjectsFromArray:allDetailCategoryItem.articleList];
[weakSelf.tableView reloadData];
if ([allDetailCategoryItem.canLoadMore isEqualToString:@"0"]) {
[weakSelf.tableView endFooterWithNoMore];
}
}
}];
}];
}
- (void)configUI
{
CGFloat scale = 365 / 750.0;
/**
* 配置tableView
*/
self.tableView = [[UITableView alloc] init];
[self.view addSubview:self.tableView];
[self.tableView mas_makeConstraints:^(MASConstraintMaker *make) {
make.edges.offset(0);
}];
/**
* 表头视图背景
*/
self.headView = [[UIView alloc] initWithFrame:CGRectMake(0, 0, YGScreenW, YGScreenW * scale)];
self.tableView.tableHeaderView = self.headView;
self.tableView.delegate = self;
self.tableView.dataSource = self;
/**
* 配置背景图片
*/
self.iconIV = [[UIImageView alloc] init];
self.iconIV.contentMode = UIViewContentModeScaleAspectFill;
self.iconIV.clipsToBounds = YES;
[self.iconIV setImageWithURL:self.imageName.yg_URL placeholder:[UIImage imageNamed:@"placeHolder1"]];
[self.headView addSubview:self.iconIV];
self.iconIV.frame = self.headView.frame;
/**
* 导航视图View
*/
self.TopNavView = [[UIView alloc] initWithFrame:CGRectMake(0, 0, YGScreenW, 64)];
self.TopNavView.backgroundColor = YGRGBColor(254, 254, 254);
/*********/
self.TopNavView.layer.shadowColor = [UIColor blackColor].CGColor;//shadowColor阴影颜色
self.TopNavView.layer.shadowOffset = CGSizeMake(0,0);
self.TopNavView.layer.shadowOpacity = 0.6;//阴影透明度,默认0
self.TopNavView.layer.shadowRadius = 5;//阴影半径,默认3
/*********/
self.TopNavView.hidden = YES;
[self.view addSubview:self.TopNavView];
/**
* 导航视图上面的标题
*/
UILabel *topLabel = [[UILabel alloc] init];
[self.TopNavView addSubview:topLabel];
topLabel.font = [UIFont systemFontOfSize:19];
topLabel.text = self.labelName;
[topLabel mas_makeConstraints:^(MASConstraintMaker *make) {
make.centerX.offset(0);
make.centerY.offset(10);
}];
/**
* 返回按钮
*/
self.backBtn = [UIButton buttonWithType:UIButtonTypeSystem];
[self.backBtn setBackgroundImage:[UIImage imageNamed:@"Action_backward_white_44x44_"] forState:UIControlStateNormal];
[self.view addSubview:self.backBtn];
self.backBtn.frame = CGRectMake(5, 20, 44, 44);
[self.backBtn addTarget:self action:@selector(goBackLastVC) forControlEvents:UIControlEventTouchUpInside];
/**
* 表视图文字
*/
self.headLabel = [[UILabel alloc] init];
self.headLabel.font = [UIFont boldSystemFontOfSize:17];
self.headLabel.textColor = [UIColor whiteColor];
self.headLabel.text = self.labelName;
[self.iconIV addSubview:self.headLabel];
[self.headLabel mas_makeConstraints:^(MASConstraintMaker *make) {
make.center.offset(0);
}];
}
#pragma mark - 返回上一界面按钮
- (void)goBackLastVC
{
[self.navigationController popViewControllerAnimated:YES];
}
#pragma mark - <UITableViewDatasource>
- (NSInteger)tableView:(UITableView *)tableView numberOfRowsInSection:(NSInteger)section
{
return self.detailCategoryArr.count;
}
- (UITableViewCell *)tableView:(UITableView *)tableView cellForRowAtIndexPath:(NSIndexPath *)indexPath
{
YGAllDetailCategoryArticlelistItem *articleItem = self.detailCategoryArr[indexPath.row];
/**
* 新闻分类
*/
if ([articleItem.objectType isEqualToString:@"1"]) {
YGAllDetailTextCell *textCell = [tableView dequeueReusableCellWithIdentifier:@"YGAllDetailTextCell" forIndexPath:indexPath];
textCell.titleLB.text = articleItem.object.title;
[textCell.iconIV setImageWithURL:articleItem.object.imgUrl.yg_URL placeholder:[UIImage imageNamed:@"placeHolder1"]];
return textCell;
}
/**
* 电影分类
*/
if ([articleItem.objectType isEqualToString:@"2"]) {
YGAllDetailMovieCell *movieCell = [tableView dequeueReusableCellWithIdentifier:@"YGAllDetailMovieCell" forIndexPath:indexPath];
[movieCell.iconIV setImageWithURL:articleItem.object.coverUrl.yg_URL placeholder:[UIImage imageNamed:@"placeHolder1"]];
movieCell.titleLB.text = articleItem.object.title;
//如果为空就用空字符串代替
if (articleItem.object.des == nil) {
movieCell.detailLB.text = @"";
} else {
movieCell.detailLB.text = articleItem.object.des;
}
return movieCell;
}
/**
* 图片分类
*/
YGAllDetailPicCell *picCell = [tableView dequeueReusableCellWithIdentifier:@"YGAllDetailPicCell" forIndexPath:indexPath];
[picCell.iconIV setImageWithURL:articleItem.object.imgUrl.yg_URL placeholder:[UIImage imageNamed:@"placeHolder1"]];
picCell.titleLB.text = articleItem.object.des;
picCell.detailLB.text = [NSString stringWithFormat:@"《%@》", articleItem.object.sourceAuthor];
return picCell;
}
#pragma mark - <UITableViewDdelegate>
- (void)tableView:(UITableView *)tableView didSelectRowAtIndexPath:(NSIndexPath *)indexPath
{
YGAllDetailCategoryArticlelistItem *articleItem = self.detailCategoryArr[indexPath.row];
/**
* 新闻分类
*/
if ([articleItem.objectType isEqualToString:@"1"]) {
YGEssenceWebController *webVC = [[YGEssenceWebController alloc] initWithAppView:articleItem.object.articleContentUrl];
// NSLog(@"%@", articleItem.object.articleContentUrl);
[self.navigationController pushViewController:webVC animated:YES];
}
/**
* 电影分类
*/
if ([articleItem.objectType isEqualToString:@"2"]) {
NSString *bgImage = @"http://img.kaiyanapp.com/65b83a4433a6a0db122cb3e1d7ff6076.jpeg?imageMogr2/quality/60/format/jpg";
YGListDetailMovieController *movieVC = [[YGListDetailMovieController alloc] initWithBgImageView:bgImage titleView:articleItem.object.coverUrl detailLabel:articleItem.object.title url:articleItem.object.videoUrl];
[self.navigationController pushViewController:movieVC animated:YES];
}
/**
* 图片分类
*/
if ([articleItem.objectType isEqualToString:@"6"]) {
YGAllDetailPhotoBrowerController *phtotVC = [[YGAllDetailPhotoBrowerController alloc] initWithImgUrl:articleItem.object.imgUrl desLB:articleItem.object.des];
[self.navigationController pushViewController:phtotVC animated:YES];
}
}
- (void)didReceiveMemoryWarning {
[super didReceiveMemoryWarning];
// Dispose of any resources that can be recreated.
}
#pragma mark - <生命周期方法>
- (void)viewWillAppear:(BOOL)animated
{
[super viewWillAppear:animated];
//去掉TableView的线
self.tableView.separatorStyle = UITableViewCellSeparatorStyleNone;
//是否隐藏导航栏
self.navigationController.navigationBarHidden = YES;
//是否隐藏电池条
[UIApplication sharedApplication].statusBarHidden = YES;
}
- (void)viewWillDisappear:(BOOL)animated
{
[super viewWillDisappear:animated];
//是否隐藏导航栏
self.navigationController.navigationBarHidden = NO;
//是否隐藏电池条
[UIApplication sharedApplication].statusBarHidden = NO;
}
//是否隐藏导航条
- (void)viewDidDisappear:(BOOL)animated
{
[super viewDidDisappear:animated];
//是否隐藏电池条
[UIApplication sharedApplication].statusBarHidden = NO;
}
#pragma mark - <UIScrollViewDelegage>
- (void)scrollViewDidScroll:(UIScrollView *)scrollView
{
CGFloat scale = 365 / 750.0;
CGPoint p = scrollView.contentOffset;
if (p.y >= YGScreenW * scale - 64) {
self.TopNavView.hidden = NO;
[self.backBtn setBackgroundImage:[UIImage imageNamed:@"Action_backward_44x44_"] forState:UIControlStateNormal];
[UIApplication sharedApplication].statusBarHidden = NO;
} else {
self.TopNavView.hidden = YES;
[self.backBtn setBackgroundImage:[UIImage imageNamed:@"Action_backward_white_44x44_"] forState:UIControlStateNormal];
[UIApplication sharedApplication].statusBarHidden = YES;
}
[self.headLabel mas_updateConstraints:^(MASConstraintMaker *make) {
make.center.offset(0);
}];
if (p.y >= 0) { //这里向上移动图片不变小
self.iconIV.frame = CGRectMake(0, 0, YGScreenW, YGScreenW * scale);
return;
}
CGRect frame = self.headView.frame;
frame.size.height = YGScreenW * scale - p.y;
frame.origin.y = p.y;
self.iconIV.frame = frame;
NSLog(@"%lf-------%lf", p.y, YGScreenW * scale - 64);
}
#pragma mark - 高性能计算行高
- (CGFloat)tableView:(UITableView *)tableView heightForRowAtIndexPath:(NSIndexPath *)indexPath
{
YGAllDetailCategoryArticlelistItem *articleItem = self.detailCategoryArr[indexPath.row];
if ([articleItem.objectType isEqualToString:@"1"]) {
return [tableView fd_heightForCellWithIdentifier:@"YGAllDetailTextCell" configuration:^(YGAllDetailTextCell *cell) {
[cell.iconIV setImageWithURL:articleItem.object.imgUrl.yg_URL placeholder:[UIImage imageNamed:@"placeHolder1"]];
}];
}
if ([articleItem.objectType isEqualToString:@"2"]) {
return [tableView fd_heightForCellWithIdentifier:@"YGAllDetailMovieCell" configuration:^(YGAllDetailMovieCell *cell) {
[cell.iconIV setImageWithURL:articleItem.object.coverUrl.yg_URL placeholder:[UIImage imageNamed:@"placeHolder1"]];
cell.titleLB.text = articleItem.object.title;
//如果为空就用空字符串代替
if (articleItem.object.des == nil) {
cell.detailLB.text = @"";
} else {
cell.detailLB.text = articleItem.object.des;
}
}];
}
return [tableView fd_heightForCellWithIdentifier:@"YGAllDetailPicCell" configuration:^(YGAllDetailPicCell *cell) {
[cell.iconIV setImageWithURL:articleItem.object.imgUrl.yg_URL placeholder:[UIImage imageNamed:@"placeHolder1"]];
cell.titleLB.text = articleItem.object.des;
cell.detailLB.text = [NSString stringWithFormat:@"《%@》", articleItem.object.sourceAuthor];
}];
}
#pragma mark - lazy
- (NSMutableArray *)detailCategoryArr {
if(_detailCategoryArr == nil) {
_detailCategoryArr = [[NSMutableArray alloc] init];
}
return _detailCategoryArr;
}
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,633 |
{"url":"https:\/\/gmatclub.com\/forum\/machines-x-and-y-can-work-at-their-respective-constant-rates-266201.html","text":"GMAT Question of the Day - Daily to your Mailbox; hard ones only\n\n It is currently 13 Dec 2019, 17:37\n\n### GMAT Club Daily Prep\n\n#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.\n\nCustomized\nfor You\n\nwe will pick new questions that match your level based on your Timer History\n\nTrack\n\nevery week, we\u2019ll send you an estimated GMAT score based on your performance\n\nPractice\nPays\n\nwe will pick new questions that match your level based on your Timer History\n\n# Machines X and Y can work at their respective constant rates\n\nAuthor Message\nTAGS:\n\n### Hide Tags\n\ne-GMAT Representative\nJoined: 04 Jan 2015\nPosts: 3158\nMachines X and Y can work at their respective constant rates\u00a0 [#permalink]\n\n### Show Tags\n\nUpdated on: 13 Aug 2018, 06:00\n2\n23\n00:00\n\nDifficulty:\n\n55% (hard)\n\nQuestion Stats:\n\n64% (01:49) correct 36% (01:38) wrong based on 358 sessions\n\n### HideShow timer Statistics\n\nSolve Time and Work Problems Efficiently using Efficiency Method! - Exercise Question #4\n\nMachines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more\/less than that of machine X?\n\n(1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does.\n(2) Machine Y, working alone, fills a production order of twice the size in 6 hrs.\n\nOption choices:\nA) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.\nB) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.\nC) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.\nD) EACH statement ALONE is sufficient.\nE) Statements (1) and (2) TOGETHER are NOT sufficient.\n\nTo read the article: Solve Time and Work Problems Efficiently using Efficiency Method!\n\n_________________\n\nOriginally posted by EgmatQuantExpert on 23 May 2018, 04:16.\nLast edited by EgmatQuantExpert on 13 Aug 2018, 06:00, edited 1 time in total.\nDirector\nJoined: 12 Feb 2015\nPosts: 966\nRe: Machines X and Y can work at their respective constant rates\u00a0 [#permalink]\n\n### Show Tags\n\n26 May 2018, 13:57\n5\n1\n1\nQuestion Stem:-\nMachines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more\/less than that of machine X?\nRephrase:-\nMachines X and Y can work at their respective constant rates of 1\/x and 1\/y respectively (where x and y indicate time taken to complete one job).\n\n$$\\frac{y}{x}-1$$ = ? i.e can we get the value of $$\\frac{y}{x}$$\n\nKindly note:-\nWhen both work together means they work at a rate of $$\\frac{1}{x}$$+$$\\frac{1}{y}$$ = $$\\frac{x+y}{xy}$$\nTime taken when both machines work together = $$\\frac{xy}{x+y}$$\n\nLets evaluate both the statements:-\nStatement (1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does.\n\nTherefore from (1) $$\\frac{xy}{x+y}$$ = $$\\frac{2y}{3}$$\nwhich implies $$\\frac{x}{x+y}$$ = $$\\frac{2}{3}$$\nor$$\\frac{y}{x} = \\frac{1}{2}$$\nSince we have got the value of $$\\frac{y}{x}$$ Statement 1 is sufficient; Not lets check statement 2 [Cross B,C & E] Evaluate between A & D:-\n\nStatement (2) Machine Y, working alone, fills a production order of twice the size in 6 hrs.\n\nThere is no mention about the rate of machine X hence statement (2) is insufficient. Hence the correct answer is option A.\n_________________\n________________\nManish\n\n\"Only I can change my life. No one can do it for me\"\n##### General Discussion\ne-GMAT Representative\nJoined: 04 Jan 2015\nPosts: 3158\nRe: Machines X and Y can work at their respective constant rates\u00a0 [#permalink]\n\n### Show Tags\n\n27 May 2018, 05:32\n\nSolution\n\nGiven:\n\u2022 Machine X and Y work at their respective constant rates to manufacture a certain production unit\n\nTo find:\n\u2022 When both machines are working alone, the time taken by machine Y is what percentage more\/less than that of machine X\n\nApproach and Working:\nIf we assume the time taken by machine X and Y individually to complete the work is $$t_1$$ and $$t_2$$ respectively, then\n\u2022 Time $$t_2$$ is more than time $$t_1$$ by (as a percentage) = $$\\frac{(t_2 \u2013 t_1)}{t_1} * 100$$\no This can be written as = ($$\\frac{t_2}{t_1}$$ \u2013 1) * 100\n[Note that if $$t_2$$ is less than $$t_1$$, then the above expression will be equal to (1 \u2013 $$\\frac{t_2}{t_1}$$) * 100\n\u2022 Hence, if we can find the value of the ratio $$\\frac{t_2}{t_1}$$, we can find out the required percentage\n\nAnalysing Statement 1\n\u2022 As per the information given in statement 1, Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does.\no The time taken by both of them together to complete the job = $$\\frac{t_1t_2}{(t_1 + t_2)}$$\n\u2022 Given that, $$\\frac{t_1t_2}{(t_1 + t_2)}$$ = $$\\frac{2}{3} t_2$$\no Simplifying, we can write $$\\frac{t_2}{t_1}$$ = $$\\frac{2}{1}$$\nHence, statement 1 is sufficient enough to answer the question\n\nAnalysing Statement 2\n\u2022 As per the information given in statement 2, Machine Y, working alone, fills a production order of twice the size in 6 hrs\no From this statement, we can say $$t_2$$ = 3 hours\no But we cannot conclude any relationship between $$t_1$$ and $$t_2$$\nHence, statement 2 is not sufficient to answer the question\n\nHence, the correct answer is option A.\n\nImportant Observation\n\n\u2022 When we are calculating by what percentage one element is more\/less than the other element, we only need to find out the ratio between those elements.\n\n_________________\nGMATH Teacher\nStatus: GMATH founder\nJoined: 12 Oct 2010\nPosts: 935\nRe: Machines X and Y can work at their respective constant rates\u00a0 [#permalink]\n\n### Show Tags\n\n30 Oct 2018, 03:15\nEgmatQuantExpert wrote:\n\nMachines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more\/less than that of machine X?\n\n(1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does.\n(2) Machine Y, working alone, fills a production order of twice the size in 6 hrs.\n\n$$?\\,\\,:\\,\\,{T_X}\\,,\\,\\,{T_Y}\\,\\,{\\rm{relationship}}\\,\\,\\,\\,\\,\\,\\left( {? = {T_X}\\mathop \\to \\limits^{\\Delta \\% } {T_Y} = {{{T_Y} - {T_X}} \\over {{T_X}}} = {{{T_Y}} \\over {{T_X}}} - 1} \\right)$$\n\nImportant: the ratio of time taken (for any given job) is the inverse of the ratio of the work done (for any given time).\n\n$$\\left( 1 \\right)\\,\\,{{{T_{X \\cup Y}}} \\over {{T_Y}}} = {2 \\over 3}\\,\\,\\,\\,\\, \\Rightarrow \\,\\,\\,\\,\\,{{{W_{X \\cup Y}}} \\over {{W_Y}}} = {3 \\over 2}\\,\\,\\,\\,\\, \\Rightarrow \\,\\,\\,\\,\\,\\left\\{ \\matrix{ \\,{W_{X \\cup Y}} = 3k \\hfill \\cr \\,{W_Y} = 2k \\hfill \\cr} \\right.\\,\\,\\,\\,\\, \\Rightarrow \\,\\,\\,{W_X} = k$$\n\n$${{{W_Y}} \\over {{W_X}}} = {2 \\over 1}\\,\\,\\,\\,\\, \\Rightarrow \\,\\,\\,\\,{{{T_Y}} \\over {{T_X}}} = {1 \\over 2}\\,\\,\\,\\,\\,\\, \\Rightarrow \\,\\,\\,\\,\\,{\\rm{SUFF}}.$$\n\n$$\\left( 2 \\right)\\,\\,{T_Y} = 3{\\rm{h}}\\,\\,\\,\\left\\{ \\matrix{ \\,{\\rm{Take}}\\,\\,{{\\rm{T}}_{\\rm{X}}} = 3{\\rm{h}}\\,\\,\\,\\, \\Rightarrow \\Delta \\% = 0 \\hfill \\cr \\,{\\rm{Take}}\\,\\,{{\\rm{T}}_{\\rm{X}}} = 4{\\rm{h}}\\,\\,\\,\\, \\Rightarrow \\Delta \\% \\ne 0 \\hfill \\cr} \\right.$$\n\nThis solution follows the notations and rationale taught in the GMATH method.\n\nRegards,\nFabio.\n_________________\nFabio Skilnik :: GMATH method creator (Math for the GMAT)\nOur high-level \"quant\" preparation starts here: https:\/\/gmath.net\nIntern\nJoined: 17 Feb 2019\nPosts: 2\nRe: Machines X and Y can work at their respective constant rates\u00a0 [#permalink]\n\n### Show Tags\n\n26 May 2019, 17:05\nKindly note:-\nWhen both work together means they work at a rate of 1\/x+1\/y = (x+y)\/xy\n\nCan somebody explain why this is?\nIntern\nJoined: 17 Feb 2019\nPosts: 2\nRe: Machines X and Y can work at their respective constant rates\u00a0 [#permalink]\n\n### Show Tags\n\n26 May 2019, 17:06\nnsato wrote:\nKindly note:-\nWhen both work together means they work at a rate of 1\/x+1\/y = (x+y)\/xy\n\nCan somebody explain why this is?\nISB School Moderator\nJoined: 08 Dec 2013\nPosts: 619\nLocation: India\nConcentration: Nonprofit, Sustainability\nSchools: ISB '21\nGMAT 1: 630 Q47 V30\nWE: Operations (Non-Profit and Government)\nMachines X and Y can work at their respective constant rates\u00a0 [#permalink]\n\n### Show Tags\n\n26 May 2019, 17:41\nnsato wrote:\nnsato wrote:\nKindly note:-\nWhen both work together means they work at a rate of 1\/x+1\/y = (x+y)\/xy\n\nCan somebody explain why this is?\n\nlet d1 be time taken by x and y together\nd2 by x alone and\nd3 by y independently.\n\n(x+y)d1 = xd2 = yd3......................(A)\n\nWe have to find d3\/d2 somehow...\n\nStatement 2.\n\ny*6 = 2(x+y)*d1, clearly insufficient.\n\nStatement 1.\n(x+y) (2\/3) *t = y*t, solving this we get x\/y as 1\/2.\n\nPutting x\/y into equation (A)\nwe can deduce the relationship between-\n1. d1 and d2\n2. d1 and d3, so sufficient.\n\nnsato if you understand equation (A) then rest of the sum will be easy for you. Check: https:\/\/gmatclub.com\/forum\/gmat-math-book-87417.html\nManager\nJoined: 04 Jun 2017\nPosts: 110\nLocation: India\nConcentration: Strategy, Operations\nGMAT 1: 500 Q39 V20\nGPA: 3.82\nRe: Machines X and Y can work at their respective constant rates\u00a0 [#permalink]\n\n### Show Tags\n\n27 Jun 2019, 07:52\nCAMANISHPARMAR wrote:\nQuestion Stem:-\nMachines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more\/less than that of machine X?\nRephrase:-\nMachines X and Y can work at their respective constant rates of 1\/x and 1\/y respectively (where x and y indicate time taken to complete one job).\n\n$$\\frac{y}{x}-1$$ = ? i.e can we get the value of $$\\frac{y}{x}$$\n\nKindly note:-\nWhen both work together means they work at a rate of $$\\frac{1}{x}$$+$$\\frac{1}{y}$$ = $$\\frac{x+y}{xy}$$\nTime taken when both machines work together = $$\\frac{xy}{x+y}$$\n\nLets evaluate both the statements:-\nStatement (1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does.\n\nTherefore from (1) $$\\frac{xy}{x+y}$$ = $$\\frac{2y}{3}$$\nwhich implies $$\\frac{x}{x+y}$$ = $$\\frac{2}{3}$$\nor$$\\frac{y}{x} = \\frac{1}{2}$$\nSince we have got the value of $$\\frac{y}{x}$$ Statement 1 is sufficient; Not lets check statement 2 [Cross B,C & E] Evaluate between A & D:-\n\nStatement (2) Machine Y, working alone, fills a production order of twice the size in 6 hrs.\n\nThere is no mention about the rate of machine X hence statement (2) is insufficient. Hence the correct answer is option A.\n\nThanks for the simplified explanation\nVeritas Prep GMAT Instructor\nJoined: 01 May 2019\nPosts: 50\nRe: Machines X and Y can work at their respective constant rates\u00a0 [#permalink]\n\n### Show Tags\n\n27 Jun 2019, 08:02\nnsato wrote:\nnsato wrote:\nKindly note:-\nWhen both work together means they work at a rate of 1\/x+1\/y = (x+y)\/xy\n\nCan somebody explain why this is?\n\nSo the rule here is that Rate of A + Rate of B = the combined Rate of A and B.\n\nHere, if x is the time taken by Machine X to complete a job, its rate is 1\/x. If y is the time taken by Machine Y to complete a job, its rate is 1\/y. So the combined Rate of Machines X and Y is 1\/x + 1\/y.\n\nLet's take this math step by step:\n\n$$\\frac{1}{x}+\\frac{1}{y}$$\n\nGet a common denominator by multiplying first fraction by y\/y and second fraction by x\/x:\n\n$$\\frac{y}{xy}+\\frac{x}{xy}$$\n\n$$\\frac{y+x}{xy}$$\nManager\nJoined: 11 Feb 2013\nPosts: 230\nLocation: United States (TX)\nGMAT 1: 490 Q44 V15\nGMAT 2: 690 Q47 V38\nGPA: 3.05\nWE: Analyst (Commercial Banking)\nRe: Machines X and Y can work at their respective constant rates\u00a0 [#permalink]\n\n### Show Tags\n\n27 Jun 2019, 08:42\nStatement 1:\nLet\u2019s assume:\nTotal work=6 unit\n\nY takes 3 days to complete the work ( ie. 2 units per day)\n\nThus, x&y combined takes 2 days to complete the work (ie 3 units per days)\n\nLet\u2019s calculate UNITS PERDAY\n\nX produces (___ )units per day\nY produces 2 units per day\n========================\n(X+Y) produce 3 units per day\n\nThus, X definitely produces 1 unit per day.\nIn other words, per day production capacity of X (1 unit ) is 50% of production capacity of Y (2 units).\n\nThat means, for any work x needs twice as much time as Y needs.\n\nSo, statement 1 is SUFFICIENT.\n\nPosted from my mobile device\nRe: Machines X and Y can work at their respective constant rates \u00a0 [#permalink] 27 Jun 2019, 08:42\nDisplay posts from previous: Sort by","date":"2019-12-14 00:38:07","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.821066677570343, \"perplexity\": 2848.6111987266004}, \"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-2019-51\/segments\/1575540569332.20\/warc\/CC-MAIN-20191213230200-20191214014200-00221.warc.gz\"}"} | null | null |
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\section{Introduction}
Recently we have found black hole solutions in the Einstein-Yang-Mills (EYM)
theory by extending the Wu-Yang ansatz to higher dimensions \cite{1,2}. Both
the YM charge and the dimensionality of the space time played crucial roles to
determine the features of such black holes. It was found long ago, within the
context of Dirac monopole theory that Wu-Yang ansatz solves the static,
spherically symmetric YM equations for $N=4$ dimensional flat space
time\cite{3}. The $SO\left( 3\right) $ gauge structure was derived from the
abelian electromagnetic (em) potential such that the internal and space time
indices were mixed together in the potential. By a similar analogy we extend
this idea to - nowadays fashionable$-N$ dimensional space times where
$SO\left( N-1\right) $ is obtained through a non-abelian gauge
transformation from the em potential within the static, spherically symmetric
metric ansatz. The YM gauge potential is chosen to depend only on the angular
variables and therefore they become independent of time ($t$) and the radial
coordinate ($r$). Upon this choice the YM potential becomes magnetic type and
by virtue of the metric ansatz the YM equations are easily satisfied. Such a
choice renders the duality principle to be automatically absent in the theory.
We note that by invoking the Birkhoff's theorem of general relativity $t$ and
$r$ can be interchanged appropriately in the metric, while the YM potential
preserves its form. The fact that the solutions obtained by this procedure
pertain to genuine non- abelian character is obvious from comparison with the
other known exact EYM solutions . The EYM\ solutions obtained by other
ansaetze\cite{4,5,6,7,8,9} constructed directly from the non-abelian character
and those obtained by our generalized Wu-Yang ansatz \cite{1,2} are the same.
We admit, however, that although our method yields exact solutions it is
restricted to spherical symmetry alone. Their solutions, on the other hand
\cite{4,5,6,7}, apply to less symmetric cases which at best can be expressed
in infinite series, and in certain limit, such as vanishing of a function,
they coincide with ours. Among other types, particle-like \cite{8} and
magnetic monopole \cite{9} solutions are discussed in even dimensions. To make
a comparison between EM and EYM solutions we refer to the different $r$ powers
in the solutions found so far. Specifically, the logarithmic term in the
metric for $N=5,$ EYM theory, for instance, is not encountered in the $N=5,$
EM theory \cite{1}. For $N=4$ it was verified on physical grounds that
although the metric remained unchanged, the geodesics particles felt the
non-abelian charges \cite{10}. We note that Ref. \cite{10} constitutes the
proper reference to be consulted in obtaining a YM solution from an EM
solution, which is stated as a theorem therein. Our study shows that the
distinction between the abelian and non-abelian contributions becomes more
transparent for $N>4.$ Let us\ note that throughout this paper by the
non-Abelian field we imply YM field whose higher dimensional version is
obtained by the generalized Wu-Yang ansatz.
It is well-known that in general relativity the field equations admit
solutions which, unlike the localized black holes can have different
properties. From this token we cite the cosmological solutions of de-Sitter
($dS$)/ Anti de-Sitter ($AdS$), the conformally flat and Bertoti-Robinson (BR)
type solutions \cite{11,12}, beside others in higher dimensions. In the EM
theory the conformally flat metric in $N=4$ is uniquely the BR\ metric whose
topology is $AdS_{2}\times S^{2}.$This extends to higher dimensions as
$AdS_{2}\times S^{N-2}$ which is no more conformally flat. The $N=4,$ BR
solution can be obtained from the extremal Reissner-Nordstrom (RN) black hole
solution through a limiting process. The latter represents a supersymmetric
soliton solution to connect different vacua of supergravity. For this reason
the BR geometry can be interpreted as a "throat" region between two
asymptotically flat space times. Also, since the source is pure homogenous
electromagnetic (em) field it is called an "em universe", which is free of
singularities. Its high degree of symmetry and singularity free properties
make BR space time attractive from both the string and supergravity theory
points of view . We recall that even for a satisfactory shell model
interpretation of an elementary particle, BR space time is proposed as a core
candidate \cite{13}. All these aspects ( and more), we believe, justifies to
make further studies on the BR\ space times, in particular for $N>4$, which
incorporates YM fields instead of the em fields.
In this paper we obtain new non-asymptotically flat dilatonic black hole
solutions and study their stability against linear perturbations\cite{14}.
Remarkably, they turn out to be stable against such perturbations. To obtain
such metrics we start with a general ansatz metric in the
Einstein-Yang-Mills-Dilaton (EYMD) theory. Our ansatz is of BR type instead of
the RN type so that in the limit of zero dilaton instead of \cite{1,2}, we
obtain BR type metrics. This leads us to a particular class of dilatonic
solutions coupled with the YM field. As expected, dilaton brings severe
restrictions on the space time which possesses singularities in general. In
the limit of zero dilaton we obtain a two parametric (i.e. Q and C) solution
which contains the BR solution as a subclass. The second parameter, which is
labeled as $C$, in a particular limit can be shown to correspond to the
quasilocal mass. Thus, keeping both $Q\neq0\neq C$ and a non-zero dilaton
gives us an asymptotically non-flat black hole model. The case $C=0$ (without
dilaton), yields a metric which is analogous to the BR metric\cite{15}.
Next, we extend our action to include the non-Abelian Born-Infeld (BI)
interaction which we phrase as Einstein-Yang-Mills-Born-Infeld-Dilaton
(EYMBID) theory. As it is well-known string / supergravity motivated
non-linear electrodynamics due to Born and Infeld \cite{16} received much
attention in recent years. Originally it was devised to eliminate divergences
due to point charges, which recovers the linear Maxwell's electrodynamics in a
particular limit (i.e. $\beta\rightarrow\infty$). Now it is believed that BI
action will provide significant contributions for the deep rooted problems of
quantum gravity. The BI action contains invariants in special combinations
under a square root term in analogy with the string theory Lagrangian. Since
our aim in this paper is to use non-Abelian fields instead of the em field we
shall employ the YM field which by our choice will be magnetic type. Some of
the solutions that we find for the EYMBID theory represent non-asymptotically
flat black holes. Unfortunately for an arbitrary dilatonic parameter the
solutions become untractable. One particular class of solutions on which we
shall elaborate will be again the BR type solutions for a vanishing dilaton.
We explore the possibility of finding conformally flat space time by choosing
particular BI parameter $\beta.$
After studying black holes in the dilatonic theory we proceed to establish
connection with the Brans-Dicke (BD) scalar field through a conformal
transformation and explore black holes in the latter as well. Coupling of BD
scalar field with YM field follows under the similar line of consideration.
The organization of the paper is as follows. In Sec. $II$ we introduce the
EYMD gravity, its field equations, their solutions and investigate their
stability. The Born-Infeld (BI) extension follows in Sec. $III$. Sec. $IV$
confines black holes in the Brans-Dicke-YM theory. The paper is completed with
conclusion in Sec. $V$.
\section{Field Equations and the metric ansatz for EYMD gravity}
The $N\left( =n+1\right) -$dimensional action in the EYMD theory is given by
$(G=1)$%
\begin{gather}
I=-\frac{1}{16\pi}\int\nolimits_{\mathcal{M}}d^{n+1}x\sqrt{-g}\left(
R-\frac{4}{n-1}\left( \mathbf{\nabla}\Phi\right) ^{2}+\mathcal{L}\left(
\Phi\right) \right) -\frac{1}{8\pi}\int\nolimits_{\partial\mathcal{M}}%
d^{n}x\sqrt{-h}K,\\
\mathcal{L}\left( \Phi\right) =-e^{-4\alpha\Phi/\left( n-1\right)
}\mathbf{Tr}(F_{\lambda\sigma}^{\left( a\right) }F^{\left( a\right)
\lambda\sigma}),\nonumber
\end{gather}
where%
\begin{equation}
\mathbf{Tr}(.)=\overset{\left( n\right) (n-1)/2}{\underset{a=1}{%
{\textstyle\sum}
}\left( .\right) ,}%
\end{equation}
$\Phi$ refers to the dilaton scalar potential (we should comment that in this
work we are interested in a spherical symmetric dilatonic potential, i.e.
$\Phi=\Phi\left( r\right) $) and $\alpha$ denotes the dilaton parameter
while the second term is the surface integral with its induced metric $h_{ij}$
and trace $K$ of its extrinsic curvature. Herein $R$ is the usual Ricci scalar
and $\mathbf{F}^{\left( a\right) }=F_{\mu\nu}^{\left( a\right) }dx^{\mu
}\wedge dx^{\nu}$ are the YM field $2-$forms (with $\wedge$ indicating the
wedge product) which are given by \cite{1,2}%
\begin{equation}
\mathbf{F}^{\left( a\right) }=\mathbf{dA}^{\left( a\right) }+\frac
{1}{2\sigma}C_{\left( b\right) \left( c\right) }^{\left( a\right)
}\mathbf{A}^{\left( b\right) }\wedge\mathbf{A}^{\left( c\right) }%
\end{equation}
with structure constants $C_{\left( b\right) \left( c\right) }^{\left(
a\right) }$ (see Appendix A) while $\sigma$ is a coupling constant and
$\mathbf{A}^{\left( a\right) }=A_{\mu}^{\left( a\right) }dx^{\mu}$ are the
potential $1-$forms. Our choice of YM potential $\mathbf{A}^{\left( a\right)
}$ follows from the higher dimensional Wu-Yang ansatz \cite{1,2} where
$\sigma$ is expressed in terms of the YM charge. Variations of the action with
respect to the gravitational field $g_{\mu\nu}$ and the scalar field $\Phi$
lead, respectively to the EYMD field equations
\begin{gather}
R_{\mu\nu}=\frac{4}{n-1}\mathbf{\partial}_{\mu}\Phi\partial_{\nu}%
\Phi+2e^{-4\alpha\Phi/\left( n-1\right) }\left[ \mathbf{Tr}\left(
F_{\mu\lambda}^{\left( a\right) }F_{\nu}^{\left( a\right) \ \lambda
}\right) -\frac{1}{2\left( n-1\right) }\mathbf{Tr}\left( F_{\lambda\sigma
}^{\left( a\right) }F^{\left( a\right) \lambda\sigma}\right) g_{\mu\nu
}\right] ,\\
\nabla^{2}\Phi=-\frac{1}{2}\alpha e^{-4\alpha\Phi/\left( n-1\right)
}\mathbf{Tr}(F_{\lambda\sigma}^{\left( a\right) }F^{\left( a\right)
\lambda\sigma}),
\end{gather}
where $R_{\mu\nu}$ is the Ricci tensor. Variation with respect to the gauge
potentials $\mathbf{A}^{\left( a\right) }$ yields the YM equations%
\begin{equation}
\mathbf{d}\left( e^{-4\alpha\Phi/\left( n-1\right) \star}\mathbf{F}%
^{\left( a\right) }\right) +\frac{1}{\sigma}C_{\left( b\right) \left(
c\right) }^{\left( a\right) }e^{-4\alpha\Phi/\left( n-1\right)
}\mathbf{A}^{\left( b\right) }\wedge^{\star}\mathbf{F}^{\left( c\right)
}=0
\end{equation}
in which the hodge star $^{\star}$ means duality. In the next section we shall
present solutions to the foregoing equations in N-dimension. Wherever it is
necessary we shall supplement our discussion by resorting to the particular
case $N=5$. Let us remark that for $N=4$ case since the YM field becomes gauge
equivalent to the em field the metrics are still of RN/BR, therefore we shall
ignore the case $N=4$.
\subsection{N-dimensional solution}
In $N\left( =n+1\right) -$dimensions, we choose a spherically symmetric
metric ansatz
\begin{equation}
ds^{2}=-f\left( r\right) dt^{2}+\frac{dr^{2}}{f\left( r\right) }+h\left(
r\right) ^{2}d\Omega_{n-1}^{2},
\end{equation}
where%
\begin{equation}
d\Omega_{n-1}^{2}=d\theta_{1}^{2}+\underset{i=2}{\overset{n-2}{%
{\textstyle\sum}
}}\underset{j=1}{\overset{i-1}{%
{\textstyle\prod}
}}\sin^{2}\theta_{j}\;d\theta_{i}^{2},\text{ \ \ }0\leq\theta_{n-1}\leq
2\pi,\text{ }0\leq\theta_{k\neq n-1}\leq\pi.
\end{equation}
while $f\left( r\right) $ and $h\left( r\right) $ are two functions to be
determined. Our gauge potential ansatz is \cite{1,2}%
\begin{align}
\mathbf{A}^{(a)} & =\frac{Q}{r^{2}}C_{\left( i\right) \left( j\right)
}^{\left( a\right) }\ x^{i}dx^{j},\text{ \ \ }Q=\text{YM magnetic charge,
\ }r^{2}=\overset{n}{\underset{i=1}{\sum}}x_{i}^{2},\\
2 & \leq j+1\leq i\leq n,\text{ \ and \ }1\leq a\leq n(n-1)/2,\nonumber\\
x_{1} & =r\cos\theta_{n-1}\sin\theta_{n-2}...\sin\theta_{1},\text{ }%
x_{2}=r\sin\theta_{n-1}\sin\theta_{n-2}...\sin\theta_{1},\nonumber\\
\text{ }x_{3} & =r\cos\theta_{n-2}\sin\theta_{n-3}...\sin\theta_{1},\text{
}x_{4}=r\sin\theta_{n-2}\sin\theta_{n-3}...\sin\theta_{1},\nonumber\\
& ...\nonumber\\
x_{n} & =r\cos\theta_{1}.\nonumber
\end{align}
We note that the structure constant $C_{ij}^{a}$ are found similar to the case
$N=5$ as described in Appendix A. The YM equations (6) are satisfied and the
field equations become%
\begin{align}
\nabla^{2}\Phi & =-\frac{1}{2}\alpha e^{-4\alpha\Phi/\left( n-1\right)
}\mathbf{Tr}(F_{\lambda\sigma}^{\left( a\right) }F^{\left( a\right)
\lambda\sigma})\\
R_{tt} & =\frac{e^{-4\alpha\Phi/\left( n-1\right) }f}{\left( n-1\right)
}\mathbf{Tr}(F_{\lambda\sigma}^{\left( a\right) }F^{\left( a\right)
\lambda\sigma})\\
R_{rr} & =\frac{4\left( \Phi^{\prime}\right) ^{2}}{\left( n-1\right)
}-\frac{e^{-4\alpha\Phi/\left( n-1\right) }}{\left( n-1\right)
f}\mathbf{Tr}(F_{\lambda\sigma}^{\left( a\right) }F^{\left( a\right)
\lambda\sigma})\\
R_{\theta_{i}\theta_{i}} & =\frac{2\left( n-2\right) Q^{2}e^{-4\alpha
\Phi/\left( n-1\right) }}{h^{2}}-\frac{h^{2}e^{-4\alpha\Phi/\left(
n-1\right) }}{\left( n-1\right) }\mathbf{Tr}(F_{\lambda\sigma}^{\left(
a\right) }F^{\left( a\right) \lambda\sigma}),
\end{align}
in which we note that the remaining angular Ricci parts add no new conditions.
A proper ansatz for $h\left( r\right) $ now is%
\begin{align}
h\left( r\right) & =Ae^{-2\alpha\Phi/\left( n-1\right) }\\
\text{(}A & =\text{constant)}\nonumber
\end{align}
which, after knowing
\begin{equation}
\mathbf{Tr}(F_{\lambda\sigma}^{\left( a\right) }F^{\left( a\right)
\lambda\sigma})=\frac{\left( n-1\right) \left( n-2\right) Q^{2}}{h^{4}}%
\end{equation}
and eliminating $f\left( r\right) $ from Eq.s (11) and (12) one gets
\begin{equation}
\Phi=-\frac{\left( n-1\right) }{2}\frac{\alpha\ln r}{\alpha^{2}+1}.
\end{equation}
Upon substitution of $\Phi$ and $h\left( r\right) $ into the Eq.s (10)-(13)
we get three new equations
\begin{gather}
\left( n-1\right) \left[ r\left( \alpha^{2}+1\right) f^{\prime}+\left(
\left( n-2\right) \alpha^{2}-1\right) f\right] -\left( \frac{\left(
n-1\right) \left( n-2\right) Q^{2}}{A^{4}}\right) \left( \alpha
^{2}+1\right) ^{2}r^{\left( \frac{2}{\alpha^{2}+1}\right) }=0\\
\left( n-1\right) \left[ r\left( \alpha^{2}+1\right) f^{\prime\prime
}+\left( n-1\right) \alpha^{2}f^{\prime}\right] -2\left( \frac{\left(
n-1\right) \left( n-2\right) Q^{2}}{A^{4}}\right) \left( \alpha
^{2}+1\right) r^{\left( -\frac{\alpha^{2}-1}{\alpha^{2}+1}\right) }=0\\
\left( \alpha^{2}+1\right) ^{2}\left( n-2\right) \left( Q^{2}%
-A^{2}\right) r^{2}+\nonumber\\
A^{4}\alpha^{2}\left( \alpha^{2}+1\right) f^{\prime}r^{\left( \frac
{3\alpha^{2}+1}{\alpha^{2}+1}\right) }+\alpha^{2}\left( \left( n-2\right)
\alpha^{2}-1\right) A^{4}fr^{\left( \frac{2\alpha^{2}}{\alpha^{2}+1}\right)
}=0.
\end{gather}
Eq. (17) yields the integral for $f\left( r\right) $%
\begin{align}
f\left( r\right) & =\Xi\left( 1-\left( \frac{r_{+}}{r}\right)
^{\frac{\left( n-2\right) \alpha^{2}+1}{\alpha^{2}+1}}\right) r^{\frac
{2}{\alpha^{2}+1}},\\
\Xi & =\frac{\left( n-2\right) }{\left( \left( n-2\right) \alpha
^{2}+1\right) Q^{2}}%
\end{align}
and the equations (18) and (19) imply that $A$ must satisfy the following
constraint%
\begin{equation}
A^{2}=Q^{2}\left( \alpha^{2}+1\right) .
\end{equation}
\ One may notice that, with the solution (20), (7) becomes a
non-asymptotically flat metric and therefore the ADM mass can not be defined.
Following the quasilocal mass formalism introduced by Brown and York \cite{17}
it is known that, a spherically symmetric N-dimensional metric solution as
\begin{equation}
ds^{2}=-F\left( R\right) ^{2}dt^{2}+\frac{dR^{2}}{G\left( R\right) ^{2}%
}+R^{2}d\Omega_{N-2}^{2},
\end{equation}
admits a quasilocal mass $M_{QL}$ defined by \cite{18,19}%
\begin{equation}
M_{QL}=\frac{N-2}{2}R_{B}^{N-3}F\left( R_{B}\right) \left( G_{ref}\left(
R_{B}\right) -G\left( R_{B}\right) \right) .
\end{equation}
Here $G_{ref}\left( R\right) $ is an arbitrary reference function, which
guarantees having zero quasilocal mass once the matter source is turned off
and $R_{B}$ is the radius of the spacelike hypersurface boundary. Applying
this formalism to the solution (20), one obtains the horizon $r_{+}$ in terms
of $M_{QL}$ as
\begin{equation}
r_{+}=\left( \frac{4\left( \alpha^{2}+1\right) M_{QL}}{\left( n-1\right)
\Xi\alpha^{2}A^{n-1}}\right) .
\end{equation}
Having the radius of horizon, one may use the usual definition of the Hawking
temperature to calculate
\begin{equation}
T_{H}=\frac{1}{4\pi}\left\vert f^{\prime}\left( r_{+}\right) \right\vert
=\frac{\Xi}{4\pi}\frac{\left[ \left( n-2\right) \alpha^{2}+1\right]
}{\left( \alpha^{2}+1\right) }\left( r_{+}\right) ^{\gamma}%
\end{equation}
where $\Xi$ and $r_{+}$ are given above and $\gamma=\frac{1-\alpha^{2}%
}{1+\alpha^{2}}$.
In order to see the singularity of the spacetime we calculate the scalar
invariants, which are tedious for general N, for this reason we restrict
ourselves to the case $N=5$ alone. The scalar invariants for $N=5$ are as
follows
\begin{align}
R & =\frac{\omega_{1}}{r^{\frac{4\alpha^{2}+1}{\alpha^{2}+1}}}+\frac
{\sigma_{1}}{r^{\frac{2\alpha^{2}}{\alpha^{2}+1}}},\\
R_{\mu\nu}R^{\mu\nu} & =\frac{\omega_{2}}{r^{\frac{6\alpha^{2}+1}{\alpha
^{2}+1}}}+\frac{\omega_{3}}{r^{2\frac{4\alpha^{2}+1}{\alpha^{2}+1}}}%
+\frac{\sigma_{2}}{r^{\frac{4\alpha^{2}}{\alpha^{2}+1}}},\\
R_{\mu\nu\alpha\beta}R^{\mu\nu\alpha\beta} & =\frac{\omega_{4}}%
{r^{\frac{6\alpha^{2}+1}{\alpha^{2}+1}}}+\frac{\omega_{5}}{r^{2\frac
{4\alpha^{2}+1}{\alpha^{2}+1}}}+\frac{\sigma_{3}}{r^{\frac{4\alpha^{2}}%
{\alpha^{2}+1}}}%
\end{align}
where $\omega_{i}$ and $\sigma_{i}$ are some constants and
\begin{align}
\underset{\alpha\rightarrow0}{\lim}\omega_{i} & =0,\text{ \ \ }%
\underset{\alpha\rightarrow0}{\lim}\sigma_{1}=\frac{2}{Q^{2}},\\
\text{\ \ }\underset{\alpha\rightarrow0}{\lim}\sigma_{2} & =\frac{20}{Q^{4}%
},\text{ \ \ }\underset{\alpha\rightarrow0}{\lim}\sigma_{3}=\frac{33}{Q^{4}%
}.\text{ }\nonumber
\end{align}
These results show that, for non-zero dilaton field (i.e. $\alpha\neq0$), the
origin is singular whereas for $\alpha=0$ (as a limit), we have a regular
spacetime. Although these results have been found for $N=5$, it is our belief
that for a general $N>5$ these behaviors do not show much difference.
\subsubsection{Linear dilaton}
Setting $\alpha=1,$ gives the linear dilaton solution (20) as%
\begin{align}
f\left( r\right) & =\frac{\left( n-2\right) }{\left( n-1\right) Q^{2}%
}\left( 1-\left( \frac{r_{+}}{r}\right) ^{\frac{n-1}{2}}\right) r,\text{
\ \ }h\left( r\right) ^{2}=2Q^{2}r\\
\text{\ \ }r_{+} & =\left( \frac{2^{\frac{7-n}{2}}M_{QL}}{\left(
n-2\right) \left( \left\vert Q\right\vert \right) ^{n-3}}\right) .
\end{align}
One can use the standard\ way to find the high frequency limit of Hawking
temperature at the horizon, which means that%
\begin{equation}
T_{H}=\frac{1}{4\pi}\left\vert f^{\prime}\left( r_{+}\right) \right\vert
=\frac{\left( n-2\right) }{8\pi Q^{2}}.
\end{equation}
Furthermore, $M_{QL}$ is an integration constant which is identified as
quasilocal mass, so one may set this constant to be zero to get the line
element
\begin{align}
ds^{2} & =-\Xi rdt^{2}+\frac{dr^{2}}{\Xi r}+2Q^{2}rd\Omega_{n-1}^{2},\\
\Xi & =\frac{\left( n-2\right) }{\left( n-1\right) Q^{2}}.
\end{align}
By a simple transformation $r=e^{\Xi\rho}$ this line element transforms into%
\begin{equation}
ds^{2}=\Xi e^{\Xi\rho}\left( -dt^{2}+d\rho^{2}+\frac{2\left( n-1\right)
Q^{4}}{\left( n-2\right) }d\Omega_{n-1}^{2}\right)
\end{equation}
which represents a conformal $M_{2}\times S_{n-1}$ space time with the radius
of $S_{n-1}$ equal to $\sqrt{\frac{2\left( n-1\right) }{\left( n-2\right)
}}Q^{2}.$
\subsubsection{BR limit of the solution}
In the zero dilaton limit $\alpha=0,$ we express our metric function in the
form of%
\begin{align}
f\left( r\right) & =\Xi_{\circ}\left( r-r_{+}\right) r,\text{ \ }%
\Xi_{\circ}=\frac{\left( n-2\right) }{Q^{2}},\\
h^{2} & =A_{\circ}^{2}=Q^{2}.
\end{align}
In $N(=n+1)-$dimensions we also set $r_{+}=0,$ $r=\frac{1}{\rho}$ and
$\tau=\Xi_{\circ}t,$ to transform the metric (7) into%
\begin{equation}
ds^{2}=\frac{Q^{2}}{\left( n-2\right) }\left( \frac{-d\tau^{2}+d\rho^{2}%
}{\rho^{2}}+\left( n-2\right) d\Omega_{n-1}^{2}\right) .
\end{equation}
This is in the BR form with the topological structure $AdS_{2}\times S^{n-1},$
where the radius of the $S^{n-1}$ sphere is $\sqrt{n-2}.$
\subsubsection{$AdS_{2}\times S^{N-2}$ topology for $0<\alpha<1$}
In this section we shall show that, the general solution given in Eq. (20),
for some specific values for $0<\alpha<1,$ may also represent a conformally
flat space time. To this end, we set $r_{+}=0,$ and apply the following
transformation
\begin{align}
r & =\left( \Xi\frac{1-\alpha^{2}}{1+\alpha^{2}}\rho\right) ^{-\frac
{1+\alpha^{2}}{1-\alpha^{2}}},\\
\Xi & =\frac{\left( n-2\right) }{\left( \left( n-2\right) \alpha
^{2}+1\right) Q^{2}},
\end{align}
to get%
\begin{equation}
ds^{2}=\left( \Xi\right) ^{-\frac{1+\alpha^{2}}{1-\alpha^{2}}}\left(
\frac{1-\alpha^{2}}{1+\alpha^{2}}\right) ^{-\frac{2}{1-\alpha^{2}}}%
\rho^{-\frac{2\alpha^{2}}{1-\alpha^{2}}}\left( \frac{-d\tau^{2}+d\rho^{2}%
}{\rho^{2}}+\Xi A^{2}\left( \frac{1-\alpha^{2}}{1+\alpha^{2}}\right)
^{2}d\Omega_{n-1}^{2}\right) .
\end{equation}
To have a conformally flat space time, we impose $\Xi A^{2}\left(
\frac{1-\alpha^{2}}{1+\alpha^{2}}\right) ^{2}$ to be one, i.e.%
\begin{equation}
\frac{\left( n-2\right) \left( 1-\alpha^{2}\right) ^{2}}{\left( \left(
n-2\right) \alpha^{2}+1\right) \left( \alpha^{2}+1\right) }=1
\end{equation}
and therefore yields, $\alpha^{2}=\frac{n-3}{3n-5}.$ The line element (42)
takes the form of a conformally flat space time, namely%
\begin{align}
ds^{2} & =a\left( \rho\right) \left( \frac{-d\tau^{2}+d\rho^{2}}{\rho
^{2}}+d\Omega_{n-1}^{2}\right) ,\\
a\left( \rho\right) & =2^{\frac{3n-5}{n-1}}\left( n-2\right) \left(
\frac{Q^{2}}{3n-5}\right) ^{2\frac{n-2}{n-1}}\left( n-1\right) ^{\frac
{n-3}{n-1}}\rho^{-\frac{2\alpha^{2}}{1-\alpha^{2}}}.
\end{align}
\subsection{Linear Stability of the EYMD black holes}
In this chapter we follow a similar method used by Yazadjiev \cite{14} to
investigate the stability of the possible EYMD black hole solutions,
introduced previously, in terms of a linear radial perturbation. Although this
method is applicable to any dimensions we confine ourselves to the
five-dimensional black hole case given by Eq. (7). To do so we assume that our
dilatonic scalar field $\Phi\left( r\right) $ changes into $\Phi\left(
r\right) +\psi\left( t,r\right) ,$ in which $\psi\left( t,r\right) $ is
very weak compared to the original dilaton field and we call it the perturbed
term. As a result we choose our perturbed metric as
\begin{equation}
ds^{2}=-f\left( r\right) e^{\Gamma\left( t,r\right) }dt^{2}+e^{\chi\left(
t,r\right) }\frac{dr^{2}}{f\left( r\right) }+h\left( r\right) ^{2}%
d\Omega_{3}^{2}.
\end{equation}
One should notice that, since our gauge potentials are magnetic, the YM
equations (6) are satisfied. The linearized version of the field equations
(10-13) plus one extra term of $R_{tr}$ are given by%
\begin{gather}
R_{tr}:\frac{3}{2}\frac{\chi_{t}\left( t,r\right) h^{\prime}\left(
r\right) }{h\left( r\right) }=\frac{4}{3}\partial_{r}\Phi\left( r\right)
\partial_{t}\psi\left( t,r\right) \\
\nabla_{\circ}^{2}\psi-\chi\nabla_{\circ}^{2}\Phi+\frac{1}{2}\left(
\Gamma-\chi\right) _{r}\Phi^{\prime}f=\frac{4\alpha^{2}e^{\frac{4}{3}%
\alpha\Phi}}{Q^{2}\left( \alpha^{2}+1\right) ^{2}}\psi\\
R_{\theta\theta}:\left( 2-R_{\circ\theta\theta}\right) \chi-\frac{1}%
{2}hh^{\prime}f\left( \Gamma-\chi\right) _{r}=\frac{8\alpha}{3\left(
\alpha^{2}+1\right) }\psi
\end{gather}
in which a lower index $_{\circ}$ represents the quantity in the unperturbed
metric. First equation in this set implies%
\begin{equation}
\chi\left( t,r\right) =-\frac{4}{3\alpha}\psi\left( t,r\right)
\end{equation}
which after making substitutions in the two latter equations and eliminating
the $\left( \Gamma-\chi\right) _{r}$ one finds%
\begin{equation}
\nabla_{\circ}^{2}\psi\left( t,r\right) -U\left( r\right) \psi\left(
t,r\right) =0
\end{equation}
where%
\begin{equation}
U\left( r\right) =\frac{4e^{\frac{4}{3}\alpha\Phi}}{Q^{2}\left(
1+\alpha^{2}\right) }=\frac{4}{Q^{2}\left( 1+\alpha^{2}\right)
r^{\frac{2\alpha^{2}}{1+\alpha^{2}}}}.
\end{equation}
To get these results we have implicitly used the constraint (22) on A. Again
by imposing the same constraint , one can show that $U\left( r\right) $ is
positive. It is not difficult to apply the separation method on (51) to get
\begin{equation}
\psi\left( t,r\right) =e^{\pm\epsilon t}\zeta\left( r\right) ,\text{
\ \ }\nabla_{\circ}^{2}\zeta\left( r\right) -U_{eff}\left( r\right)
\zeta\left( r\right) =0,\text{ \ \ }U_{eff}\left( r\right) =\left(
\frac{\epsilon^{2}}{f}+U\left( r\right) \right) ,
\end{equation}
where $\epsilon$ is a constant. Since $U_{eff}\left( r\right) $ is positive
one can easily show that, for any real value for $\epsilon$ there exists a
solution for $\zeta\left( r\right) $ which is not bounded. In other words by
the linear perturbation our black hole solution is stable for any value of
$\epsilon.$ As a limit of this proof, one may set $\alpha=0,$ which recovers
the BR case.
We remark that with little addition this method can be easily extended to any
higher dimensions. This implies that the N-dimensional EYMD black holes are
stable under the linear perturbation.
\section{Field equations and the metric ansatz for EYMBID gravity}
The $N\left( =n+1\right) -$dimensional action in the EYMBI-D theory is given
by $(G=1)$%
\begin{gather}
I=-\frac{1}{16\pi}\int\nolimits_{\mathcal{M}}d^{n+1}x\sqrt{-g}\left(
R-\frac{4}{n-1}\left( \mathbf{\nabla}\Phi\right) ^{2}+L\left(
\mathbf{F},\Phi\right) \right) -\frac{1}{8\pi}\int\nolimits_{\partial
\mathcal{M}}d^{n}x\sqrt{-h}K,\\
L\left( \mathbf{F},\Phi\right) =4\beta^{2}e^{4\alpha\Phi/\left( n-1\right)
}\left( 1-\sqrt{1+\frac{\mathbf{Tr}(F_{\lambda\sigma}^{\left( a\right)
}F^{\left( a\right) \lambda\sigma})e^{-8\alpha\Phi/\left( n-1\right) }%
}{2\beta^{2}}}\right) =\\
4\beta^{2}e^{4\alpha\Phi/\left( n-1\right) }\mathcal{L}\left( X\right)
,\nonumber
\end{gather}
where%
\begin{equation}
\mathcal{L}\left( X\right) =1-\sqrt{1+X},\text{ \ \ }X=\frac{\mathbf{Tr}%
(F_{\lambda\sigma}^{\left( a\right) }F^{\left( a\right) \lambda\sigma
})e^{-8\alpha\Phi/\left( n-1\right) }}{2\beta^{2}},\text{ \ \ }%
\mathbf{Tr}(.)=\overset{n(n-1)/2}{\underset{a=1}{%
{\textstyle\sum}
}\left( .\right) ,}%
\end{equation}
while the rest of the parameters are defined as before. Variations of the
EYMBID action with respect to the gravitational field $g_{\mu\nu}$ and the
scalar field $\Phi$ lead respectively to the correspondence EYMBID field
equations
\begin{align}
R_{\mu\nu} & =\frac{4}{n-1}\mathbf{\partial}_{\mu}\Phi\partial_{\nu}%
\Phi-4e^{-4\alpha\Phi/\left( n-1\right) }\left( \mathbf{Tr}\left(
F_{\mu\lambda}^{\left( a\right) }F_{\nu}^{\left( a\right) \ \lambda
}\right) \partial_{X}\mathcal{L}\left( X\right) \right) +\\
& \frac{4\beta^{2}}{n-1}e^{4\alpha\Phi/\left( n-1\right) }\mathcal{K}%
\left( X\right) g_{\mu\nu},\nonumber\\
\nabla^{2}\Phi & =2\alpha\beta^{2}e^{4\alpha\Phi/\left( n-1\right)
}\mathcal{K}\left( X\right) ,\text{\ \ \ \ \ }%
\end{align}
where we have abbreviated%
\begin{align}
\mathcal{K}\left( X\right) & =2X\partial_{X}\mathcal{L}\left( X\right)
-\mathcal{L}\left( X\right) \\
(\partial_{X}\mathcal{L}\left( X\right) & =-\frac{1}{\sqrt{1+X}%
})\text{.\ }\nonumber
\end{align}
Variation with respect to the gauge potentials $\mathbf{A}^{\left( a\right)
}$ yields the new relevant YM equations%
\begin{equation}
\mathbf{d}\left( e^{-4\alpha\Phi/\left( n-1\right) \star}\mathbf{F}%
^{\left( a\right) }\partial_{X}\mathcal{L}\left( X\right) \right)
+\frac{1}{\sigma}C_{\left( b\right) \left( c\right) }^{\left( a\right)
}e^{-4\alpha\Phi/\left( n-1\right) }\partial_{X}\mathcal{L}\left( X\right)
\mathbf{A}^{\left( b\right) }\wedge^{\star}\mathbf{F}^{\left( c\right)
}=0.
\end{equation}
It is remarkable to observe that the field equations (57-59) in the limit of
$\beta\rightarrow\infty,$ reduce to the Eq.s (4-6), which are the field
equations for the EYMD theory. Also in the limit of $\beta\rightarrow0$, Eq.s
(57-59) give%
\begin{align}
R_{\mu\nu} & =\frac{4}{n-1}\mathbf{\partial}_{\mu}\Phi\partial_{\nu}\Phi,\\
\nabla^{2}\Phi & =0\text{\ }%
\end{align}
which refer to the gravity coupled with a massless scalar field.
\subsection{N-dimensional solution}
In $N\left( =n+1\right) -$dimensions, we again, adopt the metric ansatz (7)
and our YM potentials are given by Eq. (9). N-dimensional YM equations (60)
are satisfied while the field equations imply the following set of four
equations%
\begin{align}
\nabla^{2}\Phi & =2\alpha\beta^{2}e^{4\alpha\Phi/\left( n-1\right)
}\mathcal{K}\left( X\right) \\
R_{tt} & =-\frac{4\beta^{2}e^{4\alpha\Phi/\left( n-1\right) }f}{\left(
n-1\right) }\mathcal{K}\left( X\right) \\
R_{rr} & =\frac{4\left( \Phi^{\prime}\right) ^{2}}{\left( n-1\right)
}+\frac{4\beta^{2}e^{4\alpha\Phi/\left( n-1\right) }}{\left( n-1\right)
f}\mathcal{K}\left( X\right) \\
R_{\theta_{i}\theta_{i}} & =\frac{-4\left( n-2\right) Q^{2}e^{-4\alpha
\Phi/\left( n-1\right) }}{h^{2}}\partial_{X}\mathcal{L}+\frac{4h^{2}%
\beta^{2}e^{4\alpha\Phi/\left( n-1\right) }}{\left( n-1\right)
}\mathcal{K}\left( X\right) .
\end{align}
in which $X$ is defined by (56). We use the same ansatz for $h\left(
r\right) $ as Eq. (14)which gives%
\begin{equation}
X=\frac{\left( n-1\right) \left( n-2\right) Q^{2}}{2\beta^{2}A^{4}}%
\end{equation}
and therefore, after eliminating $f\left( r\right) $ from Eq.s (64) and
(65), leads to (16). Upon substitution of $\Phi$ and $h\left( r\right) $
into the Eq.s (63)-(66) we find the following equations
\begin{gather}
\left( n-1\right) \left[ r\left( \alpha^{2}+1\right) f^{\prime}+\left(
\left( n-2\right) \alpha^{2}-1\right) f\right] +4\beta^{2}\mathcal{K}%
\left( X\right) \left( \alpha^{2}+1\right) ^{2}r^{\left( \frac{2}%
{\alpha^{2}+1}\right) }=0\\
\left( n-1\right) \left[ r\left( \alpha^{2}+1\right) f^{\prime\prime
}+\left( n-1\right) \alpha^{2}f^{\prime}\right] +8\beta^{2}\mathcal{K}%
\left( X\right) \left( \alpha^{2}+1\right) r^{\left( -\frac{\alpha^{2}%
-1}{\alpha^{2}+1}\right) }=0\\
\left( \alpha^{2}+1\right) ^{2}\left( 4\beta^{2}A^{4}\mathcal{K}\left(
X\right) -(4Q^{2}\partial_{X}\mathcal{L}+A^{2})\left( n-1\right) \left(
n-2\right) \right) r^{2}+\\
\left( n-1\right) A^{4}\alpha^{2}\left( \alpha^{2}+1\right) f^{\prime
}r^{\left( \frac{3\alpha^{2}+1}{\alpha^{2}+1}\right) }+\left( n-1\right)
\alpha^{2}\left( \left( n-2\right) \alpha^{2}-1\right) A^{4}fr^{\left(
\frac{2\alpha^{2}}{\alpha^{2}+1}\right) }=0.\nonumber
\end{gather}
Eq. (68) yields the integral for $f\left( r\right) $%
\begin{align}
f\left( r\right) & =\Xi\left( 1-\left( \frac{r_{+}}{r}\right)
^{\frac{\left( n-2\right) \alpha^{2}+1}{\alpha^{2}+1}}\right) r^{\frac
{2}{\alpha^{2}+1}},\\
\Xi & =-\frac{4\beta^{2}\left( \alpha^{2}+1\right) ^{2}\mathcal{K}\left(
X\right) }{\left( n-1\right) \left( \left( n-2\right) \alpha
^{2}+1\right) }%
\end{align}
in which $r_{+}$ is an integration constant connected to the quasi local mass
i.e.,%
\begin{equation}
r_{+}=\left( \frac{4\left( \alpha^{2}+1\right) M_{QL}}{\left( n-1\right)
\Xi\alpha^{2}A^{n-1}}\right)
\end{equation}
and $\mathcal{K}\left( X\right) $ is abbreviated as in (59). This solution
satisfies Eq. (69), but from Eq. (70) $A$ must satisfy the constraint%
\begin{equation}
4\mathcal{K}\left( X\right) \beta^{2}A^{4}\left( \alpha^{2}-1\right)
+\left( n-1\right) \left( n-2\right) \left( 4Q^{2}\partial_{X}%
\mathcal{L}+A^{2}\right) =0.
\end{equation}
\subsubsection{Linear dilaton}
In the linear dilaton case i.e., $\alpha=1,$ Eq. (71) yields%
\begin{equation}
f\left( r\right) =\Xi\left( 1-\left( \frac{r_{+}}{r}\right)
^{\frac{\left( n-2\right) +1}{2}}\right) r,\text{ \ \ }h\left( r\right)
=A\sqrt{r}\text{, \ \ }r_{+}=\left( \frac{8M_{QL}}{\left( n-1\right) \Xi
A^{n-1}}\right)
\end{equation}
in which
\begin{equation}
A^{2}=2Q^{2}\sqrt{1-\frac{Q_{cri}^{2}}{Q^{2}}},\text{ \ \ }\Xi=\frac{2\left(
n-2\right) }{\left( n-1\right) Q_{cri}^{2}}\left( 1-\sqrt{1-\frac
{Q_{cri}^{2}}{Q^{2}}}\right)
\end{equation}
where
\begin{equation}
Q_{cri}^{2}=\frac{\left( n-1\right) \left( n-2\right) }{8\beta^{2}}%
\end{equation}
and $Q^{2}\geq Q_{cri}^{2}.$
In this case one may set $\Xi=A=1$ to get
\begin{equation}
ds^{2}=-\left( 1-\left( \frac{r_{+}}{r}\right) ^{\frac{\left( n-2\right)
+1}{2}}\right) rdt^{2}+\frac{1}{\left( 1-\left( \frac{r_{+}}{r}\right)
^{\frac{\left( n-2\right) +1}{2}}\right) r}dr^{2}+rd\Omega_{n-1}^{2}.
\end{equation}
\subsubsection{BR limit of the solution}
In the zero dilaton limit $\alpha=0,$ we express our metric functions (71) in
the form
\begin{align}
f\left( r\right) & =\Xi_{\circ}\left( r-r_{+}\right) r,\text{ \ }%
\Xi_{\circ}=\frac{8\beta^{2}\left( n-2\right) }{\left( n-1\right) \left(
n-2\right) +8\beta^{2}Q^{2}},\\
h^{2} & =A_{\circ}^{2}=Q^{2}-\frac{\left( n-1\right) \left( n-2\right)
}{8\beta^{2}}.
\end{align}
In $N(=n+1)-$dimensions we also set $r_{+}=0,$ $r=\frac{1}{\rho}$ and
$\tau=\Xi_{\circ}t,$ to transform the metric (7) into%
\begin{equation}
ds^{2}=\frac{1}{\Xi_{\circ}}\left( \frac{-d\tau^{2}+d\rho^{2}}{\rho^{2}}%
+\Xi_{\circ}A_{\circ}^{2}d\Omega_{n-1}^{2}\right) .
\end{equation}
This is in the BR form with the topological structure $AdS_{2}\times S^{N-2},$
where the radius of the sphere is $\sqrt{\Xi_{\circ}}A_{\circ}.$ It can be
shown that%
\begin{equation}
\Xi_{\circ}A_{\circ}^{2}=\left( n-2\right) \left( \frac{8\beta^{2}%
Q^{2}-\left( n-1\right) \left( n-2\right) }{\left( n-1\right) \left(
n-2\right) +8\beta^{2}Q^{2}}\right)
\end{equation}
which, in the limit of $\beta\rightarrow\infty,$ becomes
\begin{equation}
\underset{\beta\rightarrow\infty}{\lim}\Xi_{\circ}A_{\circ}^{2}=\left(
n-2\right)
\end{equation}
such that, the solution (81) becomes the BR type solution of EYMD theory (see
Eq. (39)). We set now $\Xi_{\circ}A_{\circ}^{2}=1$, to obtain a conformally
flat metric. This claims that
\begin{equation}
\left( n-2\right) \left( \frac{8\beta^{2}Q^{2}-\left( n-1\right) \left(
n-2\right) }{\left( n-1\right) \left( n-2\right) +8\beta^{2}Q^{2}%
}\right) =1
\end{equation}
and consequently we find
\begin{align}
\beta^{2} & =\frac{\left( n-1\right) ^{2}\left( n-2\right) }%
{8Q^{2}\left( n-3\right) },\\
ds^{2} & =\frac{2Q^{2}}{\left( n-1\right) }\left( \frac{-d\tau^{2}%
+d\rho^{2}}{\rho^{2}}+d\Omega_{3}^{2}\right) .
\end{align}
This particular choice of $\beta$ casts the EYMBI metric into a conformally
flat form with the topology of $AdS_{2}\times S^{3}$
\subsubsection{$AdS_{2}\times S^{N-2}$ topology for $0<\alpha<1$}
As one may show, for $0<\alpha<1$ and $r_{+}=0,$ a similar transformation as
(40), here also leads to the line element
\begin{equation}
ds^{2}=\left( \Xi\right) ^{-\frac{1+\alpha^{2}}{1-\alpha^{2}}}\left(
\frac{1-\alpha^{2}}{1+\alpha^{2}}\right) ^{-\frac{2}{1-\alpha^{2}}}%
\rho^{-\frac{2\alpha^{2}}{1-\alpha^{2}}}\left( \frac{-d\tau^{2}+d\rho^{2}%
}{\rho^{2}}+\Xi A^{2}\left( \frac{1-\alpha^{2}}{1+\alpha^{2}}\right)
^{2}d\Omega_{n-1}^{2}\right) .
\end{equation}
Again we set $\Xi A^{2}\left( \frac{1-\alpha^{2}}{1+\alpha^{2}}\right)
^{2}=1$ which gives the conformally flat line element%
\begin{equation}
ds^{2}=a\left( \rho\right) \left( \frac{-d\tau^{2}+d\rho^{2}}{\rho^{2}%
}+d\Omega_{n-1}^{2}\right) ,
\end{equation}
with%
\begin{equation}
a\left( \rho\right) =\left( \Xi\right) ^{-\frac{1+\alpha^{2}}{1-\alpha
^{2}}}\left( \frac{1-\alpha^{2}}{1+\alpha^{2}}\right) ^{-\frac{2}%
{1-\alpha^{2}}}\rho^{-\frac{2\alpha^{2}}{1-\alpha^{2}}}.
\end{equation}
\subsection{Linear Stability of the EYMBID black holes}
Similar to the proof given in Sec. ($II.B$), here also we study the stability
of the possible black holes in EYMBID theory which undergoes a linear
perturbation. Again we give a detailed study for the 5-dimensional black holes
which is extendible to any higher dimensions. Our perturbed metric is same as
we adapted in Eq. (46). The linearized field equations plus the extra term of
$R_{tr}$ are given now by%
\begin{gather}
R_{tr}:\frac{\left( n-1\right) }{2}\frac{\chi_{t}\left( t,r\right)
h^{\prime}\left( r\right) }{h\left( r\right) }=\frac{4}{3}\partial_{r}%
\Phi\left( r\right) \partial_{t}\psi\left( t,r\right) \\
\nabla_{\circ}^{2}\psi-\chi\nabla_{\circ}^{2}\Phi+\frac{1}{2}\left(
\Gamma-\chi\right) _{r}\Phi^{\prime}f=-\frac{8}{\left( n-1\right) }%
\alpha^{2}\beta^{2}e^{\frac{4}{\left( n-1\right) }\alpha\Phi}\left(
\mathcal{L}\left( X_{\circ}\right) +4X_{\circ}^{2}\partial_{X_{\circ}}%
^{2}\mathcal{L}\left( X_{\circ}\right) \right) \psi\\
R_{\theta\theta}:\left( 2-R_{\circ\theta\theta}\right) \chi-\frac{1}%
{2}hh^{\prime}f\left( \Gamma-\chi\right) _{r}=\frac{16}{9}\alpha A^{2}%
\beta^{2}\left( 2X_{\circ}\partial_{X_{\circ}}\mathcal{L}\left( X_{\circ
}\right) -\mathcal{L}\left( X_{\circ}\right) \right) \psi
\end{gather}
in which our conventions are as before. The first equation in this set implies
that%
\begin{equation}
\chi\left( t,r\right) =-\frac{4}{3\alpha}\psi\left( t,r\right)
\end{equation}
which, after we make substitutions in the two latter equations and eliminating
the $\left( \Gamma-\chi\right) _{r}$ we find%
\begin{equation}
\nabla_{\circ}^{2}\psi\left( t,r\right) -U\left( r\right) \psi\left(
t,r\right) =0
\end{equation}
where%
\begin{equation}
U\left( r\right) =\frac{8}{3}\beta^{2}e^{\frac{4}{3}\alpha\Phi}\left[
\mathcal{L}\left( X_{\circ}\right) -2X_{\circ}\partial_{X_{\circ}%
}\mathcal{L}\left( X_{\circ}\right) -\alpha^{2}\left( \mathcal{L}\left(
X_{\circ}\right) +4X_{\circ}^{2}\partial_{X_{\circ}}^{2}\mathcal{L}\left(
X_{\circ}\right) \right) \right] .
\end{equation}
To get these results we have implicitly used the constraint (74) on $A$. Again
by imposing the same constraint , one can show that $U\left( r\right) $ is
positive definite. We follow the separation method to get
\begin{equation}
\psi\left( t,r\right) =e^{\pm\epsilon t}\zeta\left( r\right) ,\text{
\ \ }\nabla_{\circ}^{2}\zeta\left( r\right) -U_{eff}\left( r\right)
\zeta\left( r\right) =0,\text{ \ \ }U_{eff}\left( r\right) =\left(
\frac{\epsilon^{2}}{f}+U\left( r\right) \right) ,
\end{equation}
where $\epsilon$ is a constant. Here also the fact that $U_{eff}\left(
r\right) >0$ can be justified which implies in turn that the system is
stable. For $\beta\rightarrow\infty$ this reduces to the case of EYMD black
hole solution whose stability was already verified before.
\section{Black holes in the BDYM theory}
In $N\left( =n+1\right) -$dimensions we write the Brans-Dicke-Yang-Mills
(BDYM) action as%
\begin{gather}
I=-\frac{1}{16\pi}\int\nolimits_{\mathcal{M}}d^{n+1}x\sqrt{-g}\left( \phi
R-\frac{\omega}{\phi}\left( \mathbf{\nabla}\phi\right) ^{2}+\mathcal{L}%
_{m}\right) -\frac{1}{8\pi}\int\nolimits_{\partial\mathcal{M}}d^{n}x\sqrt
{-h}K,\\
\mathcal{L}_{m}=-\mathbf{Tr}(F_{\lambda\sigma}^{\left( a\right) }F^{\left(
a\right) \lambda\sigma}),\nonumber
\end{gather}
in which $\omega$ is the coupling constant, and $\phi$ stands for the BD
scalar field with the dimensions $G^{-1}$ ($G$ is the $N-$dimensional
Newtonian constant \cite{21}). Variation of the BDYM's action with respect to
the $g_{\mu\nu}$ gives
\begin{align}
\phi G_{\mu\nu} & =\frac{\omega}{\phi}\left( \nabla_{\mu}\phi\nabla_{\nu
}\phi-\frac{1}{2}g_{\mu\nu}\left( \mathbf{\nabla}\phi\right) ^{2}\right)
+2\left( \mathbf{Tr}\left( F_{\mu\lambda}^{\left( a\right) }F_{\nu
}^{\left( a\right) \ \lambda}\right) -\frac{1}{4}g_{\mu\nu}\mathbf{Tr}%
\left( F_{\lambda\sigma}^{\left( a\right) }F^{\left( a\right)
\lambda\sigma}\right) \right) +\\
& \nabla_{\mu}\nabla_{\nu}\phi-g_{\mu\nu}\nabla^{2}\phi,\nonumber
\end{align}
while variation of the action with respect to the scalar field $\phi$ and the
gauge potentials $\mathbf{A}^{\left( a\right) }$ yields
\begin{equation}
\nabla^{2}\phi=-\frac{n-3}{2\left[ \left( n-1\right) \omega+n\right]
}\mathbf{Tr}\left( F_{\lambda\sigma}^{\left( a\right) }F^{\left( a\right)
\lambda\sigma}\right) ,
\end{equation}
and%
\begin{equation}
\mathbf{d}\left( ^{\star}\mathbf{F}^{\left( a\right) }\right) +\frac
{1}{\sigma}C_{\left( b\right) \left( c\right) }^{\left( a\right)
}\mathbf{A}^{\left( b\right) }\wedge^{\star}\mathbf{F}^{\left( c\right)
}=0,
\end{equation}
respectively.
We follow now the routine process to transform BDYM action into the EYMD
action\cite{21}. For this purpose, one can use a conformal transformation
(variables with a caret $\hat{.}$ denote those in the Einstein frame)
\begin{equation}
\hat{g}_{\mu\nu}=\phi^{\frac{2}{n-1}}g_{\mu\nu}\text{ \ \ and \ \ }\hat{\Phi
}=\frac{\left( n-3\right) }{4\hat{\alpha}}\ln\phi.
\end{equation}
This transforms (97) into
\begin{equation}
\hat{I}=-\frac{1}{16\pi}\int\nolimits_{\mathcal{M}}d^{n+1}x\sqrt{-\hat{g}%
}\left( \hat{R}-\frac{4}{n-1}\left( \mathbf{\hat{\nabla}}\hat{\Phi}\right)
^{2}-e^{-4\hat{\alpha}\hat{\Phi}/\left( n-1\right) }\mathbf{Tr}\left(
\hat{F}_{\lambda\sigma}^{\left( a\right) }\hat{F}^{\left( a\right)
\lambda\sigma}\right) \right) -\frac{1}{8\pi}\int\nolimits_{\partial
\mathcal{M}}d^{n}x\sqrt{-\hat{h}}\hat{K},
\end{equation}
where
\begin{equation}
\hat{\alpha}=\frac{n-3}{2\sqrt{\left( n-1\right) \omega+n}}.
\end{equation}
This transformed action is similar to the EYMD action given by (1). Variation
of this action with respect to the $\hat{g}_{\mu\nu},$ $\hat{\Phi}$ and
$\mathbf{\hat{A}}^{\left( a\right) }$ gives%
\begin{gather}
\hat{R}_{\mu\nu}=\frac{4}{n-1}\mathbf{\hat{\partial}}_{\mu}\Phi\hat{\partial
}_{\nu}\Phi+2e^{-4\hat{\alpha}\hat{\Phi}/\left( n-1\right) }\left[
\mathbf{Tr}\left( \hat{F}_{\mu\lambda}^{\left( a\right) }\hat{F}_{\nu
}^{\left( a\right) \ \lambda}\right) -\frac{1}{2\left( n-1\right)
}\mathbf{Tr}\left( \hat{F}_{\lambda\sigma}^{\left( a\right) }\hat
{F}^{\left( a\right) \lambda\sigma}\right) \hat{g}_{\mu\nu}\right] ,\\
\hat{\nabla}^{2}\Phi=-\frac{1}{2}\hat{\alpha}e^{-4\hat{\alpha}\hat{\Phi
}/\left( n-1\right) }\mathbf{Tr}(\hat{F}_{\lambda\sigma}^{\left( a\right)
}\hat{F}^{\left( a\right) \lambda\sigma}),
\end{gather}
\begin{equation}
\mathbf{d}\left( e^{-4\hat{\alpha}\hat{\Phi}/\left( n-1\right) \star
}\mathbf{\hat{F}}^{\left( a\right) }\right) +\frac{1}{\sigma}C_{\left(
b\right) \left( c\right) }^{\left( a\right) }e^{-4\hat{\alpha}\hat{\Phi
}/\left( n-1\right) }\mathbf{\hat{A}}^{\left( b\right) }\wedge^{\star
}\mathbf{\hat{F}}^{\left( c\right) }=0.
\end{equation}
It is not difficult to conclude that, if we find a solution to the latter
equations, by an inverse transformation, we can find the solutions of the
related equations of the BDYM theory. In other words if $\left( \hat{g}%
_{\mu\nu},\Phi,\mathbf{\hat{F}}^{\left( a\right) }\right) $ is a solution
of the latter equations, then
\begin{equation}
\left( g_{\mu\nu},\phi,\mathbf{F}^{\left( a\right) }\right) =\left(
\exp\left( -\frac{8\hat{\alpha}}{\left( n-1\right) \left( n-3\right)
}\hat{\Phi}\right) \hat{g}_{\mu\nu},\exp\left( \frac{4\hat{\alpha}}{\left(
n-3\right) }\hat{\Phi}\right) ,\mathbf{\hat{F}}^{\left( a\right) }\right)
\end{equation}
is a solution of (98-100) and vice versa.
One may call $\left( g_{\mu\nu},\phi,\mathbf{F}^{\left( a\right) }\right)
,$ the reference solution and $\left( \hat{g}_{\mu\nu},\hat{\Phi
},\mathbf{\hat{F}}^{\left( a\right) }\right) $ the target solution. Hence
our solution in EYMD would be the target solution i.e.%
\begin{equation}
d\hat{s}^{2}=-\hat{f}\left( r\right) dt^{2}+\frac{dr^{2}}{\hat{f}\left(
r\right) }+\hat{h}\left( r\right) ^{2}d\Omega_{n-1}^{2},
\end{equation}
where%
\begin{align}
\hat{f}\left( r\right) & =\hat{\Xi}\left( 1-\left( \frac{\hat{r}_{+}}%
{r}\right) ^{\frac{\left( n-2\right) \hat{\alpha}^{2}+1}{\hat{\alpha}%
^{2}+1}}\right) r^{\frac{2}{\hat{\alpha}^{2}+1}},\text{ \ \ }\hat{h}\left(
r\right) =\hat{A}e^{-2\hat{\alpha}\hat{\Phi}/\left( n-1\right) },\\
\hat{\Xi} & =\frac{\left( n-2\right) }{\left( \left( n-2\right)
\hat{\alpha}^{2}+1\right) \hat{Q}^{2}},\text{ \ \ }\hat{\Phi}=-\frac{\left(
n-1\right) }{2}\frac{\hat{\alpha}\ln r}{\hat{\alpha}^{2}+1},\text{ \ \ }%
\hat{A}^{2}=\hat{Q}^{2}\left( \hat{\alpha}^{2}+1\right) ,\nonumber\\
\hat{r}_{+} & =\left( \frac{4\left( \hat{\alpha}^{2}+1\right) \hat
{M}_{QL}}{\left( n-1\right) \hat{\Xi}\hat{\alpha}^{2}\hat{A}^{n-1}}\right)
.\nonumber
\end{align}
Our reference solution would read now%
\begin{equation}
ds^{2}=-f\left( r\right) dt^{2}+\frac{dr^{2}}{f\left( r\right) }+h\left(
r\right) ^{2}d\Omega_{n-1}^{2},
\end{equation}
in which%
\begin{align}
f\left( r\right) & =\hat{\Xi}\left( 1-\left( \frac{\hat{r}_{+}}%
{r}\right) ^{\frac{\left( n-2\right) \hat{\alpha}^{2}+1}{\hat{\alpha}%
^{2}+1}}\right) r^{\frac{2\left( n-3\right) +4\hat{\alpha}^{2}}{\left(
n-3\right) \left( \hat{\alpha}^{2}+1\right) }},\text{ \ \ }h\left(
r\right) =\hat{A}e^{-\frac{2\hat{\alpha}\hat{\Phi}\left( n+1\right)
}{\left( n-1\right) \left( n-3\right) }}=\hat{A}r^{\frac{\hat{\alpha}%
^{2}\left( n+1\right) }{\left( \hat{\alpha}^{2}+1\right) \left(
n-3\right) }},\\
\phi & =r^{\frac{-2\left( n-1\right) \hat{\alpha}^{2}}{\left( n-3\right)
\left( \hat{\alpha}^{2}+1\right) }},\text{ and }\mathbf{F}^{\left(
a\right) }=\mathbf{\hat{F}}^{\left( a\right) }=\mathbf{d\hat{A}}^{\left(
a\right) }+\frac{1}{2\sigma}C_{\left( b\right) \left( c\right) }^{\left(
a\right) }\mathbf{\hat{A}}^{\left( b\right) }\wedge\mathbf{\hat{A}%
}^{\left( c\right) }%
\end{align}
where the YM potential is same as (9) with the new charge $\hat{Q}.$ Herein
one can find the Hawking temperature of the BDYM-black hole at the event
horizon as%
\begin{equation}
T_{H}=\frac{\hat{\Xi}\left[ \left( n-2\right) \hat{\alpha}^{2}+1\right]
}{4\pi\left( \hat{\alpha}^{2}+1\right) }\left( \hat{r}_{+}\right)
^{\left( -\frac{\left( n-3\right) \left( \hat{\alpha}^{2}-1\right)
-4\hat{\alpha}^{2}}{\left( \hat{\alpha}^{2}+1\right) \left( n-3\right)
}\right) }%
\end{equation}
where $\hat{r}_{+}$ is the radius of the event horizon.
\section{Conclusion}
A simple class of spherically symmetric solutions to the EYMD equations is
obtained in any dimensions. Magnetic type Wu-Yang ansatz played a crucial role
in extending the solution to N-dimension. For the non-zero dilaton the space
time possesses singularity, representing a non-asymptotically flat black hole
solution expressed in terms of the quasilocal mass. Particular case of a
linear dilatonic black hole is singled out as a specific case. Hawking
temperature for all cases has been computed which are distinct from the EMD
temperatures \cite{22}. Stability against linear perturbations for these
dilatonic metrics is proved. It has been shown that the extremal limit in the
vanishing dilaton, results in the higher dimensional BR space times for the YM
field. With the common topology of $AdS_{2}\times S^{N-2}$ for both theories,
while the radius of $S^{N-2}$ for the Maxwell case is $\left( N-3\right) ,$
it becomes $\left( N-3\right) ^{1/2}$ in the YM case. As a final
contribution in the paper we apply a conformal transformation to derive black
hole solutions in the Brans-Dicke-YM theory. It is our belief that these YMBR
metrics, beside the dilatonic ones, will be useful in the string/supergravity
theory as much as the EMBR metrics are.
\begin{acknowledgement}
We thank the anonymous referee for valuable and constructive suggestions.
\end{acknowledgement}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,706 |
\section{Introduction} \label{Introduction-Section}
In recent years, the need for broadband wireless connectivity has been steadily increasing. From online video streaming to remote vehicle piloting, new applications require reliable wireless links with high throughput and low delay. Additionally, some scenarios pose additional challenges when planning the network. In emergency scenarios, such as forest fires and earthquakes, groups of first-responders are distributed throughout a large area and need to communicate among themselves and with a remote command center \cite{zhao2019uav}. In addition to traditional voice and text services, these communications may also include broadband services requiring the exchange of multimedia content. In some circumstances, existing networks might not be able to provide reliable and broadband wireless connectivity due to failures of the base stations or lack thereof. Other scenarios that exacerbate the challenges of network planning are Temporary Crowded Events (TCEs), such as music festivals and outdoor festivities \cite{almeida2018traffic}. TCEs are characterized by a high density of users that are concentrated in predefined areas for short periods of time and generate significant and variable traffic, which is influenced by the event dynamics.
In order to satisfy the Quality of Service (QoS) requirements in these scenarios, novel network architectures are being considered. An interesting solution relies on the use of Unmanned Aerial Vehicles (UAVs) acting as aerial Wi-Fi Access Points (APs) or cellular base stations, forming aerial wireless networks \cite{zeng2016wireless, yanmaz2018drone}. Due to the mobility of the UAVs and the ability to position them in the 3D space, aerial networks can quickly adapt to the dynamic conditions of the environment and users' traffic demand. Thus, aerial networks are excellent solutions to provide on-demand wireless connectivity when there is no network infrastructure available or to enhance the capacity of existing networks with the deployment of temporary additional aerial base stations.
In \cite{almeida2018traffic} we proposed an aerial network architecture named \textbf{Traffic-Aware Multi-Tier Flying Network} (TMFN), which is illustrated in \cref{TMFN-Figure: TMFN}. The TMFN is composed of Flying Mesh Access Points (FMAPs) and Gateway (GW) UAVs, which are organized in a two-tier multi-hop architecture. The access tier consists of FMAPs, which are rotary-wing UAVs acting as aerial Wi-Fi APs that form small cells to serve the users on the ground. The backhaul tier is composed of Gateway UAVs that forward traffic from the FMAPs to the Internet. The TMFN can be dynamically repositioned and reconfigured according to the users' traffic demand, in order to improve the overall provided QoS.
To control the TMFN topology, we proposed a \textbf{Network Planning (NetPlan)} algorithm in \cite{almeida2018traffic}. The NetPlan algorithm determines the horizontal positions and Wi-Fi cell ranges of the hovering FMAPs in order to improve the TMFN's aggregate throughput. To this end, the NetPlan algorithm positions the FMAPs closer to the users generating more traffic with shorter Wi-Fi cells, with the remaining FMAPs being distributed throughout the coverage area. As a follow-up of this work, we proposed the \textbf{RedeFINE routing solution} \cite{coelho2018redefine, coelho2019routing}. RedeFINE is a predictive centralized routing protocol for high-capacity multi-hop aerial networks, which is able to determine, in advance, the forwarding tables of the FMAPs and the time instants they shall be updated in order to minimize communications disruptions. By assuming that the future trajectories of the FMAPs are known, RedeFINE is able to predict the time instants when each FMAP should update its forwarding table so that the overall network throughput is maximized. This is achieved by eliminating the process of neighbor discovery and the time wasted in updating the forwarding table in traditional routing solutions, where nodes typically recover from link failures after they occur and are detected. Finally, we proposed a \textbf{gateway UAV placement (GWP)} algorithm \cite{coelho2019traffic}. The GWP algorithm takes advantage of the knowledge of the FMAPs' future positions and offered traffic to determine the position of the gateway UAVs in order to enable communications paths with high capacity. Although the NetPlan, the RedeFINE and the GWP solutions were developed independently, they were designed to be used simultaneously. To the best of our knowledge, there are no solutions combining the UAV placement, routing and gateway placement problems in a single solution for aerial networks.
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{"TMFN/Traffic-Aware-Multi-Tier-Flying-Network"}
\caption{Traffic-Aware Multi-Tier Flying Network (TMFN) providing always-on broadband Internet connectivity to the users attending a music festival.}
\label{TMFN-Figure: TMFN}
\end{figure}
In this article, we propose a novel solution resulting from the holistic combination of the NetPlan algorithm \cite{almeida2018traffic}, the RedeFINE routing solution \cite{coelho2018redefine}, including an inter-flow interference routing metric \cite{coelho2019routing}, and the GWP algorithm \cite{coelho2019traffic} applied to the TMFN. The synergy created by the integration of the three components allows the TMFN to improve the QoS provided to the users whilst minimizing the communications disruption within the TMFN's backhaul tier. The proposed solution determines the updated TMFN topology periodically with each update cycle having the following sequence of operations. First, the NetPlan algorithm determines the updated positions and Wi-Fi cell ranges of the FMAPs for the following cycle based on the users' positions and their offered traffic. Then, the RedeFINE routing solution determines the optimal forwarding tables for the FMAPs and the time instants they shall be updated, considering their future trajectories calculated through the initial and final positions of the FMAPs. Finally, the GWP algorithm determines the optimal position of the GWs considering the FMAPs' future positions and offered traffic. Although the three components were designed to be used simultaneously, they are evaluated individually using the ns-3 simulator \cite{ns3Simulator}. This allows the evaluation of the corresponding component without the interference from the remaining ones. The NetPlan algorithm is also evaluated in an experimental testbed. In this process, we evaluate the air-to-ground and ground-to-air channel propagation models in the testbed for UAVs hovering at low altitudes in an open-air environment. This allows the verification of the theoretical models proposed in the literature \cite{khuwaja2018survey}. Moreover, using the experimental channel models, instead of the theoretical ones, in the ns-3 simulations allows a more accurate reproduction of the testbed conditions.
The contributions of this article are three-fold:
\begin{itemize}
\item A novel solution resulting from the holistic combination of the NetPlan, RedeFINE and GWP solutions for aerial networks, which improves the network performance and minimizes the communications disruptions;
\item Evaluation of the NetPlan algorithm in an experimental testbed;
\item Experimental evaluation of the air-to-ground and ground-to-air channel propagation models for UAVs hovering at low altitudes in an open-air environment.
\end{itemize}
The rest of this article is organized as follows.
\cref{RelatedWork-Section} discusses the related work.
\cref{TMFN-Section} presents the TMFN network architecture and the holistic solution proposed in this article.
\cref{NetplanAlgorithm-Section} explains the NetPlan algorithm.
\cref{NetplanAlgorithmEvaluation-Section} contains the evaluation of the NetPlan algorithm.
\cref{RedeFINE-Section} describes the RedeFINE routing protocol.
\cref{RedeFINEEvaluation-Section} contains the evaluation of RedeFINE.
\cref{GWPAlgorithm-Section} presents the GWP algorithm.
\cref{GWPAlgorithmEvaluation-Section} discusses the evaluation of the GWP algorithm.
\cref{Conclusions-Section} draws the conclusions and future work.
\section{Related Work} \label{RelatedWork-Section}
Following the emergence of aerial networks, UAV placement algorithms have been proposed to determine the positions of the UAVs that maximize a given objective function \cite{cicek2019uav, yanmaz2018drone}. In \cite{galkin2018backhaul, mozaffari2015drone, kalantari2017backhaul}, the authors propose solutions to maximize the area and number of users served by the aerial network. The determination of the UAV positions that maximize the QoS / Quality of Experience (QoE) provided to the users are the main objective of the works proposed in \cite{he2019resource, zeng2016throughput, li2017optimal, alzenad20183d}. In addition to QoS, other objectives may also be considered when designing UAV placement algorithms, including the minimization of the UAV's transmission power \cite{alzenad20173Dplacement} or the support of first-responders in emergency scenarios \cite{zhao2019uav}.
Recently, UAV placement algorithms based on Machine Learning (ML) or Reinforcement Learning (RL) techniques have been proposed \cite{wang2018machine, jiang2017machine}. The use of these artificial intelligence techniques has been proven to achieve similar or even better results than deterministic alternatives, due to the ability to automatically extract and learn the most relevant features that influence the decision-making process without human intervention. The Q-Learning technique is explored in \cite{ghanavi2018efficient, colonnese2019qsquare, liu2018deployment} in order to determine the positions of the UAVs that maximize the QoS / QoE provided to the users. The solutions presented in \cite{munaye2019uav, liu2019trajectory, balakrishnan2019deep} take advantage of deep learning techniques to design UAV placement algorithms that maximize the QoS provided to the users, by controlling the position, Tx power and OFDMA resource scheduling of the UAVs. A deep RL placement algorithm, based on Echo State Networks (ESNs), is shown in \cite{challita2018deep} to determine the trajectories of multiple UAVs, so that the interference caused in the ground network and the wireless transmission latency are minimized. ESNs are also explored in \cite{chen2017caching}, in which an algorithm for cache-enabled UAVs is proposed to determine the trajectories and content to cache at each UAV, in order to maximize the QoE provided to the users and minimize the Tx power of the on-board base stations. Moreover, an ML framework is presented in \cite{zhang2018machine} to predict congestion and traffic demand surges in cellular networks, which is used to position UAVs to enhance the capacity of local networks using minimal Tx and UAV movement power.
Overall, despite the results achieved by the UAV placement algorithms, most of them do not consider nor differentiate the users' traffic demands and optimize the SNR for all users independently of their traffic demand. Therefore, the network capacity provided by the UAVs may not be fully exploited by inactive users, who are not offering or receiving traffic.
Most of the state of the art routing solutions for aerial networks were built upon the protocols employed in Mobile Ad-hoc Networks (MANETs) and Vehicular Ad-hoc Network (VANETs) \cite{jiang2018, lakew2020}. In particular, some predictive approaches have been proposed in \cite{li2017, gankhuyag2017, song2018, khaledi2018, sliwa2019}. Predictive solutions usually consider the positions of the UAVs over time, which are inferred based on their speed, moving direction, and predetermined mobility models \cite{arafat2019}. In \cite{xianfengLi2017}, a routing protocol based on the Ad-Hoc On-Demand Distance Vector (AODV) protocol \cite{perkins2003} is proposed. It uses Global Positioning System (GPS) information and employs mobility prediction to estimate the stability of the links, aiming to minimize the delay of the routing discovery process, typical in reactive routing protocols \cite{jiang2018, sahingoz2014, tareque2015}. A similar approach is proposed in \cite{rosati2016}, where the Optimized Link State Routing (OLSR) protocol \cite{clausen2003} is improved to predict topology changes and react before link disruptions occur. Nevertheless, the overhead inherent to proactive protocols is not addressed \cite{bekmezci2013, sahingoz2014}. Moreover, both solutions have specific hardware requirements, in order to determine the location of the UAVs with high accuracy in short time intervals. In \cite{barritt2017}, a Software-Defined Networking (SDN) routing approach that anticipates topology changes is proposed; however, to the best of our knowledge, its performance evaluation has not yet been presented and the optimal placement of the UAVs is not explored.
Overall, predictive routing solutions for aerial networks employ the distributed routing paradigm; hence, the UAVs need to exchange probe packets, which may introduce high overhead and may not scale for large networks. Moreover, in aerial networks, UAVs typically need to be placed close to each other, in order to ensure high-capacity air-to-air links. This leads to interference between concurrent flows, which is not a local concept, since it depends on all the interfering nodes along a path. Therefore, a solution that performs routing decisions considering a holistic and centralized view of the network is worthy to be considered.
GW placement in wireless networks is a commonly treated problem in the literature. Over the years, different studies have been carried out \cite{maolin2009gateways, seyedzadegan2013zero, targon2010joint, aoun2006gateway, jahanshahi2019gateway}. However, most of them aim at minimizing the number of GWs while optimizing their placement, in order to meet some QoS metrics, including throughput and delay, and reducing the energy consumption. In \cite{muthaiah2008single}, the authors show how the GW placement and the transmission power affect the network throughput. However, they do not consider the traffic demand of nodes. Similarly, the work presented in \cite{oueis2019core} aims at determining the optimal placement for an Evolved Packet Core (EPC), amongst a set of BSs in a self-deployed cellular network. Nevertheless, they do not have control over the mobility of the EPC nodes and assume that the nodes have the same traffic demand. In \cite{larsen2017}, the authors show how the placement of a UAV acting as network relay between two ground nodes affects the throughput achieved; however, this study is only valid for a pair of ground nodes. A model-free approach to find the optimal positions of a relay UAV is presented in \cite{zhong2019}; its main drawback is the time required to converge to the optimal position.
Overall, state of the art work has been focused on the UAV placement, routing and GW placement problems for aerial networks. However, to the best of our knowledge, no solution proposes a holistic combination of the UAV placement, predictive routing and GW placement, leveraging the knowledge and ability to incorporate the future decisions of all components when determining the future TMFN topology, in order to improve the QoS provided to the users whilst minimizing the communications disruption.
\section{Traffic-Aware Multi-Tier Flying Network} \label{TMFN-Section}
The TMFN, originally proposed in \cite{almeida2018traffic} and illustrated in \cref{TMFN-Figure: TMFN}, consists of a multi-tier aerial network of FMAPs and Gateway UAVs which dynamically reconfigures its topology according to the users' traffic demand, in order to improve the QoS provided to users on the ground. FMAPs and Gateway UAVs are organized in a multi-hop network architecture that is able to cover large areas and provide on-demand wireless connectivity. The first tier (access network) is composed of FMAPs, which are rotary-wing UAVs acting as Wi-Fi APs; they form high-capacity small cells that can be dynamically configured and positioned according to the variable traffic demand of the moving users. FMAPs are able to continuously detect and seek the users that generate more traffic to provide them more bandwidth, so that the aggregate throughput is improved. The second tier (backhaul network) is composed of Gateway UAVs, which are responsible for forwarding traffic to the Internet using dedicated broadband wireless links. Gateway UAVs are dynamically positioned according to the FMAPs' positions and offered traffic, in order to maximize the throughput forwarded to the Internet. Due to the multi-hop architecture, FMAPs can act as relays between gateway UAVs and other FMAPs.
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{"TMFN/TMFN-Components"}
\caption{Proposed TMFN solution, illustrating the NetPlan, the RedeFINE and the GWP algorithms and their interactions.}
\label{TMFN-Figure: TMFN components}
\end{figure}
The TMFN is controlled by three components working cooperatively: i) the NetPlan algorithm; ii) the RedeFINE routing protocol; and iii) the GWP algorithm. The interactions between the three components are explained in \cref{TMFN-Figure: TMFN components}. By sharing the decisions taken among its components, the TMFN is able to quickly adapt not only to the variable users' traffic demand, but also to the movement of the UAVs themselves. To allow sharing information in advance, the components run simultaneously in a central station.
The integrated proposed solution determines the updated TMFN topology periodically with each update cycle having the following sequence of operations. The first step is to take a snapshot of the TMFN and the users. Then, all components consider this snapshot and the decisions taken by the remaining components as their inputs and determine the final updated TMFN topology as follows. First, NetPlan determines the updated positions and Wi-Fi cell ranges of the FMAPs according to the users' positions and their offered traffic. Knowing the initial and final positions of the FMAPs, RedeFINE calculates their future trajectories. Using this information, RedeFINE determines the optimal forwarding tables of the FMAPs and the time instants they shall be updated. Lastly, considering the future positions of FMAPs and their offered traffic, GWP determines the optimal position of the GW. When all components are combined, the TMFN is able to seamlessly transition into the updated topology, which provides an improved QoS to the users whilst minimizing the disruption caused by the movement of the UAVs.
\section{Network Planning Algorithm} \label{NetplanAlgorithm-Section}
The NetPlan algorithm, originally proposed in \cite{almeida2018traffic}, is explained in this section.
\subsection{System Model} \label{NetplanAlgorithm-Section: System model}
\cref{NetplanAlgorithm-Figure: NetPlan algorithm} represents the model of the system. Let the area to be covered by the TMFN be represented as a rectangle $ L_{\textrm{Cov}_\textrm{X}} \times L_{\textrm{Cov}_\textrm{Y}} $ named \emph{map}. The covered area is further subdivided into smaller fixed-size squares $ L_\textrm{Zone} $, defining \emph{zones}, which represent and aggregate all users on that geographic area. Each zone is identified by its index $ z \in \{ 1, ..., Z \} $.
The TMFN is composed of $ F $ FMAPs, which are identified by index $ f \in \{ 1, ..., F \} $. The FMAPs are hovering at a constant altitude $ H_f $ and may only move in the horizontal plane $ (x, y) $. Each FMAP's Wi-Fi cell operates in a dedicated IEEE 802.11n \SI{20}{MHz} channel in the \SI{5}{GHz} band. The channel model replicates the experimental model evaluated on the field, which is discussed in \cref{NetplanAlgorithmEvaluation-Section: Experimental channel model}. Thus, due to the dominant line-of-sight (LoS) component in the FMAP--FMAP link, this channel is modeled by the Friis path loss model \cite{khuwaja2018survey}. The FMAP--User link is modeled by the Friis path loss and Rician fast-fading characterized by the Rician K-factors $ K_U $ and $ K_D $ for the uplink and downlink directions, respectively.
$ U $ users are positioned throughout the coverage area either generating or receiving traffic from the FMAPs. The users are assumed to be associated to the closest FMAP.
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{"Netplan-Algorithm/Netplan-Algorithm"}
\caption{Proposed NetPlan algorithm, representing the map, zones, PFGs, corresponding forces applied on FMAP $ u $, and its Wi-Fi cell.}
\label{NetplanAlgorithm-Figure: NetPlan algorithm}
\end{figure}
\subsection{Overview}
The NetPlan algorithm, illustrated in \cref{NetplanAlgorithm-Figure: NetPlan algorithm}, is inspired in the concepts presented in the Potential Fields (PFs) technique \cite{khatib1986real}. In this sense, PF Generators (PFGs) are virtually deployed on the map, representing users' traffic demand hotspots -- Attractive PF Generators (AFGs) -- and areas already covered by the FMAPs -- Rejective PF Generators (RFGs). Each PFG generates a force field which applies corresponding forces on FMAPs, forcing them to move in the direction of the resulting force applied to them. The FMAPs' Wi-Fi cell ranges are determined directly as a function of the PFGs combined with the current TMFN topology. Hence, by means of the appropriate determination of the PFGs' intensities, locations and corresponding forces, the NetPlan algorithm is able to predominantly position the FMAPs establishing small cells closer to the users generating more traffic (hotspots), while the remaining FMAPs are distributed throughout the map with larger cells, so that the overall map coverage is not compromised.
The NetPlan algorithm runs on a central station that periodically determines the updated positions and Wi-Fi cell ranges of the FMAPs, in which $ T_\textrm{NetPlan} \gg \SI{1}{s} $ is the update period. The updated FMAPs' positions are determined as follows: i) calculate the intensity and location of the PFGs, based on the current TMFN topology and the users' traffic demand; ii) calculate the resulting force applied to the FMAPs; iii) calculate the corresponding displacement vector; and iv) determine the updated position as the sum of the previous coordinates with the displacement vector. The updated FMAPs' Wi-Fi cell ranges are determined directly as a function of the PFGs combined with the current TMFN topology. Finally, the central station transmits the new coordinates and Wi-Fi cell ranges to the FMAPs, which will readjust their positions and configurations accordingly. All of these steps are explained in the following sub-sections.
\subsection{Potential Field Generators}
The calculation of the PFGs' intensity is explained in this sub-section.
\subsubsection{Attractive PFGs} \label{NetplanAlgorithm-Section: Attractive PFGs}
In order to \emph{attract} FMAPs towards high concentrations of generated traffic, an Attractive PFG $ AFG_{z} $ is assigned to each zone $ z $ of the map. Each $ AFG_{z} $ represents the aggregation of all users in zone $ z $ and is located in the center of that zone. Its intensity is defined in \cref{NetplanAlgorithm-Equation: Total AFG}, which includes two components.
\begin{equation} \label{NetplanAlgorithm-Equation: Total AFG}
AFG_{z} = K_{AFG^{T}} \times AFG^{T}_{z} + K_{AFG^{C}} \times AFG^{C}_{z}
\end{equation}
The $ AFG^{T}_{z} $ component represents the aggregate users' traffic demand in zone $ z $ and is given by ${ AFG^{T}_{z} = K_{AFG^{T}_{T}} \times T_{z} + K_{AFG^{T}_\textrm{Min}} }$, where $ T_{z} $ is the mean aggregate offered throughput of the users in zone $ z $, $ K_{AFG^{T}_{T}} $ is a calibration constant and $ K_{AFG^{T}_\textrm{Min}} $ is the baseline value of $ AFG^{T}_{z} $, ensuring all AFGs have a minimum value so that all zones attract FMAPs and, thus, help maintain general coverage of the map. To limit the value of $ AFG_{z} $, the algorithm considers $ T_{z} \in [0, T_\textrm{Max}] $.
The $ AFG^{C}_{z} $ component is an additional factor that allows zones with insufficient Wi-Fi coverage to attract more FMAPs to that area, thereby ensuring that all zones have proper coverage regardless of the traffic demand. To accomplish this goal, $ AFG^{C}_{z} \in [0, 1] $ and depends on the positions of all FMAPs, as well as their cell ranges. In this sense, ${ m_{zu} = r_{u} - d_{zu} }$ is defined as the distance margin between the edge of the FMAP's Wi-Fi cell $ r_{u} $ (covered in \cref{NetplanAlgorithm-Section: FMAPs WiFi cell range}), and the distance between FMAP $ u $ and the center of zone $ z $. Then, based on the value of ${ m_{z} = \max \{ m_{z1}, ..., m_{zU} \} }$, $ AFG^{C}_{z} $ is defined as a three-branched equation:
\begin{enumerate}
\item if $ m_{z} \leq 0 $, no FMAP is covering that zone, so $ AFG^{C}_{z} = 1 $ thereby increasing the overall $ AFG_{z} $ intensity;
\item if $ m_{z} \geq L_\textrm{Zone} $, at least one FMAP is properly covering that zone, hence $ AFG^{C}_{z} = 0 $ and the overall $ AFG_{z} $ is not affected;
\item if $ 0 < m_{z} < L_\textrm{Zone} $, no FMAP provides sufficient coverage of that zone, thus ${ AFG^{C}_{z} = 1 - m_{z} / L_\textrm{Zone} }$.
\end{enumerate}
Each component is then multiplied by the calibration constants $ K_{AFG^{T}} $ and $ K_{AFG^{C}} $, respectively, to adjust the variation intervals of each component to the characteristics of the map and TMFN.
\subsubsection{Rejective PFGs}
To distribute the FMAPs across the whole map, while focusing on the zones with more traffic demand, a Rejective PFG $ RFG_{u} $ is assigned to each FMAP $ u $. In fact, the FMAPs' RFGs neutralize the AFGs of the zones covered by the FMAP, pushing away nearby FMAPs to cover other areas of the map. The intensity of $ RFG_{u} $ is given by \cref{NetplanAlgorithm-Equation: Total RFG} and revolves around a mean value $ RFG^{C}_{u} $ to which an adjustment value $ RFG^{T}_{u} $ is added. This enables the FMAPs to be predominantly positioned around the zones with higher traffic demand, while ensuring the overall coverage of the map, independently of the exact values of the users' traffic demand.
\begin{equation} \label{NetplanAlgorithm-Equation: Total RFG}
RFG_{u} = K_{RFG^{T}} \times RFG^{T}_{u} + K_{RFG^{C}} \times RFG^{C}_{u}
\end{equation}
Therefore, the adjustment value is determined as ${ RFG^{T}_{u} = \frac{1}{Z} \sum_{z=1}^{Z} AFG^{T}_{z} - \frac{1}{\left| C_{u} \right|} \sum_{z \in C_{u}} AFG^{T}_{z} }$, in which $ C_{u} = \{ z : m_{zu} \geq 0 \} $ is the set of zones $ z $ whose center is located within the Wi-Fi cell covered by FMAP $ u $. If $ C_{u} = \emptyset $, then $ RFG^{T}_{u} = 0 $. The mean value is determined as ${ RFG^{C}_{u} = \frac{1}{Z} \sum_{z=1}^{Z} AFG^{T}_{z} }$. Finally, each component is further multiplied respectively by the calibration constants $ K_{RFG^{T}} $ and $ K_{RFG^{C}} $ to adjust the relative weight of each component as well as the intensity of the final equation to the characteristics of the map and TMFN.
\subsection{Potential Field Generators' Forces}
The calculation of the resulting force applied to each FMAP is explained in this section and illustrated in \cref{NetplanAlgorithm-Figure: NetPlan algorithm}.
\subsubsection{Attractive Forces}
The force $ \vec{F}_{A_{zu}} $ applied by $ AFG_{z} $ to FMAP $ u $ is defined in \cref{NetplanAlgorithm-Equation: F Attractive}. It is directly proportional to $ AFG_{z} $ and the distance between the center of zone $ z $ and FMAP $ u $ ($ d_{zu} $), and has the direction of $ \boldsymbol{\hat{F}_{A_{zu}}} $, which is the unit vector starting at FMAP $ u $ and pointing to the center of zone $ z $. This ensures the FMAP is attracted with greater intensity by the zones located further away and/or with more intensity, so that all zones are properly covered, especially the ones with higher $ AFG_{z} $. The constant $ K_{F_{A}} $ is added to the equation to calibrate the force's intensity.
\begin{equation} \label{NetplanAlgorithm-Equation: F Attractive}
\vec{F}_{A_{zu}} = \left( K_{F_{A}} \times AFG_{z} \times d_{zu} \right) \times \boldsymbol{\hat{F}_{A_{zu}}}
\end{equation}
\subsubsection{Rejective Forces}
The force $ \vec{F}_{R_{iu}} $ applied by $ RFG_{i} $ to FMAP $ u $ is given by \cref{NetplanAlgorithm-Equation: F Rejective}. It is directly proportional to $ RFG_{u} $, but inversely proportional to the distance between FMAPs $ i $ and $ u $ ($ d_{iu} $), and has the direction of $ \boldsymbol{\hat{F}_{R_{iu}}} $, which is the unit vector starting at FMAP $ u $ and pointing in the opposite direction of FMAP $ i $. This enables FMAPs to move away from nearby and/or intense RFGs, while being mostly unaffected by distant RFGs. As a result, FMAPs will be predominantly positioned around zones with higher traffic demand, while ensuring overall coverage of the map. The constant $ K_{F_{R}} $ is added to the equation to calibrate the force's intensity.
\begin{equation} \label{NetplanAlgorithm-Equation: F Rejective}
\vec{F}_{R_{iu}} = \left( K_{F_{R}} \times RFG_{i} / d_{iu} \right) \times \boldsymbol{\hat{F}_{R_{iu}}}
\end{equation}
\subsubsection{Resulting Force}
The resulting force $ \vec{F}_{u} $ applied to FMAP $ u $ is given by the sum of all forces applied to it, as defined in \cref{NetplanAlgorithm-Equation: F Resulting}. As a result of this force, an instantaneous acceleration $ \vec{a}_{u} $ is imposed on the FMAP. Assuming the FMAP's position is fixed at the beginning of cycle $ n $, the resulting displacement vector of FMAP $ u $ is given by $ \vec{s}_{u}[n] = K_{s} \times \vec{F}_{u}[n] $, in which $ K_{s} \propto T^2_\textrm{NetPlan} / m $ summarizes the underlying Physics constants as a final calibration constant.
\begin{equation} \label{NetplanAlgorithm-Equation: F Resulting}
\vec{F}_{u} = \sum_{z=1}^{Z} \vec{F}_{A_{zu}} + \sum_{\substack{i=1 \\ i \neq u}}^{U} \vec{F}_{R_{iu}}
\end{equation}
\subsection{FMAP's Wi-Fi Cell Range} \label{NetplanAlgorithm-Section: FMAPs WiFi cell range}
As discussed in \cref{NetplanAlgorithm-Section: System model}, in order to improve the TMFN's aggregate throughput, the FMAPs closer to the users with higher traffic demand should establish smaller Wi-Fi cells, whereas the remaining FMAPs should establish larger Wi-Fi cells to maintain the overall coverage of the map. To implement this behavior, the FMAP's Wi-Fi cell range is determined according to \cref{NetplanAlgorithm-Equation: FMAPs cell range}. Similar to the FMAP's $ RFG_{u} $, it revolves around a mean value $ R_\textrm{Mean} $ to which an adjustment value $ r_{u_{\Delta}} $ is added. Since the FMAP's $ RFG^{T}_{u} $ already implements this behavior, the adjustment value of the Wi-Fi cell range $ r_{u_{\Delta}} $ is proportional to $ RFG^{T}_{u} $, in which $ K_{r} $ is the calibration constant added to the equation to adjust this value to the characteristics of the TMFN and the event.
\begin{equation} \label{NetplanAlgorithm-Equation: FMAPs cell range}
r_{u} = R_\textrm{Mean} + K_{r} \times RFG^{T}_{u}
\end{equation}
\section{Evaluation of Network Planning Algorithm} \label{NetplanAlgorithmEvaluation-Section}
\begin{figure*}[t]
\centering
\subfloat[Homogeneous traffic demand.] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Scenarios/Homogeneous-Scenario"}
\label{NetplanAlgorithmEvaluation-Figure: Homogeneous traffic demand scenario}
}
\hfill
\subfloat[Concentrated traffic demand (without NetPlan).] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Scenarios/Concentrated-Scenario-Without-NetPlan"}
\label{NetplanAlgorithmEvaluation-Figure: Concentrated traffic demand scenario without NetPlan}
}
\hfill
\subfloat[Concentrated traffic demand (with NetPlan).] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Scenarios/Concentrated-Scenario-With-NetPlan"}
\label{NetplanAlgorithmEvaluation-Figure: Concentrated traffic demand scenario with NetPlan}
}
\caption{Test scenarios depicting the FMAP positions and the associated UEs.}
\label{NetplanAlgorithmEvaluation-Figure: Test scenarios}
\end{figure*}
\begin{table*}[t]
\centering
\caption{Association map indicating the FMAP to which a UE is connected.}
\label{NetplanAlgorithmEvaluation-Table: FMAP-UE association map}
\begin{tabular}{l l l l}
\hline
& UE 1 & UE 2 & UE 3 \\
\hline
Homogeneous traffic demand & FMAP B & FMAP C & FMAP A \\
Concentrated traffic demand (without NetPlan) & FMAP B & FMAP C & FMAP C \\
Concentrated traffic demand (with NetPlan) & FMAP B & FMAP C & FMAP A \\
\hline
\end{tabular}
\end{table*}
The performance of the NetPlan algorithm was evaluated by means of simulations and an experimental testbed. The scenarios defined for the tests are explained in \cref{NetplanAlgorithmEvaluation-Section: Test scenarios}. For each scenario, Matlab simulations of the NetPlan algorithm are presented, enabling the visualization of the final positions of the FMAPs determined by the NetPlan algorithm. In addition, ns-3 simulations \cite{ns3Simulator} were performed to analyze the network performance of the User Equipment (UE) for different offered traffic types and in both the uplink and downlink flow directions.
In terms of experimental results, first the FMAP--UE communications channel was characterized in terms of Signal-to-Noise Ratio (SNR), considering different LoS distances and FMAP altitudes. This enabled the verification of the theoretical models proposed in the literature \cite{khuwaja2018survey}. Moreover, using the experimental channel models in the ns-3 simulations allows a more accurate reproduction of the testbed conditions. Then, the performance of the communications channel, considering the defined scenarios, was assessed with the the Cumulative Distribution Function (CDF) of the throughput and the histogram of the data rates of the packets generated by the FMAPs and the UEs.
\begin{table}
\centering
\caption{System and ns-3.29 simulator parameters.}
\label{NetplanAlgorithm-Table: System and ns3 parameters}
\begin{tabular}{l l}
\hline
\multicolumn{2}{c}{Coverage area and TMFN} \\
\hline
$ L_{\textrm{Cov}_\textrm{X}}$ & $ \SI{100}{m} $ \\
$ L_{\textrm{Cov}_\textrm{Y}}$ & $ \SI{100}{m} $ \\
$ L_{\textrm{Zone}} $ & $ \SI{10}{m} $ \\
$ Z $ & 100 zones \\
$ F $ & 3 FMAPs \\
$ U $ & 3 users \\
$ H_f $ & $ \SI{10}{m} $ \\
$ K_U $ & $ \SI{13}{dB} $ \\
$ K_D $ & $ \SI{40}{dB} $ \\
\hline
\multicolumn{2}{c}{ns-3.29 simulator parameters} \\
\hline
Simulation time & (\SI{30}{s} init. +) \SI{20}{s} \\
Wi-Fi standard & IEEE 802.11n \\
Wi-Fi channels & \{36, 40, 44\} \\
Channel bandwidth & \SI{20}{MHz} \\
Tx power & \SI{0}{dBm} \\
Propagation model & Friis + Rician \\
Application traffic & UDP CBR or \\
& TCP \emph{BulkSend} \\
Packet length & \SI{8000}{Bytes} \\
MAC queues & 500 Packets \\
MAC auto rate & MinstrelHt \\
\hline
\end{tabular}
\end{table}
\subsection{Test Scenarios} \label{NetplanAlgorithmEvaluation-Section: Test scenarios}
\begin{figure*}[t]
\centering
\subfloat[SNR measured in the FMAP.] {
\includegraphics[width=0.47\linewidth]{"Netplan-Algorithm-Experimental-Results/Channel-Model/SNR-Measured-FMAP"}
\label{NetplanAlgorithmEvaluation-Figure: Experimental SNR FMAP}
}
\hfill
\subfloat[SNR measured in the UE.] {
\includegraphics[width=0.47\linewidth]{"Netplan-Algorithm-Experimental-Results/Channel-Model/SNR-Measured-UE"}
\label{NetplanAlgorithmEvaluation-Figure: Experimental SNR UE}
}
\vfil
\subfloat[SNR PDF measured in the FMAP.] {
\includegraphics[width=0.47\linewidth]{"Netplan-Algorithm-Experimental-Results/Channel-Model/SNR-PDF-Measured-FMAP-10m"}
\label{NetplanAlgorithmEvaluation-Figure: Experimental SNR PDF FMAP}
}
\hfill
\subfloat[SNR PDF measured in the UE.] {
\includegraphics[width=0.47\linewidth]{"Netplan-Algorithm-Experimental-Results/Channel-Model/SNR-PDF-Measured-UE-10m"}
\label{NetplanAlgorithmEvaluation-Figure: Experimental SNR PDF UE}
}
\caption{SNR measured in the FMAP and UE. Subfigures (a) and (b) plot the SNR versus the LoS distance between each other at different altitudes. The free-space path loss and two-ray ground reflection theoretical models are represented by the dashed and dotted lines, respectively. Subfigures (c) and (d) represent the SNR PDF measured in the FMAP placed at \SI{10}{m} altitude, and the UE, considering the LoS distance of approximately \SI{20}{m}.}
\label{NetplanAlgorithmEvaluation-Figure: Experimental SNR PDF}
\end{figure*}
The test scenarios aim at evaluating the performance of the NetPlan algorithm in typical networking scenarios. They explore different traffic demands in order to demonstrate the concept and network performance gains of the NetPlan algorithm.
Two scenarios were defined for this evaluation: i) homogeneous traffic demand, which is considered as the baseline; and ii) concentrated traffic demand, which allows the evaluation of the network performance gains. Each scenario is characterized by four factors: i) the UE positions; ii) the UE offered traffic; iii) the FMAP positions; and iv) the FMAP--UE association map, indicating the FMAP to which each UE is connected. The test scenarios are illustrated in \cref{NetplanAlgorithmEvaluation-Figure: Test scenarios} and the FMAP--UE association map is indicated in \cref{NetplanAlgorithmEvaluation-Table: FMAP-UE association map}. Each scenario is further explained in the corresponding subsection.
Three offered traffic types were considered: i) TCP; ii) UDP \SI{25}{Mbit/s} constant bitrate (UDP 25M); and iii) UDP \SI{75}{Mbit/s} constant bitrate (UDP 75M). The TCP traffic flow allows the analysis of the channel in saturation, whereas the results of the UDP 25M and UDP 75M flows allow the analyses of the channel when the offered traffic is low and high, respectively. For each traffic type, both flow directions were simulated: i) UE to FMAP (uplink); and ii) FMAP to UE (downlink).
The ns-3 simulation parameters are shown in \cref{NetplanAlgorithm-Table: System and ns3 parameters}. The ns-3 results were obtained using the \emph{FlowMonitor} \cite{carneiro2009flowmonitor} module, which analyzes the traffic flows at the IP network layer. The experimental results were obtained considering 3 runs for each experiment, under the same conditions.
\subsection{Experimental Channel Model} \label{NetplanAlgorithmEvaluation-Section: Experimental channel model}
The air-to-ground and ground-to-air channel models were evaluated in the experimental setup. The FMAP was hovering at different altitudes and hence different LoS distances to the UE. The SNR received at both the FMAP and the UE was collected using the \emph{horst} software \cite{randolf2017horst}.
The channel model was analyzed in terms of the path loss and fast-fading components. \cref{NetplanAlgorithmEvaluation-Figure: Experimental SNR FMAP,NetplanAlgorithmEvaluation-Figure: Experimental SNR UE} represents the collected SNR values for different FMAP--UE distances. In order to compare the experimental values with the free-space path loss and the two-ray ground reflection models, both are represented in the plots. \cref{NetplanAlgorithmEvaluation-Figure: Experimental SNR PDF FMAP,NetplanAlgorithmEvaluation-Figure: Experimental SNR PDF UE} represents the probability distribution function (PDF) of the experimental SNRs, which was fitted with a Rician distribution.
In terms of the path loss component, it can be concluded that the free-space path loss is the most adequate model of the UE--FMAP link, as suggested in the literature \cite{khuwaja2018survey}. This is an expected conclusion, since there is a dominant LoS component between the communications nodes. Nevertheless, the two-ray ground reflection model, which in addition to the LoS component considers a component reflected on the ground and the effect of the antennas' heights, also provides a close SNR estimation, especially for UE--FMAP distances up to \SI{60}{m} and FMAP's altitudes up to \SI{30}{m}. For the same LoS distance, the angle $ \theta_{LoS} $ between the ground and the LoS ray affected the SNR on the UE and the FMAP differently. When $ \theta_{LoS} $ increased, the SNR measured on the UE increased, whereas the SNR on the FMAP decreased. This can be concluded from \cref{NetplanAlgorithmEvaluation-Figure: Experimental SNR FMAP,NetplanAlgorithmEvaluation-Figure: Experimental SNR UE}, by analyzing the two SNRs measured for the same UE--FMAP LoS distance of \SI{36}{m}, but with FMAP's altitude of \SI{20}{m} or \SI{30}{m}.
Regarding the Rician fast-fading component (K-factor), which represents the ratio of the received power in the dominant component to the non-dominant power, it presents a higher value in the UE, as observed in \cref{NetplanAlgorithmEvaluation-Figure: Experimental SNR PDF FMAP,NetplanAlgorithmEvaluation-Figure: Experimental SNR PDF UE}. The lower values in the FMAP can be justified by the obstructions to the signal caused by the airframe of the UAV and the compensation movements performed by the UAV to maintain its position, which induce changes in the antennas' tilt.
\subsection{Homogeneous Traffic Demand}
This scenario aimed at evaluating the network performance when multiple UEs generating the same amount of traffic were evenly distributed throughout the coverage area. To test this scenario, three UEs were always placed at fixed positions, each one within the coverage area of an FMAP, as illustrated in \cref{NetplanAlgorithmEvaluation-Figure: Homogeneous traffic demand scenario}. Each UE is associated to the closest FMAP, which results in each FMAP having only one UE associated. This is considered as the baseline scenario, since the use of the NetPlan algorithm does not significantly change the positions of the FMAPs when the overall traffic demand is equally distributed throughout the coverage area.
\subsubsection{Simulation Results}
\begin{figure*}[t]
\centering
\subfloat[TCP offered traffic.] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Homogeneous/Matlab-Simulation-TCP"}
\label{NetplanAlgorithmEvaluation-Figure: Homogeneous matlab simulations TCP}
}
\hfill
\subfloat[\SI{25}{Mbit/s} UDP offered traffic.] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Homogeneous/Matlab-Simulation-UDP-25M"}
\label{NetplanAlgorithmEvaluation-Figure: Homogeneous matlab simulations UDP 25M}
}
\hfill
\subfloat[\SI{75}{Mbit/s} UDP offered traffic.] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Homogeneous/Matlab-Simulation-UDP-75M"}
\label{NetplanAlgorithmEvaluation-Figure: Homogeneous matlab simulations UDP 75M}
}
\caption{Homogeneous traffic demand scenario showing the final FMAP positions determined by the NetPlan algorithm, according to different users' traffic demand.}
\label{NetplanAlgorithmEvaluation-Figure: Homogeneous matlab simulations}
\end{figure*}
\begin{figure*}[t]
\centering
\subfloat[Throughput CDF.] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Homogeneous/Throughput-CDF-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Homogeneous simulation results throughput}
}
\hfill
\subfloat[Delay CDF.] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Homogeneous/Delay-CDF-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Homogeneous simulation results delay}
}
\hfill
\subfloat[PLR CDF.] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Homogeneous/PLR-CDF-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Homogeneous simulation results PLR}
}
\caption{Network performance of UE 3 in the homogeneous traffic demand scenarios, obtained by means of ns-3 simulation.}
\label{NetplanAlgorithmEvaluation-Figure: Homogeneous simulation results}
\end{figure*}
\cref{NetplanAlgorithmEvaluation-Figure: Homogeneous matlab simulations} contains the results of Matlab simulations depicting the user positions, their offered traffic and the final FMAP positions determined by the NetPlan algorithm in the homogeneous traffic demand scenario for the three offered traffic types analyzed. Since the users are homogeneously distributed throughout the coverage area generating the same traffic demand, the FMAPs are also homogeneously distributed throughout the area.
The network performance results of UE 3 are displayed in \cref{NetplanAlgorithmEvaluation-Figure: Homogeneous simulation results}. Since each FMAP's Wi-Fi cell operates in a dedicated and orthogonal channel and each user is associated to a different FMAP, all users are provided with the full channel capacity.
For each offered traffic, both the uplink and downlink flows present similar results. Moreover, the TCP flow demonstrates that the maximum achievable throughput in this scenario is $\approx$~\SI{105}{Mbit/s}, with 0\% PLR and a delay of $\approx$~\SI{9}{ms}. The UDP 75M flow generates a high offered traffic and achieves a throughput of $\approx$~\SI{75}{Mbit/s} with 0\% PLR and a delay of \SI{0}{ms}. These results reveal that the UDP 75M flow does not saturate the channel. Unlike UDP, TCP includes a congestion control mechanism. Due to the congestion control mechanism, TCP dynamically adjusts the traffic offered to the IP layer so that the channel is fully utilized but not saturated. Moreover, TCP guarantees reliable end-to-end communications by means of acknowledgement packets and retransmissions in case of errors and packet losses. As a consequence, the PLR is 0\% but the packet delay increases relative to the UDP 75M traffic flow. The UDP 25M flow demonstrates that the channel has enough capacity to transport all the offered traffic with a throughput of $\approx$~\SI{25}{Mbit/s}, with 0\% PLR and a delay of $\approx$~\SI{0}{ms}.
\subsubsection{Experimental Results}
\begin{figure*}[t]
\centering
\subfloat[Throughput CDF.] {
\includegraphics[width=0.48\linewidth]{"Netplan-Algorithm-Experimental-Results/Homogeneous/Throughput-CDF-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Traffic results homogeneous throughput}
}
\hfill
\subfloat[Physical data rate histogram.] {
\includegraphics[width=0.47\linewidth]{"Netplan-Algorithm-Experimental-Results/Homogeneous/Data-Rate-Histogram-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Traffic results homogeneous data rate}
}
\caption{Experimental traffic results for FMAP C, considering the homogeneous traffic demand scenario. The results include the throughput CDFs and the histogram of the physical data rate of the packets generated by both the UE 3 (solid bar) and FMAP C (dotted bar) during the experiment.}
\label{NetplanAlgorithmEvaluation-Figure: Traffic results homogeneous}
\end{figure*}
In this scenario, the positions of the FMAPs were defined in order to allow that each UE on the ground was in the coverage area of a single FMAP. Since the FMAPs were configured on orthogonal channels, each UE was able to take advantage of the full channel capacity provided by a single FMAP.
The experimental throughput results are presented in \cref{NetplanAlgorithmEvaluation-Figure: Traffic results homogeneous}, represented by means of histograms of the physical data rates corresponding to the MCS for the IEEE 802.11n standard, \SI{800}{ns} guard interval, and \SI{20}{MHz} channel bandwidth, according to the configurations presented in \cref{NetplanAlgorithmEvaluation-Section: Test scenarios}.
It is possible to observe a significant asymmetry between the downlink direction (FMAP to UE) and the uplink direction (UE to FMAP), especially for the TCP traffic flow and UDP 75M traffic flow. This is denoted by the higher physical data rate values being used by most of the packets sent by the UEs to the FMAPs during the experiment. The physical data rate used to transmit a packet is selected by the MinstrelHt MAC auto-rate mechanism, which evaluates the channel conditions and selects the highest physical data rate that allows the transmission of the packet without errors. Since the conditions of the channel are variable, the selected physical data rate value will also be variable, which results in a variable throughput and PLR.
Overall, the throughput in the uplink is higher than in the downlink. This can be justified by several reasons. First, as concluded in \cref{NetplanAlgorithmEvaluation-Section: Experimental channel model} the communications link is asymmetric, since the Rician K-factor in the UE is higher than the K-factor in the FMAP. Moreover, different transmission power were used in the UE and the FMAP. Since in our testbed two commercial smartphones and a laptop were used as UEs, they were employing the default transmission power of \SI{20}{dBm}, based on the premise that our solution does not rely on modifications performed in the UEs. Conversely, in the FMAPs the transmission power was set to \SI{0}{dBm}, in order to enable short range Wi-Fi cells, required to validate the NetPlan algorithm. Link asymmetry can also be justified by the usage of different antennas in the receiver and in the transmitter. While the FMAPs were using two \SI{5}{dBi} omni-directional external antennas, the smartphones performing the role of UE were using their internal antennas, which typically have a lower reception gain. Besides the expected differences in the antennas' gain and radiation pattern, the communications performance is also affected by the firmware used to control antenna diversity, which is part of MIMO. Finally, the noise floor should not be neglected as well. It is determined by the receiver's sensitivity and by the performance of the low noise amplifier, which is in charge of amplifying weak received signals into stronger signals.
\subsection{Concentrated Traffic Demand}
This scenario, illustrated in \cref{NetplanAlgorithmEvaluation-Figure: Concentrated traffic demand scenario without NetPlan,NetplanAlgorithmEvaluation-Figure: Concentrated traffic demand scenario with NetPlan}, aimed at assessing the performance of the NetPlan algorithm and characterize the network performance when the traffic demand in a concentration area increased compared to the overall traffic demand of the coverage area. To test this scenario, the UE initially located in area A was moved to area C.
The UE--FMAP link was characterized in two cases: i) when the decisions of the NetPlan algorithm were not considered; and ii) when they were considered. In order to accommodate the traffic demand, the NetPlan algorithm positioned FMAP A near area C, which was experiencing a higher traffic demand than previously while traffic demand in area A was reduced to zero. FMAP B maintained its position, in order to provide coverage to the UE in area B. In area C, FMAP A and FMAP C enabled two cells in orthogonal channels, which were used by each UE. The UE--FMAP link was able to provide higher throughput, lower PLR, and lower Round Trip Time (RTT), measured at the application layer, when the decisions of the NetPlan algorithm were employed.
\subsubsection{Simulation Results}
\begin{figure*}
\centering
\subfloat[TCP offered traffic.] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Concentrated-With-Netplan/Matlab-Simulation-TCP"}
\label{NetplanAlgorithmEvaluation-Figure: Matlab simulations concentrated TCP}
}
\hfill
\subfloat[UDP \SI{25}{Mbit/s} constant bitrate offered traffic.] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Concentrated-With-Netplan/Matlab-Simulation-UDP-25M"}
\label{NetplanAlgorithmEvaluation-Figure: Matlab simulations concentrated UDP 25M}
}
\hfill
\subfloat[UDP \SI{75}{Mbit/s} bitrate offered traffic.] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Concentrated-With-Netplan/Matlab-Simulation-UDP-75M"}
\label{NetplanAlgorithmEvaluation-Figure: Matlab simulations concentrated UDP 75M}
}
\caption{Concentrated traffic scenario showing the final FMAP positions determined by the NetPlan algorithm, according to different users' traffic demand.}
\label{NetplanAlgorithmEvaluation-Figure: Matlab simulations concentrated}
\end{figure*}
\begin{figure*}
\centering
\subfloat[Throughput CDF (without NetPlan).] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Concentrated-Without-Netplan/Throughput-CDF-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Concentrated simulation results throughput without NetPlan}
}
\hfill
\subfloat[Delay CDF (without NetPlan).] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Concentrated-Without-Netplan/Delay-CDF-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Concentrated simulation results delay without NetPlan}
}
\hfill
\subfloat[PLR CDF (without NetPlan).] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Concentrated-Without-Netplan/PLR-CDF-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Concentrated simulation results PLR without NetPlan}
}
\vfil
\subfloat[Throughput CDF (with NetPlan).] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Concentrated-With-Netplan/Throughput-CDF-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Concentrated simulation results throughput with NetPlan}
}
\hfill
\subfloat[Delay CDF (with NetPlan).] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Concentrated-With-Netplan/Delay-CDF-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Concentrated simulation results delay with NetPlan}
}
\hfill
\subfloat[PLR CDF (with NetPlan).] {
\includegraphics[width=0.3\linewidth]{"Netplan-Algorithm-Simulation-Results/Concentrated-With-Netplan/PLR-CDF-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Concentrated simulation results PLR with NetPlan}
}
\caption{Network performance of UE 3 in the concentrated traffic demand scenario, obtained by means of ns-3 simulation. The first row represents the results without the NetPlan algorithm, whereas the second row represents the results with the NetPlan algorithm.}
\label{NetplanAlgorithmEvaluation-Figure: Concentrated simulation results}
\end{figure*}
The Matlab simulations for the concentrated traffic demand scenario are illustrated in \cref{NetplanAlgorithmEvaluation-Figure: Matlab simulations concentrated}. The images show the UE positions, their offered traffic and the final FMAP positions determined by the NetPlan algorithm for the three offered traffic types analyzed. The baseline for this scenario, in which the NetPlan algorithm is not used, consists in evenly distributing the FMAPs throughout the coverage area adopting the same positions as in \cref{NetplanAlgorithmEvaluation-Figure: Concentrated traffic demand scenario without NetPlan}. Since the UEs are concentrated in a small area, the FMAPs are also concentrated around that area, without compromising the overall coverage of the area.
In order to analyze the network performance gains in the concentrated traffic demand scenario due to the NetPlan algorithm, UE 3 is analyzed since this is the UE that benefits the most with the FMAPs' repositioning. \cref{NetplanAlgorithmEvaluation-Figure: Concentrated simulation results} presents the network performance results of UE 3 with and without the NetPlan algorithm. In order to analyze the network performance gains, the TCP flow is analyzed. As previously explained, when the NetPlan algorithm is not used, UE 2 and UE 3 are both associated to FMAP C. Hence, the capacity of FMAP C has to be shared among both UEs. However, when the NetPlan algorithm is used, FMAP A is repositioned closer to UE 3, so that this UE can associate to this FMAP. As a result, since both FMAPs now only have one UE, each UE can take advantage of the full FMAP channel capacity.
The analysis and comparison of the median values of the QoS metrics obtained with and without the NetPlan algorithm demonstrate that the theoretical expectations are valid. In fact, for the TCP flow the median throughput of UE 3 increased to $\approx$~2x when the TMFN was positioned according to the NetPlan algorithm, compared to the baseline of not using the NetPlan algorithm. Furthermore, the median delay reduced to $\approx$~0.4x when not using the NetPlan algorithm. The PLR was 0\% for both cases, since TCP guarantees reliable packet delivery.
Similar to the homogeneous traffic demand scenario, the UDP 25M flow does not demonstrate performance gains, since the channel still has capacity to transport the traffic being offered by the three UEs. In both cases, UE 3 achieves a throughput of $\approx$~\SI{25}{Mbit/s}, with a delay of $\approx$~\SI{0}{ms} and a PLR of $\approx$~0\%. Moreover, the downlink and uplink flows have similar results.
The UDP 75M traffic flow saturates the channel when the NetPlan algorithm was not used, but does not saturate when the NetPlan algorithm is used, since each UE was associated to a different FMAP. For the downlink flow (FMAP to UE), the median throughput increased to $\approx$~1.7x compared to the baseline of not using the NetPlan algorithm, the delay reduced from $\approx$~\SI{150}{ms} to $\approx$~\SI{0}{ms} and the PLR reduced from $\approx$~65\% to $\approx$~0\%. For the uplink flow (UE to FMAP), the median throughput increased to $\approx$~1.7x compared to the baseline of not using the NetPlan algorithm, the delay reduced from $\approx$~\SI{350}{ms} to $\approx$~\SI{0}{ms} and the PLR reduced from $\approx$~70\% to $\approx$~0\%. In order to control the delay of the UDP traffic flows, active queue management applied to the MAC queues could be used at the expense of an increased PLR.
Similar to the TCP flow, the performance gains are explained by the repositioning of FMAP A. Moreover, as analyzed in \cref{NetplanAlgorithmEvaluation-Section: Experimental channel model}, the channel is modeled by the Friis propagation loss model with a Rician fast-fading characterized by the Rician K-Factor, which is the ratio between the Rx power of the LoS component and the sum of the Rx power of the Non Line-of-Sight (NLoS) components. Since the downlink Rician K-factor (\SI{40}{dB}) is much higher than the uplink Rician K-factor (\SI{13}{dB}), the downlink channel benefits from better propagation conditions. In this sense, when the FMAP is transmitting to the UE, there is a higher probability of using higher physical data rates, thus improving the network performance.
\subsubsection{Experimental Results}
\begin{figure*}
\centering
\subfloat[Throughput CDF (without NetPlan).] {
\includegraphics[width=0.48\linewidth]{"Netplan-Algorithm-Experimental-Results/Concentrated/Throughput-CDF-Without-Netplan-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Traffic results concentrated throughput without NetPlan}
}
\hfill
\subfloat[Physical data rate histogram (without NetPlan).] {
\includegraphics[width=0.47\linewidth]{"Netplan-Algorithm-Experimental-Results/Concentrated/Data-Rate-Histogram-Without-Netplan-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Traffic results concentrated data rates without NetPlan}
}
\vfil
\subfloat[Throughput CDF (with NetPlan).] {
\includegraphics[width=0.48\linewidth]{"Netplan-Algorithm-Experimental-Results/Concentrated/Throughput-CDF-With-Netplan-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Traffic results concentrated throughput with NetPlan}
}
\hfill
\subfloat[Physical data rate histogram (with NetPlan).] {
\includegraphics[width=0.47\linewidth]{"Netplan-Algorithm-Experimental-Results/Concentrated/Data-Rate-Histogram-With-Netplan-UE3"}
\label{NetplanAlgorithmEvaluation-Figure: Traffic results concentrated data rates with NetPlan}
}
\caption{Experimental traffic results of FMAP C for the concentrated traffic demand scenario with and without the NetPlan algorithm. The results include the throughput CDFs and the histogram of the physical data rates of the packets generated by both the UE 3 (solid bar) and FMAP C (dotted bar) during the experiments.}
\label{NetplanAlgorithmEvaluation-Figure: Traffic results concentrated}
\end{figure*}
\begin{figure*}
\centering
\subfloat[UDP \SI{25}{Mbit/s} constant bitrate flow.] {
\includegraphics[width=0.47\linewidth]{"Netplan-Algorithm-Experimental-Results/Experimental-PLR/PLR-CDF-UDP-25M-FMAPC"}
}
\hfill
\subfloat[UDP \SI{75}{Mbit/s} constant bitrate flow.] {
\includegraphics[width=0.47\linewidth]{"Netplan-Algorithm-Experimental-Results/Experimental-PLR/PLR-CDF-UDP-75M-FMAPC"}
}
\caption{Packet Loss Ratio (PLR) CDF in FMAP C for different traffic demands, considering the homogeneous traffic demand and the concentrated traffic demand (with and without the NetPlan algorithm).}
\label{NetplanAlgorithmEvaluation-Figure: Experimental PLR}
\end{figure*}
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{"Netplan-Algorithm-Experimental-Results/Experimental-RTT/RTT-CDF-FMAPC"}
\caption{Round Trip Time (RTT) CDF in FMAP C considering the homogeneous traffic demand and the concentrated traffic demand (with and without the NetPlan algorithm).}
\label{NetplanAlgorithmEvaluation-Figure: Experimental RTT}
\end{figure}
In this scenario, two UEs were generating traffic in the same area. This scenario motivates the usage of the NetPlan algorithm, in order to position the FMAPs according to the traffic demand, in order to improve the network performance. When the NetPlan algorithm was not employed, the two UEs generating traffic in the same area were sharing the same Wi-Fi channel. This resulted in one of the FMAPs being overloaded with two UEs, whereas the second FMAP did not have any user associated. Hence, the UEs could not take full advantage of the aggregate network capacity provided by the two FMAPs, resulting in a degraded network performance. When the decisions of the NetPlan algorithm were considered, the FMAPs were positioned in order to meet the traffic demand of the UEs. In this case, each UE was able to take advantage of the full channel capacity provided.
In the concentrated traffic demand scenario without the NetPlan algorithm, two UEs inside area C (\cref{NetplanAlgorithmEvaluation-Figure: Concentrated traffic demand scenario without NetPlan}) were associated to FMAP C simultaneously. On the other hand, in the concentrated traffic demand scenario with the NetPlan algorithm (\cref{NetplanAlgorithmEvaluation-Figure: Concentrated traffic demand scenario with NetPlan}), a single UE was associated to FMAP C, since the other UE, previously associated to FMAP C, became client of FMAP A, which has been moved closer to area C, in order to enhance the network capacity and meet the traffic demand of the UEs inside this area. The performance results for both scenarios (with and without NetPlan) are depicted in \cref{NetplanAlgorithmEvaluation-Figure: Traffic results concentrated}.
The results with the NetPlan algorithm significantly outperform those when the NetPlan algorithm is not used. By comparing the 25th, 50th, and 75th percentiles of the throughput CDFs (\cref{NetplanAlgorithmEvaluation-Figure: Traffic results concentrated throughput without NetPlan,NetplanAlgorithmEvaluation-Figure: Traffic results concentrated throughput with NetPlan}), it can be concluded that the NetPlan algorithm allows a throughput improvement up to 1.84x, 1.63x, and 1.52x, respectively. Nevertheless, the link asymmetry is once again observed, which is justified by the same reasons pointed out in the homogeneous scenario. In \cref{NetplanAlgorithmEvaluation-Figure: Traffic results concentrated throughput without NetPlan}, the lower throughput values of some flows, including the UDP 75M flow between the UE and FMAP C, is justified by the simultaneous exchange of traffic in both directions, with both traffic flows competing to access the Wi-Fi medium.
Regarding the RTT, which is depicted in \cref{NetplanAlgorithmEvaluation-Figure: Experimental RTT}, the results for the concentrated traffic demand scenario denote the superior performance of the NetPlan algorithm (yellow diamond) compared to the case where the NetPlan is not employed (orange cross). This can be concluded by observing the 50th and 75th percentiles of the RTT CDFs, for which the RTT is 0.24x and 0.1x lower, respectively. The higher RTT when the NetPlan algorithm is not employed denotes packets being held longer in the transmission queue and packet retransmissions due to link congestion. The same behavior is observed for PLR, which is represented in \cref{NetplanAlgorithmEvaluation-Figure: Experimental PLR}, considering UDP flows with different bitrates, for which there is no packet loss. Overall, the network performance when the NetPlan algorithm is used in a concentrated area is similar to the one obtained for the baseline scenario, which considers homogeneous traffic demand in the different network areas; this is the main contribution of the proposed solution.
\section{RedeFINE Routing Solution} \label{RedeFINE-Section}
RedeFINE, which was initially proposed in~\cite{coelho2018redefine, coelho2019routing}, is presented in this section.
\subsection{Problem Formulation} \label{RedeFINE-Section: Problem Formulation}
In the following, we formulate the problem addressed by RedeFINE. At a time instant $t_k = k \cdot \Delta t, k \in N_0$ and $\Delta t \in \mathbb{R}$, which is defined according to the TMFN update period imposed by the NetPlan algorithm, the TMFN is represented by a graph $G(t_k)=(V, E(t_k), w(t_k))$, where $V=\{0, ..., N-1\}$ represents the set of UAVs forming the TMFN, $E(t_k) \subseteq V \times V$ represents the communications links, and $w(t_k)$ represents the cost assigned to the communications links of $G$. $(i,j)_{t_k} \in E(t_k)$ represents the directional communications link from\ $i$ to $j$ available at $t_k$, where $i,j \in V$, and $w_{i,j}(t_k)$ represents the cost of link $(i,j)_{t_k}$. $X_i(t_k)$ represents the position of UAV $i$ at time $t_k$ and depends on its initial position at instant $t_0$ and its associated velocity and acceleration vectors defined by the CS that controls the UAV positions.
The availability of the wireless links connecting the UAVs changes along the time. Hence, the directional wireless communications link $(i,j)_{t_k}$ exists if and only if the power $P_{R_i}(t_k)$ received by UAV $i$ at time $t_k$ divided by the noise power $N_i$ satisfies \cref{RedeFINE-Equation: SNR Threshold}, that is, if the Signal-to-Noise Ratio (SNR) is higher than a threshold $S$. The received power at UAV $i$, $P_{R_i}(t_k)$, results from the Free-space path loss model defined in \cref{RedeFINE-Equation: Friis propagation model}, where $P_{T_j}(t_k)$ describes the power transmitted by UAV $j$ at time $t_k$, $c$ represents the speed of light in vacuum, $f_{i,j}$ denotes the carrier frequency, and $d_{i,j}(t_k)$ expresses the Euclidean distance between UAV $i$ and UAV $j$ at time $t_k$.
\begin{equation}
\frac{P_{R_i}(t_k)}{N_i} > S
\label{RedeFINE-Equation: SNR Threshold}
\end{equation}
\begin{equation}
\frac{P_{R_i}(t_k)}{P_{T_j}(t_k)}= \left[ \frac{c}{4\pi \times d_{i,j}(t_k) \times f_{i,j}} \right]^2
\label{RedeFINE-Equation: Friis propagation model}
\end{equation}
We define a path as a set of adjacent links connecting UAV $i$ to the GW. Multiple paths may be available for UAV $i$ at time $t_k$, but only one of them is used. We also define $C_{i,j}(t_k)$ as the maximum capacity, in bit/s, of the communications link available between UAV $i$ and UAV $j$ at time $t_k$, considering a constant value for the link bandwidth $B_{i,j}$ in \SI{}{\hertz}; Shannon-Hartley theorem is used for this purpose, as given by~\cref{RedeFINE-Equation: Shannon-Hartley theorem}.
\begin{equation}
C_{i,j}(t_k) = B_{i,j} \times \log_{2} \left[ 1+\frac{P_{R_i}(t_k)}{N_i} \right]
\label{RedeFINE-Equation: Shannon-Hartley theorem}
\end{equation}
Considering the throughput $R_i(t_k)$, in bit/s, as the bitrate of the flow from UAV $i$ received at the GW at time $t_k$, and $N$ UAVs generating traffic towards the GW, we aim at maximizing at any time instant $t_k$ the amount of bits received by the GW during time interval $\Delta t$. As such, our objective function can be defined as:
\begin{equation}
\text{maximize} \qquad R(t_k) = \sum_{i=0}^{N-1}R_i(t_k)
\label{RedeFINE-Equation: Objective function}
\end{equation}
The factors influencing $R_i(t_k)$ include the capacity of the path used by UAV $i$, which should be limited by the link in the path having the smallest capacity, the number of flows traversing the links, medium access protocol behaviour, and interference between the communications nodes. This is a complex optimization problem since the last two factors are not easily characterized.
In order to solve this problem we will attempt to find a path for each UAV $i$ for each time instant $t_k$, so that we meet \cref{RedeFINE-Equation: Objective function}.
\subsection{Concept} \label{RedeFINE-Section: Concept}
RedeFINE was designed to take advantage of the centralized view of the TMFN available at the CS. By considering a) the future positions of the FMAPs composing the TMFN, which are defined by the NetPlan algorithm to fulfill the traffic demand of the UEs on the ground, and b) the velocity of the FMAPs following a straight line between source and destination, RedeFINE selects periodically the best path for each FMAP. We will define the best path as the path that has the smallest cost, according to metrics that will be discussed later on.
RedeFINE assumes a strong LoS component between the nodes, which is characteristic of the links between UAVs flying dozens of meters above the ground. To find the shortest path between UAVs, RedeFINE employs the Dijkstra's algorithm~\cite{walker1992implementing}.
\subsection{Analysis of a Reference Case} \label{RedeFINE-Section: Analysis of reference case}
\begin{figure}[t]
\centering
\includegraphics[width=1\linewidth]{"RedeFINE-Scenarios/Conceptual-Scenario"}
\caption{Scenario used for the theoretical validation of RedeFINE. For the initial position of FMAP 3, the wireless links between FMAP 3 and both FMAP 2 and GW are not available, due to the SNR threshold constraint.}
\label{RedeFINE-Figure: Conceptual Scenario}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=1\linewidth]{"RedeFINE-Concept/RedeFINE-Concept"}
\caption{Theoretical capacity values for the paths between FMAP 3 and the GW. In order to reach the GW, FMAP 3 uses as relay nodes FMAP 1 until $t=\SI{60}{\second}$ and FMAP 2 from $t=\SI{60}{\second}$ to $t=\SI{130}{\second}$. The path with the highest capacity at each instant is highlighted by the circle symbol.}
\label{RedeFINE-Figure: RedeFINE concept}
\end{figure}
In order to demonstrate the RedeFINE concept and perform a preliminary evaluation, a theoretical validation is made herein. For the sake of simplicity, we consider the scenario depicted in~\cref{RedeFINE-Figure: Conceptual Scenario}. It is formed by: 1) a static GW; 2) two static relay FMAPs (FMAP 1 and FMAP 2); and 3) a moving FMAP (FMAP 3). This scenario aims at illustrating a TMFN reconfiguration that causes link disruptions. In particular, FMAP 3 follows a straight line at \SI{0.5}{m/s} in the direction from FMAP 1 to FMAP 2, in order to reach the new location defined by the NetPlan algorithm. FMAP 1 and FMAP 2 remain in the same positions and they are able to forward the traffic received from FMAP 3 towards the GW, while simultaneously providing connectivity to users on the ground.
The initial position of FMAP $i$ is represented by $X_i(0)$ and the constant velocity is denoted by $v_i$. The initial cost of the wireless link between FMAP $i$ and FMAP $j$ is represented by $w_{i,j}(0)$, which for demonstration purposes is the linear Euclidean distance between their initial positions. The wireless link availability is restricted by a \SI{5}{dB} SNR, that is $S \approx 3.16$ threshold (cf.~\cref{RedeFINE-Equation: SNR Threshold}). The SNR is derived from the Free-space path loss model (cf.~\cref{RedeFINE-Equation: Friis propagation model}). We assume that the maximum capacity for the wireless links is given by the Shannon-Hartley theorem (cf.~\cref{RedeFINE-Equation: Shannon-Hartley theorem}). The maximum capacity of a wireless link is computed considering an average noise power equal to \SI{-85}{dBm}.
In turn, the capacity of a path is restricted by the link with lower capacity among the set of links forming the path. Additionally, we consider the transmission power equal to \SI{0}{dBm}, the carrier frequency equal to \SI{5250}{MHz}, and the channel bandwidth equal to \SI{160}{MHz}, which are values compatible with the IEEE 802.11ac standard.
Based on these assumptions, the theoretical maximum capacity values for the paths between FMAP 3 and the GW are plotted in \cref{RedeFINE-Figure: RedeFINE concept}.
With RedeFINE, in order to reach the GW, FMAP 3 uses as relay nodes FMAP 1 until $t=\SI{60}{\second}$ and FMAP 2 from $t=\SI{60}{\second}$ to $t=\SI{130}{\second}$. These are the highest-capacity paths, which are highlighted by the circle symbol in \cref{RedeFINE-Figure: RedeFINE concept}.
Considering as baseline the static routing configuration that uses FMAP 1 as relay node for the communications between FMAP 3 and the GW during \SI{130}{s}, RedeFINE allows a gain of $\approx$~20\% regarding the total amount of bits received in the GW. The areas under the curves in \cref{RedeFINE-Figure: RedeFINE concept} give the total amount of bits carried by the respective path. We compute the amount of information received on each case (static and RedeFINE) as $\sum_{k=0}^{130}R_0(t_k)\times\Delta t$, considering $\Delta t=\SI{1}{\second}$. In this analysis, FMAP $1$ and FMAP $2$ do not generate traffic. They only forward traffic received from FMAP $0$.
\subsection{Interference Model} \label{RedeFINE-Section: Interference model}
Taking into account the IEEE 802.11 MAC protocol, for a packet transmission to be successful neither the transmitter nor the receiver should be interfered by other nodes. Hence, the transmissions on links $(i, j)_{t_k}$ and $(k, l)_{t_k}$ are both successful at $t_k$ if and only if both $i$ and $j$ are outside the interference range of $k$ and $l$ at $t_k$. This is expressed by the Transmitter-Receiver Conflict Avoidance (TRCA) interference model~\cite{houaidia2017inter}.
In order to demonstrate how the selection of relay nodes affects the network performance, let us analyze a reference case. For the sake of simplicity, we consider the scenario depicted in~\cref{RedeFINE-Figure: Interference model}. It is formed by: 1) two FMAPs generating traffic -- FMAP 1 and FMAP 4; 2) a GW; and 3) six FMAPs able to forward traffic. The interference range of each node is represented by a dashed circumference around that node.
Firstly, we consider two paths for the flows between the FMAPs generating traffic and the GW: $p_1$:$<$FMAP 1, FMAP 2, FMAP 3, GW$>$ and $p_2$:$<$FMAP 4, FMAP 5, FMAP 6, FMAP 8, GW$>$. For these paths, there is no inter-flow interference, excluding the nodes competing for the access to the GW, which is addressed by the MAC protocol. Hence, the throughput achieved by each flow is only limited by the link with the lowest capacity among the ones forming the path. Conversely, if FMAP 8 is chosen to be part of a path $p_1'$:$<$FMAP 1, FMAP 2, FMAP 8, GW$>$, then inter-flow interference will be introduced in the network. For instance, since FMAP 8 is in the interference range of FMAP 6, the links $<$FMAP 2, FMAP 8$>$ and $<$FMAP 5, FMAP 6$>$ become mutually interfered. Therefore, the network performance is reduced up to 50\%, when compared with the previous routing configuration.
This reference case motivates the definition of an inter-flow interference-aware routing approach to improve the performance of RedeFINE. In fact, by using the Euclidean distance as routing metric in the reference scenario depicted in~\cref{RedeFINE-Figure: Interference model}, it becomes indifferent selecting FMAP 7, or FMAP 2 and FMAP 6, respectively, to forward the traffic from FMAP 1 and FMAP 5, since the minimal Euclidean distance is equal for both in this reference case.
\begin{figure}
\centering
\includegraphics[width=0.70\linewidth]{"RedeFINE-Scenarios/Interference-Model"}
\caption{Network graph illustrating the TRCA interference model. If FMAP 8 is used as relay node, the network performance will be reduced up to 50\%, since FMAP 8 is in the interference range of FMAP 2 and FMAP 6.}
\label{RedeFINE-Figure: Interference model}
\end{figure}
\subsection{I2R Routing Metric} \label{RedeFINE-Section: I2R concept}
Motivated by the problem presented in~\cref{RedeFINE-Section: Interference model}, an inter-flow interference-aware routing metric tailored for centralized routing in TMFNs with controllable topology, named I2R, was incorporated into RedeFINE.
I2R consists of two factors: the distance-aware factor and the inter-flow interference-aware factor. Both factors are fed by the centralized view of the TMFN provided by the CS running the NetPlan algorithm, which defines the future locations of the FMAPs that will serve the mobile UEs on the ground. Since a strong LoS component characterizes the wireless links between the UAVs flying dozens of meters above the ground, we use Free-space path loss to model the links between the FMAPs, and estimate the SNR and number of neighboring FMAPs. This holistic knowledge avoids the usage of control packets for neighbor discovery and interference estimation. The distance-aware factor is based on the Euclidean distance of the links between each pair of FMAPs, at time instant $t_k$, which is denoted by $d_{i,j}(t_k)$. As such, this factor includes the sum of the Euclidean distances of the set of links forming a path $p$, considering in advance the future trajectories that FMAPs will follow, which were calculated and pre-defined by the CS to fulfill the traffic demand of the ground users. Using the Euclidean distance as part of the routing metric is compliant with the objective of selecting high-capacity paths, since the link capacity increases as the Euclidean distance decreases, according to the Shannon-Hartley theorem. $d_{i,j} (t_k)$ is normalized to the maximum Euclidean distance among all the usable links of the TMFN, at $t_k$. In turn, the inter-flow interference aware factor is a value $\gamma(t_k)$ that is added to the Euclidean distance of the link between FMAP $i$ and FMAP $j$, at $t_k$. $\gamma_j(t_k)$ represents the number of neighboring nodes of FMAP $j$, excluding FMAP $i$, at $t_k$. We assume as neighboring nodes the FMAPs in carrier-sense range that are generating or forwarding traffic. $\gamma_j(t_k)$ considers that the level of interference is equal either the neighboring nodes are close or far away, as the TRCA model denotes. $\gamma_j(t_k)$ is normalized to the maximum number of neighbors that any FMAP composing the TMFN has at $t_k$.
The path cost using I2R is defined in \cref{RedeFINE-Equation: Routing metric}, where $0 \leq \alpha \leq 1$ is a tunable parameter that weights the influence of the distance-aware and interference-aware factors. To calculate the path between any FMAP and the GW, the Dijkstra's algorithm~\cite{walker1992implementing} is used. Considering the reference case depicted in~\cref{RedeFINE-Figure: Interference model}, I2R uses the factor $\gamma$ to increase the cost of the links $<$FMAP 2, FMAP 8$>$ and $<$FMAP 6, FMAP 8$>$, since FMAP 8 is in the interference range of FMAP 2 and FMAP 6.
\begin{equation}
I2R = (1-\alpha)\times\sum_{\forall (i,j) \in p}d_{i,j}(t_k) + \alpha \times \sum_{\forall j \in p} \gamma_{j}(t_k)
\label{RedeFINE-Equation: Routing metric}
\end{equation}
\section{RedeFINE Evaluation} \label{RedeFINEEvaluation-Section}
The performance evaluation of RedeFINE is presented in this section, including the simulation setup, the simulation scenarios, and the performance metrics considered.
\subsection{Simulation Setup} \label{RedeFINEEvaluation-Section: Simulation setup}
The ns-3 simulator was used to evaluate RedeFINE in complex networking scenarios formed by a TMFN composed of 1 GW and 20 FMAPs. In each node, a Network Interface Card (NIC) was configured in Ad Hoc mode, using the IEEE 802.11ac standard in channel 50, which allows \SI{160}{\mega\hertz} channel bandwidth. The data rate was defined by the \emph{IdealWifiManager} mechanism. The wireless links were modeled by the Free-space path loss model; only links with SNR above \SI{5}{\deci\bel} were considered as usable. The transmission power of the NICs was set to \SI{0}{dBm}.
One IEEE 802.11ac spatial stream was used for the wireless links. With one spatial stream, the data corresponding to the maximum Modulation and Coding Scheme (MCS) index is \SI{780}{Mbit/s}, considering \SI{800}{\nano\second} Guard Interval. Taking into account the dimensions of the simulated scenarios, we assume an average number of 2 hops between the FMAPs generating traffic and the GW, in order to calculate the maximum achievable data rate per flow; this results in $(\frac{780}{N_{tx}} / 2) \SI{}{Mbit/s}$, where $N_{tx}$ denotes the number of FMAPs generating traffic. Based on that, the maximum offered load for each scenario was set to 75\% of the maximum achievable data rate per flow, for a total number of FMAPs generating traffic between 5 and 10. The traffic generated was UDP with arrival process modeled as Poisson, for a constant packet size of 1400 bytes; the traffic generation was only triggered after \SI{30}{\second} of simulation, in order to stabilize the OLSR routing tables. In addition, different values for the tunable parameter $\alpha$, between 0.2 and 1, were considered.
A summary of the ns-3.27 simulation parameters used is presented in \cref{RedeFINEEvaluation-Table: ns-3 simulation parameters}.
\begin{table}
\centering
\caption{Summary of the ns-3.27 simulation parameters.}
\label{RedeFINEEvaluation-Table: ns-3 simulation parameters}
\begin{tabular}{l l}
\hline
Simulation time & (\SI{30}{\second} init. +) \SI{130}{\second} \\
Wi-Fi standard & IEEE 802.11ac \\
Wi-Fi mode & Ad Hoc \\
Wi-Fi Channel & 50 [\SI{5250}{\mega\hertz}] \\
Channel bandwidth & \SI{160}{\mega\hertz} \\
Guard interval & \SI{800}{\nano\second} \\
Tx power & \SI{0}{dBm} \\
Propagation delay & Constant speed \\
Propagation loss & Friis \\
Remote station manager & IdealWifiManager \\
Mobility model & Waypoint \\
Traffic type & UDP Poisson \\
Packet size & 1400 Bytes \\
Traffic control & CoDel \\
\hline
\end{tabular}
\end{table}
\subsection{Simulation Scenarios} \label{RedeFINEEvaluation-Section: Simulation scenarios}
Five scenarios, in which the UAVs were moving according to the Random Waypoint Mobility (RWM) model, were generated to evaluate the performance of RedeFINE in typical crowded events. Under the RWM model, each UAV chooses a random destination and a speed uniformly distributed between a minimum and a maximum value. Then, the UAV moves to the chosen destination at the selected speed; upon arrival, the UAV stops for a specified period of time and repeats the process for a new destination and speed~\cite{camp2002survey}.
Since RedeFINE relies on knowing in advance the movements of the UAVs, instead of generating the random movements during the ns-3 simulation, we used BonnMotion~\cite{aschenbruck2010bonnmotion}, which is a mobility scenario generation tool. BonnMotion was set to create random waypoint 3D movements for 21 nodes (20 FMAPs and 1 GW) within a box of dimensions \SI{80}{\meter} $\times$ \SI{80}{\meter} $\times$ \SI{25}{\meter} during \SI{160}{\second}, considering a velocity between \SI{0.5}{m/s} and \SI{3}{m/s} for the UAVs. These scenarios were used to calculate in advance the forwarding tables and the instants they shall be updated. Both the forwarding tables and the generated scenarios were finally imported to ns-3 with a sampling period of \SI{1}{\second}. To apply mobility to the UAVs, based on the generated scenarios, the \emph{WaypointMobilityModel} model of ns-3 was used.
\subsection{Performance Metrics} \label{RedeFINEEvaluation-Section: Performance metrics}
RedeFINE using the Euclidean distance, Airtime, and I2R routing metrics was evaluated against two state of the art distributed routing protocols representative of the reactive and proactive routing paradigms -- AODV~\cite{aodv-etx-repository} and OLSR~\cite{olsr-etx-repository}, respectively, using the ETX routing metric. ETX is a link quality-based routing metric that represents the expected number of transmissions required to send a packet over a link, including retransmissions. Airtime, which is the default routing metric specified in the IEEE 802.11s standard~\cite{hiertz2010ieee}, expresses the amount of channel resources consumed for transmitting a frame over a link. Since the theoretical calculation of the Airtime resulting costs is not straightforward, we exported them from ns-3, by running previous simulations for each one of the generated scenarios. Afterwards, we employed the Dijkstra's algorithm to find the shortest paths between each FMAP and the GW, considering a sampling period of \SI{1}{\second} and the corresponding routing metric. The Airtime routing metric was used in our evaluation to ensure that I2R is able to outperform a metric that uses real measurements to estimate data rate, overhead, and frame error ratio of the communications links.
Our performance evaluation considers two metrics:
\begin{itemize}
\item Aggregate throughput: The mean number of bits received per second by the GW.
\item End-to-end delay: The mean time taken by the packets to reach the application layer of the GW since the instant they were generated at a given FMAP, measured at each second, including queuing, transmission, and propagation delays.
\end{itemize}
\subsection{Simulation Results} \label{RedeFINEEvaluation-Section: Simulation results}
\begin{figure}
\centering
\subfloat[End-to-end delay Cumulative Distribution Function (CDF).]{
\includegraphics[width=1\linewidth]{"RedeFINE-Simulation-Results/Delay-CDF-5-TX-Nodes"}
\label{RedeFINEEvaluation-Figure: Delay CDF 5 TX nodes}
}
\hfill
\subfloat[Throughput Complementary Cumulative Distribution Function (CCDF).]{
\includegraphics[width=1\linewidth]{"RedeFINE-Simulation-Results/Throughput-CCDF-5-TX-Nodes"}
\label{RedeFINEEvaluation-Figure: Throughput CCDF 5 TX nodes}
}
\hfill
\subfloat[The 25th, 50th, and 75th percentiles of both the throughput CCDF and end-to-end delay CDF.]{
\includegraphics[width=1\linewidth]{"RedeFINE-Simulation-Results/Throughput-vs-Delay-5-TX-Nodes"}
\label{RedeFINEEvaluation-Figure: Throughput vs. Delay 5 TX nodes}
}
\caption{Results for throughput and end-to-end delay in the GW. The results were obtained considering 5 FMAPs generating traffic, and $\alpha=1$.}
\label{RedeFINEEvaluation-Figure: Results 5 TX nodes}
\end{figure}
\begin{figure}
\centering
\subfloat[End-to-end delay Cumulative Distribution Function (CDF).]{
\includegraphics[width=1\linewidth]{"RedeFINE-Simulation-Results/Delay-CDF-10-TX-Nodes"}
\label{RedeFINEEvaluation-Figure: Delay CDF 10 TX nodes}
}
\hfill
\subfloat[Throughput Complementary Cumulative Distribution Function (CCDF).]{
\includegraphics[width=1\linewidth]{"RedeFINE-Simulation-Results/Throughput-CCDF-10-TX-Nodes"}
\label{RedeFINEEvaluation-Figure: Throughput CCDF 10 TX nodes}
}
\hfill
\subfloat[The 25th, 50th, and 75th percentiles of both the throughput CCDF and end-to-end delay CDF.]{
\includegraphics[width=1\linewidth]{"RedeFINE-Simulation-Results/Throughput-vs-Delay-10-TX-Nodes"}
\label{RedeFINEEvaluation-Figure: Throughput vs. Delay 10 TX nodes}
}
\caption{Results for throughput and end-to-end delay in the GW. The results were obtained considering 10 FMAPs generating traffic, and $\alpha=1$.}
\label{RedeFINE-Figure: Results 10 TX nodes}
\end{figure}
The results were obtained after 20 simulation runs, using using $RngSeed = 10$ and $RngRun = \{1, ..., 20\}$, for each experimental combination, including different I2R's $\alpha$ values and different number of FMAPs generating traffic. The results are expressed using mean values, considering five random scenarios, as stated in~\cref{RedeFINEEvaluation-Section: Simulation scenarios}. They are represented by means of the CDF for the end-to-end delay and by the complementary CDF (CCDF) for the aggregate throughput, including the values for the 25th, 50th, and 75th percentiles. The CDF $F(x)$ represents the percentage of simulation time for which the mean end-to-end delay was lower than or equal to to $x$, while the CCDF $F'(x)$ represents the percentage of simulation for which the mean aggregate throughput was higher than $x$.
Finally, the influence of the tunable parameter $\alpha$ on the TMFN performance is also evaluated.
When 5 FMAPs are used as traffic sources (cf.~\cref{RedeFINEEvaluation-Figure: Results 5 TX nodes}), the usage of the I2R routing metric improves the end-to-end delay achieved by RedeFINE using the Euclidean distance in approximately 22\%, OLSR and AODV using ETX in 21\% and 15\%, respectively, and RedeFINE using Airtime in 10\%. These values are obtained considering the mean end-to-end delay of the packets received in the GW for the different solutions. The outperforming results of RedeFINE using the I2R routing metric are justified by the selection of paths formed by FMAPs with reduced number of neighbors that are generating or forwarding traffic. Regarding the total amount of bits received in the GW, RedeFINE using the I2R routing metric provides a gain up to 7\% when compared with RedeFINE using the Euclidean distance. In turn, when compared with AODV and OLSR using the ETX routing metric, and with RedeFINE using Airtime, the gains are even more relevant: approximately 45\%, 17\%, and 28\%, respectively.
When 10 FMAPs are generating traffic (cf.~\cref{RedeFINE-Figure: Results 10 TX nodes}), RedeFINE using the I2R routing metric improves end-to-end delay in approximately 10\% with respect to RedeFINE using the Euclidean distance, while the gain over AODV and OLSR using ETX is approximately 18\% and 13\%, respectively. The gain in end-to-end delay of I2R over the Airtime routing metric applied to RedeFINE is negligible.
Regarding the total amount of bits received in the GW, the gain of RedeFINE using I2R over OLSR using ETX is still approximately 18\%, and over RedeFINE using the Euclidean distance is negligible ($\approx$~4\%). Conversely, the gain over AODV using ETX is increased to approximately 68\%, while with respect to RedeFINE using Airtime it is approximately 31\%.
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{"RedeFINE-Simulation-Results/Throughput-vs-Delay-Multiple-Alpha"}
\caption{The 25th, 50th, and 75th percentiles of both the throughput CCDF and delay CDF, considering different I2R's $\alpha$ values. The results consider 5 FMAPs generating traffic.}
\label{RedeFINEEvaluation-Figure: Throughput vs. Delay Multiple Alpha}
\end{figure}
The relation between aggregate throughput and end-to-end delay for the different combinations of protocols and routing metrics is depicted in~\cref{RedeFINEEvaluation-Figure: Throughput vs. Delay 5 TX nodes} and~\cref{RedeFINEEvaluation-Figure: Throughput vs. Delay 10 TX nodes}, where the 25th, 50th, and 75th percentiles of both the throughput CCDF and delay CDF are represented. Overall, the gains in end-to-end delay and throughput of RedeFINE using I2R are reduced when the number of transmission FMAPs increases.
The performance evaluation carried out allowed to conclude that I2R selects preferably as relay nodes the FMAPs that are also sources of traffic; for instance, in a scenario where 5 FMAPs are generating traffic, if any of these FMAPs need a relay to reach the GW, then I2R will give preference to any of the remaining 4 FMAPs that are generating traffic, thus avoiding that a sixth FMAP introduces interference in the TMFN. This effect is faded when the number of FMAPs in the TMFN increases.
Regarding the tunable parameter $\alpha$ of I2R, it must be set to a value close to 1 for higher throughput and lower end-to-end delay values. As $\alpha$ decreases, the performance worsens, as exacerbated by $\alpha=0.2$, in~\cref{RedeFINEEvaluation-Figure: Throughput vs. Delay Multiple Alpha}. This demonstrates how the selection of paths formed by the minimum number of neighboring FMAPs in carrier-sense range contributes to improve the performance of a TMFN, rather than the selection based only on the Euclidean distance.
\section{Traffic-Aware GW Placement Algorithm} \label{GWPAlgorithm-Section}
Even though users are directly affected by the QoS and QoE provided by the access network, the backhaul network, including the GW placement, needs to be carefully designed in order to meet the variable traffic demand of the access network. In this section, a centralized traffic-aware GW Placement (GWP) algorithm for the TMFN, which takes advantage of the knowledge of the placement of the FMAPs and offered traffic to enable communications paths with high enough capacity is presented.
\subsection{Problem Formulation} \label{GWPAlgorithm-Section: Problem formulation}
In the following, the problem addressed in this section is formulated. At time $t_k = k \cdot \Delta t, k \in N_0$ and $\Delta t \in \mathbb{R}$, which is defined according to the TMFN update period imposed by the NetPlan algorithm, the TMFN is represented by a directed graph $G(t_k)=(V, E(t_k))$, where $V=\{0, ..., N-1\}$ is the set of UAVs $i$ positioned at $P_i=(x_i, y_i, z_i)$ inside a cuboid $ X \times Y \times Z$, $E(t_k) \subseteq V \times V $ is the set of directional links between UAVs $i$ and $j$ at $t_k$, $i, j \in V$, and $(i,j)\in E(t_k)$. The wireless channel between two UAVs is modeled by the Free-space path loss model, since a strong LoS component dominates the links between UAVs flying dozens of meters above the ground.
Let us assume that $\textrm{UAV}_i$, $i\in \{1, ..., N-1\}$, performs the role of FMAP and transmits or forwards from other FMAP a traffic flow of bitrate $T_i(t_k)$~\si{bit/s} during time slot $t_k$ towards $\textrm{UAV}_0$ that performs the role of GW. In this case, we have a tree $T(V, E_T)$ that is a subgraph of $G$, where $E_T \subset E$ is the set of direct links between $\textrm{UAV}_i$ and $\textrm{UAV}_0$. This sub-tree defines the TMFN active topology. The flow $F_{0,i}$ is received at $\textrm{UAV}_0$ from $\textrm{UAV}_i$ with bitrate $R_i(t_k)$ bit/s. The wireless medium is shared and we assume that every $\textrm{UAV}_i$ is in the same collision domain, including $\textrm{UAV}_0$. The Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) mechanism is employed for Medium Access Control (MAC), which enables transmissions only when the channel is sensed to be idle, in order to avoid collisions of network packets.
Considering the throughput $R_i(t_k)$ as the bitrate of the flow $F_{0,i}$ at time $t_k$, and $N-1$ FMAPs generating or forwarding traffic towards $\textrm{UAV}_0$, we aim at determining at any time instant $t_k$ the position of $\textrm{UAV}_0$, $P_0 = (x_0, y_0, z_0)$, and the transmission power $P_T$ of the UAVs, such that the aggregate throughput, $R(t_k) = \sum_{i=1}^{N-1} R_i(t_k)$ is maximized. Our objective function is defined in \cref{GWPAlgorithm-Equation: Objective funtion}.
\begin{equation} \label{GWPAlgorithm-Equation: Objective funtion}
\begin{aligned}
& \underset{P_T, (x_0, y_0, z_0)}{\textrm{maximize}} && R(t_k)=\sum_{i=1}^{N-1}R_i(t_k) \\
& \textrm{subject to:} \\
& && \hspace{-4em} (0, i), (i, 0) \in E(t_k), & \hspace{-2em} i \in \{1, ..., N-1\} \\
& && \hspace{-4em} T_i(t_k) > 0, & \hspace{-2em} i \in \{1,...,N-1\} \\
& && \hspace{-4em} R_i(t_k) \leq T_i(t_k), & \hspace{-2em} i \in \{1,...,N-1\} \\
& && \hspace{-4em} 0 \leq x_i \leq X, & \hspace{-2em} i \in \{0,...,N-1\} \\
& && \hspace{-4em} 0 \leq y_i \leq Y, & \hspace{-2em} i \in \{0,...,N-1\} \\
& && \hspace{-4em} 0 \leq z_i \leq Z, & \hspace{-2em} i \in \{0,...,N-1\} \\
& && \hspace{-4em} (x_0, y_0, z_0) \neq (x_i, y_i, z_i), & \hspace{-2em} i \in\{1,...,N-1\}
\end{aligned}
\end{equation}
\subsection{Rationale} \label{GWPAlgorithm-Section: Rationale}
The GWP algorithm takes advantage of the centralized view of the TMFN provided by the NetPlan algorithm. For the sake of simplicity we omit $t_k$ thereafter. Considering the future positions of $\textrm{UAV}_i$ and the bitrate of the traffic flow $F_{0,i}$, $T_i$, we aim at guaranteeing that the wireless link between $\textrm{UAV}_i$ and $\textrm{UAV}_0$ (GW) has a minimum SNR, $SNR_i$, which enables the usage of a MCS index, $\textrm{MCS}_i$, capable of transmitting $T_i$~\SI{}{bit/s}. Conceptually, if $\textrm{MCS}_i$ is ensured by the network, then $R_i \approx T_i$ and $R_i$ is maximized; this is according to the objective function defined in~\cref{GWPAlgorithm-Equation: Objective funtion}.
The minimum $SNR_i$ required for using $\textrm{MCS}_i$ imposes a minimum received power $P_{R_0,i}$. Then, if the transmission power $P_{T_i}$ is known, we can calculate the maximum distance $d_{\max_i}$ between $\textrm{UAV}_i$ and $\textrm{UAV}_0$, using the Free-space path loss model defined in~\cref{GWPAlgorithm-Equation: Free-space Path Loss Model}.
\begin{equation}
\frac{P_{R_{0,i}}}{P_{T_i}}=\left( \frac{c}{4\pi \times d_{\max_i} \times f_i} \right) ^2
\label{GWPAlgorithm-Equation: Free-space Path Loss Model}
\end{equation}
In the three-Dimensional (3D) space, $d_{\max_i}$ corresponds to the radius of a sphere, centered at $\textrm{UAV}_i$, inside which $\textrm{UAV}_0$ should be placed. Considering $N-1$ UAVs, the placement subspace for positioning $\textrm{UAV}_0$ is defined by the intersection of the corresponding spheres $i \in \{1, ..., N-1\}$; we refer to this subspace as the Gateway Placement Subspace, $S_G$. In order to simplify the process of calculating $S_G$, we follow Algorithm~A, which iteratively allows obtaining the point $P_0 = (x_0, y_0, z_0)$ for positioning $\textrm{UAV}_0$ and the transmission power $P_T$ which we assume to be the same for all UAVs.
\begin{algorithm}[t]\label{GWPAlgorithm-Algorithm: GWP Algorithm}
\renewcommand{\thealgorithm}{A}
\caption{-- GWP Algorithm}
\begin{algorithmic}[1]
\State $P_T = 0$ \Comment{\SI{0}{dBm} Tx power}
\While {true}
\State $P_{T_i} = P_T, i\in \{1, ..., N-1\}$ \Comment{Same UAVs' Tx power}
\State Calculate $(x_0, y_0, z_0)$ \Comment{System of equations~\cref{GWPAlgorithm-SystemOfEquations: Gateway Placement Subspace}}
\If{$(x_0, y_0, z_0) \neq \oslash$} \Comment{i.e., $(x_0, y_0, z_0) \in S_G$}
\State \textbf{return} $P_T, (x_0, y_0, z_0)$ \Comment{Tx power, GW pos.}
\Else
\State $P_T = P_T + 1$ \Comment{Increase Tx power by \SI{1}{dBm}}
\EndIf
\EndWhile
\end{algorithmic}
\end{algorithm}
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{"GWP-Algorithm/Gateway-Placement-Subspace"}
\caption{Gateway Placement Subspace ($S_G$) in a two-Dimensional (2D) space, which results from the intersection of the circumferences, centered at each FMAP, with radius equal to the maximum distance compliant with a minimum wireless link's SNR.}
\label{GWPAlgorithm-Figure: Gateway Placement Subspace}
\end{figure}
The GWP algorithm provides the same output whether downlink or uplink traffic is considered, since all the nodes are configured with the same transmission power and the wireless channel is assumed to be symmetric.
\subsection{Numerical Analysis} \label{GWPAlgorithm-Section: Numerical Analysis}
Without loss of generality, we now exemplify the execution of Algorithm A for the simple scenario shown in \cref{GWPAlgorithm-Figure: Gateway Placement Subspace}; the algorithm is generic and may be applied to any traffic demand and number of FMAPs. The scenario of \cref{GWPAlgorithm-Figure: Gateway Placement Subspace} is composed of 4 FMAPs that are placed within a square of \SI{30}{\meter} sideways, hovering at \SI{10}{\meter} altitude. The capacity of the shared wireless medium is assumed to be equal to the maximum MCS index of the IEEE 802.11ac technology, which is \SI{780}{Mbit/s}, considering one spatial stream, \SI{800}{\nano \second} Guard Interval (GI), and \SI{160}{\mega\hertz} channel bandwidth (channel 50 at \SI{5250}{\mega\hertz}). Since the wireless medium is shared by four FMAPs generating traffic, and assuming a single hop between the FMAPs and the GW ($\textrm{UAV}_0$), this results in a fair share $L = \frac{780}{4} = \SI{195}{Mbit/s}$ for the capacity of the wireless channel between each $\textrm{FMAP}_i, i \in \{1, 2, 3, 4\}$, and the GW. In the scenario of \cref{GWPAlgorithm-Figure: Gateway Placement Subspace}, the FMAPs on the left-side have traffic demand equal to 25\% of the FMAPs' fair share of the wireless channel capacity, and the righ-side FMAPs have traffic demand equal to 75\% of the FMAPs' fair share of the wireless channel capacity. Accordingly, the FMAPs on the left-side transmit at bitrate $T_1 = T_2 = 0.25 \times 195 \approx \SI{49}{Mbit/s}$, and the right-side FMAPs transmit at bitrate $T_3 = T_4 = 0.75 \times 195 \approx \SI{146}{Mbit/s}$.
Taking into account the mapping between SNR, theoretical data rate of the IEEE 802.11ac MCS indexes, and the link capacity for 4 FMAPs sharing the transmission time, from \cref{GWPAlgorithm-Table: Mapping Between SNR Data Rate and Link Capacity} we conclude that the target SNR values in \si{\decibel}, considering a \SI{-85}{dBm} noise floor power, are respectively \SI{20}{\deci\bel} for the left-side FMAPs and \SI{35}{\deci\bel} for the right-side FMAPs. Note that the rationale to calculate the capacity of each individual link, which is presented in the third column of \cref{GWPAlgorithm-Table: Mapping Between SNR Data Rate and Link Capacity}, results from the fact that the average transmission time assigned to each FMAP, as a result of the MAC protocol, is quarter of the transmission time available in the shared wireless channel. For two FMAPs with traffic demand equal to $0.25 \times 195 \approx \SI{49}{Mbit/s}$ and two FMAPs with traffic demand equal to $0.25 \times 195 \approx \SI{146}{Mbit/s}$, this results in $\SI{390}{Mbit/s}$ as the aggregate throughput. Since the shared channel provides $2 \times \SI{78}{Mbit/s}$ $+$ $2 \times \SI{176}{Mbit/s} = \SI{468}{Mbit/s}$ as the maximum capacity, the channel will be occupied during $\frac{390}{468} \approx 0.83$ of the available transmission time.
\begin{table}
\centering
\caption{Extract of the mapping between SNR, data rate of the IEEE 802.11ac MCS indexes, and the link capacity values for 4 FMAPs sharing the transmission time~\cite{MCSIndex14:online}.}
\label{GWPAlgorithm-Table: Mapping Between SNR Data Rate and Link Capacity}
\begin{tabular}{l l l}
\hline
SNR & MCS data rate & Link capacity \\
(\si{dB}) & (\si{Mbit/s}) & (\si{Mbit/s}) \\
\hline
12 & 58.5 & $58.5 / 4 \approx 15 $ \\
\circled{20} & 234 & 58.5 \\
\mymk{35} & 702 & 175.5 \\
37 & 780 & 195 \\
\hline
\end{tabular}
\end{table}
\begin{equation} \label{GWPAlgorithm-SystemOfEquations: Gateway Placement Subspace}
\begin{cases}
\begin{aligned}
& (x_0-30)^2+y_0^2+(z_0-10)^2 \leq 10^{\left(\dfrac{K+P_T-\mymk{35}}{20} \right)^2} \\
& (x_0-30)^2+(y_0-30)^2 \\
& \qquad + (z_0-10)^2 \leq 10^{\left(\dfrac{K+P_T-\mymk{35}}{20} \right)^2} \\
& x_0^2+(y_0-30)^2 + (z_0-10)^2 \leq 10^{\left(\dfrac{K+P_T-\circled{20}}{20} \right)^2} \\
& x_0^2+y_0^2+(z_0-10)^2 \leq 10^{\left(\dfrac{K+P_T-\circled{20}}{20}\right)^2} \\
& K = -20 \times \log_{10}\left(\frac{4\pi}{3\times10^8}\right)\\
& \qquad -20 \times \log_{10}(5250\times10^6) - (-85)\\
\end{aligned}
\end{cases}
\end{equation}
Solving the system of equations \cref{GWPAlgorithm-SystemOfEquations: Gateway Placement Subspace}, which is derived from \cref{GWPAlgorithm-Equation: Free-space Path Loss Model} in logarithmic scale, we conclude that an optimal placement for the GW is $(x_0,y_0,z_0) \approx (23.3, 15.4, 3.3)$ for a transmission power $P_{T} = $ \SI{22}{dBm}. Note that $P_T$ is the fine tuning parameter in the system of equations \cref{GWPAlgorithm-SystemOfEquations: Gateway Placement Subspace}, so that we can find at least a point $(x_0, y_0, z_0) \in S_G$; otherwise, we may have a system of equations without solution. $P_T$ is initially set to \SI{0}{dBm}; then, it is iteratively increased by \SI{1}{dBm} until a valid solution for the GW position is found. In \cref{GWPAlgorithm-SystemOfEquations: Gateway Placement Subspace}, the carrier frequency $f$ being used is considered: \SI{5250}{\mega\hertz} in this article; however, our conclusions are independent of $f$.
In the GWP algorithm we assume that the overhead introduced by the UDP, IP, and MAC packet headers is negligible; this is compliant with emerging wireless communications technologies, such as IEEE 802.11ax, where Orthogonal Frequency-Division Multiple Access (OFDMA) and frame aggregation mechanisms improve the MAC efficiency~\cite{afaqui2016}.
\section{Evaluation of the GWP Algorithm} \label{GWPAlgorithmEvaluation-Section}
The TMFN performance achieved using the GWP algorithm is presented in this section, including the simulation setup, the simulation scenarios, and the performance metrics considered.
\subsection{Simulation Setup} \label{GWPAlgorithmEvaluation-Section: Simulation setup}
In order to evaluate the TMFN performance achieved with the GWP algorithm, the ns-3 simulator was used. A Network Interface Card (NIC) was configured on each node in Ad Hoc mode, using the IEEE 802.11ac standard in channel 50, with \SI{160}{\mega\hertz} channel bandwidth, and \SI{800}{\nano\second} guard interval. One spatial stream was used for all wireless links. The traffic generated was UDP Poisson for a constant packet size of \SI{1400}{bytes}, during \SI{100}{\second} simulation time. The data rate was automatically defined by the \emph{IdealWifiManager} mechanism. The Controlled Delay (CoDeL) algorithm~\cite{nichols2012}, which is a Linux-based queuing discipline that considers the time that packets are held in the transmission queue to discard packets, was used; it allows mitigating the bufferbloat problem. The default parameters of CoDeL in ns-3 were employed, including 1000 packets as queue size and \SI{5}{\milli\second} as target queue delay \cite{CoDel:online}.
\subsection{Simulation Scenarios} \label{GWPAlgorithmEvaluation-Section: Simulation Scenarios}
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{"GWP-Algorithm-Scenarios/Baseline-Scenario"}
\caption{Scenario A, in which different positions for the GW were evaluated. Position 8 corresponds to the optimal GW position, while position 5 corresponds to the baseline -- GW placed in the FMAPs center.}
\label{GWPAlgorithmEvaluation-Figure: Baseline Scenario}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{"GWP-Algorithm-Scenarios/Complex-Scenario"}
\caption{Scenario B, in which 10 FMAPs were randomly positioned in order to form two zones with different traffic demand: $\lambda_1$ and $\lambda_2$. The baseline corresponds to the GW placed in the FMAPs center, which is represented by a dashed circumference.}
\label{GWPAlgorithmEvaluation-Figure: Complex Scenario}
\end{figure}
In addition to the optimal GW position, which was obtained using the GWP algorithm, other positions for the GW in the venue depicted in ~\cref{GWPAlgorithm-Figure: Gateway Placement Subspace} were evaluated, in order to show the performance gains obtained when using the GWP algorithm; the seven additional positions considered are depicted in ~\cref{GWPAlgorithmEvaluation-Figure: Baseline Scenario} and hereafter referred to as Scenario A. Position 1 to position 7 were defined to allow an inter-position distance of \SI{7.5}{\meter}; they aimed at exploring the vertical and horizontal corridors of the venue. We define as baseline the GW placed in the FMAPs center (i.e.,
three-coordinates average considering all FMAPs). Position 8 represents the optimal GW placement, which was derived from~\cref{GWPAlgorithm-SystemOfEquations: Gateway Placement Subspace}.
\begin{figure*}[t]
\centering
\subfloat[Throughput (R) CCDF.]{
\includegraphics[width=0.47\linewidth]{"GWP-Algorithm-Simulation-Results/Baseline-Scenario/Throughput"}
\label{GWPAlgorithmEvaluation-Figure: Baseline Scenario Throughput}
}
\hfill
\subfloat[End-to-end delay CDF.]{
\includegraphics[width=0.47\linewidth]{"GWP-Algorithm-Simulation-Results/Baseline-Scenario/Delay"}
\label{GWPAlgorithmEvaluation-Figure: Baseline Scenario Delay}
}
\caption{Scenario A - Aggregate Throughput (R) and End-to-end delay results measured in the GW. Position 8 corresponds to our proposal for the GW position.}
\label{GWPAlgorithmEvaluation-Figure: Baseline Scenario Results}
\end{figure*}
In order to evaluate the performance achieved when using the GWP algorithm in a typical crowded event, a more complex scenario, depicted in \cref{GWPAlgorithmEvaluation-Figure: Complex Scenario} and hereafter named as Scenario B, was also considered. It represents a TMFN composed of 10 FMAPs and 1 GW, inside a cuboid of dimensions \SI{80}{\meter} $\times$ \SI{80}{\meter} $\times$ \SI{20}{\meter}. The FMAPs were randomly positioned in order to form two zones with different traffic demand: $\lambda_1$ and $\lambda_2$ bit/s.
Since the GWP algorithm relies on knowing in advance the positions of the FMAPs, provided by the NetPlan algorithm in a real-world deployment, instead of generating the random waypoints during the ns-3 simulation we used BonnMotion~\cite{aschenbruck2010bonnmotion}, which is a mobility scenario generation tool. These waypoints were considered to calculate in advance the forwarding tables and the optimal GW position. We considered as baseline the GW placed in the FMAPs center. Finally, the forwarding tables and the GW position along the time, as well as the generated scenarios were imported to ns-3, with a sampling period of \SI{1}{\second}. The \emph{WaypointMobilityModel} model of ns-3, which places the UAVs in the positions generated by BonnMotion, was used. Two different traffic demand combinations were considered: a) $\lambda_1$ $= 0.1 \times L$ and $\lambda_2 = 0.9 \times L$; and b) $\lambda_1$ $= 0.25 \times L$ and $\lambda_2 = 0.75 \times L$, where $L$ is the capacity of the wireless medium divided by the number of FMAPs.
\subsection{Performance Metrics} \label{GWPAlgorithmEvaluation-Section: Performance Metrics}
\begin{figure*}[t]
\centering
\subfloat[Throughput (R) CCDF.]{
\includegraphics[width=0.47\linewidth]{"GWP-Algorithm-Simulation-Results/Complex-Scenario/Throughput-10-90"}
\label{GWPAlgorithmEvaluation-Figure: Complex Scenario Throughput 10-90}
}
\hfill
\subfloat[End-to-end delay CDF.]{
\includegraphics[width=0.47\linewidth]{"GWP-Algorithm-Simulation-Results/Complex-Scenario/Delay-10-90"}
\label{GWPAlgorithmEvaluation-Figure: Complex Scenario Delay 10-90}
}
\caption{Scenario B - Aggregate Throughput (R) and End-to-end delay results measured in the GW for $\lambda_1 $ and $\lambda_2$ equal to 10\% and 90\% of the channel capacity, respectively.}
\label{GWPAlgorithmEvaluation-Figure: Complex Scenario Results 10-90}
\end{figure*}
\begin{figure*}[t]
\centering
\subfloat[Throughput (R) CCDF.]{
\includegraphics[width=0.47\linewidth]{"GWP-Algorithm-Simulation-Results/Complex-Scenario/Throughput-25-75"}
\label{GWPAlgorithmEvaluation-Figure: Complex Scenario Throughput 27-75}
}
\hfill
\subfloat[End-to-end delay CDF.]{
\includegraphics[width=0.47\linewidth]{"GWP-Algorithm-Simulation-Results/Complex-Scenario/Delay-25-75"}
\label{GWPAlgorithmEvaluation-Figure: Complex Scenario Delay 25-75}
}
\caption{Scenario B - Aggregate Throughput (R) and End-to-end delay results measured in the GW for $\lambda_1 $ and $\lambda_2$ equal to 25\% and 75\% of the channel capacity, respectively.}
\label{GWPAlgorithmEvaluation-Figure: Complex Scenario Results 25-75}
\end{figure*}
The performance of the GWP algorithm was evaluated considering two performance metrics:
\begin{itemize}
\item Aggregate Throughput (R): The mean number of bits received per second by the GW.
\item End-to-end delay: The mean time taken by the packets to reach the application layer of the GW since the instant they were generated by the FMAPs, including queuing, transmission, and propagation delays.
\end{itemize}
\subsection{Simulation Results} \label{GWPAlgorithmEvaluation-Section: Simulation Results}
The results were obtained after 20 simulation runs for each traffic demand combinations that were considered (cf. \cref{GWPAlgorithmEvaluation-Section: Simulation Scenarios}), under the same networking conditions, using $RngSeed = 10$ and $RngRun = \{1, ..., 20\}$. The results are expressed using mean values and they are represented using the CDF for the end-to-end delay and by the CCDF for the aggregate throughput. The CCDF $F'(x)$ represents the percentage of time for which the mean aggregate throughput was higher than $x$, while the CDF $F(x)$ represents the percentage of time for which the mean end-to-end delay was lower than or equal to to $x$.
Regarding Scenario A, when the GW is placed in the optimal position (Position 8 in \cref{GWPAlgorithmEvaluation-Figure: Baseline Scenario}), the aggregate throughput is improved 24\% for the 90th percentile and 21\% for the 50th percentile (median), with respect to the baseline (i.e., the GW placed in the FMAPs center). In parallel, the end-to-end delay is decreased 26\% for both the 90th and 50th percentiles (cf. \cref{GWPAlgorithmEvaluation-Figure: Baseline Scenario Results}). The similar performance results obtained for Position 2 and Position 8, which are depicted in \cref{GWPAlgorithmEvaluation-Figure: Baseline Scenario Results}, are justified by the closer distance between these positions; note that Position 2 was obtained by chance, while Position 8 resulted from the GWP algorithm.
In order to meet the higher traffic demand of the right-side FMAPs, the GWP algorithm places the GW closer to them, in order to improve the SNR of the communications links and enable the selection of higher MCS indexes. This improves the overall TMFN performance and the shared medium usage -- the packets are held in the transmission queues for shorter time, the transmission delay decreases, and the throughput increases. The difference between the traffic demand of the FMAPs and the aggregate throughput in the GW are justified by the action of the auto rate mechanism, which control the MCS indexes being used by the FMAPs over time, as well as by the overhead introduced by the UDP, IP, and MAC packet headers.
With respect to Scenario B, when $\lambda_1 $ and $\lambda_2$ are respectively equal to 10\% and 90\% of $L$, an optimal placement for the GW is $(x_0,y_0,z_0) \approx (6.2, 31.0, 8.8)$ for a transmission power $P_{T} = $ \SI{26}{dBm}; this allows to improve the aggregate throughput up to 27\%, considering the 90th and 50th percentiles, while the end-to-end delay is reduced up to 4\% (cf. \cref{GWPAlgorithmEvaluation-Figure: Complex Scenario Results 10-90}). When $\lambda_1 $ and $\lambda_2$ are respectively equal to 25\% and 75\% of the channel capacity, the GWP algorithm defines $(x_0,y_0,z_0) \approx (9.0, 31.1, 2.8)$ as the optimal GW placement for transmission power $P_{T} = $ \SI{24}{dBm}. This allows to improve the aggregate throughput in 18\% with respect to the 90th percentile and 19\% for the 50th percentile, while the end-to-end delay is reduced 12\% for the 90th percentile and 8\% for the 50th percentile (cf. \cref{GWPAlgorithmEvaluation-Figure: Complex Scenario Results 25-75}). These results validate the effectiveness of the GWP algorithm and corroborate our research hypothesis: the TMFN performance can be improved by dynamically adjusting the position of the GW, considering both the positions and the offered traffic of the FMAPs.
\section{Conclusions} \label{Conclusions-Section}
This article proposed an integrated solution to control the Traffic-Aware Multi-Tier Flying Networks (TMFN). The synergy created from the combination of the NetPlan algorithm, the RedeFINE routing solution and the GWP algorithm allows the TMFN to seamlessly update its topology according to the users' traffic demand and minimizing the disruption caused by the movement of the UAVs. Therefore, this solution enables the TMFN to be used as an on-demand network, which is able to provide an improved QoS to the users, even in scenarios with a high-density of users and variable traffic demand.
Even though the three components were designed to be used simultaneously, they were evaluated individually, in order to obtain results that were not affected by the remaining components. The results obtained showed that each component was able to improve the QoS provided to the users, when compared to baselines and state of the art counterparts in the scenarios tested in this article. Also, the experimental results of NetPlan demonstrated the gains obtained by means of simulation. Furthermore, the evaluation of the air-to-ground and ground-to-air channel propagation models for low altitudes demonstrated that both channels are best modeled by the Friis path loss with Rician fast-fading, which corresponds to the theoretical studies proposed in the literature. Moreover, the asymmetry between the air-to-ground and the ground-to-air channels was also confirmed.
As future work, we plan to develop a prototype of the proposed solution with the NetPlan algorithm, the RedeFINE routing solution and the GWP algorithm fully integrated. Moreover, the RedeFINE solution can be improved by considering the positions of the gateway UAVs determined by GWP in addition to the FMAPs. Finally, we plan to evaluate the performance of the prototype by means of simulation and experimental scenarios.
\section*{Acknowledgments}
The authors would like to thank Filipe Rodrigues and Filipe Rosa from Tekever for their help setting up the testbed and piloting the UAVs.
This work is financed by the ERDF -- European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation -- COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT -- Fundação para a Ciência e a Tecnologia within project POCI-01-0145-FEDER-016744.
The first author thanks the funding from FCT under the PhD grant PD/BD/113819/2015.
The second author thanks the funding from FCT under the PhD grant SFRH/BD/137255/2018.
\bibliographystyle{elsarticle-num}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,798 |
THIS IS A BORZOI BOOK
PUBLISHED BY ALFRED A. KNOPF, INC.
Copyright © 1991 by Philip Levine
All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by Alfred A. Knopf, Inc., New York, and simultaneously in Canada by Random House of Canada Limited, Toronto. Distributed by Random House, Inc., New York.
www.randomhouse.com/knopf/poetry/
My thanks to the editors of the following publications in which these poems first appeared:
_Antaeus_ ("Soloing")
_The Atlantic Monthly_ ("Among Children")
_The Georgia Review_ ("Coming Homeward from the Post Office")
_The Gettysburg Review_ ("The Seventh Summer")
_Michigan Quarterly Review_ ("My Grave")
_The New England Review_ ("The Sweetness of Bobby Hefka," "Facts," & "Coming of Age in Michigan")
_The New Yorker_ ("Fear and Fame," "Coming Close," "Fire," "Every Blessed Day," "What Work Is," "Snails," "Perennials," "Above the World," "M. Degas Teaches Art & Science at Durfee Intermediate School," and "On the River")
_Poetry_ ("Burned" and "The Right Cross")
_Western Humanities Review_ ("Growth" and "Scouting")
_Zyzzyva_ ("Gin")
My special thanks to my friends who helped me with these poems and encouraged me to complete them, especially to Larry Levis, Garrett Hongo, Edward Hirsch, Donald Hall, Sharon Olds, and C.K. Williams.
Library of Congress Cataloging-in-Publication Data
Levine, Philip, 1928–
What work is : poems / Philip Levine.
p. cm.
eISBN: 978-0-307-76195-8
I. Title.
PS3562.E9W47 1991
811'.54—dc20 90–53421
Reprinted Twelve Times
v3.1
_FOR LARRY LEVIS_
# CONTENTS
_Cover_
_Title Page_
_Copyright_
_Dedication_
I
_Fear and Fame_
_Coming Close_
_Fire_
_Every Blessed Day_
_Growth_
_Innocence_
_Coming Home from the Post Office_
_Among Children_
_What Work Is_
II
_Snails_
_My Grave_
_Agnus Dei_
_Facts_
_Gin_
_Perennials_
_Above the World_
_M. Degas Teaches Art & Science at Durfee Intermediate School_
III
_Burned_
IV
_Soloing_
_Scouting_
_Coming of Age in Michigan_
_The Right Cross_
_The Sweetness of Bobby Hefka_
_On the River_
_The Seventh Summer_
_About the Author_
_Other Books by This Author_
# I
## FEAR AND FAME
Half an hour to dress, wide rubber hip boots,
gauntlets to the elbow, a plastic helmet
like a knight's but with a little glass window
that kept steaming over, and a respirator
to save my smoke-stained lungs. I would descend
step by slow step into the dim world
of the pickling tank and there prepare
the new solutions from the great carboys
of acids lowered to me on ropes—all from a recipe
I shared with nobody and learned from Frank O'Mera
before he went off to the bars on Vernor Highway
to drink himself to death. A gallon of hydrochloric
steaming from the wide glass mouth, a dash
of pale nitric to bubble up, sulphuric to calm,
metals for sweeteners, cleansers for salts,
until I knew the burning stew was done.
Then to climb back, step by stately step, the adventurer
returned to the ordinary blinking lights
of the swingshift at Feinberg and Breslin's
First-Rate Plumbing and Plating with a message
from the kingdom of fire. Oddly enough
no one welcomed me back, and I'd stand
fully armored as the downpour of cold water
rained down on me and the smoking traces puddled
at my feet like so much milk and melting snow.
Then to disrobe down to my work pants and shirt,
my black street shoes and white cotton socks,
to reassume my nickname, strap on my Bulova,
screw back my wedding ring, and with tap water
gargle away the bitterness as best I could.
For fifteen minutes or more I'd sit quietly
off to the side of the world as the women
polished the tubes and fixtures to a burnished purity
hung like Christmas ornaments on the racks
pulled steadily toward the tanks I'd cooked.
Ahead lay the second cigarette, held in a shaking hand,
as I took into myself the sickening heat to quell heat,
a lunch of two Genoa salami sandwiches and Swiss cheese
on heavy peasant bread baked by my Aunt Tsipie,
and a third cigarette to kill the taste of the others.
Then to arise and dress again in the costume
of my trade for the second time that night, stiffened
by the knowledge that to descend and rise up
from the other world merely once in eight hours is half
what it takes to be known among women and men.
## COMING CLOSE
Take this quiet woman, she has been
standing before a polishing wheel
for over three hours, and she lacks
twenty minutes before she can take
a lunch break. Is she a woman?
Consider the arms as they press
the long brass tube against the buffer,
they are striated along the triceps,
the three heads of which clearly show.
Consider the fine dusting of dark down
above the upper lip, and the beads
of sweat that run from under the red
kerchief across the brow and are wiped
away with a blackening wrist band
in one odd motion a child might make
to say No! No! You must come closer
to find out, you must hang your tie
and jacket in one of the lockers
in favor of a black smock, you must
be prepared to spend shift after shift
hauling off the metal trays of stock,
bowing first, knees bent for a purchase,
then lifting with a gasp, the first word
of tenderness between the two of you,
then you must bring new trays of dull,
unpolished tubes. You must feed her,
as they say in the language of the place.
Make no mistake, the place has a language,
and if by some luck the power were cut,
the wheel slowed to a stop so that you
suddenly saw it was not a solid object
but so many separate bristles forming
in motion a perfect circle, she would turn
to you and say, "Why?" Not the old _why_
of _why must I spend five nights a week_?
Just, "Why?" Even if by some magic
you knew, you wouldn't dare speak
for fear of her laughter, which now
you have anyway as she places the five
tapering fingers of her filthy hand
on the arm of your white shirt to mark
you for your own, now and forever.
## FIRE
A fire burns along the eastern rim
of mountains. In the valley we
see it as a celestial prank, for
in the summer haze the mountains
themselves are lost, but as the night
deepens the fire grows more golden
and dense. On this calm ground
the raw raging of burning winds
that cuts the eyes and singes the hair
is seen as a pencil-line of light
moving southward. I know my son
is there, has been for four days,
moved in and out by helicopters
with his squad of fire fighters.
By now, without sleep, they've
gone beyond exhaustion. Some can't
waken, some are crazed, a few go
on—the oldest—working steadily.
I know this from the stories he
has told me of other famous fires
from which he returned as from
a dream, his eyes glazed with seeing,
his sense of time and place gone.
He would raise his shaking right arm
above his head, and with his palm
open sweep it toward me again
and again and speak without grammar,
sometimes without words, of what
had taken place. I knew it was true.
Now in the cool of evening I catch
a hint of the forest, of that taking
of sudden breath that pines demand;
it's on my skin, a light oil, a sweat
born of some forgotten leaning into fire.
## EVERY BLESSED DAY
First with a glass of water
tasting of iron and then
with more and colder water
over his head he gasps himself
awake. He hears the _cheep_
of winter birds searching
the snow for crumbs of garbage
and knows exactly how much light
and how much darkness is there
before the dawn, gray and weak,
slips between the buildings.
Closing the door behind him,
he thinks of places he
has never seen but heard
about, of the great desert
his father said was like
no sea he had ever crossed
and how at dusk or dawn
it held all the shades of red
and blue in its merging shadows,
and though his life was then
a prison he had come to live
for these suspended moments.
Waiting at the corner he feels
the cold at his back and stamps
himself awake again. Seven miles
from the frozen, narrow river.
Even before he looks he knows
the faces on the bus, some
going to work and some coming back,
but each sealed in its hunger
for a different life, a lost life.
Where he's going or who he is
he doesn't ask himself, he
doesn't know and doesn't know
it matters. He gets off
at the familiar corner, crosses
the emptying parking lots
toward Chevy Gear & Axle # 3.
In a few minutes he will hold
his time card above a clock,
and he can drop it in
and hear the moment crunching
down, or he can not, for
either way the day will last
forever. So he lets it fall.
If he feels the elusive calm
his father spoke of and searched
for all his short life, there's
no way of telling, for now he's
laughing among them, older men
and kids. He's saying, "Damn,
we've got it made." He's
lighting up or chewing with
the others, thousands of miles
from their forgotten homes, each
and every one his father's son.
## GROWTH
In the soap factory where I worked
when I was fourteen, I spoke to
no one and only one man spoke
to me and then to command me
to wheel the little cars of damp chips
into the ovens. While the chips dried
I made more racks, nailing together
wood lath and ordinary screening
you'd use to keep flies out, racks
and more racks each long afternoon,
for this was a growing business
in a year of growth. The oil drums
of fat would arrive each morning,
too huge for me to tussle with,
reeking of the dark, cavernous
kitchens of the Greek and Rumanian
restaurants, of cheap hamburger joints,
White Towers and worse. They would
sulk in the battered yard behind
the plant until my boss, Leo,
the squat Ukrainian dollied them in
to become, somehow, through the magic
of chemistry, pure soap. My job
was always the racks and the ovens—
two low ceilinged metal rooms
the color of sick skin. When I
slid open the heavy doors my eyes
started open, the pores
of my skull shrivelled, and sweat
smelling of scared animal burst from
me everywhere. Head down I entered,
first to remove what had dried
and then to wheel in the damp, raw
yellow curls of new soap, grained
like iris petals or unseamed quartz.
Then out to the open weedy yard
among the waiting and emptied drums
where I hammered and sawed, singing
my new life of working and earning,
outside in the fresh air of Detroit
in 1942, a year of growth.
## INNOCENCE
Side by side against the trunks of the gray oaks
that lined US 24 we sat while Michelangelo concocted
from tomatoes, hot peppers, onions, salami,
his long blade flashing along the blocks of cheese,
laying the slices precisely down the two slabs
of coarse white bread crafted from a single loaf.
Seriously and in silence we watched, and when he raised
the huge original sandwich to the first bite,
we raised our quarts of milk in a dumb salute
to the sullen gods of time for a thank you
for our mid-day rest. Our Michelangelo was not
the painter, long dead and forgotten by those
beside the road to Toledo during the summer of '50
just before the republic went back to its wars,
but Michelangelo the furious lopper of tree limbs
who leapt all day from branch to leafy branch
to strip those poor old oaks before the earthmovers
dragged them down so that there might be
two smooth new concrete lanes all the way
to the empires of Ohio. (It's there now, the road,
a permanent work of the human imagination,
lined colorfully as all great ways must be,
with the arches of triumph over good taste.)
Each noon Michelangelo told the same joyous tales
of surrender to the 3rd Army Corps in North Africa,
as though he personally had handed over his sword
to Omar Bradley, and then the long sea voyage
to serene Michigan and his second Italian family,
the prosperous cousins in complicated brickwork,
experts in drainage, masters of tree removal
whose thankful apprentice he now was.
We toasted the girls who each night lavished
their cares on his long knotted body topped
perfectly with a roof of black curly thatch.
We even lied back in return, inventing squadrons
of blondes and serious brunettes driven by love
to wait on our doorsteps until we returned
by bus, filthy and broken by the long days
of breaking the earth, women with new cars
and old needs content to take their turns.
Michelangelo would smile, the wise European
come to these innocent shores in a time
of innocence. Later, when the yellow Le Tourneau
earthmovers gripped the chained and stripped trunks,
hunched down and roared their engines, the earth
held and trembled before it gave, and the stumps
howled as they turned their black, prized groins
skyward for the first times in their lives,
turned and rocked back and forth just once
in the heavy wet dirt of late afternoon.
We smiled, not to hide our tears from ourselves
or each other, but because the day was ending,
if there were lamentations they were not ours
but the starlings gathering in the oaks,
the starlings and bobolinks and the vireos
chanting and bowing in the darkening branches
all along the road to Ohio and the coming night.
## COMING HOME FROM THE POST OFFICE
On Sunday night we would
see the women returning
from an evening with God,
their faces glowing with faith
and the hard sweat of their faith.
They would sing separately
or together, and when the bus
stopped and one got carefully
off the sisters would shout
news of the good days ahead
and the joys of handmaidenship.
I remember an evening in April
when I passed in and out of
sleep, and the woman who stood
above me stared into my eyes
as though searching for a sign
that might bring light softly
falling among the dark houses
we stuttered by. When I closed
my eyes I saw cards, letters,
small packages, each bearing
a particular name and some
burden of grief or tidings
of loss. Names like my own
passed moment by moment
into the gray sacks that slumped
open mouthed. On strong legs
she stood easily, swaying
from side to side, a woman
in a green suit, a purse held
in one hand, a hankie folded
in the other. Her pale eyes
held mine easily each time
I wakened, and so I wakened
not into the colorless light
from overhead but into
the twin mysteries of a life
in God. When I fell back
into my light sleep I saw
a great clear river running
between the houses I knew
and a bright shore of temples,
glowing public squares, children
in long robes flowing, those I
loved climbing a high hill
toward a new sun. Hours later
the driver softly wakened
me with a hand on my head
and a single word, and I
stepped lightly into the world,
my shoulders hunched, my collar
turned up against the hour,
and headed down the still street.
The new spring winds groaned
around me, the distant light
of no new star marked me home.
## AMONG CHILDREN
I walk among the rows of bowed heads—
the children are sleeping through fourth grade
so as to be ready for what is ahead,
the monumental boredom of junior high
and the rush forward tearing their wings
loose and turning their eyes forever inward.
These are the children of Flint, their fathers
work at the spark plug factory or truck
bottled water in 5 gallon sea-blue jugs
to the widows of the suburbs. You can see
already how their backs have thickened,
how their small hands, soiled by pig iron,
leap and stutter even in dreams. I would like
to sit down among them and read slowly
from _The Book of Job_ until the windows
pale and the teacher rises out of a milky sea
of industrial scum, her gowns streaming
with light, her foolish words transformed
into song, I would like to arm each one
with a quiver of arrows so that they might
rush like wind there where no battle rages
shouting among the trumpets, Ha! Ha!
How dear the gift of laughter in the face
of the 8 hour day, the cold winter mornings
without coffee and oranges, the long lines
of mothers in old coats waiting silently
where the gates have closed. Ten years ago
I went among these same children, just born,
in the bright ward of the Sacred Heart and leaned
down to hear their breaths delivered that day,
burning with joy. There was such wonder
in their sleep, such purpose in their eyes
closed against autumn, in their damp heads
blurred with the hair of ponds, and not one
turned against me or the light, not one
said, I am sick, I am tired, I will go home,
not one complained or drifted alone,
unloved, on the hardest day of their lives.
Eleven years from now they will become
the men and women of Flint or Paradise,
the majors of a minor town, and I
will be gone into smoke or memory,
so I bow to them here and whisper
all I know, all I will never know.
## WHAT WORK IS
We stand in the rain in a long line
waiting at Ford Highland Park. For work.
You know what work is—if you're
old enough to read this you know what
work is, although you may not do it.
Forget you. This is about waiting,
shifting from one foot to another.
Feeling the light rain falling like mist
into your hair, blurring your vision
until you think you see your own brother
ahead of you, maybe ten places.
You rub your glasses with your fingers,
and of course it's someone else's brother,
narrower across the shoulders than
yours but with the same sad slouch, the grin
that does not hide the stubbornness,
the sad refusal to give in to
rain, to the hours wasted waiting,
to the knowledge that somewhere ahead
a man is waiting who will say, "No,
we're not hiring today," for any
reason he wants. You love your brother,
now suddenly you can hardly stand
the love flooding you for your brother,
who's not beside you or behind or
ahead because he's home trying to
sleep off a miserable night shift
at Cadillac so he can get up
before noon to study his German.
Works eight hours a night so he can sing
Wagner, the opera you hate most,
the worst music ever invented.
How long has it been since you told him
you loved him, held his wide shoulders,
opened your eyes wide and said those words,
and maybe kissed his cheek? You've never
done something so simple, so obvious,
not because you're too young or too dumb,
not because you're jealous or even mean
or incapable of crying in
the presence of another man, no,
just because you don't know what work is.
# II
## SNAILS
The leaves rusted in the late winds
of September, the ash trees bowed
to no one I could see. Finches
quarrelled among the orange groves.
I was about to say something final
that would capture the meaning
of autumn's arrival, something
suitable for bronzing,
something immediately recognizable
as so large a truth it's totally untrue,
when one small white cloud—not much
more than the merest fragment of mist—
passed between me and the pale
thin cuticle of the mid-day moon
come out to see the traffic and dust
of Central California. I kept quiet.
The wind stilled, and I could hear
the even steady ticking of the leaves,
the lawn's burned hay gasping
for breath, the pale soil rising
only to fall between earth and heaven,
if heaven's there. The world would escape
to become all it's never been
if only we would let it go
streaming toward a future without
purpose or voice. In shade the ground
darkens, and now the silver trails
stretch from leaf to chewed off leaf
of the runners of pumpkin to disappear
in the cover of sheaves and bowed grass.
On the fence blue trumpets of glory
almost closed—music to the moon,
laughter to us, they blared all day
though no one answered, no one
could score their sense or harmony
before they faded in the wind and sun.
## MY GRAVE
Just outside Malaga, California,
lost among the cluster of truckstops
there is a little untended plot
of ground and weeds and a stone
that bears my name, misspelled,
and under the stone is dirt, hardpan,
more dirt, rocks, then one hundred
and one different elements
embracing each other in every way
they can imagine so that at times
they remind me of those photographs
I saw as a boy and which I was assured
were expensive and stimulating
and meant nothing. There are also
over a thousand beer bottle caps
one of my sons was saving until
he calculated that he would never
reach a million and so quit. (Quit
saving, not drinking.) One document
is here, ceremoniously labeled
"My Last Will & Testament." My sister
so hated it she threw it into
the bare hole and asked that it be
shovelled under. Not one foolish hope
of mine is here, for none was real
and hard, the hope that the poor
stalked from their cardboard houses
to transform our leaders, that our flags
wept colored tears until they became
nothing but flags of surrender.
I hoped also to see my mother
a long distance runner, my brother
give his money to the kids of Chicago
and take to the roads, carless, hatless,
in search of a task that befits a man.
I dreamed my friends quit lying
and their breath took on the perfume
of new-mown grass, and that I came
to be a man walking carelessly
through rain, my hair tangled, my one
answer the full belly laugh I saved
for my meeting with God, a laugh I
no longer need. Not one nightmare
is here, nor are my eyes which saw
you rise at night, barefoot and quiet,
and leave my side, and my ears which heard
you return suddenly, your mouth tasting
of cold water. Even my forehead
is not here, behind which I plotted
the overthrow of this our republic
by means of the refusal to wipe.
My journals aren't here, my right hand
that wrote them, my waist that strained
against so many leather belts and belts
of cloth that finally surrendered.
My enormous feet that carried me safely
through thirty cities, my tongue
that stroked and restroked your cheek
roughly until you said, "Cat." My poems,
my lies, my few kept promises, my love
for morning sunlight and dusk, my love
for women and the children of women,
my guiding star and the star I wore
for twenty seven years. Nothing of me
is here because this is not my house,
this is not the driver's seat of my car
nor the memory of someone who loved me
nor that distant classroom in which I
fell asleep and dreamed of lamb. This
is dirt, a filled hole of earth, stone
that says return to stone, a broken fence
that mumbles _Keep Out_ , air above nothing,
air that cannot imagine the sweet duties
of wildflowers and herbs, this is cheap,
common, coarse, what you pass by
every day in your car without a thought,
this is an ordinary grave.
## AGNUS DEI
My little sister created the Lamb of God.
She made him out of used-up dust mops
and coat hangers. She left him whitewashed
at the entrance to the Calvin Coolidge branch
of the public library, so as to scare
the lady librarian who'd clucked at each of us,
"Why do you want to read a grown-up book?"
The lamb sagged against the oaken doors,
high and dark in the deep vault of morning,
and said nothing as we scampered off
across the dew-wet lawns, our shoes darkening.
The rest of our adventure made the _Times_ ,
how Officer German took in the lamb and made
a morning meal of milk and mucilage
and wrapped him warmly in out-of-town papers.
How he slept unnoticed for hours and wakening
rose in a shower of golden dust, bellowing
in rage, and sent Miss Greenglass running
to the Ladies Restroom where she fainted
and, waking, changed her life. Books scattered.
There was weeping and gnashing. The lamb escaped
through an expensive, leaded windowpane
and entered the late afternoon flying low
over the houses of the middle class
until clouds obscured the world, and it was done.
My brother Leopold read this all out loud
on Sunday morning while our parents slept
above us in a high dark room we never entered,
and the cellar moaned and rumbled, warming
us the best it could. A fresh wind rapped
at the front windows, and we stared in silence
as, bloodred and wrinkled, the new elm unleaved
in public, shuddering with the ache of its growing.
## FACTS
The bus station in Princeton, New Jersey,
has no men's room. I had to use one like mad,
but the guy behind the counter said, "Sorry,
but you know what goes on in bus station men's rooms."
If you take a '37 Packard grill and split it down
the center and reduce the angle by 18° and reweld it,
you'll have a perfect grill for a Rolls Royce
just in case you ever need a new grill for yours.
I was not born in Cleveland, Ohio. Other people
were, or so I have read, and many have remained,
which strikes me as an exercise in futility
greater even than saving your pennies to buy a Rolls.
F. Scott Fitzgerald attended Princeton. A student
pointed out the windows of the suite he occupied.
We were on our way to the train station to escape
to New York City, and the student may have been lying.
The train is called "The Dinky." It takes you only
a few miles away to a junction where you can catch
a train to Grand Central or—if you're scared—
to Philadelphia. From either you can reach Cleveland.
My friend Howie wrote me that he was ashamed
to live in a city whose most efficient means of escape
is called "The Dinky." If he'd invest in a Rolls,
even one with a Packard grill, he'd feel differently.
I don't blame the student for lying, especially
to a teacher. He may have been ill at ease
in my company, for I am an enormous man given
to long bouts of silence as I brood on facts.
There are two lies in the previous stanza. I'm small,
each year I feel the bulk of me shrinking, becoming
more frail and delicate. I get cold easily as though
I lacked even the solidity to protect my own heart.
The coldest I've ever been was in Cleveland, Ohio.
My host and hostess hated and loved each other
by frantic turns. To escape I'd go on long walks
in the yellowing snow as the evening winds raged.
The citizens of Cleveland, Ohio, passed me sullenly,
benighted in their Rolls Royces, each in a halo
of blue light sifting down from the abandoned
filling stations of what once was a community.
I will never return to Cleveland or Princeton, not
even to pay homage to Hart Crane's lonely tower
or the glory days of John Berryman, whom I loved.
I haven't the heart for it. Not even in your Rolls.
## GIN
The first time I drank gin
I thought it must be hair tonic.
My brother swiped the bottle
from a guy whose father owned
a drug store that sold booze
in those ancient, honorable days
when we acknowledged the stuff
was a drug. Three of us passed
the bottle around, each tasting
with disbelief. People paid
for this? People had to have
it, the way we had to have
the women we never got near.
(Actually they were girls, but
never mind, the important fact
was their impenetrability.)
Leo, the third foolish partner,
suggested my brother should have
swiped Canadian whiskey or brandy,
but Eddie defended his choice
on the grounds of the expressions
"gin house" and "gin lane," both
of which indicated the preeminence
of gin in the world of drinking,
a world we were entering without
understanding how difficult
exit might be. Maybe the bliss
that came with drinking came
only after a certain period
of apprenticeship. Eddie likened
it to the holy man's self-flagellation
to experience the fullness of faith.
(He was very well read for a kid
of fourteen in the public schools.)
So we dug in and passed the bottle
around a second time and then a third,
in the silence each of us expecting
some transformation. "You get used
to it," Leo said. "You don't
like it but you get used to it."
I know now that brain cells
were dying for no earthly purpose,
that three boys were becoming
increasingly despiritualized
even as they took into themselves
these spirits, but I thought then
I was at last sharing the world
with the movie stars, that before
long I would be shaving because
I needed to, that hair would
sprout across the flat prairie
of my chest and plunge even
to my groin, that first girls
and then women would be drawn
to my qualities. Amazingly, later
some of this took place, but
first the bottle had to be
emptied, and then the three boys
had to empty themselves of all
they had so painfully taken in
and by means even more painful
as they bowed by turns over
the eye of the toilet bowl
to discharge their shame. Ahead
lay cigarettes, the futility
of guaranteed programs of
exercise, the elaborate lies
of conquest no one believed,
forms of sexual torture and
rejection undreamed of. Ahead
lay our fifteenth birthdays,
acne, deodorants, crabs, salves,
butch haircuts, draft registration,
the military and political victories
of Dwight Eisenhower, who brought us
Richard Nixon with wife and dog.
Any wonder we tried gin.
## PERENNIALS
Winter. The marketplace of the village
of Fuengirola. A tattered mongrel,
tan, brown, and black with a white muzzle.
The stubby, bowed forelegs set apart
in a stance suitable for a short advance
or a sudden retreat. I know this beast,
I think, I know this dirty, box-like head
ringed with curls, this dry, foolish bark
that scares off nothing. "Marilyn," I say,
remembering one who scorned me years before.
Each day my son John calls out, "Marilyn!"
as stamping we wait our turn in line
before the black oildrums of burning fat
where the _churros_ fry. "Marilyn," he calls
until she comes to beg bread from his hand.
*
Under the windows onto the gray yard
a green glass wine bottle with one branch
of blood-tipped bursting plum. The odor
of mid-summer hanging in winter.
The room thickens around the living core
as I pass and stop. Where was I going
that I should ignore the heart of my house,
this new intruder come in another
dark season to tell me the year won't wait?
I was on the way to the kitchen
for a glass of water, and now I have wine.
I was looking for a brown paper sack
of sleep, an old pillow of forgetting,
a way out before the world got in,
and found the dining room in riot
from one black branch as arched as I.
## ABOVE THE WORLD
Up through miles of twisting pines, past
a town of brightly painted caves, their windows
curtained and open, the doors ajar revealing
the heavy furniture of entrepreneurs, carpets,
television sets; on the roofs, antennas poking
in all directions and the day's laundry strung
from cave to cave. Up another hour or more
winding through dense woods to a high plateau,
then truck farms greening in December, fenced
fields of grazing cattle right to the outskirts
of the new town, raw, unfinished, with wide streets
of crowded shops hawking garter belts, canes,
fountain pens, goatskin jackets, peeled rabbits.
The women, in dark print dresses, clutched
their leather purses with both hands, the men
smoked in small circles. At the center, a maze
of wires and tracks sprouting from a compound
of ancient trolleys leaning into silence,
their windows gone, the cane seats unravelling,
the paint cracked and flaking. One road led
up the mountain, and we took it and left
the trucks, the clouds of black soot, the roar
of motorcycles to enter something
far older, and found the place and parked.
We registered at the Hotel of Heaven,
a father, a mother, three upright blond sons
in American jeans, blue-eyed and suspicious.
Would my kids now remember the parapets
that hung out over the edge of the world
that spread before us—the fabled Mare Nostrum
we never saw—as everything below dissolved
in smoke and dust? The tangled gardens
of a long-gone magistrate, their paths clogged
with weeds, the roses blown and climbing
everywhere, the famous court of stone lions
each as large and fierce as a happy dog,
each facing away from his brothers to guard
nothing from no one. Even the tall, graying
Englishman stooped before his easel was not
a dream, nor was the painting itself, still
largely canvas, though it caught the green
exactly, shadowed with black, and a sky
of distant clouds, small and bored,
floating away. That man would be ninety
or older now and still at the task
of rendering the magic and nonsense of lives
lived at great height, still not answering
the unanswerable questions of high mist,
brain cells fighting for breath, our bondage
to a line of perfect crows marking the way up.
Make no mistake, for even here you could still
go up along ragged stone trails that wound
their way into a gray world and from there
into thin air. Or you could descend
in summer to the music of water on the narrow
cobbled streets, or in silent December,
as we did, the mother leading the way,
the father taking up the rear in Spanish style,
laboring over a newspaper of local filth.
There was darkness. It fell even before
the cold fell, even before the late sun
vanished behind the mountains, it fell
into the corners of sight slowly
like stained snow. In the restaurant
there was more cold and darkness. A fine layer
of dust had settled on plates and silverware.
I wondered if anyone else saw it
sifting down but was scared to ask. One rear door
stood open on the night, though no animals
entered or left. We sent the soup back,
a clear broth of boiled water dotted
with islands of fat. We tried the bread
that gleamed like old china, we even tried
the thin burned steaks. We tried. And then
we walked the streets to a little square
where the children sold white paper dolls
you could explode with a lighted cigarette
and necklaces of wooden beads meant
for Christmas angels, who were sure to come,
for everything is answered in the Old World,
the Gypsy peddler told us as he wrapped
the chestnuts six to a triangled pack,
his stubby burned fingers working deftly.
"Everything!" he promised. I turned away
from the laughter and threats, turned away
from my wife and kids. Suddenly alone,
believing he was right, I turned to behold
the sky I'd always lived under bulging
with huge, unfamiliar stars closer
than I'd ever seen them and moving, frozen,
in that ancient, secret dance. Who could
have guessed how everything was answered
before the night ended? At the hotel a room
for each of us, windowless and sealed,
a private cell for sleep or prayer,
and seven more for those who never came—
a dozen tiny rooms in all, circling
a low-ceilinged common room that held
one great round table with attendant chairs,
equitably, as they never are in this life.
Beside the table and below the portrait
of God, the iron stove a boy filled with twigs,
broken crates, garbage, while we watched.
This, too, was answered. The grandfather,
smiling sideways at his audience, lit the blaze
and leaped back, laughing, for even here
above the world we would have all that night,
even unto the clear break of day, steam heat.
## M. DEGAS TEACHES ART & SCIENCE AT DURFEE INTERMEDIATE SCHOOL _Detroit, 1942_
He made a line on the blackboard,
one bold stroke from right to left
diagonally downward and stood back
to ask, looking as always at no one
in particular, "What have I done?"
From the back of the room Freddie
shouted, "You've broken a piece
of chalk." M. Degas did not smile.
"What have I done?" he repeated.
The most intellectual students
looked down to study their desks
except for Gertrude Bimmler, who raised
her hand before she spoke. "M. Degas,
you have created the hypotenuse
of an isosceles triangle." Degas mused.
Everyone knew that Gertrude could not
be incorrect. "It is possible,"
Louis Warshowsky added precisely,
"that you have begun to represent
the roof of a barn." I remember
that it was exactly twenty minutes
past eleven, and I thought at worst
this would go on another forty
minutes. It was early April,
the snow had all but melted on
the playgrounds, the elms and maples
bordering the cracked walks shivered
in the new winds, and I believed
that before I knew it I'd be
swaggering to the candy store
for a Milky Way. M. Degas
pursed his lips, and the room
stilled until the long hand
of the clock moved to twenty one
as though in complicity with Gertrude,
who added confidently, "You've begun
to separate the dark from the dark."
I looked back for help, but now
the trees bucked and quaked, and I
knew this could go on forever.
# III
## BURNED
I have to go back into the forge room
at Chevy where Lonnie still calls
out his commands to Sweet Pea and Packy
and stare into the fire
until my eyes are also fire
and tear away some piece of my face
because we're all burning in the blood
and it's too late.
I have to walk
the long road from here to Bessemer,
Alabama, and arrive on a June night in '48
after work when the men have crowded
around a stalled car and tell them
there's no place to go and
let them take turns beating me
with hands turned to pig iron.
I have to
climb the shaking ladder to the roof
of the Nitro plant and tear off
my respirator and breathe the yellow air
the Chaldeans called "the air you must not breathe,"
and sing in the voices
of my fathers calling the children
into prayer while below the stubby canisters
pass labelled, "Chicago," "Amsterdam,"
"Belsen," "Toronto."
I have to swim out
into the flat waters of the great sea
at dawn when the small fishing boats
are coming in and climb aboard the one
with the face of a goddess and the tail
of a goat and let my left cheek
brush against the rough, unshaven cheek
of the old man whose tears—mixed with wine—
watered the beach twenty one years ago.
And
keep going past the last marker
until I am lost forever, until the sea
and the sky are one, the waves have ceased,
no tide pulls us toward
the cries of the drowned.
I have to climb
the slag hills again, but this time not
as a child, and look out over the river of iron,
and hold it all in my eyes,
the river, the iron mountains, the factories
where our brothers burned. I have to repeat
the prayer that we will all go back
to earth one day soon to become earth,
that our tears will run to the sea
a last time and open it, and our fires
light the way back home for someone.
*
In the fullness of a season someone
had to go first into the other kingdom.
Summer in Detroit. The light scattered
into tiny flares at the end of a day
of hard work. Stanley walked his dog,
talking as always to himself, Dorothy
sat on the front porch alone, excited
by the knowledge of her changing body.
Blocks away Leo read _The Tempest_ slowly
to himself, stopping now and then to announce
a line out loud—"Thy turfy mountains
where live nibbling sheep"—, his skin
chilled with the glory of language.
I have not brought them together
so their hearts might stutter or stop
with love they can't bear. It is 1944,
Moradian has landed on a Pacific atoll
to become his life forever, Esther's husband
sees the Sherman twenty yards ahead
go up in a flash and knows his is next.
Past midnight Bernard and Arthur vow
to give themselves to music and to poetry.
I do not call out, I do not step forward
out of the chaos of my 16 years to ask
to take their place. I'm too young,
too exhausted, too busy. In the kitchen
I stand at the counter slicing cheese,
salami, rye bread, spreading mayonnaise,
tamping down the lettuce, wrapping
the sandwiches carefully in waxed paper
for tomorrow's lunch the exact way
my grandmother taught me years before,
humming one of my grandfather's tunes,
one he groans out when he sings himself
to sleep, tapping his foot, swinging
from side to side as though he were burning.
*
A burned car left in a field
of sassafras, the long green shoots
through the windows and doors where no
doors remain. The kids don't come by
after school to carve their names
on the dashboard or pull the steering wheel
to avoid the inevitable. Rocks, tires,
cases of empties, an old couch sagging
into weeds, the cushions blooming.
I lived here once, in a house
now gone. A friend visited me
at dusk, and she brought a paper parcel
of cookies tied with a ribbon. Even then
we were scared of the silence that followed
whatever we gave each other. I would
walk her to the bus stop on Second Avenue,
and we'd wait in silence in the dense air
of a March night as slow rain
fell into the last snow. I'd come back
alone, sober, singing to a starless sky,
singing recklessly out of a boy's
throat, past the darkened rows
of sleeping two storey houses
that have all gone up in smoke.
*
Yom Kippur
in the New World.
Los Angeles hums
a little tune—
trucks down
the coast road
for Monday market
packed with small faces
blinking in the dark.
My mother dreams
by the open window.
On the drainboard
the gray roast humps
untouched, the oven
bangs its iron jaws,
but it's over.
Before her on the table
set for so many
her glass of fire
goes out.
The childish photographs,
the letters and cards
scatter at last.
The dead burn alone
toward dawn.
*
Why am I going away from the glass of wine
from the loaf of bread
Why am I not mourning the tiny death
of the sparrow
who leaped on the lowest branches
of the atlas cedar
until one afternoon he was drawn
into tall burning grass
What will I say when the nights grow
longer and longer
the dawn is barely visible, a grudging
of yellow light
The day dies into the violet halos
of exhaust
No one takes my hand and leads me to bed
to the mouth to mouth agonies of darkness
When this passes
how will I know I was and I was alive
Who will take my hand
smelling of earth and
burning now to autumnal rust
Who will lead me to the ceremonies of sorrow
who will lead me
*
I was burned,
she said, and lifted her blouse to show
me the curious pale mottling along
the lines of her belly, still smooth. "He
said he adored my white skin, creamy.
Can a Jew imagine what a real
white woman looks like all over? All
your life you dream of someone like me,
every night of your life." Her green eyes
on fire with her own memories
of herself 40 years ago. She shakes her head
awake and still goes on. "Not with cigarettes,
you moron, would a man like that, richer
than God, burn his only beloved with
cigarettes? Cigars, imported Havanas, nothing
but the best!"
And she's gone, thank God,
slamming the door on me, gone back
to the one life she clings to. The room
is quiet, ashamed, the books gawk down
from their shelves, not one
with a word to tell me what it is like
to enter the fires of your own making, naked,
day after day, until the burning becomes
a sweetness.
*
The day you left I walked
alone for hours down the crowded streets
hearing and seeing no one until I
caught the cries of a drunken woman
behind me. She had lost her husband,
left him in a bar, was alone, frightened,
calling for help. I kept walking
with her behind me, calling.
The houses along the canals were closing
up, turning their eyes inward,
listening to the rumbling of their fires
or their human groans. This day will end,
I told myself, this pain will pass.
I will waken to my life. The evening
spread from the great oaks
that lined the emptying boulevards
or descended in bits of ashes and dust
from a deepening sky. I turned at last
to behold the woman whose grief
was louder than mine. There was
only a child, her right hand closed
tight on a handkerchief, knotted at one end
with some coins and a note, a little girl
who seeing my eyes filled with tears
began to cry as she smiled.
*
Two ten-inch phonograph records, _Bluebirds_ ,
going white, that won't give up their music.
My uncle's perfect cloth bound book
that opened the secret of electric growth.
My mother's gap-toothed tortoise combs.
My father's Victoria Cross he brought back
from an automobile parts convention
in Chicago. His white gold pocket watch,
a Howard, that runs and stops and runs
to keep his time. His naturalization papers
claiming he was born in 1898 in Poland,
without a single mention of his years at war.
My brother's smeared grade school drawings
of Spitfires, Stukas, ME 109s,
his "Withdrawal from Dunkirk," the beach
crisscrossed with small black lines
that could be abandoned arms or the arms
of boys hugging. My stillborn sister's
wish to walk with us on Sunday afternoons,
to breathe the stained air that blows
in at dusk from the parking lots,
to mother a child. Your finger prints
on the final application for release.
A bitten fountain pen, a dry stamp pad.
Two clear drops of fluid that catch
and hold the artificial light, that glow
with their own light when that's gone
as eyes in stories are said to do.
Now in the dark they could be you,
they could be me, they could be anyone.
*
I stop at the borders of dreams.
I ask who you are, whispering
in my ear all these years, you
to whom I've said all I can say.
I hold my two hands upward
toward the light now sifting
from the air. That is the shape
of eternity: five long fingers
and a palm broadened and carved
by use. When I looked
in my heart and found only
questions, when I walked
beside the ditch at dusk
and asked the sun,
the answer was curled
quietly in my pocket. "Look at
them both," you say, "turn them
over and place them on the table
before you. Don't be afraid.
They are you, familiar, at times
overlooked, despised. Now,
go back the way you came, down
the same old streets where you
grew to a name and a single face.
That was home, you said, and today
it is nothing, not even a closet
of unread books. Here is home.
Close your eyes. You are on
a dark plain. The hot winds
breathe in and out. You're laughing!
You asked for a home, you crossed
the earth, you sat speechless,
you questioned the closed door,
'Are you there?' No one answered
because all the time it was you."
*
If I called you "my soul," you'd
laugh in my face. If I went
down on my knees to you as to
a god or a beloved, you'd turn
to the window, shake your head,
and talk to the last of the garden.
At the end of September I may
ask the trees to hold still
in the west wind. I may scold
the flicker hiding in the shade
of an orange tree. His feathers
scatter and settle in the trough
of each wave. He is not
a religious object nor is
the wind sacred, smelling
as it does of cold salt
and sea life. I have been here
so long the bleached hairs
quivering on my hands remember
the years before the flood.
The whites of my eyes, no longer
white, stared into fire when fire
was mine, and I am only
so much salt, water, and stone
smelling of iron. I can talk
to you and though my answers
will scatter like feathers in wind,
you may write them down on paper
that burns even in sunlight.
Get what you can, says the flicker;
remorseless, he shoulders his way
into light and then into air.
What does he care that the year
winds down? That the west wind
smells of ice? That what went out
as lies and so much bad breath
came home as the final truth?
*
The outskirts of our least favorite city,
the one bombed and burned from the inside
by its own citizens—along the fence
small climbing roses bloom in April,
the hardier ones hang on long
past the better days, and late autumn
brings tiny crystals glistening
on the cheeks of the blackened petals.
Spading the gray soil, I think
of begonias and how their buds redden
even without rain and of the wild iris—
flags we called them—that won't live
in the rich beds though they survive
fire and hail outbattling tough weeds
to spring up where houses once were.
Poking among these ruins for rocks
for the garden, I unearth bricks
from a familiar fireplace or a slab
of stone that crowned a hearth, remnants
of my lost neighbors. Spilling
the kernels of carrot seeds
into my palm and the black pips
of radishes, I know something
will come from this root and wood
thickened ground. With a stick I scrape
a trough for planting. I remember
the unloved lamb become a sheep I saw
on his way to slaughter. Like me, he shook
his lowered head as though he knew
the way home, that head dirty with curls.
*
I was small once, hardly bigger
than the laughter of a lemon and like
a lemon I had come into a life
no one would question, an oily rind,
closed volumes of flesh, and seeds
as smooth as pearls. Even then
you could talk, you were immense
with the desire to touch each leaf,
each small animal that rose
from his lair. Later,
even you who could love rind,
seeds, oil, flesh, let your name
slip from your tongue to become
nonsense, let salt rain down
into the fields and surrendered
all you'd seen, you who had
eaten the earth gave back ashes.
So, it is time we left.
Take the small, empty purse
your mother carried across an ocean,
take the little book of songs
the children taught you, take
your teeth and your fingernails
and the white scars on your belly
and meet me where the road
vanishes into the hillside.
How will you know me?
I won't be tall or dressed
for dinner or carrying a dark bag,
I won't be whistling like a bird
or your father coming home from work,
I won't be anyone you ever
spoke to or fell asleep beside
or wakened to. I won't be sorry
for you, I won't take your hand
or come forward and touch
your hair or kiss your cheek.
There, between the two sullen elms
without leaves, the ones that died
years ago, do you see a shadow?
It could be the birth we gave
back to the rain. It could be
the silence after love or just pain
without hope or the need to dance.
It looks alive, even in the darkness,
it looks as though it were growing
smaller and smaller, but it's
not a patch of snow. It could be
a whisper, a secret never kept,
everything your heart knew
and you forgot. Don't ask.
*
Give me your hand, and I'll count
each finger twice and put them to sleep
with a name more cold and remote
than a star's. They don't move,
not even to breathe, not even
to search for water or to embrace
another hand. This is the way
things become as we return closer
and closer to air that simply is,
stained by a day not yet here.
A woman gets out of bed and goes
to the window to see if the birds
have wakened and sees the houses
have gone, the trees have turned
inward to become so many pages
unmarked by mistakes. She says
nothing to herself. She makes the bed
and washes the one plate, the cup,
the little spoon and fork. She dries
them carefully and lets them fall
one by one into the garbage.
*
Here it comes.
It's been quiet. If you'd bothered
you'd have heard finches in the trees
and the wind sighing out back and wires
humming in the voices of wire, you
could have heard a country asleep
except for the people down under
stoking the furnaces and the ones
way up changing the light bulbs.
No more. Because here it is,
the big wave the moon's been holding
back and the Rocky Mountains
of ice water. Now the clouds of locusts
waiting since _Genesis_ sweep over Kansas
and eat wheat and carry off the cows.
And the constant hum? It's California
on its knees chanting to keep safe
our vintage wines and swimming pools,
the false Gods of our movies
and the true dead ones in our hearts.
Los Angeles, Seattle, New York City,
Detroit, Washington, gone to sea.
Now you can hear again, finches
in the golden voices of finch, the wind
saying it best as only the old wind
can, blowing over the centuries of nothing,
blowing every which way it wants, blowing.
*
Once in a park in Paris an old woman
seized two coins nesting on my open palm.
I grabbed the offending hand, closed
now like a tiny steel cage, and twisted
while she gasped and tore at my hand
with her nails. At last one dark tear
dripped from her nose and the two coins fell
into the grass. When I put a shoe over them
she cried to the low clouds scudding overhead
that all men were strangers and sons of whores.
Leaving the coins, I stood and walked away.
I did not have to turn to know that smile—
I'd seen it on my own face, I'd known
the same hump in my shoulders, the cold
gleaming in my eyes, and wanted not to see.
"What if grass were bread?" my son asked me
a week before when the plane broke through
the dense rain and we beheld the green world.
I had no answer. When we landed
I bought money with money, forgetting
that each dollar spent was so much time
staring into faces that answered nothing.
Later, in the hotel, my kids played
with the elevator until the old concierge
hissed at them in French, and they roared
out the laughter of boys and refused to stop.
When he came to my door to complain
I answered that in the West grass was bread.
He held his pudgy hands over his breast
to deliver his truths of waste and use.
How many years had he gone faithfully
from room to room turning out lights,
searching for loose change? How many days
had he ended by reheating lunch and praying?
I consider the long fields that blaze
in early March across the lower hills
of the great Sierras. I cannot answer.
I remember a warm bakery in winter north
of the village of Lorca where I bought bread,
the women smiling at me and giving me
the first place in line. Bread so stale
it shattered into shards as sharp as glass
when we tried to break it. My kids,
my wife, and I howled with glee.
The father had returned, his face full
of trust, bearing the gifts of earth.
It was afternoon, cold, and we had hours to go,
we had sour red wine and empty stomachs.
*
To enter the fire
is to be burned, said Leo Maryk, slumped
on the loading dock behind Kelsey-Hayes.
He'd read it somewhere, maybe the Epistles
of Paul or one of the early Fathers,
Augustine or Ambrose. On a night like this
they all ran together in his head.
"Some kind of priest I'll make," he laughed.
Even in the cold I could see the sweat
running down the long, jagged nose, the steam
rising from his enormous chest as from
an oven as he clenched and unclenched
his gloved hands. "A man the size
of me terrified of every little woman,
afraid to live the life my father lived,
I even changed my name." Marikowski asking me
what was love if he couldn't feel it
with his body? what was it? Asking me,
a kid more ignorant than he. Above us a low sky,
the slag heaps burning slowly toward a day
that never came, the others—men and women—
passing in and out of the same fires
they never saw into the world.
*
Once I believed I lived these closed
rows of tenements, the shotgunned houses
bunched uselessly against the coming
of another day. Now the stars settle
down, easing themselves into the river.
Shivering with delight, they almost
go out, but a high wind fans the little
separate points of flame. An ore boat
passes upriver. Riding soundlessly
the other way, another parts the waters
toward seven oceans and an older world.
*
The slow windward motion of the stars.
Late rain falling for hours
between the squat, closed houses.
Then silence, the town asleep, the light
not yet arrived where a single shade is torn
or a door leans ajar. A wagon pulled
down the bricked alley, and there is milk,
bread in cold packages, white, untouched.
Imagine the darkness drawn away,
the new day falling equitably
in the valleys of the living. Imagine
all the long morning fathers rising
with their wives, children making way
for children at sink and table on a day
without work or school until dusk
shatters the golden windows.
Imagine it.
*
The first time we entered
the city, it was late afternoon, Friday,
behind miles of trucks and old cars spewing
everywhere. Past closed warehouses
of gray cotton cloth, factories, low-built
laboratories grinding out antibiotics
and corn plasters. Each time the traffic
stalled we sat in stunned silence. This
would be home. Before long we
found a room and entered the darkness
together, holding each other
as long as we could in the hope
we would be home.
Morning. On the streets
a tiny man leans back planting
his heels as six greyhounds tug him
toward the single tree. Our old friends
the sparrows busy in the gutters turning
yesterday's papers for a hint of the truth.
A blue sky enters from nowhere. A truck
delivers oranges and red sacks of milk.
Air so clear I can see all the way down
the Ramblas to where the sea goes out
on its one voyage, all the way up
to the Holy Mountain from which the devil
said, "Behold, it shall be yours, all
the kingdoms below," and we made our choice.
*
Rain falling into the dry canals
east of here. Old couches, magazines,
dinettes—their legs skyward—, car seats
unstick slowly from the gray mud and drift
spinning toward the little dams and weirs.
A skirt, stained with wine or blood, fills
with water and swirls to the surface,
a carton of empty beer cans like trophies.
A black setter comes toward me, springing
easily along the bank, his long head
hung low, his coat soaked and heavy,
and passes without a sign.
Another day.
The sun still up past six, the dark clouds
gone into the foothills or farther,
the clear sky darkening. The water
moves swiftly past islands of calm
and darkness. I glimpse a root, bare
and silvery, groping upward through air,
an open hand of black branches breaks
the surface for a moment and then
turns under and closes up. Somewhere
a light comes on in a living room,
someone I don't know pauses at
the window before the last light goes
and speaks to me.
One great room, the moon
sliding through the trailing wisps
of clouds or dust clouds. The child
gone under in clear water years ago,
the sad yelps of brothers and sisters
that went on and on until morning
quiet at last. The earth's own sighs,
the day's last breath going out,
my own silent cry of denial. They're
all asleep, all the windows from here
to the end of the world are open,
I can hear the even breathing
of all that is wordless and final.
# IV
## SOLOING
My mother tells me she dreamed
of John Coltrane, a young Trane
playing his music with such joy
and contained energy and rage
she could not hold back her tears.
And sitting awake now, her hands
crossed in her lap, the tears start
in her blind eyes. The TV set
behind her is gray, expressionless.
It is late, the neighbors quiet,
even the city—Los Angeles—quiet.
I have driven for hours down 99,
over the Grapevine into heaven
to be here. I place my left hand
on her shoulder, and she smiles.
What a world, a mother and son
finding solace in California
just where we were told it would
be, among the palm trees and all-night
super markets pushing orange
back-lighted oranges at 2 A.M.
"He was alone," she says, and does
not say, just as I am, "soloing."
What a world, a great man half
her age comes to my mother
in sleep to give her the gift
of song, which—shaking the tears
away—she passes on to me, for now
I can hear the music of the world
in the silence and that word:
soloing. What a world—when I
arrived the great bowl of mountains
was hidden in a cloud of exhaust,
the sea spread out like a carpet
of oil, the roses I had brought
from Fresno browned on the seat
beside me, and I could have
turned back and lost the music.
## SCOUTING
I'm the man who gets off the bus
at the bare junction of nothing
with nothing, and then heads back
to where we've been as though
the future were stashed somewhere
in that tangle of events we call
"Where I come from." Where I
came from the fences ran right
down to the road, and the lone woman
leaning back on her front porch as she
quietly smoked asked me what did
I want. Confused as always, I
answered, "Water," and she came to me
with a frosted bottle and a cup,
shook my hand, and said, "Good luck."
That was forty years ago, you say,
when anything was possible. No,
it was yesterday, the gray icebox
sat on the front porch, the crop
was tobacco and not yet in, you
could hear it sighing out back.
The rocker gradually slowed as
she came toward me but never
stopped and the two of us went on
living in time. One of her eyes
had a pale cast and looked nowhere
or into the future where without
regrets she would give up the power
to grant life, and I would darken
like wood left in the rain and then
fade into only a hint of the grain.
I went higher up the mountain
until my breath came in gasps,
my sight darkened, and I slept
to the side of the road to waken
chilled in the sudden July cold,
alone and well. What is it like
to come to, nowhere, in darkness,
not knowing who you are, not
caring if the wind calms, the stars
stall in their sudden orbits,
the cities below go on without
you, screaming and singing?
I don't have the answer. I'm
scouting, getting the feel
of the land, the way the fields
step down the mountainsides
hugging their battered, sagging
wire fences to themselves as though
both day and night they needed
to know their limits. Almost still,
the silent dogs wound into sleep,
the gray cabins breathing steadily
in moonlight, tomorrow wakening
slowly in the clumps of mountain oak
and pine where streams once ran
down the little white rock gullies.
You can feel the whole country
wanting to waken into a child's dream,
you can feel the moment reaching
back to contain your life and forward
to whatever the dawn brings you to.
In the dark you can love this place.
## COMING OF AGE IN MICHIGAN
New Year's Eve, 1947, the old one's ending
or the new beginning on a familiar note.
His name is McDonald, his father owns a dairy
down the block from Brass Craft where I polish
flexible plumbing tubes by the hour. "Sol and Abie,"
he says, "Fe're not open yet for bizniz," then holds
his nose against that awful smell, the "Abie" smell
no one asked for. Noel Baker begins to cry.
How did the night end? I can't remember it ending.
I can remember counting the house, an even dozen
of them and two of us. My brother threw his drink
against the wall, and no one moved on him, no one
said a thing. McDonald was dragged off laughing
to a bedroom in his fancy suite we'd been invited
into by some genuine innocent who didn't know
a Jew from Commodore Vanderbilt without his yacht.
I remember my joy at seeing Noel Baker for the first time
since the 8th grade, a skinny whiz at math and English
in penny loafers and monogrammed sweaters. (I saw her
only once after that in a liquor store in early June
years later, she was talking too much and too loudly,
but he didn't mind, he'd left the motor running—
a white LaSalle convertible they floated off in
while we waited in line.) I forget all the rest.
*
Have I taken something away from you? Noel Baker
did not become a famous woman: it was too late
to enter the fiction of F. Scott Fitzgerald, too early
for her to become the governor of Michigan,
which hardly makes you famous. My brother and I
did not throw McDonald from a 7th story window
of the Book Cadillac and into _The Detroit Free Press_ ,
we did not even have the good taste to have our teeth
knocked loose, to come home with our best white shirts
blood smeared, our ties torn to shreds, cigarettes
dangling from swollen lips. Don't blame us.
The Book Cadillac is still going, though it smells
like a steam bath, and the rooms are tiny and gray.
(Down the boulevard the Statler, boarded over and serene,
did not compromise, the Fox Theatre around the corner—
a rip-off of the great mosque of Cordoba—became
a car park, and even the bus station got up one morning
and moved to the suburbs.) No one that night turned
into literature, nothing that we did or didn't
entered the mythology of boys growing into men
or girls fighting to be people. Everyone went home
because that was how the world was before God
tuned to prime-time TV and kids still rose early
to catch the bus for school and everyone was innocent.
## THE RIGHT CROSS
The sun rising over the mountains
found me awake, found an entire valley
of sleepers awake, dreaming of a few hours
more of sleep. Though the Great Central Valley
is home for the homeless, the fruit pickers
of creation, for runaway housewives
bored by their husbands, and bored husbands,
the rising sun does not dip back behind
the Sierras until we're ready. The Valley sun
just comes on. We rise, drop our faces
in cold water, and face the prospects
of a day like the last one from which we
have not recovered. All this month I've
gone in search of the right cross, the punch
which had I mastered it forty years ago
might have saved me from the worst. The heavy bag
still hangs from the rafters of the garage,
turning in no wind, where my youngest son
left it when he went off ten years ago
abandoning his childish pursuits to me.
After tea, dry toast, and some toe-touching,
I'm ready to work. I pull on the salty
bag gloves, bow my head, dip one shoulder
into the great sullen weight, and begin
with a series of quick jabs. I'm up
on my toes, moving clockwise, grunting
as the blows crumple, the air going out
and coming back in little hot benedictions.
I'm remembering Nate Coleman barking
all those years ago, "Straight from the shoulder,
Levine," as though describing his own nature.
The gentlest man I ever knew, perfect
with his fists, our master and mentor,
who fought only for the love of it,
living secretly by day in suit and tie,
vending copper cookware from the back seat
of his black Plymouth. The dust rises
from the sour bag, and I feel how fragile
my left wrist has become, how meek the bones
of my shoulders as the shocks come home,
the bag barely moving. "Let it go!"
Nate would call, urging the right hand out
against the big light heavies, Marvin
with his sudden feints and blunt Becker,
his face grim and closed behind cocked fists.
Later, the gym gone silent in the half-dark,
Nate would stand beside me, left hand
on my shoulder, and take my right wrist
loosely in his right hand, and push it out
toward an imagined foe, his right knee
pressed behind my right knee until my leg
came forward. I could feel his words
—"like this"—falling softly on my cheek
and smell the milky sweetness of his breath
—"you just let it go"—, the dark lashes
of his mysterious green eyes unmoving.
The bag is going now, swinging easily
with the force of jabs and hooks. The garage
moans as though this dance at its center
threatened to bring it down. I throw a right,
another, and another before I take my rest
in the cleared space amid the detritus
of five lives: boxes of unanswered letters,
school papers, report cards, scattered parts
of lawn mowers and motorcycles gone to ground.
The sky is coming through the mismatched boards
of the roof, pure blue and distant, the day
rising from the oily cement of the floor
as again I circle the heavy bag throwing out
more punches until I can't. If my sons
were here they'd cheer me on, and I'd
keep going into the impossible heat
and before I quit I might throw, just once,
for the first time, the perfect right cross.
They say it's magic. When it lands
you feel the force of your whole body,
even the deeper organs, the dark fluids
that go untapped for decades, the tiny
pale microbes haunting the bone marrow,
the intricate patterns that devised
the bones of the feet, you feel them
finally coming together like so many
atoms of salt and water as they form
an ocean or a tear, for just an instant
before the hand comes back under the chin
in its ordinary defensive posture.
The boys, the grown men dreaming
of the squared circle into which the light
falls evenly as they move without effort
hour after hour, breathing easily, oiled
with their own sweat, fight for nothing
except the beauty of their own balance,
the precision of each punch.
I hated to fight. I saw each blow
in a sequence of events leading
finally to a winner and a loser.
Yet I fought as boys were told to do,
and won and lost as men must. That's over.
Six months from my sixtieth year, doused
in my own juices, I call it quits
for the day, having earned the rituals—
the long bath, the shave, the laundered clothes,
the afternoon muse as the little clots
of stiffness break up and travel down
the channels of the blood. After dinner
and before sleep, I walk behind the garage
among grape vines and swelling tomatoes
to where the morning glories close down
in the rising darkness and the cosmos
flare their brilliant whites a last time
before the moon comes out. From under
the orange trees the click and chuckle
of quail; the tiny chicks dart out
for a last look and scurry back again
before the earth goes gray. A dove moans,
another answers from a distant yard as though
they called each other home, called each of us
back to our beds for the day's last work.
## THE SWEETNESS OF BOBBY HEFKA
What do you make of little Bobby Hefka
in the 11th grade admitting to Mr. Jaslow
that he was a racist and if Mr. Jaslow
was so tolerant how come he couldn't
tolerate Bobby? The class was stunned.
"How do you feel about the Jews?"
asked my brother Eddie, menacingly.
"Oh, come on, Eddie," Bobby said,
"I thought we were friends." Mr. Jaslow
banged the desk to regain control.
"What is it about Negroes you do not like?"
he asked in his most rational voice,
which always failed to hide the fact
he was crazy as a bed bug, claiming
Capek's _RUR_ was far greater than _Macbeth._
Bobby was silent for a long minute, thinking.
"Negroes frighten me," he finally said,
"they frighten my mother and father who never
saw them in Finland, they scare my brother
who's much bigger than me." Then he added
the one name, Joe Louis, who had been
busy cutting down black and white men
no matter what their size. Mr. Jaslow
sighed with compassion. We knew that
before the class ended he'd be telling us
a great era for men and women was imminent
if only we could cross the threshold
into humanitarianism, into the ideals
of G. B. Shaw, Karel Capek, and Mr. Jaslow.
I looked across the room to where Bobby
sat in the back row next to the windows.
He was still awake, his blue eyes wide.
Beyond him the dark clouds of 1945
were clustering over Linwood, the smokestack
of the power plant gave its worst
to a low sky. Lacking the patience to wait
for combat, Johnny Mooradian had quit school
a year before, and Johnny was dead on an atoll
without a name. Bobby Hefka had told the truth
—to his own shame and pride—and the rains
came on. Nothing had changed for a roomful
of 17 year olds more scared of life than death.
The last time I saw Bobby Hefka he was driving
a milk truck for Dairy Cream, he was married,
he had a little girl, he still dreamed
of going to medical school. He listened
in sorrow to what had become of me. He handed
me an icy quart bottle of milk, a gift
we both held on to for a silent moment
while the great city roared around us, the trucks
honking and racing their engines to make him move.
His eyes were wide open. Bobby Hefka loved me.
## ON THE RIVER
My brother has an old row boat
moored to a dock at the foot
of Jefferson Avenue, Detroit.
Once a week in decent weather
he rows out to get a better
look at the opposite shore
as though Canada truly were
a foreign country. It isn't easy
what with the ore boats' lazy
crawl toward salt water, the launches
of tourists and cops, the lunchers
spread out on barges, docks, rafts,
waiting for the oiled clouds to lift
a moment and unveil the sun,
waiting for the fumes of exhaustion
to blow off in the poor gusts
of our making—collective breaths,
passing trucks, running dogs loath
to return to their chains.
On schedule he comes at noon
or not at all—his only free time—
so he can see with a painter's eye
the hulking shapes of warehouses define
themselves, the sad rusts and grays
take hold and shimmer a moment
in the blur of air until the stones
darken like wounds and become nothing.
He does this for our father
who parked each week exactly here
to stare at that distant shore
as though it were home, and then
passed quietly to a farther one.
He does this for me, who long ago
stopped seeing beneath the shadows
of concrete and burned brick towers
the flickering hints of life, the colors
we made of fresh earth and flowers
coming through the wet smells of houses
fallen in upon themselves. I suppose
he does this also so that somewhere
on the face of the black waters
he can turn, feathering one oar
slowly, to behold his own life
come into view brick by dark brick,
bending his back for all it's worth,
as the whole thing goes up in smoke.
## THE SEVENTH SUMMER
How could I not know God had a son?
the biggest kid asked. I considered.
No one told me. Did I ever go to church?
Yes, but they spoke a language I didn't
actually understand. The three stared at me.
I could have answered that it was possible
God did not have a son and that this picture
over what was to be my bed was a fake—
for one thing it wasn't a photograph,
for another it looked like an ad from _Life_ ,
but I was already sorry I'd said, "Who
is he?" referring to the figure displayed
behind glass in a plain wooden frame.
What I truly wanted to know was why God
had let anyone do such a thing to his son,
nail his hands and feet to a huge wooden cross
from which he sagged in what appeared
to be less discomfort than I would have felt.
"The Jews done it," the biggest one said, as though
reading my mind. I felt a chill run through me,
sure that once more I was going to be blamed
for what I had not done or what I'd done
but done without meaning to do, but the boys
—the oldest was sixteen, over twice my age—left
me to myself, for it was early to bed for everyone.
I lay awhile in the silent dark of the farmhouse
wondering if it could be so, that God had
a son he had let die, and if this were so why
no one had told me so that I might understand
why life could be so puzzling for all of us.
Days passed before Lars, the fourteen year old,
told me that it was OK, this Jesus had died
so that all of us could be saved, in the end
things turned out for the best. That was Sunday,
after the boys had returned from church—
to which I did not go—, and before we walked
into town to swim in the big public place.
I remember best how sweet was the lake water
we swam in, how I could even swallow
little gulps of it and not feel ill and how large
the bodies around me were, Lars and Sven thrashing
after the girls in their dark wool suits, the girls
squealing with mock hurt when they would catch
them up in their pale arms, for though their faces
were deeply browned their bodies were ghostly.
Sven, Lars, and Thomas, three boys as big as men,
who let me climb to their secret room beside
the hay loft, where they smoked and spoke of women,
the laughter rushing out of their great throats,
the strange words I had never heard before coughed
out in sudden spasms, and such hopes uttered
as they moved about the room in a half-dance,
half-sword-fight, calling out the magic names
of the absent girls as they stroked their own bodies
at chest and crotch or rolled on the floor
in mock death agony. August in Michigan,
the world spinning around me, my mother gone
in the grief of final loss, from which one day
she would awaken in daylight, one year
before the wars in Ethiopia, Spain, and China
could give my growing up its particular name,
and yet I sat at their table that night, head bowed
in the grace I did not say, thankful for corn,
beans, and poisonous pork, and understood it all.
# A NOTE ABOUT THE AUTHOR
Philip Levine was born in 1928 in Detroit and was formally educated there, at the public schools and at Wayne University (now Wayne State University). After a succession of industrial jobs he left the city for good and lived in various parts of the country before settling in Fresno, California. He currently teaches in the creative writing program at New York University. Three of his books have been nominated for the National Book Critics Circle Award, and two of them, _Ashes_ and _7 Years from Somewhere_ , have received it. _Ashes_ also received the American Book Award in 1980. In 1987 he received the Ruth Lilly Poetry Prize "for distinguished poetic achievements," awarded by _Poetry_ magazine and the American Council for the Arts. His _New Selected Poems_ was published simultaneously with _What Work Is_ , which won the National Book Award for Poetry in 1991. _The Simple Truth_ (1994), received the Pulitzer Prize for poetry. His latest book of poems is _The Mercy_ , and two earlier titles, _They Feed They Lion_ and _The Names of the Lost_ have been recently reissued in a combined volume.
# BOOKS BY PHILIP LEVINE
THE MERCY 1999
THEY FEED THEY LION and
THE NAMES OF THE LOST (reissue) 1999
THE SIMPLE TRUTH 1994
WHAT WORK IS 1991
NEW SELECTED POEMS 1991
A WALK WITH TOM JEFFERSON 1988
SWEET WILL 1985
SELECTED POEMS 1984
ONE FOR THE ROSE 1981
7 YEARS FROM SOMEWHERE 1979
ASHES: POEMS NEW AND OLD 1979
THE NAMES OF THE LOST 1976
1988 1974
THEY FEED THEY LION 1972
RED DUST 1971
PILI'S WALL 1971
NOT THIS PIG 1968
ON THE EDGE 1963
| {
"redpajama_set_name": "RedPajamaBook"
} | 5,140 |
Love is the most beautiful feeling that good has created, and probably the most powerful one too. We all need a strong love relationship in order to keep ourselves motivated. When we are in an intimated relationship it makes us feel motivated and gives us power to face the challenges of daily life. A powerful relationship not only connects you with your partner but also with the world too. When we are in strong relationship we not only feel satisfied, but at the same time, we also become kinder to other people.
The research also reveals that the strong love relationship directly affects the physical health and work performance of a person. When we are in a good relationship, our efficiency increased and we perform better in our professional life. The scientific research also shows that strong relationship always has a positive impact on the immune system and cardiovascular functions of our body. It is also pertinent to mention here that all the strong love relationships are based on the mutual understanding and self respect to each other. A relationship is like a two way traffic in which both sides have to perform well and respect the feelings of each other.
This entry was posted in Relationship and tagged love, partner, physical health, relationship. Bookmark the permalink. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,224 |
Q: font-weight for custom fonts I'm using my custom fonts defined like this:
@font-face {
font-family : 'LatoWeb';
src : url('../resources/fonts/Lato-Regular.woff') format('woff');
font-style : normal;
font-weight : normal;
text-rendering : optimizeLegibility;
}
What's interesting is that I don't have font-weight variations for this font. However, starting from font-weight: 600 the font gets bolder, how's that possible? Where does it take the font if it's not loaded?
A: @font-face {
font-family : 'LatoWeb';
src : url('../resources/fonts/Lato-Regular.woff') format('woff');
font-weight : normal;
font-style : normal;
text-rendering : optimizeLegibility;
}
also you can use:
for example :
font-weight:normal
font-weight:bold
100 Extra Light or Ultra Light
200 Light or Thin
300 Book or Demi
400 Normal or Regular
500 Medium
600 Semibold, Demibold
700 Bold
800 Black, Extra Bold or Heavy
900 Extra Black, Fat, Poster or Ultra Black
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,543 |
This bronze sculpture, at Corinth Contraband Camp, is known as "Woman and Child Reading." The bronze figures in the park all depict some facet of daily life, from when the camp was active. This photograph provides a view over the young girl's right shoulder, as she reads. There is embossed text on the pages of the book. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,199 |
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