text:
\section{Introduction}
This demo file is intended to serve as a ``starter file" for the
Robotics: Science and Systems conference papers produced under \LaTeX\
using IEEEtran.cls version 1.7a and later.

\section{Section}

Section text here.

\subsection{Subsection Heading Here}
Subsection text here.

\subsubsection{Subsubsection Heading Here}
Subsubsection text here.

\section{RSS citations}

Please make sure to include \verb!natbib.sty! and to use the
\verb!plainnat.bst! bibliography style. \verb!natbib! provides additional
citation commands, most usefully \verb!\citet!. For example, rather than the
awkward construction

{\small
\begin{verbatim}
\cite{kalman1960new} demonstrated...
\end{verbatim}
}

\noindent
rendered as ``\cite{kalman1960new} demonstrated...,''
or the
inconvenient

{\small
\begin{verbatim}
Kalman \cite{kalman1960new}
demonstrated...
\end{verbatim}
}

\noindent
rendered as
``Kalman \cite{kalman1960new} demonstrated...'',
one can
write

{\small
\begin{verbatim}
\citet{kalman1960new} demonstrated...
\end{verbatim}
}
\noindent
which renders as ``\citet{kalman1960new} demonstrated...'' and is
both easy to write and much easier to read.

\subsection{RSS Hyperlinks}

This year, we would like to use the ability of PDF viewers to interpret
hyperlinks, specifically to allow each reference in the bibliography to be a
link to an online version of the reference.
As an example, if you were to cite ``Passive Dynamic Walking''
\cite{McGeer01041990}, the entry in the bibtex would read:

{\small
\begin{verbatim}
@article{McGeer01041990,
  author = {McGeer, Tad},
  title = {\href{http://ijr.sagepub.com/content/9/2/62.abstract}{Passive Dynamic Walking}},
  volume = {9},
  number = {2},
  pages = {62-82},
  year = {1990},
  doi = {10.1177/027836499000900206},
  URL = {http://ijr.sagepub.com/content/9/2/62.abstract},
  eprint = {http://ijr.sagepub.com/content/9/2/62.full.pdf+html},
  journal = {The International Journal of Robotics Research}
}
\end{verbatim}
}
\noindent
and the entry in the compiled PDF would look like:

\def\tmplabel#1{[#1]}

\begin{enumerate}
\item[\tmplabel{1}] Tad McGeer. \href{http://ijr.sagepub.com/content/9/2/62.abstract}{Passive Dynamic
Walking}. {\em The International Journal of Robotics Research}, 9(2):62--82,
1990.
\end{enumerate}
where the title of the article is a link that takes you to the article on IJRR's website.

Linking cited articles will not always be possible, especially for
older articles. There are also often several versions of papers
online: authors are free to decide what to use as the link destination
yet we strongly encourage to link to archival or publisher sites
(such as IEEE Xplore or Sage Journals).  We encourage all authors to use this feature to
the extent possible.

\section{Conclusion}
\label{sec:conclusion}

The conclusion goes here.

\section*{Acknowledgments}

\bibliographystyle{plainnat}

\section{Introduction}
\subsection{Motivation}
Safe and reliable operation of a robot in a cluttered environment can
be difficult to achieve due to noisy and partial observations of the
state of both the world and the robot. As autonomous systems leave the
factory floor and become more pervasive in the form of drones and
self-driving cars, it is becoming increasingly important to understand
how to design systems that will not fail under these real-world
conditions. While it is important that these systems be safe, it is
also important they do not operate so conservatively as to be
ineffective. They must have a strong understanding of when they take
risks so they can avoid them, but still operate efficiently.

While most previous work focuses on robot state uncertainty, this
paper focuses on safe navigation when the locations and geometries of
these obstacles are uncertain. We focus on algorithms that find safety
``certificates"---easily verifiable proofs that the trajectory or
policy is safe. We examine two implications of the algorithms. First,
the computational complexity of reasoning about uncertainty can be
quite low. Second, the mathematics surrounding robot safety can have
surprising behavior. We demonstrate how these tools can be used to
design a motion planner guaranteed to give only safe plans, and inform
the design of more general systems that make decisions under
uncertainty.

\begin{figure}
\centering
\includegraphics[width=\columnwidth]{planning-traj-hq-crop.pdf}
\caption{The desired trajectory found by the planner shown with its specialized shadows that certify the probability of collision as less than $0.26\%$.}
\label{fig:safetraj}
\end{figure}

\subsection{Problem Formulation}
We consider two settings.  In the {\em off-line} setting we have a
fixed set of information about the environment and are searching for
an open-loop trajectory. In the {\em on-line} setting the robot has
access to a stream of observations and can change its trajectory as a
function of new information; the problem is to find a policy, a
function from observations to actions, that allow the robot to adapt
to changing circumstances.  We show that different notions of safety
are required for the two cases to ensure that the robot can guarantee
a low probability of collision throughout its entire execution.

Safety in the offline setting amounts to staying out of regions likely
to be contained within obstacles, and can be analyzed by computing
geometric bounds on obstacles for which we have only partial
information. Safety in the online setting builds on offline safety by
requiring that the robot respect a contract with respect to the
aggregate lifetime risk of operation while always having a guaranteed
safe trajectory available to it.

We develop a general framework for analyzing safety and provide an
example of applying this framework to a specific model of random
geometry. We wish to emphasize that this framework can be applied to a
wide variety of models beyond the example shown here.

Our framework operates in generality in $\mathbb R^n$ and assumes that
obstacles are polytopes in $\mathbb R^n$. In this paper we focus on
examples of typical robotic domains in $\mathbb R^2$ and $\mathbb
R^3$. We ensure safety by verifying that the swept volume of a robot's
trajectory is unlikely to collide with any obstacles. These swept
volumes can be computed geometrically, or, for dynamical systems, via
SOS programs \cite{majumdar2012algebraic}.

We say that a trajectory, a map from time to robot configurations
${\mathcal Q}$, $\tau: [0,\infty) \rightarrow \mathcal Q$ is
$\epsilon-$safe if the swept volume of the robot along trajectory $\tau$
intersects an obstacle with probability less than
$\epsilon$. Formally, if $A$ is the event that the swept volume of
$\tau$ intersects an obstacle, then $\tau$ is \textit{$\epsilon-$safe}
in the offline sense if $P(A \mid \tau) \le \epsilon$.

We say that a policy, a map from observation history $O$, state history $H$
and time to a trajectory $\tau$, $\pi: O \times H \times
[0,\infty)\rightarrow \tau$ is $\epsilon-$safe if,  under all sequences of
observations, $P(A \mid \pi) \le \epsilon$. This notion of safety will
be referred to as \textit{policy safety}; it is a departure from
previous models of robot safety, capturing
the notion of a contract that the total risk over the
lifetime of the system always be less than $\epsilon$.
\label{sec:policySafety}

The requirement that the safety condition hold under all observations
sequences is more conservative than the natural definition of
$P(A \mid \pi )$.  It crucial to prevent undesirable behavior that can
``cheat'' the definition of safety; this is discussed in detail in
section~\ref{sec:onlinesafety}.

\subsection{Related Work}
Planning under uncertainty has been studied extensively. Some
approaches operate in generality and compute complete policies
\cite{kaelbling1998planning} while operate online, computing a
plausible open-loop plan and updating it as more information is
acquired \cite{platt2010belief}.

Generating plans that provide formal non-collision (safety) guarantees
when the environment is uncertain has proven difficult. Many methods
use heuristic strategies to try to ensure that the plans they generate are
unlikely to collide. One way of ensuring that a trajectory is safe is
simply staying sufficiently far away from obstacles. If the robot's
pose is uncertain this can be achieved by planning with a robot whose
shape is grown by an uncertainty
bound~\cite{bry2011rapidly}. Alternatively, if the
obstacle geometry is uncertain, the area around estimated obstacles
can be expanded into a shadow whose size depends on the magnitude of
the uncertainty~\cite{kaelbling2013integrated,lee2013sigma}.

Another approach focuses on evaluating the probability that a
trajectory will collide. Monte-Carlo methods can evaluate the
probability of collision by sampling, but can be computationally
expensive when the likelihood of failure is very
small~\cite{montecarloLJESMP2015}. When the uncertainty is restricted
to Gaussian uncertainty on the robot's pose, probabilistic collision
checking can yield notable performance improvements~\cite{sun2016safe}\cite{Park2016EfficientPC}\cite{Park2016FastAB}.

Another perspective is finding a plan that is safe by construction. If
the system is modeled as a Markov Decision Process, formal
verification methods can be used to construct a plan that is guaranteed
to be safe~\cite{ding2013strategic}\cite{feyzabadi2016multi}. Recent
work on methods that are based on signal temporal logic (STL) model have also
uncertainty in obstacle geometry. With PrSTL \citet{prstl} explicitly
model uncertainty in the environment to help generate safe plans but
offer weaker guarantees than our work.

\subsection{Contributions}
This paper makes three contributions.
the first is a formal definition of online safety that provides risk
bounds on the entire execution of a policy.

The second contribution is an algorithm for efficiently verifying
offline safety with respect to polytopes with Gaussian distributed
faces (PGDFs) that is then generalized to the online case. In
comparison to previous methods, the quality of the resulting bound is
not dependent on the number of obstacles in the environment. The
presented algorithms produce a certificate, which allows another
system to efficiently verify that the actions about to be taken are
safe. For a maximal collision probability of $\epsilon$, the
runtime of the algorithm grows as $\log \frac 1 \epsilon$ making
 it efficient even for very small $\epsilon$'s.

The third contribution is a modification to the RRT algorithm that
generates safe plans.  For any fixed $\epsilon$, the resulting planner
is guaranteed to only return trajectories for which the probability of
failure is less than $\epsilon$. We note that for $n$ obstacles, the
runtime of the RRT is increased only by a $\log n \log \frac 1
\epsilon$ factor, which suggests that reasoning about uncertainty can
come at a low computational cost.  A result of running this algorithm
is shown in figure~\ref{fig:safetraj}.

\section{Model for Random Geometry}

Previous work on planning under uncertainty has often relied on the
notion of a shadow~\cite{kaelbling2013integrated, lee2013sigma}, which
is a volume that represents an uncertain estimate of the pose of an
object and the space that it may occupy.  A proper shadow is likely to
contain the true object; and even if the exact location of the object
is not known, it is sufficient to avoid the obstacle's shadow in order
to avoid the true obstacle. A shadow is essentially the geometric
equivalent of a confidence interval.

In order to provide strong guarantees about the safety of robot
trajectories we first formalize this notion of a shadow.
\begin{defn}\label{def:shadow} A set $X$ is said to be an {\em
    $\epsilon-$shadow} of a random obstacle $O$ if $P( O \subset X)
  \ge 1 - \epsilon$.
\end{defn}
To be able to generate shadows with desired properties, we need to
place some restrictions on the class of distributions from which
obstacles are drawn.

One way to arrive at a distribution on the shape and position of
obstacles is to imagine that sensor data is obtained in the form of
point clouds in which the points are segmented according to the face of
the obstacle to which they belong. Then, the points belonging to a
particular obstacle face can be used to perform a Bayesian linear
regression on the parameters of the
plane containing the face; given a Gaussian prior on the face-plane
parameters and under reasonable assumptions about the noise-generation
process, the posterior on the face-plane parameters will also be
Gaussian~\cite{bishop2006pattern, rasmussen2006gaussian}.

Recalling that a polytope $X$ is the intersection of halfspaces, we
can define a distribution over the parameters of polytopes with a
fixed number of faces. For $\bm x$
represented in homogeneous coordinates, a polytope $X$ can be
represented as
$$X = \bigcap \bm n_i ^T \bm x \le 0\;\;.$$
When these normal vectors $\bm n_i$ are drawn from a Gaussian
distribution $\mathcal N \left ( \bm \mu_i, \bm
  \Sigma_i \right ) $, we will call this a polytope with
Gaussian distributed Faces (PGDF) with parameters $\bm \mu_i, \bm
\Sigma_i$. We do not assume that the normal vectors are drawn
independently and show that an independence assumption would yield
little additional tightness to our bounds.

Using the PGDF model, we will be able to identify shadow regions that
are guaranteed to contain the obstacle with a probability greater than
$1 - \epsilon$ in most cases of interest.  There are degenerate
combinations of values of $\epsilon$, $\mu$, and $\Sigma$ for which
there is no well-defined shadow (consider the case in which the means
of all the face-planes go through the origin, for example).  In
addition, there are some cases in which the bounds we use for
constructing regions are not tight and so although a shadow region
exists, we cannot construct it.  Details of these cases are discussed
in the proofs in the supplementary material.

If we consider a single face, theorem~\ref{lemma:lgshape} identifies a
shadow region likely to contain the corresponding half-space.

 \begin{thm}\label{lemma:lgshape} Consider $\epsilon \in (0,1)$,
   $\bm n \sim \mathcal N \left  (\bm \mu, \bm \Sigma \right)$ such
   that the combination of $\epsilon, \bm \mu, \bm \Sigma$ is
   non-degenerate. There exists a shadow $S$ s.t. $\{ \bm x \mid \bm n^T \bm x \ge 0 \}$ is
   contained within $S$ with probability at least $1 -
   \epsilon$. \end{thm}

 While a detailed constructive proof is deferred to the supplemental
 materials, we present a sketch here. First, we identify a
 sufficiently high probability-mass region of half-spaces $\bm n$,
 which, by construction corresponds to a linear cone $C$ in the space
 of half-space parameters. We then take the set of $\bm x$'s in
 homogeneous coordinates that these half-spaces contain. The set of
 points not contained by any half-space is the polar cone of
 $C$. Converting back to non-homogeneous coordinates yields conic
 sections as seen in figure~\ref{fig:lgshape}.

 \begin{comment}\begin{proofatend}
\textit{Preliminaries:} In order to avoid a constant term in the definition of halfspaces we use homogeneous coordinates, and thus our shadow will be defined asinvariant under positive scaling. $x$ will always refer to these coordinates. Likewise, parameterizations of hyperplanes that go through the origin are positive scale invariant $\alpha$ will always refer to a hyperplane parametrization.

It is important to note that $\alpha$'s act on the $x$'s. They belong to different spaces, even though they may share geometric properties and dimensionality.

We will for the convenience of applying standard theorems from geometry, sometimes treat these spaces by looking at the representation as a subset of $\mathbb R^{n}$, where the sets will be closed under positive scaling. This will also prove convenient when working with the gaussian distribution, as it is not typically defined on such spaces.

After the proof, we will provide an interpretation of the theorem in standard coordinates ($\mathbb R^{n-1}$) in order to provide intuition for the shape of the generated shadows.

\textit{Proof Sketch:}
\begin{enumerate}
\item Identify a set of parameters, as a scaled covariance ellipsoid around the mean, that has probability mass of $1 - \epsilon$.
\item Consider the set of hyperplanes they form. This will be a linear cone.
\item Take any $x \in \mathbb R^{n}$ that is contained in by any $\alpha$ in the previous set of hyperplanes. This will be the shadow. Its complement will also be a linear cone.
\item Converting back to non-homogeneous coordinates will reveal that the shape of the complement of a shadow is a conic section.
\end{enumerate}

First we note that the squared radius values of the $n-d$ standard multivariate Gaussian distribution is distributed as a chi-squared distribution with $n$ degrees of freedom. Let $\phi(k)$ be the corresponding cumulative distribution function. Then it follows that the probability mass of $A = \{ \bm \alpha | (\bm \alpha - \bm \mu)^T \bm \Sigma^{-1} (\bm \alpha - \bm \mu \le \phi^{-1}(1 - \epsilon)\}$ is $1 - \epsilon$.

We note, however, that since $\alpha$'s are invariant under positive scaling, the resulting hyperplanes form a linear cone, $C$. This is the minimal cone with axis $\bm \mu$ that contains the above ellipsoid.

We consider the polar of this cone, $C^0$. A polar cone $C^0$ of $C$ is $\{ x | x^T y \le 0 \forall y \in C\}$. Since every element of $C^0$ has a positive negative dot product with every element of $C$, ${C^0}^C$ is the set of points which have a positive dot product with at least one element of $C$. ${C^0}^C$ is the set that is contained by at least a single $\alpha \in A$ and an $\epsilon-$shadow. We note that $C^0$, the complement of the shadow, is also a linear cone since the polar cone of a linear cone is also a linear cone.

In order to understand the geometry this induces on non-homogeneous coordinates we take a slice where the last coordinate is equal to $1$. Since our set has an equivalence class of positive scaling, this slice will contain exactly one representative of every point. This set is a standard conic section---giving us the familiar curves we see throughout the paper.

If this slice has finite (ex. 0) measure in $\mathbb R^{n-1}$ we say that the shadow is degenerate---it did not provide us with a useful shadow. One example of a degenerate case is when the set $A$ contained the origin. A neighborhood of the origin in parameter space produces halfspaces that contain all of $\mathbb R^n$. The distribution being close to centered about the origin represents having little to no information about the points contained within the half-space.
\end{proofatend} \end{comment}

\begin{figure}[tp]
\centering
\includegraphics[width=0.4\columnwidth]{oneside-crop.pdf}
\caption{An example of the region defined by theorem \ref{lemma:lgshape}. The darker region is the "mean" obstacle and the orange region contains 95\% of the obstacles generated by these parameters.}
\label{fig:lgshape}
\end{figure}

In lemma \ref{lemma:polybuild} we generalize this notion to
polytopes. For an obstacle with $m$ faces, we can take the
intersection of the resulting $\frac \epsilon m$-shadows. A union bound
guarantees that the probability of any face not being contained in its
corresponding region is less than $\epsilon$. Thus the probability
that the polytope is not contained in this region is less than
$\epsilon$. In other words, lemma \ref{lemma:polybuild} constructs
an $\epsilon$ shadow.

\begin{lemma}\label{lemma:polybuild} Consider a polytope defined by
  $\bigcap\limits_i \bm n^T \bm x \le 0$. Let $X_i$ be a set that
  contains the halfspace defined by $\bm n_i$ with probability at
  least $ 1- \epsilon_i$ (for example as in theorem
  \ref{lemma:lgshape}). Then $\bigcap\limits_i X_i$ contains the
  polytope with probability at least $1 - \sum\limits_i \epsilon_i$.
\end{lemma}
\begin{comment}
    \begin{proofatend}
We note that $\bigcap\limits_i X_i$ contains the polytope if every $X_i$ contains its corresponding halfspace. Since the probability that $X_i$ does not contain its corresponding halfspace is $\epsilon_i$, a union bound gives us that the probability that any $X_i$ does not contain its corresponding halfspace is bounded by $\sum\limits_i \epsilon_i$. $\bigcap\limits_i X_i$ containing the polytope is the complement of this event, thus the probability that $\bigcap\limits_i X_i$ contains the polytope is at least $ 1 - \sum\limits_i \epsilon_o$
\end{proofatend}
\end{comment}
\subsection{Computing Obstacle Shadows}

\begin{figure}[tp]
\centering
\begin{tikzpicture}
  \node[anchor=south west,inner sep=0] at (0,0) {\includegraphics[width=0.3\textwidth]{twosquares-crop.pdf}};
  \node[draw,align=left] at (1.3,3) {$P(A) = 0.5$};
  \node[draw,align=left] at (4.1,3) {$P(A^C) = 0.5$};
  \end{tikzpicture}
\caption{Both the blue and black squares are valid $0.5$-shadows, while the union of the two yellow areas is the set of points with probability at least $0.5$ of being in the square.}
\label{fig:shadowquirk1}
\end{figure}

\begin{figure}[tp]
\centering
\includegraphics[width=0.7\columnwidth]{growing-crop.pdf}
\caption{The blue square represents the ``mean" estimated obstacle. Each outline in the red set represents a different probability shadow of the obstacle.}
\label{fig:manyshadows}
\end{figure}

We will use theorem~\ref{lemma:lgshape} and lemma~\ref{lemma:polybuild}
to construct regions which we can prove are shadows.
Before we continue, however, we note that obstacle shadows need not be
unique, or correspond to the set of points with probability greater
than $\epsilon$ of being inside the obstacle. Consider the case where
a fair coin flip determines the location of a square as shown in
figure \ref{fig:shadowquirk1}.
While there have been previous attempts to derive unsafe regions for
normally-distributed faces~\cite{prstl}, this lemma is stronger in
that it constructs a set that is likely contain the obstacle as
opposed to identifying points which are individually likely to be
inside the obstacle.

Recall that a PGDF obstacle is a random polytope with $m$ sides,
that is, the intersection of $m$ halfspaces. We can provide a shadow for
each halfspace using theorem \ref{lemma:lgshape}, and use lemma
\ref{lemma:polybuild} to combine their intersection into a shadow for
the estimated obstacle. The result is a $\epsilon-$shadow for a PGDF
obstacle. An sequence of such increasingly tight $\epsilon-$shadows is
shown in figure \ref{fig:manyshadows}.

\begin{lemma}\label{lemma:myshadow} If an obstacle is PGDF with
  nondegenerate parameters and $m$ sides, we can construct an
  $\epsilon$-shadow as the intersection of the $\frac \epsilon m$ shadows of
  each of its sides.
\end{lemma}
\begin{comment}
\begin{proofatend}
Let $X_i$ be the shadow constructed by Lemma 1 with parameter
$\epsilon/m$ for side $i$. Then the shadow $X = \bigcap\limits_i X_i$
contains the PGDF with probability at least $1 -
\sum\limits_i\epsilon_i/m = 1 - \epsilon$.
\end{proofatend}
\end{comment}

\subsection{Shadows as Safety Certificates}

Above we showed that for a given $\epsilon$, we can easily compute a
shadow for an obstacle under our model. Since a shadow is likely to
contain the real object, the non-intersection of an $\epsilon-$shadow
with the swept volume of a trajectory guarantees that the probability
of colliding with the given obstacle is less than $\epsilon$.
Theorem
\ref{lemma:multiobstacle} generalizes this notion to multiple
obstacles using a union bound.

\begin{thm}\label{lemma:multiobstacle}
Let $X$ be the volume of
  space that the robot may visit during its lifetime. If for a given set of
  obstacles, indexed by $i$, and their corresponding $\epsilon_i$
  shadows, $X$ does not intersect any shadow, then the probability of
  collision with any obstacle over the lifetime of the system is at
  most $\sum \epsilon_i$.
\end{thm}
{\bf Proof:} Please see the supplementary material.

\begin{comment}
\begin{proofatend}
Let $A_i$ be the event that the intersection of $X$ and obstacle $i$ is nonempty. Since the shadow of obstacle $i$ did not intersect $X$, this means that obstacle $i$ must not be contained by its shadow. The probability of this is less than $\epsilon_i$ by definition of $\epsilon-$shadow. Thus the probability of $A_i$ must be at most $\epsilon_i$.

Applying a union bound gives us that $P(\bigcup A_i) \le \sum \epsilon_i$.
\end{proofatend}
\end{comment}

It is important that theorem~\ref{lemma:multiobstacle} does not depend
on anything but the intersection of the swept volume with the
obstacle shadows; it is independent of the trajectory's length and of
how close to the shadow it comes. The guarantees of the theorem hold
regardless of what the robot chooses to do in the space not occupied
by a shadow.

Computing a shadow requires solving a relatively simple system of
equations;  then given a set of shadows and their corresponding
$\epsilon$'s, a collision check between the visited states and the
shadows is sufficient to verify that the proposed trajectory is
safe. This implies that safety is easy to verify computationally,
potentially enabling redundant safety checks without much
computational power. Alternatively, a secondary system can verify that
the robot is fulfilling its safety contract.

One potential concern is the tightness of
theorem~\eqref{lemma:multiobstacle}. If the union bound is loose, it may
force
us to fail to certify trajectories that are safe in practice. The
union bound used in the proof of theorem~\eqref{lemma:multiobstacle}
assumes the worst case correlation. If we assume that the system is to
certify that collisions are rare events, and the events are
independent, the union bound here ends up being almost tight.

\begin{lemma} \label{lemma:uniontight}
Given $n$ obstacles and their shadows, if
\begin{itemize}
\item the events that each obstacle is not contained in its
  shadow are independent,
\item the probability that obstacles are
  not contained in their shadows is less than $\epsilon$, and
\item $\epsilon = O(\frac{\sqrt \delta}{n})$
\end{itemize}
then the difference between the true
probability of a shadow not containing the object, and the union
bound in theorem~\ref{lemma:multiobstacle} is less than $\delta$.
\end{lemma}
{\bf Proof:} Please see the supplementary material.

\begin{comment}
\begin{proofatend}
We note that the union bound is only loose when at least two events
happen at the same time, so it is sufficient to bound the probability
that two shadows fail to contain their corresponding PGDF.

The probability of this happening for two given obstacles is at most $\epsilon^2$, and there are $n \choose 2$ such combinations. Thus by a union bound, the probability of two shadows failing to contain their obstacle is at most $n \choose 2 \epsilon^2$. If $\epsilon \le k \frac{\sqrt \delta}{n}$ for $k \ge \frac{1}{\sqrt 2}$, then the probability of this happening is at most $\delta$.

Since the probability of more than one event happening at the same time is bounded by $\delta$, the probability given by the union bound is within $\delta$ of the true probability.
\end{proofatend}
\end{comment}
Another way of interpreting lemma \ref{lemma:uniontight} is that if the probability of failure is small, the union bound is close to tight.

Theorem \ref{lemma:multiobstacle} highlights a problem with systems that
do not search for a set of optimal shadows. If we allocate equal
$\epsilon$'s for every obstacle, then we are forced to pay as much for
an object far away and irrelevant to the trajectory as we are for
obstacles close to the trajectory. Figure~\ref{fig:farawaysafe}
suggests that it is optimal to have large shadows with very small
$\epsilon$'s for such irrelevant obstacles, and larger $\epsilon$'s
for obstacles that may present significant risk. Doing so requires
finding a good $\epsilon$-shadow pair for every obstacle. We present
an algorithm that finds this optimal certificate in the next section.

\begin{figure}[tp]
\centering
\includegraphics[width=0.5\columnwidth]{FarAwaySafe-crop.pdf}
\caption{This figure overlays several possible instances of the real obstacles given a single observation. The trajectory is much more likely to collide with a draw of the bottom left obstacle than the bottom right one. The two obstacles do not affect the safety of the trajectory equally. }
\label{fig:farawaysafe}
\end{figure}

\section{Algorithm For Finding Optimal Shadows}
We will verify that trajectories are safe by finding a set of shadows
that proves the swept volume of the trajectory is unlikely to collide with an
obstacle.
In order to minimize the number of scenarios in which a trajectory is
actually safe, but our system fails to certify it as such, we will search for
the optimal set of shadows for the given trajectory, allowing shadows
for distant obstacles to be larger than those for obstacles near the trajectory.
In order to understand the search for shadows of multiple obstacles we
first examine the case of a single obstacle.

\subsection{Single Obstacle}
For a single obstacle with index $i$, we want to find the smallest
$\epsilon_i$ risk bound, or equivalently, largest shadow that contains
the estimate but not the volume of space that the robot may
visit. That is, we wish to solve the following optimization problem:
\begin{equation*}
\begin{aligned}
& \underset{\epsilon \in (0,1)}{\text{minimize}}
&  \epsilon\\
& \text{subject to}
& &\mathrm{shadow}(\epsilon) \cap X = \varnothing
\end{aligned}
\end{equation*}
If we restrict ourselves to the shadows obtained by lemma
\ref{lemma:myshadow}, a shadow with a larger $\epsilon$ is strictly
contained in a shadow with a smaller $\epsilon$. This implies that the
intersection is monotone in $\epsilon$, allowing us to solve the above
problem with a line search as shown in
figure~\ref{fig:linesearch}. While we restrict our attention to the
general case, in certain cases, such as where $X$ is a collection of
points, this optimization can be solved analytically.

Essentially we are growing the size of the shadow until it almost touches the states that the robot can visit, $X$.
\begin{figure}[tp]
\centering
\begin{subfigure}{0.5\columnwidth}
  \centering
  \begin{tikzpicture}
  \node[anchor=south west,inner sep=0] at (0,0) {\includegraphics[width=\textwidth]{growing-step1-hq-crop.pdf}};
  \node[draw,align=left] at (1.05,4.2) {Iteration 1};
  \end{tikzpicture}
\end{subfigure}%
\begin{subfigure}{0.5\columnwidth}
  \centering
  \begin{tikzpicture}
  \node[anchor=south west,inner sep=0] at (0,0) {\includegraphics[width=\textwidth]{growing-step2-hq-crop.pdf}};
  \node[draw,align=left] at (1.05,4.2) {Iteration 2};
  \end{tikzpicture}
\end{subfigure}
\begin{subfigure}{0.49\columnwidth}
  \centering
  \begin{tikzpicture}
  \node[anchor=south west,inner sep=0] at (0,0) {\includegraphics[width=\textwidth]{growing-step-over-hq-crop.pdf}};
  \node[draw,align=left] at (1.05,4.1) {Iteration 3};
  \end{tikzpicture}
\end{subfigure}
\begin{subfigure}{0.49\columnwidth}
  \centering
  \begin{tikzpicture}
  \node[anchor=south west,inner sep=0] at (0,0) {\includegraphics[width=\textwidth]{growing-step3-hq-crop.pdf}};
  \node[draw,align=left] at (1.05,4.1) {Iteration 4};
  \end{tikzpicture}
\end{subfigure}
\caption{A line search for the maximal shadow. The shadow ``grows'' and
  ``shrinks'' until it contacts the green space visited by the robot.}
\label{fig:linesearch}
\end{figure}

We define {\sc FIND\_MAXIMAL\_SHADOW}($\epsilon_p, \bm
\mu_i, \bm \Sigma_i, V$), which takes the precision $\epsilon_p$, PGDF
parameters $\bm \mu_i, \bm \Sigma_i$, and swept volume $V$, and
uses a standard bisection search to find and return the largest
$\epsilon$ for which the shadows are non-intersecting with $V$.
This requires $O( \log 1/{\epsilon_p})$ calls of
intersection---proportional to the number of
digits of precision required. The runtime grows very slowly as the
acceptable probability of collision goes to zero.

\subsection{Multiple Obstacles}
In order to extend the algorithm to multiple obstacles we imitate the
union bound in theorem \ref{lemma:multiobstacle}. We run the line search
to determine the largest allowable $\epsilon$ for every obstacle, and
sum the resulting $\epsilon$'s to get the ultimate bound on the
risk. The psuedocode is presented in algorithm \ref{alg:multiobj}.

\begin{algorithm}
 \caption{FIND\_MAXIMAL\_SHADOW\_SET}
 \begin{algorithmic}[1]
   \renewcommand{\algorithmicrequire}{\textbf{Input:}}
   \renewcommand{\algorithmicensure}{\textbf{Output:}} \Require
   $\epsilon_p, \bm \mu_i, \bm \Sigma_i, V$ \Ensure $\epsilon$,
   s.t. the path generating volume $V$ is at least $\epsilon$ safe and
   each shadow is less than $\epsilon_p$ away from the minimal
   $\epsilon$ for which this class of bound may be obtained.
  \For {i = 1...n}
  \State $\epsilon_i$ = \Call{find\_maximal\_shadow}{$\epsilon_p, \bm
    \mu_i, \bm \Sigma_i, V$}
  \EndFor\\
 \Return $\sum \epsilon_i$
 \end{algorithmic}
  \label{alg:multiobj}
 \end{algorithm}

This algorithm is embarrassingly parallel because every $\epsilon_i$
can be computed independently without increasing the total amount of
required computation. To obtain a
total accumulated numerical error less than $\delta$ we only need
to set $\epsilon_p = \delta /n$. If $\omega$ is the complexity of a
single call of intersection, our algorithm runs in $O( \omega n \log n
\log 1/\delta)$ time. However, since the search for shadows can be
done in parallel in a work-efficient manner, the algorithm can run in
$O( \omega \log n \log 1/\delta)$ time on $\Theta(n)$ processors.

If the intersection check is implemented with a collision checker then finding a safety certificate is only $\log$ factors slower than running a collision check--suggesting that systems robust to uncertainty do not necessarily have to have significantly more computational power.

Furthermore, since the algorithm computes a separate $\epsilon$ for every obstacle, obstacles with little relevance to the robot's actions do not significantly affect the resulting risk bound. This allows for a much tighter bound than algorithms which allocate the same risk for every obstacle.

\subsection{Experiments}
We can illustrate the advantages of a geometric approach
by certifying a trajectory with a probability of failure
very close to zero. For an allowable chance of failure of $\epsilon$,
the runtime of sample-based, Monte-Carlo methods tends to depend on $
\frac 1 \epsilon$ as opposed to $\log 1/\epsilon$. Monte-Carlo based
techniques rely on counting failed samples requiring them to run
enough simulations to observe many failed samples. This means that
they have trouble scaling to situations where $\epsilon$ approaches
zero and failed samples are very rare. For example, Janson et al.'s
method takes seconds to evaluate a simple trajectory with $\epsilon =
0.01$, even with variance reduction techniques
\cite{montecarloLJESMP2015}.

We demonstrate our algorithm on a simple domain with $\epsilon = 2.2
\times 10^{-5}$. Our algorithm required just 6 calls to a collision
checker for each obstacle. We also demonstrate that our algorithm can
certify trajectories which cannot be certified as safe with shadows of
equal sizes. Figures~\ref{fig:expequalalloc} and \ref{fig:expoptalloc}
show the problem domain. Figure~\ref{fig:expequalalloc} shows that the
trajectory cannot be certified as safe with a uniform risk assigned to
each obstacle. Figure \ref{fig:expoptalloc} shows the shadows found by
our algorithm that prove the trajectory is safe.

\begin{figure}[tp]
\centering
\includegraphics[width=0.6\columnwidth]{offline-even-hq-crop.pdf}
\caption{Computing the optimal equal allocation of probabilities fails to certify the safety of the path. }
\label{fig:expequalalloc}
\end{figure}

\begin{figure}[tp]
\centering
\includegraphics[width=0.6\columnwidth]{offline-opt-hq-crop.pdf}
\caption{Computing the optimal probability for each shadow allows us to successfully verify that the trajectory is safe. }
\label{fig:expoptalloc}
\end{figure}
\section{Online Safety}\label{sec:onlinesafety}
The bounds in the previous section do not immediately generalize to a
setting where the robot acquires more information over time and can be
allowed to change its desired trajectory. Additional care must be
taken to ensure that the system cannot ``trick" the notion of safety
used, and not honor the desired contract on aggregate lifetime risk of
the execution instance. Consider the case where,  if a fair coin turns
up as heads the robot takes a path with a $1.5\epsilon$ probability of
failure and it takes a trajectory with a $0.5 \epsilon$ probability of failure
otherwise. This policy takes an action that is unsafe, but the
probability of failure of the policy is still less than
$\epsilon$. Furthermore, the history of actions is also important in
ensuring aggregate lifetime safety. In figure \ref{fig:trickingsafety}
we illustrate a example of how the robot can always be committed to some
trajectory that is $\epsilon$-safe but have more than an
$\epsilon$ probability of collision over the lifetime of the execution.

\begin{figure}[tp]
\centering
\begin{subfigure}{\columnwidth}
  \centering

  \begin{tikzpicture}
    \node[anchor=south west,inner sep=0] at (0,0) {\includegraphics[width=\columnwidth]{online-first-hq-crop.pdf}};
    \node[draw,align=left] at (1.9,3) {$P(A_1) = 0.2$};
  \node[draw,align=left] at (4.5,3) {$P(A_2) = 0.05$};
  \node[draw,align=left] at (7.2,3) {$P(A_3) = 0.05$};
  \end{tikzpicture}
  \caption{At first the robot chooses the thin black trajectory which is has a probability of collision of only 0.3. It is more likely to collide with the first obstacle than the remaining obstacles.}
  \label{fig:sub1}
\end{subfigure}%
\\
\begin{subfigure}{\columnwidth}
  \centering
  \begin{tikzpicture}
    \node[anchor=south west,inner sep=0] at (0,0) {\includegraphics[width=\columnwidth]{online-second-hq-crop.pdf}};
    \node[draw,align=left] at (1.9,3) {$P(A_1) \approx 0$};
  \node[draw,align=left] at (4.5,3) {$P(A_2) = 0.2$};
  \node[draw,align=left] at (7.2,3) {$P(A_3) = 0.1$};
  \end{tikzpicture}
  \caption{After observing that it had not collided with the first obstacle, it readjusts the plan to follow the bold trajectory so that the probability of collision is still less than 0.3. However, a system that follows this policy will collide with probability 0.51 even though at every point it was following a trajectory with probability of collision less than 0.3. In other words, for this set of observations $O$, $P( A | \pi, O) > 0.3$. A system that is allowed to change its action after seeing additional information (in this case the fact that it did not collide) must properly account for the risk already taken. }
  \label{fig:sub2}
\end{subfigure}
\caption{Tricking "safety" by changing paths once more information is acquired. Note that even knowing that the system did not collide can serve as information.}
\label{fig:trickingsafety}
\end{figure}

Figure \ref{fig:trickingsafety} highlights the need to ensure low
probability of failure under all sets of observations. If this
scenario is run multiple times the failure rate will be much greater
than acceptable. In order to propose an algorithm that allows the
robot to change the desired trajectory as a function of a stream of
information, we develop an alternative criteria for safety that
accounts for risks as they are about to be incurred. We let $p_t$
denote the probability of collision at time $t$, given the information
available at time $t$, given that we follow the trajectory currently
predicted by the policy $\pi$. We note that since the information
itself is random, $p_t$ is a random variable for future times. We say
that a policy $\pi$ is \textit{absolutely safe} if for all times $t$,
equation \eqref{eqn:abssafe} is satisfied. The expectation in the
integral is with respect to the information available at the current
time $t$.
\begin{align}
\int\limits_{0}^\infty E[p_t \mid \pi ] dt &= \int\limits_0^t p_t dt + \int\limits_t^\infty E[p_t \mid \pi]\;  dt   \le \epsilon \label{eqn:abssafe}
\end{align}
We note that the $\int\limits_0^t p_tdt$ can be evaluated as an accumulation with standard numerical techniques for evaluating integrals.

The second term, $\int\limits_t^\infty E[p_t \mid \pi]\; dt$, is exactly the probability that the remaining part of the trajectory will collide and can be evaluated with the method for solving the offline safety problem.

\subsection{Absolute Safety vs Policy Safety}

Algorithm \ref{alg:onlinesafety} provides a method for performing safe
online planning in the case that the PGDF parameters are updated
during execution. While it shows that absolute safety can
be verified efficiently, it is not clear how to efficiently verify
policy safety. However, unlike absolute safety, policy safety
(introduced in section~\ref{sec:policySafety}) is a
very direct condition on aggregate lifetime probability of collision
and can be easier to interpret. In this section we compare policy
safety to absolute safety in order to identify when they are
equivalent.

First we show that absolute safety is a strictly stronger condition
than policy safety in theorem \ref{thm:absoluteimpliespolicy}. This
comes by integrating the probability of failure over time to get the
total probability of failure. Since the absolute safety condition in
equation \eqref{eqn:abssafe} must always be satisfied, regardless of
the observation set, the probability of failure for that information
set will always be sufficiently small.

\begin{thm}\label{thm:absoluteimpliespolicy} If a policy is absolutely safe, then it is also safe in the policy safety sense.
\end{thm}
{\bf Proof:} Please see the supplementary material.

\begin{comment}
\begin{proofatend}
Assume for the sake of contradiction that a policy is absolutely safe, but not policy safe. That means there exists a set of observations $O$ and time $t$ for which policy safety does not hold, but absolute safety does not.

The probability of collision conditioned on these observations is $\int\limits_0^t p_t | O dt + \int\limits_{t}^\infty E[p_t | O] dt$. Since the integral is less than $\epsilon$ so must the probability of collision. However, this implies that the system is policy safe for this set of observations $O$ and time $t$, yielding a contradiction.

Thus if a policy is absolutely safe it must also be policy safe.
\end{proofatend}
\end{comment}

Absolute safety, however, is not always equivalent to policy safety. The key difference lies in how the two conditions allow future information to be used. Absolute safety requires that the system always designate a safe trajectory under the current information while policy safety allows the robot to postpone specifying a complete, safe trajectory if it is certain it will acquire critical information in the future.

In order to formalize when policy safety and absolute safety are
equivalent, we introduce the notion of an information adversary. An
information adversary is allowed to (1) see the observations at the same
time as the agent, (2) access the policy used by the agent, and (3)
terminate the agent's information stream at any point. Policy safety
under an information adversary is guaranteed by the policy
safety conditions if the information stream can stop naturally at any
point. Theorem \ref{thm:infoadv} shows that policy safety with an
information adversary is equivalent to absolute safety.

\begin{thm}\label{thm:infoadv} A policy that is safe at all times
  under an information adversary is also absolutely safe.
\end{thm}
{\bf Proof:} Please see the supplementary material.

\begin{comment}
\begin{proofatend}
Assume for the sake of contradiction that there exists set of observations $O$ and a time $t$ for which absolute safety does not hold. That is to say that conditioned on these observations
\begin{align*}
\int\limits_{0}^t p_t dt + \int\limits_t^\infty E[p_t | \pi] dt > \epsilon
\end{align*}
Let the information adversary stop the flow of information to the robot at time $t$. Let $A_1$ denote the event that the system fails during times $(0, t]$ and $A_2$ denote the event that the systems fails during times $(t, \infty)$. We note that a system can fail at most once, so $A_1, A_2$ are exclusive.

Utilizing the fact that $\int\limits_t^\infty E[p_t| O] dt = P(A_2 | O)$ and $\int\limits_0^t p_t | O dt = P(A_1 | O)$, we get that the probability of failure $P(A_1 \cup A_2) = P(A_1) + P(A_2) \ge \epsilon$ violating our assumption that the system is policy safe under the set of observations $O$.

Thus if a system is policy safe under an information adversary, it is also absolutely safe.
\end{proofatend}
\end{comment}

\begin{algorithm}[tp]
 \caption{FIND\_MAXIMAL\_SHADOWS\_ONLINE}

\label{alg:onlinesafety}
 \begin{algorithmic}[1]
 \renewcommand{\algorithmicrequire}{\textbf{Input:}}
 \renewcommand{\algorithmicensure}{\textbf{Output:}}
 \Require intersects$_i$, $\epsilon_p$, $t$, $\{p_{t'} |  \forall t' \in [0,t] \}$
 \Ensure  $\epsilon$, s.t. $\epsilon$ is greater than the sum cumulate risk taken before the current time $t$ and the future risk. $\epsilon$ is at most $\epsilon_p$ away from the minimal $\epsilon$ for which a bound of this class may be obtained.
\State $\epsilon_1  = \int\limits_0^t p_t dt$
\State $\epsilon_2 =$ \Call{find\_maximal\_shadow\_set}{$\epsilon_p, \bm \mu_{1...n}, \bm \Sigma_{1...n}$} \\
 \Return $\epsilon_1 + \epsilon_2$
 \end{algorithmic}
 \end{algorithm}

\subsection{Experiments}
We demonstrate a simple replanning example based on the domain
presented in figure \ref{fig:expoptalloc}. Once the robot gets halfway
through,  it will receive a new observation that helps it refine its
estimate of the larger, second obstacle. This allows it to shrink the
volume of the shadow corresponding to the same probability and certify
a new, shorter path as safe. This new path is shown in figure
\ref{fig:replanexample}. It takes this new trajectory without taking
an unacceptable amount of risk.

\begin{figure}[tp]
\centering
\includegraphics[width=\columnwidth]{online-replan-example-hq-crop.pdf}
\caption{Once the robot reached the top of the old trajectory it got a new observation regarding the second obstacle. This allows it to shrink the shadow around the second obstacle and take the less conservative path that is shown above.}
\label{fig:replanexample}
\end{figure}

\section{Enabling Safe Planning using Safety Certificates}
The safety certification algorithms we presented above can be used for more than just checking safety. It can enable safe planning as well. We present a modification to the RRT algorithm that restricts output to only safe plans \cite{lavalle1998rapidly}. Every time the tree is about to be expanded, the risk of the trajectory to the node is computed. The tree is only grown if the risk of the resulting trajectory is acceptable.

\begin{algorithm}[tp]
\caption{SAFE\_RRT}

\label{alg:saferrt}
 \begin{algorithmic}[1]
 \renewcommand{\algorithmicrequire}{\textbf{Input:}}
 \renewcommand{\algorithmicensure}{\textbf{Output:}}
 \Require $\epsilon_{safe}$, $\epsilon_p,t, q_s,q_f, \bm \mu_{1...n}, \bm \Sigma_{1...n}$
 \Ensure  A sequence of waypoints from $q_s$ to $q_f$, such that the trajectory going through these waypoints has a probability of less than $\epsilon_{safety}$ of collision.
\State $tree = $ new \Call{tree}{$q_s$}
\For {$\mathrm{iteration} = 1...n$}
\State $x_{rand} =$ \Call{random\_state}{}
\State $x_{near} =$ \Call{nearest\_neighbor}{TREE}
\State $x_{new} =$ \Call{extend}{$x_{near}, x_{rand}$}
\State $X =$ \Call{get\_trajectory}{$tree, x_{near}, x_{new}$}
\State $risk =$\\ \hspace{0.9cm}\Call{find\_maximal\_shadow\_set}{$X, \epsilon_p, \bm \mu_{1...n}, \bm \Sigma_{1...n}$}
\If {$ risk \le \epsilon_{safe}$}
\State \Call{add\_child}{$tree, x_{near}, x_{new}$}
\EndIf
\EndFor \\
\Return $tree$
 \end{algorithmic}
 \end{algorithm}

We note that it is not necessary to check the safety of the entire
trajectory every time the tree is extended. Since the bounds for each
obstacle are determined by a single point in the trajectory, it is
sufficient to consider the following two risks: the trajectory from the
root of the tree to $x_{near}$ and the trajectory from $x_{near}$ to
$x_{new}$. Finally we note that analyzing probabilistic completeness
is quite different in the risk constrained case from the original
case. We do not believe this method is probabilistically
complete. Unlike the deterministic planning problem, the trajectory
taken to reach a point affects the ability to reach future
states---breaking down a crucial assumption required for RRTs to be
probabilistically complete.

We demonstrate the safe-RRT algorithm on a point robot trying to escape a box. The box has two exits. While the robot can safely pass through the larger exit, it cannot safely pass through the smaller exit. The planner is run to only return paths with a probability of failure less than $0.5\%$. Figure \ref{fig:safeplan} shows a safe tree from the red dot inside the box to the red dot above the box. Figure \ref{fig:safetraj} shows just the ultimate trajectory with its corresponding shadows that certify the probability of failure as less than $0.26\%$. Note that some shadows did not extend all the way to the trajectory as their risk was already below the numerical threshold.

The experiment shown in figure \ref{fig:safeplan} demonstrates offline-safety. If the robot were given additional information during execution, we could use the equations for online-safety to re-run the RRT with the new estimates of obstacles while preserving the safety guarantee.

\begin{figure}[tp]
\centering
\includegraphics[width=\columnwidth]{planning-rrt-hq-crop.pdf}
\caption{A tree of safe trajectories branching from the red dot in interior of the box. Equally sized shadows are shown for reference.}
\label{fig:safeplan}
\end{figure}

\section{Conclusion}

We presented a framework to compute shadows, the geometric equivalent
of a confidence interval, around observed geometric objects. Our bounds are
tighter than those of previous methods and, crucially, the tightness of the
bounds does not depend on the number of obstacles. In order to achieve
this tightness we rely on computing a bound specific to a trajectory
instead of trying to identify a generic ``safe" set.

We present offline and online variants of algorithms that can verify safety with respect to the shadows identified above for both trajectories and policies. The online method highlights nuances and potential issues with a mathematical definition of safety, and presents a strong, but still computationally verifiable notion of safety. These algorithms do not have a computational complexity much larger than a collision check, and are only a $O\left (\log n \log \frac 1 \epsilon \right )$ factor slower than a collision check for $n$ obstacles and an $\epsilon-$safety guarantee. Finally the output of these algorithms is easy to verify, allowing the output to serve as a safety certificate.

These safety certification algorithms are an important not only in ensuring that a given action is safe, but also in enabling the search for safe plans. We demonstrate an extension to the RRT algorithm that only outputs safe plans.

Future work includes using other models of random geometry. A model for occupancy would match the information of interest to a motion planner more closely, and may be easier to apply to real world data sets. The presented algorithms are compatible with mixture models---a potentially interesting and useful direction that should be evaluated empirically. Another direction of interest is the development of safe planning algorithms with strong theoretical guarantees such as optimality and probabilistic completeness.

\section*{Acknowledgements}
BA would like to thank Gireeja Ranade, Debadeepta Dey and Ashish Kapoor for introducing him to the safe robot navigation problem during his time at Microsoft Research.

We gratefully acknowledge support from the Thomas and Stacey Siebel Foundation, from NSF grants 1420927 and 1523767, from ONR grant N00014-14-1-0486, and from ARO grant W911NF1410433. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of our sponsors.

\bibliographystyle{plainnat}

redpajama_set_name: RedPajamaArXiv


text:
Small-Business Outlook Improves
Hard times at larger corporations are boosting business for small firms, a survey finds.
By Angus Loten
After a prolonged downturn in recent months, economic optimism among the nation's small-business owners improved in August, SurePayroll reported this week.
Based on payroll data from over 20,000 companies nationwide, small employers increased hiring last month by 0.42 percent, according to the Chicago-based payroll firm.
At the same time, average small-business salaries declined by 0.33 percent from July to $32,182.39. So far this year, average salaries have fallen by 1.3 percent, the report said.
More owners in August also said they were optimistic about the economy, adding that the situation isn't as bas as depicted in the media. While a lot of larger firms were going bankrupt, smaller businesses were holding on, they said.

redpajama_set_name: RedPajamaCommonCrawl


text:
The Diner Booth
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By Max Pizarro | September 25, 2017, 10:05 am | in City Confidential
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"When I saw things developing as they were, I stepped away," he said. "It was September or October o flast year, way before the indictment. I said 'I can't be part of this. I have four kids. This is not what we talked about. So I resigned and thanked him for the opportunity. I want to manage this town in a decent way, and we have experience. Everybody we have supported has won, including Wilda Diaz in PErth Amboy, and candidates in Hackensack and Saddle Brook. We have the know how and we will have the money."
The son of a barber, Rodriguez first came to Paterson when he was 12. Factory workers, his grandparents lived in the 4th ward. His four boys attend the Paterson Public Schools.
"I've been preparing myself for this for a long time," he told InsiderNJ. "I served as commissioner on the school board, and on the zoning and planning boards, and as deputy mayor. In the private sector, I oversaw a larger budget and personnel than the city. I elect to live here. The difference between us and others is no one will be able to pull a chain. Look at the direction of the city now. Our kids don't have safe parks to play in, and all the city council people just approved a dog park.
"A dog park," he repeated with incredulity.
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text:
The Gordian
By early February 1972 the events to be described in this book had resulted in my being in a state of continual, severe pressure, and I was in need of a good rest. It was for this reason that on the morning of February 13, Uri Geller drove me to Lod International Airport where I was to catch a plane for Rome.
As Uri and I parted at the escalator going up to the Immigration Section, a customs official came up to me and insisted on escorting me. I waved good-bye to Uri as I ascended, little knowing that I was walking into a trap. The official took me into an office where, without saying a word, he carefully checked my passport. Then he asked me to follow him; we went right through Immigration and Inspection without being stopped. Suddenly I realized I was in trouble. I was led into a small room, where waiting for me were four tough-looking men in their forties.
They identified themselves as Israeli Army Counterintelligence (Shin Beth) officers. One of them politely requested my permission to search me and all of my effects. I protested vigorously and asked to see their search warrant. One of them said they were exercising normal wartime powers. I asked for permission to call one of my many acquaintances in the Israeli Army. They refused. So I consented to the search, feeling secure in the knowledge that they would find no evidence that I was any kind of "spy." However, they not only thoroughly searched my person, camera bag, and briefcase but also took possession of almost all of the contents. I became furious when they confiscated my three volumes of research journals containing data on Uri. Again I protested vigorously. One of the men look at me grimly and said, "I hope, for your sake, that we do not find what we are looking for."
After he had taken my research journals, movie films, telephone book, and letters, the leader of the group said that this material would eventually be returned to me. "Where shall we send it?" he asked. I gave him a close friend's address in Tel Aviv. He gave me a receipt for my property, and I was escorted by two men aboard the waiting plane.
As the plane took off from the soil of Israel, I looked down at the Holy Land and wondered if I would ever be permitted to return. I was suddenly aware that I was alone, all alone, for the first time in several months.
When I arrived in Rome, I telephoned friends in New York and discovered that an immense rumor mill had been started which said that I had gone mad. Many even believed that Uri was a Mephistophelian character and that I had made some kind of pact with this "devil." I was able to reach Uri in Israel by phone, and he told me that all hell had broken loose there. The Army was constantly interrogating him, in order to get more information about me. He told me that they were convinced I was a master spy and that they were now trying to figure out what country I worked for. They had also come to his apartment where I had stored my research equipment, tapes, and film documentation and seized them all for intelligence analysis. Uri told me to plan to stay away for a long time, but to keep in touch. After four days in Rome, I assessed my situation and found it to be one where I was not welcome either at home or in Israel, and I decided to take a long rest.
I left Rome by a devious route, checking to see if I was being followed. When I was sure that I was not being followed, I found my way to the Italian Dolomite Alps and the town of Cortina. I scouted around and found a small, totally isolated hotel, the Tre Croci, on the top of a mountain pass. It was the essence of Old World charm presided over by Signor Menardi and his wife.
Realizing that I might never see my confiscated journals again, I decided to try to reconstruct from memory those events that led me to be suspected as a threat to the security of a nation. On February 19, 1972, on my fifty-fourth birthday, I sat down at my desk in the Tre Croci Hotel to begin this task.
My first trip to Israel was in March 1970 to train a research group at the Tel Aviv University Medical School in my technique of electrostimulation of hearing for the deaf. I would lecture a few hours a day to the staff at the Tel H'ashomer Communications Research Unit and then rush off to see the sights of Israel. One of the places I wanted to see was the Qumran site, near the Dead Sea, where the Dead Sea scrolls had been discovered in 1947. I was fascinated by the doctrines and writings of the Essenes who had lived there.
I rented a car and drove from Tel H'ashomer to Qumran. It was a warm, balmy day, and the scent of spring was very much in the desert air. There were no tourists at Qumran, only one Arab boy as a tour guide. He volunteered to take me into each of the caves where the scrolls had been found. This was a great thrill for me, since I am an amateur archaeologist. Finally the boy left me alone, and I sat on the rocks of the community site, drinking in the smell of the Dead Sea and the sights of the Jordan Valley to the north. For me it was a happy and exhilarating hour in the sun. When it was 5 P.M., I reluctantly moved toward my car to drive back to Tel Aviv
As I started to drive, I felt a heaviness come over me that was like anesthesia. I reasoned that it must be due to all the fresh spring air and the altitude, which was about three hundred meters below sea level. But, then, why had I felt so good a few moments earlier? I checked the car's exhaust system for leaks, but it was all right. My health was perfect, and I had not used any medicines or drugs. I could not account for the sleepiness.
I had great difficulty getting through Jerusalem. Something was putting me to sleep, and I was fighting it like a punch-drunk boxer who doesn't know when to quit. I have never had to fight sleep so hard in my life. In another hour of slow, sleepy driving, I reached the town of Ramla and finally succumbed to sleep in the car. I woke up an hour later, drank a lot of coffee, got into the car, and barely made it to my hotel room in Tel Aviv, where I fell asleep on my bed fully clothed, with all the lights on. I slept for twelve hours.
When I awakened, I tried to analyze what had happened. I could only conclude that some external force had had this hypnotic effect on me. It might have been a positive ion effect in the air, but it was not the hamsin season, when the hot wind blows through the desert. But one thing was clear: I had never, in any other part of the world, experienced this sensation. It was not until eighteen months later that I was to know the reason for my sleepiness.
On my return to New York from Israel, I was offered the opportunity of being the chairman of an international conference, "Exploring the Energy Fields of Man." The purpose of this conference was to explore the energies involved in certain psychic phenomena. I welcomed the opportunity to bring together a distinguished group of scientists to evaluate these problems so close to my work. At the conference, Itzhaak Bentov, an Israeli researcher from Boston, gave a report on a young man named Uri Geller, who had recently done some amazing psychic feats in Israel. Bentov read a letter from a friend in Israel, whose son had recently graduated from the Technion. The letter said in summary: "His son saw Uri Geller, a 23 year old stage performer, do some amazing things for a group of students and their professors. He made it clear that his son does not believe in these things as being paranormal. His son thinks some kind of a trick is involved, but nobody knows the trick, not even the magicians."
His son's friend had held a gold ring clenched in his hand while Geller held his left hand over this hand for about thirty seconds. When his son's friend opened his hand, the ring was split. Geller also held his hand over the face of a wristwatch belonging to a student, and when he moved his hand away, the watch hands were displaced two hours forward. The third thing Geller did was to drive through Haifa traffic while blindfolded, with the windshield of the car on the driver's side masked with cardboard. It seems someone was required to be in the car with Geller so that Geller could "see" through this person's eyes.
This report was greeted with both incredulity and skepticism by the conference scientists. I made contact with Uri Geller in Israel by letter. Geller agreed to see me in August 1971 and to give me an opportunity to test his alleged talents. I planned to see him the week before I was to go to a conference in France.
Two weeks before I was to leave for Israel, I was suddenly faced with a catastrophic series of events much too complex and personal to report here. There were grave family problems, financial difficulties, and severe illness. For two weeks I felt stressed and stretched to the limits. I felt that I was under some kind of test, that I had to choose between my self-imposed duty to get to Israel and my personal health and comfort. Against all advice I went on to Israel on August 17, 1971. Curiously enough, as soon as I got on the plane, my illness improved, and by the time I landed in Israel I felt healthy again.
I was met at Lod Airport by the father of the boy who had witnessed Uri Geller's feats (I shall call him Jacov, since he does not wish to be identified). Jacov was a balding, sandy-haired, freckle-faced man of deep calm and quiet dignity. He explained at some length that he had arranged for the use of a friend's apartment for me in Tel Aviv. He brought me up to date on his further investigations of Uri Geller. He was frankly skeptical of Geller's powers because there had not been a decent opportunity for satisfactory private demonstrations. He welcomed my presence, just to resolve the nagging question as to whether or not these were genuine powers.
Jacov told me that Geller was performing at 11 P.M. that night at a discotheque called the Zorba in Jaffa. Would I like to go and see Geller or get some rest? In spite of my recent illness, I could not think of conserving myself; I had to go and meet Geller. After dinner, we arrived at the Zorba. It was a huge barn of a place, put together out of crepe and tinsel for the tourist trade. While waiting in the foyer for the show to start, a young man who recognized Jacov came up to us. It was Uri Geller. He introduced himself in perfect English, welcomed me to Israel, and apologized for our having to meet under the squalid roof of the Zorba.
I greeted him in return by saying I had waited for a year to meet him. I was surprised at his healthy appearance. I had expected to find some kind of a strange nebbish somehow not related to this world. Instead he was tall and very handsome, with a quick, sharp, here-and-now sense of presence. His manner was easy, even gentle. He didn't look like a man who broke metal rings by sheer willpower.
Uri soon excused himself to get ready to go on stage. Jacov and I got ringside seats and suffered through a series of rock numbers, jugglers, clowns, and comedians. Uri was the last to appear, since he was the star of this show.
He was simply introduced as Uri Geller as he appeared on stage. The crowd of youngsters went wild with applause. He was evidently very popular. He announced, "With the cooperation of the audience, I am going to try to demonstrate simple telepathy and psychokinesis. I hope I will succeed."
He then did a series of telepathic demonstrations wherein members of the audience wrote numbers, the names of cities, and the names of colors on a blackboard. Blindfolded, he would try to guess what they had written. He was correct on every attempt. I was not impressed, because any magician could do the same thing in a number of different ways by trickery, mostly by having collaborators in the audience. However, I reserved judgment on this subject because I could easily test this talent when we met privately.
Finally he came to the big event of his demonstration. He said that if anyone would volunteer a ring, he would attempt to break it. A lady sitting near us volunteered her costume jewelry ring for the test. She went up on stage, took the ring off her hand, and held it up for all to see; it appeared intact. Uri then told her to clutch the ring in her hand and to make sure that he could not touch it. This she did. Uri then placed his left palm over the lady's clenched fist for about thirty seconds. He asked her to open her hand and to examine the ring. She gasped, "The ring is broken." She held it up for all to see. There was wild applause as Uri ended his demonstration. The lady returned to her seat, and Jacov asked her in Hebrew if we could inspect the ring. She handed it over to us. It was split in two pieces, with no signs of any tool marks. The lady assured Jacov that she was not in collusion with Geller. All this was intriguing, but not convincing, since a magician with the assistance of a confederate could do the same thing.
We met Geller after the show. He was very boyish in his eagerness to find out if I liked his show. I assured him that I enjoyed his part of the show, but would have to work with him privately to assess what he was doing. He readily agreed to meet me at my apartment the next day at 1 P.M. to discuss my research interests and find out what I wanted to do.
I did not realize then how lucky I was. Later I found out that Uri had steadfastly resisted all offers by research people to do experiments. He, too, was surprised at how readily he had consented, especially since I was a total stranger.
By the time Uri arrived at the apartment the next afternoon, all of my equipment was operative and in place. Two of my Israeli friends were present, Jacov and Ms. Shifra Mor. I began by asking Uri to show me those talents of his that he felt the most sure of and to do them in his own way. Uri said he would like to do some simple telepathy for me. He said, "Think of one number from one to nine. Don't tell anyone, just keep it in mind. Got it?"
"Yes," I said. I had thought of the number four.
"Now think of another number."
"I have it," said I, having thought of the number three.
"Now the last number," Uri said.
I had selected two for this number.
Uri looked at me intently as though he were checking his own impressions Then he said very abruptly to me, "Pick up the pad on the table before you, the one I wrote on before you selected your first number. Did you notice that I had written on it then and haven't touched it since?"
"Yes, Uri, I noticed what you had done and that you haven't touched it since or tried to switch it. After all, that is part of my business as an investigator."
I picked up the pad, which was face down, turned it over, and read what Uri had written down before I had thought of my first number. It read, "4 3 2."
Uri laughed, obviously pleased with his coup.
I responded with some admiration. "That's pretty clever; you told me this would be telepathy, and I, of course, thought you were going to be the receiver. But you pulled a switch on me."
"Ah, you got it quick!" interrupted Uri. "I wanted to send you the numbers, but I knew that if I told you to try to receive the numbers, you would fight me. In this way you participated in the experiment without prejudice, and proved that you have telepathy, when I send or pass to you."
I realized now that Uri had an unusual power of influencing others' thoughts. At this point I asked Uri's permission to use my tape recorder and movie camera.
"Of course, if it is easier for you," he replied quickly. "But you probably think that since I sent those numbers to you so easily, I might also hypnotize you to see and do things that are not really there!"
"You are so right, Uri," I laughingly replied. "I can see that we're going to get along just fine."
Now that we had tested each other's mettle, we were able to settle down to some serious work. I then asked Uri to do some more telepathy with my Israeli friends. I might say that these two people were highly trained observers.
After an hour of doing Uri's telepathy with simple units of information such as numbers, letters, colors, and single words, we stopped for a break. We openly discussed our opinion of Uri's demonstration. I led off by stating without equivocation that this was genuine telepathy and I would state so anywhere.
Shifra and Jacov concurred in this opinion. They asked if Uri could get or give more complex information by telepathic means. He replied, "I can't do things like that. I stick to the simplest bits of things, so that it is like two times two equals four. Then people have to say I am right or I am wrong. If I do whole stories, it's hard to score what I do. This way it is either zero, or a hundred, and no in-between."
"Now what would you like to do?" I asked Uri.
"Does anyone happen to have a watch that does not work? I will try to fix it," said Uri.
Shifra replied first. "I have a watch that is not broken; it is not working because I haven't wound it in a few days. Can you start it without touching it?"
"Well, I'll try," said Uri. I interrupted, "Shifra, first let me inspect the watch before anything is done." She handed me the watch. It was a well-known Swiss-brand watch. I listened to it. I shook it. This made it tick a few cycles and then it stopped. I then took a motion picture of the face.
Uri said, "I don't want to touch it. Let Shifra hold it in her clenched fist."
I placed the watch in Shifra's open palm. She closed it, and then Uri placed his left hand palm down over her hand without touching it. After thirty seconds Uri said, "Okay, check it. I think it's running."
I took the watch from Shifra and inspected it. The watch ticked now and continued to do so. The hands moved for several minutes normally. Shifra agreed to let me keep the watch to see how long it would run. The watch ran for thirty minutes before it stopped.
Uri then asked if I would take my watch off and just hold it in my hand. I noted the time. It was 2:32 P.M. I placed the watch in my right hand. Uri placed his hand over mine without touching it. He concentrated for about ten seconds, then said, "Check it."
I looked at the watch. The hands now stood at 3:04 P.M., an advance of thirty-two minutes. My watch is a Universal Geneve Chronometer, with additional dials to add up stopwatch time. I noticed that two of these dials had also shown an advance of thirty-two minutes. But the stopwatch sweep-second hand should have been running for thirty-two minutes, but the stopwatch sweep-second hand was motionless. There is no known way to advance these two dials thirty-two minutes except to run the stopwatch for thirty-two minutes. This complex feat of psychokinesis was unparalleled in my experience, or in the literature, for that matter.
This ended our research session for the first day. I had only one reservation: I must wait until my motion pictures were developed to make sure that my companions and I were not hallucinating. One month later when the film was developed I had my confirmation; the film had seen the same thing as had my eyes.
The next day I repeated the telepathy tests and found the same positive results. Then I asked Uri to concentrate on a pair of identical thermometers of the bimetal type. He was able to raise selectively the temperature of one thermometer six to eight degrees Fahrenheit, while the other one remained at the room temperature. I found that he could do this equally well from across the room as when near the thermometer.
There was now no question in my mind that Uri Geller's powers of telepathy and psychokinesis were extraordinary. I now wanted to know more about him as a person: What were his interests and his motivation?
"Uri, you must have thought a great deal about your powers. What is your idea about where they come from? Or how do you think it works?"
"Yes, I have thought about them. You see, my ideas may seem funny to you because I have only had a high school education. I don't read books. But my ideas are my own, and I don't like to discuss them. I believe that in telepathy I am passing the light speed. I feel that telepathic waves travel at a speed of light or faster. Every object gives off radiation which moves out into the universe. When we pass the light barrier, we can see into the past or into the future, and we can transmute materials one into the other. Everything is based on the light speed, and once beyond that there is no end to what can be done. But as yet, we cannot find the particles beyond the light speed because they are too small. I also believe that there is no limit to the smallness of particles. This is the way I think, but let us not get into theories that we cannot work with."
I was quite taken with the depth of Uri's ideas, especially since they were so unexpected. "Someday," I said, "when we have time, I would like to tell you about Dr. Vinod, a man from India who taught me many things. One of them had to do with superconscious states of mind being due to, or related to, velocities near to the speed of light. What you say about telepathy strikes a responsive chord in me."
"There is an interesting thing I have noticed, Dr. Puharich," Uri interrupted. "Sometimes when I break a ring, it loses some of its material. With the breaking of a chain, sometimes a link disappears."
"Uri, I saw you break metals with your willpower at the Zorba. Would you try to show me that?" I asked.
"Yes, I would like to do that for you, but a little later," he said.
I asked Uri when he had first decided to show his powers in public.
"It slowly started in late 1969 when I did some small things for a friend of mine, Shipi Strang. But I really had my first show, with promotion and advertising and all that, in March 1970, because an agent said I could make a lot of money. It was in a movie house in Bat Yam. After a week of this I knew it was easy and I enjoyed it. Then I found that I really need the stimulation of working in front of people in order to do these things. When I am by myself, nothing happens. Now, there are also many people who are opposed to me. They say it is all a fraud and a trick and that I should admit it. But I don't really care whether they believe or don't believe; as you see, I have two things going for me. First, there is my plain, naive appearance. Second, I am a showman and I do have powers."
To this candid immodesty, I had to add my honest opinion about Uri. "You have not realized your full powers yet. You are just at the beginning."
"Thank you, Dr. Puharich, but what else is there for me to do? Everything is written. If we go out of the route, and we leave the third or fourth dimension, we go on into another dimension and another form of life. I believe there is life everywhere in the universe. There are advanced beings who can pass the light barrier, who can travel millions of light-years in an instant. They can transfer themselves to different dimensions; they can change themselves into any form they wish, and appear as ants, birds, people, or even UFOs. These space people now know that earth people are finally advanced enough so that they can show newer forms than they used to take in biblical times. That is, they take different forms now."
"Uri, did you ever see these things that you are talking about?" I asked.
"No, to tell you the truth, I never have. I just believe in these things, but I don't know why I do."
Uri went on. "I'm talking about these things because I see them in my mind. I believe them. I believe that we live other lives. When our energy runs out in this life, it goes into another dimension. You see, I believe that if you have telepathy, you pass the light barrier, and you go into other dimensions. People ask me, 'Why do you have powers, and I don't?' I have an explanation, and I suppose you can say it comes out of four theories, or any one of them.
"Maybe on our own earth before the Ice Age, there was a civilization, very advanced. All that I do now, they once did. Somehow they have remained, not incorporated in a body, and I somehow have their powers."
"Then maybe I am a descendant; my ancestors were people not from earth. They landed in a flying saucer. They had these powers, and somehow they came up in me. This is like a science fiction theory, that I was planted on earth."
"Or somehow while growing up, my mind split. Basically it appears okay, but something turned a little away, a little sharper. There is a warp in its makeup."
"The last one, I don't even want to say it. They are somewhere out there. They have their reasons. This is related to my second idea."
"Now I will try to split a ring for you," Uri announced in the face of our silence. Jacov's wife, Sara, had joined us. She offered her gold wedding band. I think she felt that it was perfectly safe; no one could break a ring without touching it. Uri asked her to clench the ring in her fist. He held his left hand, palm open and down, over Sara's fist.
Uri said, "I know this ring is precious to you. I won't break it badly; I'll just crack it lightly. Tell me, do you feel anything?"
Sara said after about thirty seconds, "I feel some tingling in my palm."
"Okay, I think it is broken. Open your fist," said Uri.
We all crowded around Sara. I picked up the ring first. There, clearly across the yellow gold, was a crack in the metal! Now I felt the full impact of Uri's powers. The Gordian Knot had been cut! (Several months later I got a report on the ring from the metallurgist at the Stanford University Department of Materials Science. It stated that there was no known way to cause this kind of fracture and that the electron microscope pictures were unique. )
I spent my remaining few days repeating each of the tests with Uri that I had already done, just to make sure that I was not being fooled. I wanted to make arrangements for future research with Uri. He was quite willing to work with me. I decided that the preliminary research should be done right in Israel, and Uri concurred. Before I left Israel, Uri proudly showed me his scrapbook of news clippings. One story from Israel's leading newspaper, Ma'Ariv, of February 19, 1971, caught my eye. It was about "Captain Edgar D. Mitchell, the Uri Geller of the astronauts." I told Uri that I would be talking to Captain Mitchell on my return to the States.
Since I had to be in France on August 24, I did not have much time. I had to reach key figures in the government to make sure that I would have their cooperation. Jacov understood totally what had to be done in Israel, and he undertook to be my emissary. I left for France on the understanding that if he could arrange a meeting for me with certain key figures, I would return to Israel.
At the International Conference in St. Paul de Vence, I was especially interested in a report by Dr. Hans Bender on a phenomenon that involved recording on a tape recorder voices whose origin was unknown. Dr. Bender told me of a man in Germany, Dr. Konstantin Raudive, who was doing such work. I decided to go see Dr. Raudive right after the conference.
At the conference I met a young parapsychologist from the University of Wisconsin, Ila Ziebell, who impressed me very much with her quick wit and good judgment. But more of her later, when she enters this story as a principal. I did not report on my work with Geller at the conference, since I felt it was premature to say anything about his startling powers. I knew that, paradoxically, the bigger his powers, the more proof it would take to be convincing.
From the conference I flew to Zurich, where I met my friend and assistant of many years, Melanie Toyofuku, to do some work with Dr. Raudive. I phoned Dr. Raudive and found that he was able to see me for the coming week. Since I had all my research equipment with me from the work in Israel, I was prepared to join Dr. Raudive immediately.
Melanie and I drove down along the Rhine to Bad Krozingen where Dr. Raudive lived and worked. Bad Krozingen is a spa built for chronically ill people, and I did not like its atmosphere. Therefore, as was my habit, I simply drove around the area looking for an inn that suited my mood. At sunset I drove into a small town which was guarded by a castle high on a hill. It had a warm rustic atmosphere. I found an inn that had rooms free, and Melanie and I settled in. The next morning we were having breakfast at a sidewalk cafe in the village square when we inquired as to the name of the town. The waiter informed us that it was Staufen and was famous as the place in which Dr. Johannes Faustus had lived in the sixteenth century.
Dr. Konstantin Raudive was a Latvian philosopher living in Bad Krozingen because of his wife's disability. Although he spoke many languages, English did not come easily to him, so we settled on French for our discussions with Melanie serving as the interpreter. Dr. Raudive explained how he was able to record the "voices" of people who had died. He used an ordinary tape recorder with a diode placed in series with the input jack. Sometimes he used the tape recorder with an ordinary microphone input, but this created too much noise in the recording, with the result that the "voices" were buried in the noise level of the electronic system. Therefore, one had to train oneself to hear the signal in the noise. It took me about twelve hours of such training to hear the voices that Dr. Raudive said were there. At last Melanie and I were able to hear the voices without any help from Dr. Raudive.
On August 31, 1971, Dr. Raudive conducted an experimental session in which we would try to record "spirit" voices on my Sony TC 120 tape recorder. The procedure was simple: The tape recorder was placed on a coffee table, and we sat around it. The recorder was started, and Dr. Raudive simply said, "We would like to have a message for Miss Melanie." We waited two minutes and then played back the tape recording. All of us distinctly heard the words "Melanie," "yes," following Dr. Raudive's last words. Melanie said the two words had the voice quality of her deceased Japanese grandmother who had never learned to speak English properly.
Following this attempt, the tape recorder was started again, and I asked for my mother, Rose, who had died in 1956, but I spoke in Croatian, the language in which she and I had spoken so often. When the tape was played back, we heard the phrase in Croatian "To Rosalija," and to my ear it had the voice quality of my mother as I remembered it. The phrase meant "This is Rose."
We went on working in this fashion for two more days with similar results. I was totally convinced that the effect was genuine. However, I was forced to the conclusion that in order for the effect to occur, Dr. Raudive's presence was required. This meant that we were dealing with a two-termed process in which one term was an instrument, the tape recorder, and the other term was a human being, Dr. Raudive. For example, the same effect did not occur with me at this time. A person who has such a special effect is called a medium. A medium serves as a bridge between this material world and the world of the unknown, from which the voices came. The fact that one needed a medium did not make the effect less valid; it just introduced the factor of special human dependency.
After our final sessions with Dr. Raudive, I left for London and from there drove to Cambridge University to discuss my findings on Uri Geller with a group of friends whom I considered to be on the "cutting edge" of knowledge advancement. I met with Ted Bastin, a physicist; Chris Clarke, a cosmologist; Margaret Masterman, a philosopher and linguist; and Richard Braithwaite, a philosopher; and others. My data on the Geller effects were received with great interest as a possible contribution to a fundamental revision in philosophy and in science. We began to make plans for the kind of research that we would have to do in future years, just to build a new data base for the new science to come.
On September 12 I got a phone call in London from Jacov, who was in Israel. He said he had made contact with the right Israeli authorities and that I should return immediately for a discussion. On September 13 I had extensive discussions with a key government figure in Tel Aviv about research with Uri. He told me that there was a consensus among his colleagues that the kind of things Uri Geller was doing should be taken seriously from a scholarly point of view and that I could count on cooperation in my program from his government. I was encouraged to return to Israel, to try to organize a research program on my own.
On September 14 I picked up a copy of the Herald Tribune in Tel Aviv and read a story by Walter Sullivan. It said that some American and Soviet scientists had called an international conference "to consider the possibility of communicating with life on other worlds." The meeting had been held in Byurakan in the Soviet Union. Many distinguished scientists were in attendance, including Dr. Charles Townes, Nobel Laureate from the University of California, Berkeley. This was the first time that such a conference had ever been held at so high a level.
I did not try to do any research with Uri on this trip, but spent our time together simply trying to get to know him better. I also met his two closest friends, Hannah and Shipi Strang. It was easy to see that a tight bond held these three together, and I knew that any plans for work with Uri in the future would necessarily have to include Hannah and Shipi.
By September 20 I was back in my home in Ossining. The next two months were a blur of activity in which I saw people all over the United States and Canada, trying to enlist their interest and support for the Geller research in Israel. Most of my professional colleagues simply did not accept my data on Geller, even after viewing my films of his effects on watches, metal breakage, etc. I soon discovered the reason: they were threatened. If Geller were true, then the very foundations of science would have to be questioned.
One of the more open minds was that of Captain Edgar D. Mitchell, who had just completed the Apollo 14 mission to the moon in February. He and I met for the first time in Houston, where he told me that he had completed the first moon:earth telepathy experiment. He had been the sender in space to four human receivers based on earth. He told me that the results had been just as I had predicted ten years earlier in my book Beyond Telepathy. He was most enthusiastic about the prospects of doing research with Uri, and we made some plans to do so.
By November 17 I had completed all the complex tasks necessary to launch a long-term research effort in Israel with Uri, and was on my way back to Israel. My goals were now quite clear. I had to make arrangements with the institutes of higher learning in Israel to get them to work with Uri. It was essential that others participate in the process of validating Uri's powers; and Uri had to become accustomed to working with scientists.
By 7:30 P.M. November 19, 1971, I was settled in Reuven's apartment in Tel Aviv. The next day I was scheduled to start a series of meetings with Uri, Jacov, Reuven, and others to plan how to accomplish all the goals I had set. Little did I know at this moment as I settled into bed that my lifelong quest for true knowledge was about to commence.


text:
Ölands län was tussen 1819 en 1826 een provincie van Zweden. De provincie bestond uit het eiland en landschap Öland. De hoofdstad van de provincie was Borgholm. Voordat Ölands län ontstond maakte de provincie deel uit van Kalmar län, toen de provincie in 1826 werd opgeheven ging Öland opnieuw deel uitmaken van deze provincie.

Gouverneur
Axel Adlersparre (1819-1821)
Erik Gustaf Lindencrona (1821-1826)

Voormalige provincie van Zweden

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Panna Cotta is versatile so it was perfect for experimenting with. My biggest worry with Panna Cotta is that it doesn't set, so I kept to a ratio of 2 cups of liquid to 4 sheets of Gelatin and it turned out fine. I find that anything more than 2 tablespoons of rose-water is a little too strong for me ,but I suppose you could experiment with that yourself and adjust it to your taste. I was lucky enough to take a 6 week dessert course at the Culinary Institute in Dubai and one of the tips I picked up is to always use a whisk to stir any dairy (milk, cream, cheese etc.) you put on the stove, so do use a whisk to stir the cream to prevent it from becoming lumpy.
I've used fresh raspberries to keep it light and to counter the sweetness of the Panna Cotta, but you could make a raspberry sauce or include raspberries in the cream after cooking and before setting it in the fridge – like I said, Panna Cotta is versatile, so happy experimenting!
Submerge the Gelatin sheets in a bowl of cold water for about 10 minutes.
In a saucepan, combine the cream, coconut milk and sugar.
Slowly bring this to a boil, stirring the whole time with a whisk, until the mixture starts to boil. Turn it off and leave it on the heat for a few seconds.
Take the saucepan off the heat , drain & squeeze the Gelatin sheets (try to get out as much water as you can) and then add it to the cream mixture.
Stir until the Gelatin is fully melted into the cream.
Pour the mixture into the moulds, you can pretty much use any shape or size.
Leave the moulds in the fridge for at least 3 hours.
Run a sharp knife along the edge of the Panna Cotta, separating it from the mould.
Place the mould almost to the top in a bowl of hot water (be careful it's not boiling as the top of the Panna Cotta may melt).
Then turn it over onto a plate and tap the bottom of the mould to get the Panna Cotta out. Top with raspberries and rose petals.
I picked up this great tip from thekitchn.com – dampen the plate before turning the Panna Cotta out onto it, so you can adjust its' position before serving. It's difficult to move the Panna Cotta around on a dry plate.
Alternatively, you could garnish it beautifully and serve it up directly in the mould, for a small twist on the traditional way of serving it.
Davidlebovitz.com has a lot of information on working with Gelatin, so do take a look if you want to try this with powdered Gelatin instead.


text:
Q: Restore Xcode 7.3.1 after Xcode 8 upgrade Last night I went into my Application directory and renamed the Xcode.app to Xcode7.app
I then upgraded to Xcode 8 overnight.
When I came back in the morning, Xcode7.app was gone!! Nowhere to be found.
Now my project doesn't work on Xcode 8, upgrading to Swift 3.0 is impossible as many of my dependencies don't support it yet - and upgrading to swift 2.3 also doesn't work for some reason.
What happened to my Xcode 7 ? How do I get it back now?

A: I did not have this problem, and I also renamed Xcode (to Xcode-7.app) before updating.
I'm guessing it's because rather than choosing 'update' from the app store, I went to apple's downloads page and downloaded from there.
Try renaming your new Xcode to Xcode8.app, then go to https://developer.apple.com/download/more/ and download Xcode 7.3.1.dmg.

A: You can try this program:
https://github.com/KrauseFx/xcode-install
This program lets you install any Xcode version.
$ gem install xcode-install
$ xcversion list --all

...
7.0.1
7.1
7.1.1
7.2
7.2.1
7.3
7.3.1
8

$ xcversion install 7.3.1

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