text:
\subsection*{Introduction}

In a series of papers \cite{JoyDisproof1, JoyReply1, JoyConsolidations1, JoyIllusion1, JoyBell1, JoyBound1, JoyDisproof2, JoyCausality1}, Joy Christian claims to have constructed a local and realistic hidden variable theory able to reproduce quantum mechanics' correlations in the case of an EPR-Bohm experiment with spin one half particles. Joy Christian's model was received with serious criticisms \cite{Marcin1}, \cite{Holman1}, \cite{Grangier1}, \cite{Tung1}, \cite{Moldoveanu1}, but no single analysis could provide a decisive argument against it. Interestingly, the first comment \cite{Marcin1} came very close to uncover the first mathematical problem discussed below. In his reply \cite{JoyReply1} Joy Christian stated: ``With hindsight, however, it would have been perhaps better had I not left out as an exercise an explicit derivation of the CHSH inequality in Ref.~[1]. Let me, therefore, try to rectify this pedagogical deficiency here.''. This reply unfortunately managed to discourage other people from trying to check the validity of the mathematical results which are actually very easy to find.

Here are some key statements from subsequent critics' replies showing that the mathematical correctness was not the main focus of the criticisms:

``the model formally manages to reproduce some quantum theoretical expectation values correctly'' \cite{Holman1}

``and here we will assume that the content of these papers is correct'' \cite{Grangier1}

``The first comment on Christian's paper, [9] by Marcin Pawlowski, is also different from the current paper. That comment seems to say that in Clifford-algebra-valued hidden variable theory it is unable to derive Bell's inequalities. This is not true since they are indeed derivable, as is explicitly shown in [2].'' \cite{Tung1}

"By providing an explicit factorizable model, Joy Christian's example only disproves the importance of Bell's theorem as an argument against contextual hidden variable theories.'' \cite{Moldoveanu1}.

In the meantime, a new challenge to Joy Christian's work came from informal physics blogs: if Joy Christian's claim of a local realistic theory able to reproduce quantum correlations is right, then a computer simulation on a classical computer would be possible. The author of this paper proceed to do just that: model Joy Christian's theory on a computer to clarify its claims of local realism. In order to translate the model to computer code, all results had to be systematically double checked and this led to the big surprise of finding out the elementary but critical mathematical mistakes presented below.

\subsection*{Error 1: losing part of the correlation result by incorrect averaging}

In his first paper \cite{JoyDisproof1}, Joy Christian introduces his hidden variable $\mu$ as a random handedness of the basis for his geometric algebra basis. If $\{e_1, e_2, e_3\}$ are a set of fixed orthonormal vectors, the hidden variable $\mu$ is defined as follows
\begin{equation}
\mu \triangleq \pm I = \pm e_1 e_2 e_3 = \pm e_1 \wedge e_2 \wedge e_3
\end{equation}
(see Eq.~14 of Ref.~\cite{JoyDisproof1})

Then Joy Christian proceeds on computing the Clifford product of two bivectors $\mu \cdot a$, $\mu \cdot b$ obtaining in Eq.~17:

\begin{equation}
(\mu \cdot a)(\mu \cdot b) = - a \cdot b - a \wedge b
\end{equation}
which is correct (please note that the plus and minus factors in the two $\mu$'s cancel each other out and the expression is equivalent with $(I \cdot a)(I \cdot b)$). However, the last line of Eq.~17 is incorrect. By a well-known identity (Hodge duality):
\begin{equation}
a \wedge b = I \cdot (a \times b)
\end{equation}
it is now easy to see that  the last line of Eq.~17 is incorrect when $\mu = -I$. Because $I$ is incorrectly replaced by $\mu$ and gains an illegal minus sign when $\mu = -I$, this leads to an incorrect canceling of the $a \wedge b$ term when averaging over all $\mu$'s in the oriented vector manifold ${\cal{V}}_3$.

In Ref.~\cite{Marcin1}, Pawlowski criticized Christian's proposal for the presence of Clifford Algebra valued observables if we are to get a scalar in the RHS of the CHSH inequality. Joy Christian responded \cite{JoyReply1} by stating that the average on ${\cal{V}}_3$ removes the $a \wedge b$ element. However, Eq.~3 of Ref.~\cite{JoyReply1} is incorrect just like the last line of Eq.~17 in Ref.~\cite{JoyDisproof1}

Even without spelling in detail the error, it is easy to see that the exterior product term should not vanish on any handedness average because handedness is just a paper convention on how to consistently make computations. For example one can apply the same incorrect argument to complex numbers because there is the same freedom to choose the sign of $\sqrt{-1}$ based on the two dimensional coordinate handedness in this case. Then one can compute the average of let's say $z = 3+2i$ for a fair coin random distribution of handedness and arrive at the incorrect answer: $<z> = 3$ instead of $<z> = z$.

One advertised strength of geometric algebra is the ability to make computations in a coordinate-free fashion. If breaking up an object in its components and performing an average results in elimination of some components, then we are guaranteed that the operation is mathematically illegal.

The same mistake is present in the minimalist paper \cite{JoyDisproof2} in Eq.~4. Given a {\it fixed} bivector basis $\{\beta_i, \beta_j, \beta_k\}$, Eq.~3 of Ref.~\cite{JoyDisproof2} is correct. The corresponding $\lambda$-dependent basis product however should be the same as Eq.~3 of Ref.~\cite{JoyDisproof2} because $\beta_i (\lambda) \beta_j (\lambda) = \beta_i \beta_j \lambda^2  = \beta_i \beta_j$ and not gain an illegal $\lambda$ term for the cross product.

So how it was possible to have such an elementary mistake undetected? Most of Joy Christian's papers suffer from a convention ambiguity: in some cases the computations are done using the $\mu = \pm I$ convention with $I$ arising from a {\it fixed} basis, while in others the computations are done using the $\mu = I$ convention (indefinite Hodge duality) which means that $I$ is the current trivector and does not arise from a fixed basis. Illegally mixing the conventions during one computation yields the supposedly agreement with quantum mechanics.

Another way this mistake can arise can be seen in Eqs.~23 and 24 of Ref.~\cite{JoyBound1}. In there Eq.~23 is correct and Eq.~24 is derived by switching $I$ to $-I$ for a change of handedness. It is true that changing handedness (or equivalent performing a reflection) changes the sign of the pseudoscalar $I$, but what is incorrect in Eq.~24 is that $a \times b$ is a pseudovector who should change sign as well. The corrected Eq.~24 should be:
\begin{equation}
(-I \cdot a)(-I \cdot b) = - a\cdot b - (-I)(-(a \times b))
\end{equation}

The same mechanism for producing the error probably occurred in deriving  Eq.~4 of Ref.~\cite{JoyDisproof2} due to an incorrect replacement of $\beta (\lambda)$ in Eq.~3 without appropriately switching the sign of the Levi-Civita pseudotensor.

Also there are two additional physics objections as well. First, associating a hidden variable to an abstract computation convention is completely unphysical. Second, by doing it so, the theory predicts the same correlation {\it regardless} of the spin state of the particles in the EPR-Bohm experiment.

\subsection*{Error 2: Isotropically weighted averages of non-scalar part of correlations and measurement outcomes cannot be both zero}

Specifically, Eq.~18 and Eq.~19 of paper \cite{JoyDisproof1} cannot be both right. Let us count how many factors of $\mu$ are in Eq.~18 and Eq.~19. In Eq.~18 there are two factors of $\mu$, one from $\mu \cdot n$ and the other from $d \rho (\mu)$. Eq.~19 has three factors of $\mu$ from $\mu \cdot a$, $\mu \cdot b$, and $d \rho (\mu)$. As the factors are even and odd, integrating on a manifold ${\cal{V}}_3$ where $\mu$ changes signs evenly, only one of the two equations can be zero. Expanding the $(\mu \cdot a)(\mu \cdot b)$ term and using Hodge duality it follows that isotropically weighted averages of non-scalar part of correlations and measurement outcomes cannot be both zero.

By the prior error we already know Eq.~19 is incorrect and the statement that Eq.~18 and Eq.~19 cannot be both right is not a surprise. The new content of this error is that fixing Eq.~19 by any hypothetical generalization of the manifold ${\cal{V}}_3$ breaks Eq.~18. Both Eqs.~18 and 19 are needed to be right if the model is to reproduce experimental results. Therefore the handedness mistakes conclusively rule out both Joy's model and all its potential Clifford algebra generalizations.

\subsection*{Error 3: Illegal limit for a bivector equation}
In Ref.~\cite{JoyCausality1}, Joy Christian attempts to implicitly answer Holman's criticisms \cite{Holman1} that the final answer in Eq.~19 of Ref.~\cite{JoyDisproof1} has a wrong sign and that the outcome of the experiments is always the same resulting in perfect correlations. Joy Christian first seems to agree that the outcome for any pairs of experimental results is the same, but then tries to prove the opposite in an explanation marred by mathematical mistakes.

The discussion of this problem takes place around Eqs.~42-46 of that paper. Citing Joy Christian: {\it ``Furthermore, we have taken the randomness $\mu = + I$ or $- I$ shared by Alice and Bob to be the initial orientation (or handedness) of the entire physical space, or equivalently that of a 3-sphere. Consequently, once $\mu$ is given as an initial state, the polarizations along all directions chosen by Alice and Bob would have the same value, because $\mu$ completely fixes the sense of bivectors $\mu \cdot n$ belonging to $S2 \subset S3$ , regardless of direction.''} In other words, the correlation of the experimental outcome is always $+1$ contradicting quantum mechanics predictions. Up to this point Joy Christian is correct.

Still, Joy Christian continues: ``However, and this is an important point, the polarization $( +\mu \cdot a )$ observed by Alice is measured with respect to the analyzer $(- I \cdot a )$, whereas the polarization $( +\mu \cdot b )$ observed by Bob is measured with respect to the analyzer $(+ I \cdot b )$.''

It will be shown below in this and next section that the mathematical arguments supporting this (in an attempt to produce both the minus cosine correlation and all the four experimental outcomes $(+,+), (-,-), (+,-), (-,+)$) are mathematically incorrect.

First let us note that the change in sign between Alice and Bob is illegal because they both use the same kind of apparatus during measurement and swapping them should not change anything. Therefore we could stop the analysis here because Joy Christian's model is obviously wrong as it does not respect this basic symmetry. However let's follow along Joy Christian's argument and discover where the mistakes occur.

To solve the problem, Joy Christian considers two almost parallel vectors instead of one at each detector: $a a^{'}$ for Alice and $b b^{'}$ for Bob. The two vectors form a bivector and starting from an aligned vector configuration ($a$ aligned with $b$ and $a^{'}$ aligned with $b^{'}$) the goal is  to move the second pair ($b b^{'}$) at  Bob's location in the final detector position using a rotor. In general, a rotor can be expressed as follows:
\begin{equation}
R = \cos \Omega + \hat{B} \sin \Omega
\end{equation}

with $\hat{B}$ a unit bivector defined as:
\begin{equation}
\hat{B} = \frac{m \wedge n}{\sin~ \Omega}
\end{equation}
where $m$ and $n$ are two unit vectors and $\Omega$ is the angle between them. In the case of Eq.~45 of Ref.~\cite{JoyCausality1}, the unit bivector corresponds to an axial vector $c$ of unit norm:
\begin{equation}
c = \frac{a \times a^{'}}{|a \times a^{'}|}
\end{equation}

Then at the end of the rotation, after applying a simple trigonometric identity composing bivectors (multiplying two exponential expressions corresponding to the $a \wedge a^{'}$ and the $a \wedge b$ bivectors) Joy Christian takes the limit $a \rightarrow a^{'}$ and claims that this makes the bivector component of the final result zero as $a \wedge a^{'}$ becomes zero. The end result is that only the cosine factor survives the operation therefore a rotation by ``parallel transport'' in a ``twisted manifold'' allows to recover the cosine of the angle between Alice and Bob in their correlation as predicted by quantum mechanics.

The limit operation above is mathematically illegal. To see why, recall that the axial vector $c$ is of unit norm and as such it is normalized by the sine of the angles between $a$ and $a^{'}$. As $a^{'}$ approaches $a$, the wedge product goes to zero as sine of the angle, but the denominator goes to zero by the same sine of the angle factor. As such the two sines cancel each other and the bivector maintains its magnitude. This is nothing but a restatement of the geometric algebra fact that the magnitude of a bivector does not depend on the shape of the parallelepiped defining it. But maybe there is a discontinuity at the limit when $a = a^{'}$ and the bivector $\hat{B}$ does become zero. We can see that this is not the case as follows. Suppose $a$, $a^{'}$, $b$, $b^{'}$ are four unit vectors in the same plane, and vector $c$ is a unit vector orthogonal to this plane:
\begin{equation}
c = \frac{a \times a^{'}}{|a \times a^{'}|}  = \frac{a^{'} \times b}{| a^{'} \times b|}
\end{equation}
let $\epsilon \Omega$ be the angle between $a$ and $a^{'}$, and $(1 - \epsilon) \Omega $ the angle between $a^{'}$ and $b$.
If $\hat{B}$ is the unit bivector
\begin{equation}
\hat{B} = B_{a a^{'}} = B_{a^{'}b} = I c = \frac{a \wedge a^{'}}{\sin (\epsilon \Omega)} = \frac{a^{'} \wedge b}{\sin (1 - \epsilon \Omega)}
\end{equation}
then Joy Christian's incorrect argument is as follows:
\begin{eqnarray}
&\cos \Omega + \hat{B} \sin \Omega = \nonumber \\
&R(ab) = R(aa^{'}) R(a^{'}b) = \nonumber \\
&(\cos (\epsilon\Omega) + \hat{B}\sin (\epsilon\Omega))(\cos ((1- \epsilon)\Omega) + \hat{B}\sin ((1-\epsilon)\Omega)) = \nonumber \\
&\cos(\epsilon\Omega) \cos ((1- \epsilon)\Omega) - \sin(\epsilon\Omega) \sin ((1- \epsilon)\Omega) + \nonumber\\
&B_{a a^{'}}(\sin (\epsilon\Omega) \cos ((1- \epsilon)\Omega) + \cos (\epsilon\Omega) \sin ((1-\epsilon)\Omega)) = \nonumber \\
&\cos \Omega  \nonumber \\
\end{eqnarray}

The last equality comes from taking the exact limit $a = a^{'}$ which makes $B_{a a^{'}}$ vanish due to $a \wedge a = 0$. Comparing the first and last rows, it is clear that there is no discontinuity even when $a$ is strictly $a^{'}$ and the limit result is illegal.

It is also easy to see the mistake another way. Just compare Eq.~46 with the definition of the rotor following Eq.~45. In line two of Eq.~46 the term following the rotor computes to $-\lambda$ and the final answer in Eq.~46 up to the $-\lambda$ factor should be the entire value of the rotor and not just its cosine part.

\subsection*{Error 4: Incorrect parallel transport rotor direction}
In the problem above Joy Christian attempts to eliminate a bivector by an illegal limit. Taking the limit correctly still results in the wrong result because the first line of Eq.~46 should be equal with the last line of the same equation. The error is in using the incorrect rotor to perform the parallel transport. In geometric algebra any object $G$ transforms under a rotation by a rotor $R$ as $G \rightarrow R^{\dagger}GR$  with $R=ab$ and $R^{\dagger}=ba$. The angle of rotation is double the angle between vectors $a$ and $b$. This formula is completely general and works for scalars, vectors, bivectors, pseudoscalars, or any of their linear combinations. Let us try to apply this general formula to Eq.~46. $R_{ab}$ reads:
\begin{equation}
R_{ab} = \exp \{ (I \cdot c) \theta_{ab}/2\} = \cos (\theta_{ab}/2) + (I\cdot c)  \sin (\theta_{ab}/2)
\end{equation}

and the correct computation in Eq.~46 is:

\begin{eqnarray}
& \lim_{b^{'} \to b} [(+ I \cdot b) (+ \mu \cdot b^{'})] = - \lambda  \nonumber \\
& = \lim_{a^{'} \to a} \{R_{ab}^{\dagger} [(+ I \cdot a)  (+ \mu \cdot a^{'})] R_{ab}\} \nonumber \\
& = \lim_{a^{'} \to a}\{R_{ab}^{\dagger} [(-\lambda)(\exp \{ (I \cdot c) \theta_{aa^{'}}\})]  R_{ab}\} = \nonumber \\
& = \lim_{a^{'} \to a} \{R_{ab}^{\dagger} R_{ab} [(-\lambda)(\exp \{ (I \cdot c) \theta_{aa^{'}}\})]\} = \nonumber \\
& = \lim_{a^{'} \to a} [(+ I \cdot a) (+ \mu \cdot a^{'})] = -\lambda \nonumber \\
\end{eqnarray}

The final result after parallel transport is still $-\lambda$ because $\lambda$ is a scalar. The fourth line in the equation above comes from the fact that vector $c$ commutes with itself. There is another way to understand why the final result was not changed even when the limit is not taken. A bivector is an oriented surface characterized only by direction, magnitude, and sense of rotation. The vectors $a$, $a^{'}$, $b$, $b^{'}$ are in the same plane and the bivector $[(+ I \cdot a) (+ \mu \cdot a^{'})]$ and $[(+ I \cdot b) (+ \mu \cdot b^{'})]$ are actually identical because they have the same orientation, magnitude, and sense of rotation.  Rotating the pair $a a^{'}$ into $b b^{'}$ by the angle $\theta_{ab}$ preserves the orientation, magnitude, and sense of rotation.

The second mistake in Eq.~46 (when computing the limit correctly) comes from applying incorrectly the law of rotation for rotors. This formula is different than the general multivector formula and it applies only for rotors. Specifically the mistake in Joy Christian's paper is in the orientation of his rotor $\cal{R}$: instead of rotating around the vector $c$ (or equivalently $a \times a^{'}$), the correct direction is $(a \times a^{'})\times ( b \times b^{'})$. This is the correct direction because we are trying to rotate an $a\wedge a^{'}$ bivector with orientation $a \times a^{'}$ into a $b\wedge b^{'}$ bivector with orientation $b \times b^{'}$ and the rotation needs to align the two directions. Therefore the correct rotation direction is $(a \times a^{'})\times ( b \times b^{'})$. With this correct direction one can prove that the rotor law of rotation and the multivector law of rotation produce the same result (for example one can use a tedious brute force expansion of the two formulae and show they are identical in components). Applied to the discussion in the paper, since $(a \times a^{'})$ is parallel with $(b \times b^{'})$ the rotor reduces to identity in this case.

Computed correctly with the right limit and the right rotor, we can now see that the outcome at Alice's and Bob's detectors is always the same and the results are completely correlated contradicting quantum mechanics.  The reason is that the outcome results are nothing but the negative of the local bivectors' magnitude - a fixed value regardless of direction. Holman's analysis \cite{Holman1} is therefore proven correct: ``Because $\mu$ is a local deterministic hidden variable, its value cannot depend on the choice made by the experimenter. If this value is left unchanged by the first measurement, performing the second measurement in the $e_x$-direction would result in ``spin up'' in this direction with certainty, in contradiction with the usual quantum predictions.''. Flipping of the signs on Alice's and Bob's experimental outcomes is also without merit.

\subsection*{Conclusion}
Any of the four mathematical mistakes presented above can reject Joy Christian's claims of a disproval of Bell's theorem by counterexample. Another error is that computing Eq.~16 of Ref.~\cite{JoyBell1} yields Eq.~3 and not Eq.~15 as claimed: ``we believe the experiment will vindicate prediction (15) and refute prediction (3).''. This was proven both analytically and by computer simulation. Since this impacts only a particular claim of a paper and not the viability of the whole research program it was not presented here. (A similar computer simulation was carried out earlier by Stephen Lee \cite{Lee1}, but the source code was not made publicly available.) After those mistakes were found the systematic checking of Joy Christian's mathematical claims was stopped.

Joy Christian's model is not correct, but can Bell's theorem be invalidated by another non-commutative ``beables'' theory? Two theorems by Clifton \cite{Clifton1} answer this in the negative for non-contextual hidden variable theories and for relativistic quantum field theories with bounded energy. During computer simulations, several other non-commutative models which correctly realize the minus cosine correlations were discovered. However, the simulation also showed that any transition from non-commutative beables to discrete experimental outcomes destroys this correlation and yields the classical correlations as expected from Bell's theorem. It is therefore essential for a hidden variable model to predict both quantum correlations and the experimental outcomes. Any commutative beable hidden variable theory is ruled out by Bell's theorem. Any non-commutative non-contextual beable hidden variable theory is ruled out by Clifton's analysis. The only remaining way out is to construct a non-commutative contextual beable hidden variable theory. But contextual hidden variable theories are not really considered physical theories as no experimental evidence ever backed them out. It is debatable if Bell's theorem is important to rule out some contextual hidden variable theories as well, or only non-contextual ones. Bell's theorem is not the only result ruling out non-contextual hidden variable theories, but only Bell's result is robust enough (because involves an inequality) to be put to an experimental test.

\subsection*{Appendix: Relevant Clifford algebra tutorial}
After this preprint was originally published, several developments occurred. First, Joy Christian uploaded a rebuttal of this preprint \cite{JoyRebutalFlorin}, Richard Gill re-discovered error number one \cite{Gill1} in Joy Christian's minimalist one pager paper \cite{JoyDisproof2}, and Joy Christian rebutted that as well \cite{JoyRebutalGill}. There is no point going back and forth in an endless cycle of claims and counterclaims and instead this appendix will present in a hopefully clear pedagogical way the key ideas of Joy Christian's research, his mistakes (old and new), and why this program cannot be salvaged. The aim is to give any reader interested in this topic, even if not an expert in Clifford algebras, the tools to check Joy Christian's claims.

Before starting I also want to make a minor correction based on Joy Christian's rebuttal. The only valid criticism in \cite{JoyRebutalFlorin} was that complex numbers don't have handedness. This is correct, and also completely inconsequential to the conclusions of this paper.

The hidden variable model in Joy Christian's proposal is based on Clifford algebra, also known as geometric algebra. In the $19^{th}$ century, Clifford himself called his algebra ``geometric algebra''. The term was popularized by David Hestenes in the 60s and Hestenes had a famous expression: ``Geometry without algebra is dumb! Algebra without geometry is blind! ''\cite{HestenesQuote}. But what is a Clifford algebra? One example is the algebra of Dirac's gamma matrices. Skipping the rigorous definition, a Clifford algebra is an algebra satisfying:
\begin{equation}
uv + vu = 2<u,v>
\end{equation}
with the scalar product defined by the polarization identity:
\begin{equation}
<u,v>=(Q(u + v) - Q(u) - Q(v))/2
\end{equation}
and $Q$ a quadratic form.

In particular Clifford algebra $Cl(3,0)$ used in Joy Christian's model satisfies:
\begin{equation}
e_i e_j + e_j e_i = 2 \delta_{ij}
\end{equation}
with $(e_1, e_2, e_3)$ the usual $x, y, z$ unit vectors of the ordinary three dimensional space.

From this one extracts two very important practical rules:
\begin{equation}
e_1 e_1 = e_2 e_2 = e_3 e_3 = 1
\end{equation}
and
\begin{equation}
e_1 e_2 = -e_2 e_1 , e_1 e_3 = - e_3 e_1 , e_2 e_3 = -e_3 e_2
\end{equation}

Therefore when computing expressions in $Cl(3,0)$, one has to keep proper track of the order of terms, and use the two practical rules to simplify the expressions. This is all there is to it and everything else follows from here. It is easy to see that the basis of $Cl(3,0)$ is: $\{1, e_1, e_2, e_3, e_1 e_2, e_2 e_3, e_3 e_1, e_1 e_2 e_3\}$ with $1$ being the scalar, $\{ e_1, e_2, e_3 \}$ the vector basis, $\{e_1 e_2, e_2 e_3, e_3 e_1 \}$ the bivector basis, and $e_1 e_2 e_3$ the trivector (pseudo-scalar). As a shorthand notation, the bivectors are represented by the exterior product $e_1 e_2 = e_1 \wedge e_2$, and the trivector is usually named $I = e_1 e_2 e_3$.

From the definition of Clifford algebra one can extract the scalar product:
\begin{equation}
a \cdot b = \frac{1}{2} (ab + ba)
\end{equation}
and from the definition of exterior product one has:
\begin{equation}
a \wedge b = \frac{1}{2} (ab - ba)
\end{equation}

Summing the two equations results in this fundamental identity:
\begin{equation}
ab = a\cdot b + a \wedge b
\end{equation}

In terms of geometry, the scalar corresponds to a point, the vectors to lines, the bivectors to oriented surfaces, and the trivector with an oriented parallelepiped. In general, in Clifford algebras Hodge duality maps $k$-vectors with $(n-k)$-vectors by multiplication with the pseudo-scalar. In particular, in $Cl(3,0)$, Hodge duality maps bivectors (oriented areas) to pseudo-vectors (the cross product vector orthogonal to the area):
\begin{equation}
a \wedge b = +I (a \times b)
\end{equation}

Now we have all the mathematical preliminaries to understand Joy Christian's model. Let us compute the following expression: $(I a)(I b)$ with $a$ and $b$ vectors. First, what is $I I$? Let us apply the two practical rules: $I I = e_1 e_2 e_3 e_1 e_2 e_3 = - e_1 e_2 e_3 e_1  e_3 e_2 = + e_1 e_2 e_3  e_3 e_1 e_2 = + e_1 e_2 e_1 e_2 = - e_1 e_1 e_2 e_2 = -1$. Then let us prove $Ia = aI$. We can show it component by component and we will compute only the ``x'' component leaving the rest as an exercise to the reader: $I a_1 e_1 = a_1 I e_1 = a_1 e_1 e_2 e_3 e_1 = + a_1 e_1 e_1 e_2 e_3 = a_1 e_1 I $ by hopping $e_1$ twice from right to left. So now $(I a)(I b) = I I a b = -ab = -a\cdot b -a\wedge b = -a\cdot b - I a \times b$.

But why do we care about the computation above? Because the EPR-B singlet correlation is $-a\cdot b$ with $a$ and $b$ the spin measurement directions for Alice and Bob. If we can somehow eliminate the $-I a \times b$ term, we could claim we have a hidden variable theory reproducing quantum mechanics correlations. {\bf  This is the essence of Joy Christian's program. The essence of this tutorial is that this hope cannot be realized in any mathematical consistent way.}

So let us follow Joy Christian again and introduce the hidden variable $\mu = \pm I$:
\begin{equation}
(Ia)(Ib) = -a\cdot b - \mu a\times b
\end{equation}
and the sign of $\mu$ being $+1$ $50\%$ of the time and $-1$ the other $50\%$ of the time. Is this equation correct?

At first, Joy Christian's program seems feasible. The sign of the pseudoscalar/trivector $I$ is arbitrary and corresponds to the handedness of the reference frame $e_1, e_2, e_3$. So maybe the hidden variable is the sign of $I$ and we can average out somehow the troubled $I (a \times b)$ term. To see why this is impossible we need to clarify in the process the confusions between handedness, the sign of the determinant ($O(n)$ vs. $SO(n)$) and adjoin representations.

During the many papers presenting his model, Joy Christian attempted several approaches to average out the $\mu a \times b$ term. This is what Richard Gill calls: ``moving the bump in the carpet''. We'll follow along the ``bump'' in historical fashion from Joy Christian's papers. However, before we embark on this endeavor, there is a very simple way to see that this term cannot vanish. We start with $(Ia)(Ib)$ which equals $-ab$ and no matter how this is decomposed and averaged in components, in the end is still $-ab$ which remains $-a\cdot b -a \wedge b$ and the $a \wedge b$ term cannot be eliminated in any consistent mathematical argument.

Now we will introduce a few algebra preliminary statements without proofs. All Clifford algebras have even subalgebras. Handedness exists only in three dimensions (it is a property of the human hand: ``lefty loosy, righty tighty''), but it is generalized to any dimensions to a definite determinant sign which preserves orientation and distinguishes between $SO(n)$ and $O(n)$ by mirror reflections. All associative algebras have matrix representations (matrix multiplication is associative). A $n \times n$ matrix can multiply a column vector (ket) from the {\it left}, or a row vector (bra) from the {\it right}. For complex numbers and the even subalgebras of $Cl(3,0)$ those left/right algebra representations are adjoints (the usual transposed and complex conjugation, but without complex conjugacy for complex numbers because the representations are over real numbers). In Geometric Algebra, those adjoints correspond to reversing the order of the $e_i$ elements in products.

Now let start illustrating those statements with complex numbers both in Clifford algebra and in matrix representations. Let us start with this Clifford algebra in two dimensions: $\{1, e_1, e_2, e_1 e_2\}$. It has a  right subalgebra: $\{1, e_1 e_2\}$ and a left subalgebra $\{1, -e_1 e_2\}$.

Now consider two elements $A$ and $B$ as follows:
\begin{equation}
A = a_1 + a_2 e_1 e_2
\end{equation}
\begin{equation}
B = b_1 + b_2 e_1 e_2
\end{equation}
Let us multiply them:
$AB = (a_1 + a_2 e_1 e_2)( b_1 + b_2 e_1 e_2) = a_1 b_1 + a_2 b_2 e_1 e_2 e_1 e_2 + a_1 b_2 e_1 e_2 + a_2 b_1 e_1 e_2$ and using the two simple Clifford algebra rules one gets: $AB = (a_1 b_1 - a_2 b_2) + (a_1 b_2 + a_2 b_1) e_1 e_2$ so this is a Clifford algebra representation of complex numbers.

Similarly consider
$M$ and $N$ as follows:
\begin{equation}
M = m1 +m2 (-e_1 e_2)
\end{equation}
\begin{equation}
N= n1 + n_2 (-e_1 e2)
\end{equation}
and after multiplication $MN = (m_1 n_1 - m_2 n_2) + (m_1 n_2 + m_2 n_1) (-e_1 e_2)$, so again this is the other a Clifford algebra representation of complex numbers. Please note that it is nonsense to add or multiply numbers in the two representations. Also the two representations are adjoint: ${(e_1 e_2)}^{\dagger} = e_2 e_1 = -e_1 e_2$.

Now let's illustrate complex numbers in the two left/right matrix and ket/bra representations which correspond to the two above subalgebra representations.

The ket representation is as follows:
\begin{equation}
| z > = \left( \begin{array}{c}
a\\
b\\
\end{array}
\right)
\end{equation}
with this multiplication rule
\begin{equation}
| z_1 > * | z_2 > = \left( \begin{array}{c}
a_1 a_2 - b_1 b_2\\
a_1 b_2 + a_2 b_1\\
\end{array}
\right)
\end{equation}
and the left matrix representation is
\begin{equation}
Z_{left} = \left( \begin{array}{cc}
a&-b\\
b&a\\
\end{array}
\right)
\end{equation}

Then the following identities hold justifying the name (left representation)\cite{GrginBook}:
\begin{equation}
A B C | d > = A B |c d> = A B |c> * |d> = A |b c d>
\end{equation}

Similarly the bra representation is as follows:
\begin{equation}
< z | = \left( a , b \right)
\end{equation}
with this multiplication rule
\begin{equation}
< z_1 | * < z_2 | = \left( a_1 a_2 - b_1 b_2 ,
a_1 b_2 + a_2 b_1 \right)
\end{equation}
and the right matrix representation is
\begin{equation}
Z_{right} = \left( \begin{array}{cc}
a&b\\
-b&a\\
\end{array}
\right)
\end{equation}

Then the following identities hold justifying the name (right representation):
\begin{equation}
< d | C B A = <d c | B A = <d| * <c| B A = <d c b | A
\end{equation}

Please note:
\begin{equation}
|z>^{\dagger} = <z|
\end{equation}
and
\begin{equation}
Z_{left}^{\dagger} = Z_{right}
\end{equation}

The reason for this mathematical detour is to clarify the left/right mathematical representations because in the case of the even subalgebras of $Cl(3,0)$ Joy Christian incorrectly calls them left/right handedness \cite{JoyRebutalFlorin}. In general, for an associative algebra the left/right ket/bra representations are distinct from the adjoint representations, and also different from chiral representations. For complex numbers and for $Cl(3,0)$ subalgebras, the adjoint and left/right matrix representations are identical (as it was already shown for complex numbers and will be later shown for the even subalgebras of $Cl(3,0)$). In case of Joy Christian's subalgebras we have four distinct classes: left algebra left handedness, left algebra right handedness, right algebra left handedness, right algebra right handedness. Recall that a handedness change corresponds to a mirror reflection, and an adjoint change corresponds to flipping the order of the basis. So here are the four classes of algebras one can encounter in Joy Christian's model:
Start with a {\it fixed} right hand basis $\{ e_1 , e_2 , e_3\}$

Right algebra right handed basis:
\begin{equation}
\left\{ 1, e_2 e_3 , e_3 e_1 , e_1 e_2 \right\}
\end{equation}
then mirror say $e_2$ to get a right algebra in a left handed basis
\begin{equation}
\left\{ 1, (-e_2 ) e_3 , e_3 e_1 , e_1 (-e_2 ) \right\}
\end{equation}
From right/right flip the order of all basis vectors (take a geometric algebra adjoint) to get a left algebra in a right handed basis:

\begin{eqnarray}
\left\{ 1, {(e_2 e_3 )}^{\dagger} , {(e_3 e_1 )}^{\dagger}, {(e_1 e_2 )}^{\dagger}\right\} = \nonumber \\
\left\{ 1, e_3 e_2 , e_1 e_3 , e_2 e_1 \right\} = \\
\left\{ 1, - e_2 e_3 , -e_3 e_1 , -e_1 e_2 \right\} \nonumber
\end{eqnarray}

Last, to obtain a left algebra in a left handed basis, flip the sign of $e_2$ for example in the equation above:
\begin{equation}
\left\{ 1, e_2  e_3 , (-e_3 e_1 ) , e_1 e_2 \right\}
\end{equation}

Let us now defines some useful shorthand notations: $B_{1R} = e_2 e_3$, $B_{2R} = e_3 e_1$, $B_{3R} = e_1 e_2$ and the corresponding adjoints $B_{L}=B_{R}^{\dagger}$: $B_{1L} = -e_2 e_3$, $B_{2L} = -e_3 e_1$, $B_{3L} = -e_1 e_2$. Let us compute the product of the three elements in both algebras: $B_{1R} B_{2R} B_{3R} = +1$ and $B_{1L} B_{2L} B_{3L} = -1$. For proof, please see this sequence $e_2 e_3 e_3 e_1 e_1 e_2 = e_2 e_3 e_3 e_2 = e_2  e_2 = +1$. Again, Joy Christian incorrectly calls this right and left handedness, but the name actually comes from the matrix representation, and mixing them in a computation amounts to adding column with row vectors.

The general rule for multiplying the $B$ elements is as follows:
\begin{equation}
B_{iR} B_{jR} = - \delta_{ij} - \epsilon_{ijk} B_{kR}
\end{equation}
and
\begin{equation}
B_{iL} B_{jL} = - \delta_{ij} + \epsilon_{ijk} B_{kL}
\end{equation}

The relations between the two algebras are:
\begin{equation}
B_{R}^{\dagger} = B_{L} = - B_{R}
\end{equation}

Below are the ket/bra and left and right matrix representations of those two algebras (over complex numbers). Other representations are possible. In particular the representations over real numbers involve $4 \times 4$ matrices. The way to obtain the complex representations are either from Pauli matrices (those algebras are actually quaternions and the $B$s are the $\pm i$, $\pm j$, $\pm k$ quaternionic elements) or from the Cayley-Dickson construction (which was used below). The advantage of the Cayley-Dickson construction is that it also gives the ket/bra representations right away.

Left algebra ($B_{iL} B_{jL} = - \delta_{ij} + \epsilon_{ijk} B_{kL}$):

\begin{equation}
| B_{1L} > = \left( \begin{array}{c}
i\\
0\\
\end{array}
\right)
\end{equation}

\begin{equation}
| B_{2L} > = \left( \begin{array}{c}
0\\
1\\
\end{array}
\right)
\end{equation}

\begin{equation}
| B_{3L} > = \left( \begin{array}{c}
0\\
-i\\
\end{array}
\right)
\end{equation}

\begin{equation}
B_{1L} = \left( \begin{array}{cc}
i&0\\
0&-i\\
\end{array}
\right)  = i \sigma_3
\end{equation}

\begin{equation}
B_{2L} = \left( \begin{array}{cc}
0&-1\\
1&0\\
\end{array}
\right)  = - i \sigma_2
\end{equation}

\begin{equation}
B_{3L} = \left( \begin{array}{cc}
0&-i\\
-i&0\\
\end{array}
\right) = -i \sigma_1
\end{equation}

Right algebra ($B_{iR} B_{jR} = - \delta_{ij} - \epsilon_{ijk} B_{kR}$):

\begin{equation}
< B_{1R} | = \left( -i , 0 \right)
\end{equation}

\begin{equation}
< B_{2R} | = \left( 0 , 1 \right)
\end{equation}

\begin{equation}
< B_{3R} | = \left( 0 , i \right)
\end{equation}

\begin{equation}
B_{1R} = \left( \begin{array}{cc}
-i&0\\
0&i\\
\end{array}
\right) = -i \sigma_3
\end{equation}

\begin{equation}
B_{2R} = \left( \begin{array}{cc}
0&1\\
-1&0\\
\end{array}
\right) = i \sigma_2
\end{equation}

\begin{equation}
B_{3R} = \left( \begin{array}{cc}
0&i\\
i&0\\
\end{array}
\right) = i \sigma_1
\end{equation}

By inspection, in ket/bra or left/right matrix representation, the same relationship holds as in the case of Clifford algebra representation:
\begin{equation}
B_{R}^{\dagger} = B_{L} = - B_{R}
\end{equation}
and this time the adjoint involves also a complex conjugation as well because the representation is over complex numbers.

We are almost ready to discuss Joy Christian's mathematical mistakes and conclude that his program cannot succeed. Having clarified the left/right name and the relationship between Clifford $Cl(3,0)$ subalgebras in three representations, we need to understand how handedness enters the picture and how the sign of the Hodge duality changes or not in the four combinations: left/right representation with left/right handedness. To avoid unnecessary confusions we have considered and continue to consider only a {\it fixed} right handed basis $\{ e_1 , e_2 , e_3\}$. Any mirror reflection changes handedness and there is no restriction on which direction the mirror reflection can take place. We have seen that the left and right subalgebra representations obey different mathematical identities: $B_{1R} B_{2R} B_{3R} = +1$ and $B_{1L} B_{2L} B_{3L} = -1$. Let us first show that those identities have nothing to do with handedness contrary to Joy Christian's claims. Start with a right subalgebra in a fixed right handed basis $\{ e_1 , e_2 , e_3\}$. Perform three mirror reflections for $e_1$, $e_2$, and $e_3$. All three $e_i$ elements change signs and the $B$ elements do not because they are an even product of the unit vectors. As such the triple product $B_{1R} B_{2R} B_{3R}$ maintains the same $+1$ sign. But the handedness flipped three times in the process. Therefore the sign of the triple product has absolutely no relevance on the basis handedness (the sign of $I$).  Drawing a right hand basis on paper and successfully drawing the three consecutive mirror reflections shows how the final basis can change signs for the pseudoscalar.

Now the final piece of the puzzle: the sign in the Hodge duality. By direct computation in components and term identification, it is easy to see that in a right handed right algebra:
\begin{equation}
a \wedge b = +I (a \times b)
\end{equation}
The question is: does this equation changes signs by a mirror reflection as Joy Christian seems to imply in his first paper? Now we can either compute it in components, or observe instead that in a mirror reflection $I$ changes signs as a pseudo-scalar, but so does $a \times b$ because it is a pseudo-vector. As such, Hodge duality maintains its sign on a handedness change as long as the algebra is kept the same. Leaving the proof as an exercise to the reader, in a right handed left algebra the Hodge duality becomes:
\begin{equation}
a \wedge b = -I (a \times b)
\end{equation}
and again, this relation does not change signs on any mirror reflection.

So now we have all the mathematical results needed to understand the question posed earlier: is the following equation correct?
\begin{equation}
(Ia)(Ib) = -a\cdot b - \mu a\times b
\end{equation}

Now let us look in chronological order to Joy Christian's papers and see the "bump in the carpet" moving. Starting with the first paper \cite{JoyDisproof1}, we have a case of the same algebra and different handedness. But Hodge duality does not change signs on a handedness change in the same algebra and the last line of Eq.~17 of the paper is inconsistent with Eq.~14 of the same paper.

When confronted in public blog debates with the proof of this mathematical fact, Joy Christian used the ambiguity in his framework and claimed that this is a ``straw man'' argument and he actually meant left and right algebras. This is consistent with his rebuttal argument for this paper. Citing Joy Christian \cite{JoyRebutalFlorin}:

``To this end, right-multiply both sides of Eq. (7) by $\beta_l$, and then use the fact that ${(\beta_l)}^{2} = -1$ to arrive at
\begin{equation}
\beta_j \beta_k \beta_l = +1 \hspace{0.5in} [12] \nonumber
\end{equation}
The fact that this ordered product yields a positive value confirms that $\{\beta_x , \beta_y , \beta_z \}$ indeed forms a right-handed
frame of basis bivectors. This is a universally accepted convention, found in any textbook on geometric algebra [14].''

I hope now it is easy to spot the serious confusions in Joy Christian's text snippet. The overall sign of the triple product has nothing to do whatsoever with handedness. Instead it has to do with row or column representations or with multiplying kets from the left and bras from the right in matrix representations, and any handedness can be picked by whatever convention one wants.

So if we no longer consider the handedness to change the sign of the Hodge duality, we can now investigate the next move in "bump in the carpet" as displayed in Joy Christian's one-pager paper \cite{JoyDisproof2} which Richard Gill investigated in \cite{Gill1}. In this paper, following Eq.~3, Joy introduces lambda-dependent bivector basis: $\beta_j ( \lambda ) = \lambda \beta_j$. Apart from this dangerously confusing notation, we can see that this is nothing but the relationship between the left and right algebras (ignore the left most term):
\begin{equation}
B_{R}^{\dagger} = B_{L} = - B_{R}
\end{equation}

At this juncture, it is hard to understand Joy Christian's intent as we reached a decision point: is Joy Christian mixing the two representations in the same computation, or not? Either way it leads to bad outcomes. In public blog debates, Joy Christian opted for the first choice: adding the two betas. If this is the case the entire model evaporates. By substituting $\beta_j ( \lambda ) = \lambda \beta_j$ into his Eq.~3, Joy Christian obtains his Eq.~4:
\begin{equation}
\beta_j \beta_k = -\delta_{jk} - \lambda \epsilon_{jkl} \beta_l
\end{equation}

Now if this equation is always valid (for both values of lambda) by adding the two equations for both values of lambda one can immediately see that all betas must be zero. In this appendix formalism, when using the ket/bra representation, it is obvious that it is nonsensical to add row with column vectors and Joy Christian's Eq.~4 cannot be considered holding at the same time.

So now let us move the "bump" along one more time and argue that in $50\%$ of the cases the equation with $\lambda = +1$ holds, and in the other $50\%$  of the cases the equation with $\lambda = -1$ holds.

Then the problem moves to deriving Eq.~7 from Eq.~6 in Joy Christian's one pager. Here the error is subtle and if the reader loves a mathematical challenge, please try to identify the issue without reading on.

To get from Eq.~6 to Eq.~7, Joy Christian is substituting Eq.~4 into Eq.~6. But while in Eq.~4 lambda is a variable, in Eq.~6 is an index and the substitution in one step is illegal. To do the proper substitution, we need to keep proper tabs on the two kinds of betas in Eq.~6: row or column vectors and add like terms in two substitutions. Then use the conversion law: $B_R = -B_L$ to combine the two sums. This additional minus sign from the conversion now makes the trouble sum term in Eq.~7 no longer vanish and the correct final result is (no surprise):  $-a \cdot b - a \wedge b = -ab$

So no matter which road one takes computing $-ab$, the final result must be $-ab$ and not $-a\cdot b$.

We have reached the end of the mathematical road hopefully illuminating the mathematics involved in Joy Christian's research program and despite its unusual Clifford algebra setting, the math involved is really trivial. It is a matter of indifference on which representation one chooses for $Cl(3,0)$ and its subalgebras, be it standard geometric algebra, ket and bra representations, or matrix representations. The practical rules given by Eqs.~16 and 17 are all one needs to know to be able to check Joy Christian's claims. A larger detour was given here to put things in perspective and understand the left and right representations, mirror reflection impact, and spelling out the four classes of algebras: left/right representation times left/right handedness.

\subsection*{Appendix: Final developments}
After writing the appendix above and before this paper was made public, important developments occurred changing completely the author's perspective. Tung Ten Yong's original analysis \cite{Tung1} invalidated the entire program of challenging Bell's by ``topological complete'' hidden variable models, but his argument was not understood until James Owen Weatherall managed to construct a model (not based on Clifford algebras) which achieves precisely the aims of Joy's program: $-a\cdot b$ correlation and zero average for both Alice and Bob's outcomes \cite{Weatherall1}. In particular, Weatherall's model respects outcome and parameter independence but it cannot be modeled on a computer according to Sascha Vongehr's quantum Randi challenge \cite{Vongehr1}. So what goes wrong as James Weatherall discovered independently of Tung Ten Yong, is the need to compute the correlations not in a generalized statistical theory in the space of the hidden variable model, but in the usual way {\it after} the experimental outcomes are obtained. The conclusion of those developments is that Bell's locality: outcome and parameter independence has to be augmented with the requirement to compute the correlations after obtaining the experimental outcomes. Therefore the Clifton's theorems \cite{Clifton1} are no longer needed to prevent challenges to Bell's theorem.

More developments followed. ``Error 1'' presented in this paper was discovered independently not only by Richard Gill and the author, but by Marc Holman and David Hestenes as well but they were not published. I did not want to change anything in the original sections of this paper to let the readers have a clear history of this debate. However, the earlier statement: `` but no single analysis could provide a decisive argument against it'' is clearly false and reflected the author's understanding at the time of writing the first version. All four original critics: Pawlowski, Holman, Grangier, and Yong provided decisive arguments (and Holman's analysis provided two independent decisive arguments against the model). Marc Holman even prepared a paper on ``Error 1'' \cite{MarcPrivate} which was never published. To date, Joy Christian still disagrees with all his critics, calling their arguments: ``straw men arguments'', and stating that he will not accept anyone's judgment on his work ``but that of Nature'' reiterating his call for the experiment proposed in \cite{JoyBell1}. In the author's opinion, demanding an experiment while failing basic mathematical consistency amounts to an unacceptable departure from basic scientific norms. Hopefully the appendix will allow the reader reach an informed decision on the mathematical consistency of Joy Christian's mathematical argument.

\subsection*{Acknowledgement}
I want to thank Cristi Stoica for his help in computer modeling of Joy Christian's proposed experiment in Ref.~\cite{JoyBell1} and for useful discussions. I also want to thank Marc Holman, Richard Gill, David Hestenes, James Weatherall, and Sascha Vongehr for useful discussions. I want to thank Scott Aaronson for helping decide on the usefulness of writing the Clifford algebra tutorial.

redpajama_set_name: RedPajamaArXiv


Please note that in order to create a new page or edit an existing wiki page, you must be a logged-in member of the society. Non-members are welcome to submit material to the wiki Editorial Board using the wiki submission form.
If you are new to working with the wiki, you should read the new article tutorial and the how to edit a wiki page tutorial. The links give basic steps for creating a new wiki page, including screen shots of making an example page and how to edit existing pages.. You should also read the wiki style guidelines page as it explains several important formatting conventions and advanced editing features.
Before creating a new article, it is a good practice to make sure that one doesn't already exist by using the search function or viewing the title list.


text:
HANDS AND DAYLIGHT PODCAST
E85: BEARDS, BROS, AND BOOTS
Maine's newest resident, Ryan Michler, joins us as at the studio for a great conversation about his experience building boots recently at the Origin factory. We deep dive into all things Maine.
America was forged. From nothing came everything we believe in. But the America our grandparents once knew is not the America we now know. Pete Roberts explores how our ancestors used their minds, hands and daylight to build this great nation. Have you forgotten your history? Have you forgotten that you and me, men and women are the ones who drive true change. Have you forgotten that our independence was won through the sacrifice of our ancestors. That what we have is the sum of their works. A movement of the people is the true power we have. But the greatest legacy they left is not the bridges and buildings, it's this thing we call Freedom. That unified we can move mountains. It's not business as usual, Pete builds parallels between the past, the present and the future. He discusses how to reconstruct the grit, values, and work ethic through his personal experiences and of those who have been there.
© © 2018 Origin Holdings, LLC

redpajama_set_name: RedPajamaCommonCrawl


text:
HMS Albion fends off Spanish jets during Baltic exercises
10 June 2021 Topic: Fighting armsSurface Fleet Storyline: HMS Albion
HMS Albion fended off attacks from Spanish jets as they tested their air defence skills in the Baltic Sea.
Plymouth-based Albion is currently at the centre of the UK's Littoral Response Group (North) deployment, which is now participating in large-scale NATO exercises – Baltops – alongside 17 other nations.
But before linking up with the Baltops task group, Albion came under simulated attack from two Spanish Typhoons of NATO's Baltic Air Policing mission, which fired mock anti-ship missiles at them.
The assault ship sprang into action as the jets were detected and the operations room coordinated their defence to thwart the inbound fighters.
Upper deck weapons crews and Phalanx operators were called on to report inbound aircraft or missiles and engage under the direction of the Principal Warfare Officer, Lieutenant Commander Natalie Burns.
She said: "The aircraft flew simulated missile profiles against the ship in order to test our reactions and defensive procedures before conducting Combat Air Support (CAS) training with the Joint Terminal Attack Controller (JTAC) team from 29 Commando. During an air defence exercise the Operations Room will be at the fullest state of readiness to enable us to fight the ship and protect the people within it.
"Personnel will be closed up to report incoming threats to the Principle Warfare Officer and Command, and the Electronic Warfare team will advise on how best to employ the ship's decoys in order to protect the ship.
"Training with live assets is really beneficial as it adds a crucial element of realism, especially for the upper deck weapons crew and Bridge team who are able to practice calling in 'real threats'.
"The ability to train with NATO partner nations also provides excellent opportunities for embarked staff to hone their skills in the maritime environment, ensuring that the ship and her staff, are continually prepared for deployed operations."
The Spanish jet are currently on a four-month operation working with Italy and Turkey on NATO's Baltic Air Policing mission, which has seen them guard the skies over the region since May.
The jets are kept on quick reaction alert 24/7 to fly security sorties in the Baltic skies.
Prior to the fending off the jets, Albion had been working with the Finnish military and visited capital Helsinki.
Royal Marines trained with the Finnish Navy and two Jehu-class landing craft used Albion's spacious dock for the first time.
The exercises also include navigational manoeuvres and UK and Finnish landing craft working closely together.
Lieutenant Emily Witcher, Deputy Navigator on HMS Albion, said: "During our recent patrol to the Baltic Sea, we had the pleasure of working with the Finnish Navy.
"It was a great opportunity to work together and demonstrate the flexibility of our capabilities by embarking their landing craft into our well dock whilst they conducted training with our landing craft. It is important to maintain and progress these international relationships whenever we get the opportunity to."
While in Helsinki, Albion hosted the Finnish Chief of Defence, UK Ambassador, Defence Attaché and Naval Academy Commandant.
Sailors and Royal Marines also demonstrated some of the capabilities of the UK's Littoral Response Group, including new tactics being adopted.
Stephen Boyle, British Embassy Helsinki's Defence Attaché, said: "Albion's visit to Helsinki was a great success with excellent training conducted by our two Navies and productive discussions held with the Finnish Chief of Defence.
"Completing her second visit in two years, Albion's Captain and crew are looking forward a time when she can renew her ties with the city with the opportunity to spend some time ashore in beautiful Helsinki."
Surface Fleet HMS Albion
Continue reading about HMS Albion
Royal Navy and French Navy combine to test new support ship
One of Britain's biggest warships was towed through the Channel to help the French test...
The Princess Royal joins assault ship Albion on exercises in Scotland
The Princess Royal, Sponsor of HMS Albion, visited her warship to watch the largest...
Albion's sailors remember one of the Thames' darkest hours
Sailors from HMS Albion paid their respects to 38 civilians killed when the ship's...
HMS Albion meets her Royal Sponsor and pays her 'Dues'
Amphibious assault ship HMS Albion visited the Tower of London to participate in the...


text:
Porosz Mór, születési és 1900-ig használt nevén Popper Mór (Alberti, 1867. október 22. – Budapest, 1935. december 9.) bőrgyógyász, urológus, venerológus, szexológus, szakíró.

Életpályája
Popper Ignác (1836–1924) hitközségi vezető és Schweiger Éva fiaként született zsidó családban. Középiskolai tanulmányait a budapesti V. kerületi Királyi Katolikus Főgimnáziumban végezte (1878–1886), majd a Budapesti Tudományegyetem Orvostudományi Karának (1886–1892) hallgatója lett, ahol 1892. január 9-én avatták orvosdoktorrá. Később megszerezte a középiskolai egészségtan tanári és iskolaorvosi képesítést és letette a tisztiorvosi vizsgát. 1895 januárjától a Bőr- és Bujakórtani Tanszék gyakornokának nevezték ki, ahol Schwimmer Ernő mellett dolgozott. Rész vett az 1904–1905-ös pesti szexuálpedagógiai konferencián.

Az első világháború idején, 1915 júliusában ezredorvossá léptették elő. A budapesti honvédkerület bőr- és nemibeteg kórházának parancsnoka volt és értékes szolgálataiért több kitüntetésben részesült. A háború után magángyakorlatot folytatott a Vilmos császár út 64. szám alatti rendelőjében. Állandó munkatársa volt magyar, német és amerikai orvosi szaklapoknak, amelyekben több száz cikke és tanulmánya jelent meg bőr- és nemibetegségekkel kapcsolatos és szexuális vonatkozású kérdésekről. Halálát tüdőrák okozta.

Tagja volt az Izraelita Magyar Irodalmi Társulatnak.

A Kozma utcai izraelita temetőben nyugszik.

Családja
Felesége Leitner Ilona (1874–) volt, Leitner Fülöp kereskedő és Wertheimer Rozália lánya, akivel 1893. augusztus 15-én Jászkiséren kötött házasságot.

Gyermekei:
 Porosz Julianna (1894–?). Férje Kramer Miksa (1890–?) bankhivatalnok, a Magyar Bank és Kereskedelmi Rt. tisztviselője.
 Porosz Ambrus (1898–1943) fogorvos. Munkaszolgálatosként vesztette életét az orosz fronton. Felesége Halpern Sarolta (1903–?).
 Porosz Éva Lilla (1900–1977). Férje Gesztes (Schlesinger) Sándor (1897–?).
 Porosz Rózsa Magdolna (1906–?). Férje dr. Bálint (Breisach) Géza (1893–?) orvos.

Művei
 A prostata lobos bántalmainak és hypertrophiájának, továbbá az alvási pollutio-, prostatorrhoea- és spermatorrhoeának faradicus árammal való gyógyításáról. (Gyógyászat, 1897, 50–51.)
 A rendellenes magömlésről. (Gyógyászat, 1898, 36., 38., 40., 42., 44–45, 47., 49.)
 Az ondófolyás és egyes prostata bántalmak villamárammal való gyógyításáról. Budapest, 1898
 A rendellenes magömlésről. Budapest, 1899
 A rendellenes vizelésről. (Gyógyászat, 1899, 32–33; 35.)
 Atonia prostatae. Előadta a Magyar Orvosok és Természetvizsgálók szabadkai vándorgyűlésén. (Gyógyászat, 1899, 43.)
 Epididymitis sympathica és a kankóval járó mellékherelobról. (Gyógyászat, 1900, 24.)
 A kankó gyógyítása légenysavval. Jegyzetek a kankókezelésről. (Gyógyászat, 1900, 32.)
 A pityriasis versicolor (májfolt) eltávolításáról. (Gyógyászat, 1900, 41.)
 A Tonogen suprarenale sec. Richter némely sikeres alkalmazásáról. (Gyógyászat, 1904, 32.)
 Tonogen mint hányáscsillapító szer. (Gyógyászat, 1904, 38.)
 Az onania következményeiről. (Gyógyászat, (Gyógyászat, 1905, 10., 13., 16., 22.)
 A húgycsőszűkületekről. (Gyógyászat, 1905, 36., 38., 40. )
 Végbélféreg okozta urethrorrhoea és fokozott libido. (Gyógyászat, 1909, 39.)
 Prostata okozta pollutio, spermatorrhoea és impotentia. (Orvosi Hetilap, 1909, 51.)
 A húgycső hyperaemiás kezelésének methodikája. (Orvosi Hetilap, 1911, 31.)
 Adatok a prostata anatómiájához. (Orvosi Hetilap, 1912, 13–16.)
 Az impotentia és perverzitás törvényszéki orvosi megállapítása. (Budapesti Orvosi Ujság, 1912, 21.)
 A hadi venerologia köréből. (Gyógyászat, 1915, 36.)
 Pseudofrenulum praeputii. (Gyógyászat, 1921, 29.)
 A prostata tultengés (hypertrophia) gyógykezelése. (Gyógyászat, 1921, 43.)
 A Seautocontemptio. Az önlekicsinylés (Die Selbstgeringschätzung) mint sexualis psychicus állapot. (Gyógyászat, 1922, 36.)
 Rosszul festett harisnyától keletkezett bőrgyulladás a lábon. (Gyógyászat, 1923, 25.)
 A modern syphilis kezelésről. (Gyógyászat, 1923, 37–39.)
 Gyors ejaculatiós (prostata atonján alapuló) impotentia meggyógyítása. (Gyógyászat, 1929, 37.)
 A prostatitisről és gyógyításáról. (Gyógyászat, 1932, 45.)

Jegyzetek

Források

 Gergely András: Jeles magyar zsidó orvosok lexikona. Budapest, Makkabi, 2001

Magyar bőrgyógyászok
Magyar urológusok
1867-ben született személyek
1935-ben elhunyt személyek
Albertirsaiak
Családi nevüket magyarosított személyek

redpajama_set_name: RedPajamaWikipedia


Stacy Wading Pool is located at 1401 Sunset Lane in Austin, Texas. View all City of Austin pools and splash pads.
Lott Splash Pad is a splash pad located at 1108 Curves in Austin, Texas. View all City of Austin pools and splash pads.
Mabel Davis Pool is a Regional Aquatic Center located at 3427 Parker Lane in Austin, Texas. View all City of Austin pools and splash pads.
Martin Pool is a neighborhood pool located at 1626 Nash Hernandez Sr Drive in Austin, Texas. View all City of Austin pools and splash pads.
Metz Pool is a neighborhood pool located at 2407 Canterbury Street in Austin, Texas. View all City of Austin pools and splash pads.
Metz Splash Pad is a splash pad located at 2400 Canterbury St. in Austin, Texas. View all City of Austin pools and splash pads.
Montopolis Pool is a neighborhood pool located at 1200 Montopolis Drive in Austin, Texas. View all City of Austin pools and splash pads.
Murchison Pool is a neighborhood pool located at 3700 North Hills Drive in Austin, Texas. View all City of Austin pools and splash pads.
Beverly S. Sheffield Northwest Pool is a Regional Aquatic Center located on 7000 Ardath Street in Austin, Texas. View all City of Austin pools and splash pads.
Parque Zaragosa Pool is a neighborhood pool located at 741 Pedernales Street in Austin, Texas. View all City of Austin pools and splash pads.


Kieru is a unique first person multiplayer stealth game, set in a stark, high contrast world where life and death is literally black and white. Kieru's world is monochrome, as are the two teams of stealthy Ninjas who occupy it. A black Ninja in shadow or a white Ninja in the light are completely invisible to their oblivious opponents. Stealth, deception and sudden, surprise aggression will win the day. The single splash of colour in this severe and uncompromising world are the blood trails left by wounded opponents. But do they lead to an easy kill or an ambush?


Morning Break is a meet up group for parents! Morning Break will meet during the week to share an informal discussion on the topic of a "spiritual nugget" (Bible verse, poem, book excerpt, etc.) followed by light refreshments and fellowship. CHILDREN ARE WELCOME and will be provided simple entertainment (but feel free to bring your own).
Advent III- Special Whole Church Event- Light the Way to Bethlehem with Joy- Meet and Potatoes!


text:
Need of Cybersecurity as viewed by the Educational Boards of India
OWASP Top 10 Vulnerabilities IoT Security: Lack of Physical Hardening
Web Cache Poisoning – A Modern Methodology of Attacking Large User-Base
India desperately needs more cyber-heroes to defend its web-fronts(and backs)! As one of the major economies of the world, India has and sincerely contributed to the large scale digitalization and virtualization of its economic, financial, governance as well as administrative systems. On its way to emerge as one of the software product-making powers, India as a whole is in a dire state of need to invest in reliable cybersecurity resources to protect its digital assets. Even though the imperative and prompt necessity to upgrade our cybersecurity defenses at par with developed economies cannot be overstated, a grounded solution of introducing cybersecurity as a part of the IT curriculum might just be the most efficient one for the long run.
Concerningly so, India was ranked the third-most cyber-attacked country in the world.
It is alarmingly evident that India being the world's second-largest internet-connected country needs to bring more cyber-heroes to the forefront to face these inevitable threats posed to its IT-driven product and services infrastructure and systems.
Cybersecurity is not network security:
Cybersecurity and network security, though seemingly having branched out from the same philosophy of internet security, are very much distinct from each other. They are more than often mistakenly perceived as one and the same. The most significant difference can be chalked up to the fact that while network security focuses on securing the authenticity of IT frameworks, cybersecurity predominantly pertains to protect internet-linked structures and networks as well as defend against targetted attacks at accessing and sabotaging sensitive data with mal-intents to extort credit form either users or organizations. Additionally, network security involves managing and deploying firewalls, VPNs, routers, switches, and other network-monitoring tools while the benefits of installation and upgrading safety software, monitoring of networks to detect security breaches, and simulation of attacks to identify vulnerabilities are provided with the appropriate engagement of cybersecurity practices. These perceptible differences between the very essence of these services very much speak for themselves as to why there is an urgent need for cybersecurity to have an individual and more structured course in colleges and universities. Conventionally, the closest that IT curriculums came to regarding cybersecurity was the standard and consistent integration of network security subjects. Majors such as computer engineering, software engineering, network engineering, software testing, hardware testing, etc as a part of BTech/BE, MTech, and MSc courses hardly do justice to the vast case of network security and, in-extension, cybersecurity with the subject being primarily limited to college and university classrooms.
Are Your Cybersecurity Awareness Programs Perfect?
An exhilarating demand for academic cybersecurity:
Distressing as it may, our current battles against COVID-19 and the ultimate shift towards the work from home and distance education scenarios have given rise to the inevitable and ever-rising online security threats that come with them. The importance and implementation of cybersecurity measures are, now, more prevalent than ever. Albeit not particularly enough to fulfil the rise in demand, many private, as well as government institutions, have introduced specialized and standalone courses on cybersecurity. These diverse provisions for a degree, diploma, and certification programs have refreshingly found enthusiasm and popularity among students as well as professionals. One can easily find convenient options for engaging in these courses that vary from part-time to distance learning to full-time online modes.
The government's involvement in mainstreaming the subject is currently playing an important role to educationalize and commercialize it on a large scale. If certain academic monitoring websites are to be considered there are currently 204 colleges that offer UG and PG level programs in cybersecurity. IIT Madras has also taken an initiative to launch a Certified Cyber Warriors course to dabble into academizing cybersecurity. The National Institute of Electronics and Information Technology has been instructed to commence courses on cybersecurity with its 24 centres that span across the country. Furthermore, other initiatives by the government also include the training of law enforcement and judicial officers by launching an online PG diploma in cyberlaw, crime investigation, and digital forensics by the National eGovernance Division in partnership with the National Law Institute University, Bhopal.
Are we able to meet the demands?
Evidently, it is high time that IT syllabi and curriculums start integrating cybersecurity and all its sub-disciplines as one of the utmost important components of today's world or as we call 'the new normal'. We also need to look into the matter of upgrading the quality of STEM graduates for the sake of reinforcing and boosting the relevant human resources. However positive the increasing consideration of the cybersecurity courses for professional as well as career choices, it is still not as sufficient as it requires to be. Astonishing research reveals that against an estimated demand for a million cybersecurity experts, India has less than 10,000 professionals. Since the cybersecurity industry is expected to grow to a whopping $3 billion by 2022, only an obvious and significant increase in the number of cybersecurity professionals would be able to respond to the demands.
Niranjana Dhumal
Niranjana Dhumal, a zealous technical content and blog writer. She is the writer for many technical blogs online. Her creative and technical experience has given her a new form of writing experience with which her articles accommodate the readers. As a people person, she believes in a perpetual commutation of information.
The Top 5 Penetration Testing Service Companies
Does SOC 2 Type II Require Penetration Testing?
The Complete SOC2 Compliance Checklist


When will I have achieved this goal? When I am able to put together a few basic Photoshop actions that achieve my 'style' (which is still a work-in-progress!).
Why did I choose this goal? I spend too much time individually processing/editing pictures, and would like more consistency in my sets.


text:
Q: Can't bind variable to select Query Builder on Laravel I can't bind variable to DB::select() but can't tell what I'm doing wrong.
Below is my code;
$id = 1;
return DB::select('SELECT
    a.id,
    a.tender_name, (SELECT COUNT(id)
FROM
    merging_vendor_project
WHERE
    planning_id=a.id) as count_participants
FROM
    planning as a
WHERE a.id=?',[$id]);

What am I doing wrong and how can I fix it?

A: What you are trying to do via an SQL statement can easily be done by Laravel's Eloquent.
First lets create the Model:
php artisan make:model Planning

Following conventions, we don't use Planning but more like Plan but for the simplicity sake I will use Planning.
class Planning extends Model
{
    public $table = 'planning'

    public function merging_vendor_project(){
       return $this->hasMany(MergeVendorProject::class)
    }
}

Now you can a simple withCount on the model like:
$id = 1
Planning::where('id', $id)->select('id', 'name', 'tender_name', 'merging_vendor_project_count')->withCount('merging_vendor_project')->get();

Boom... There you go. You have your inital query made in Laravel style. Taylor Otwell would be proud of you for using Eloquent and not DB::select

redpajama_set_name: RedPajamaStackExchange


text:
using System.IO;

namespace Crane.Core.Templates
{
    public static class FileInfoExtensions
    {
        public static bool IsTextFile(this FileInfo fileInfo)
        {
            return !fileInfo.Extension.Equals(".exe") &&
                   !fileInfo.Extension.Equals(".dll");
        }
    }
}

redpajama_set_name: RedPajamaGithub


The life of Robert Schumann seems to capture the essence of the glory and tragedy of the "Romantic artist." He was brilliant, a talented pianist and extraordinary composer, obsessed with the "art" of music. He loved another brilliant pianist, Clara Wieck; against her father's wishes, he prevailed and married her.
In all that Romantic living, Schumann created some of the most beautiful of piano works, of which the Introduction and Allegro Appassionato is a glowing testament.
Another of Schumann's remarkable talents was writing about music. He brought to the field a masterfulness and inventiveness of a high standard. His publication Neue Zeitschrift fur Musik (1834-1844) offered his and others' essays, reviews, and general musical articles that carried important influence in their day.
All these qualities are evident in the Introduction and Allegro, completed in 1853 and premiered in 1855. The piece opens with tenderness and beauty in one of the most supremely Romantic themes ever penned. From the Introduction flows a life-affirming Allegro filled with invention, fancy, and energy – delicious chocolate.
It hardly seems possible that in 1854, between the composition and the premiere of this beautiful and lively composition, Schumann committed himself to the asylum in Endenich, where he remained until his death in 1856.


The hubs and I both had iPhone 3s in Otterbox cases, and when my hubby was in Atlantic City on business (same day we had an earthquake, which we never have here!) he dropped the phone, and it landed just right to crack the screen. I managed to find him a kit on Ebay to replace it, and it broke again shortly after. I really didn't want him to be without a phone going back & forth to work until we tried to fix it again, so we ended up upgrading to the 4S and again, bought Otterbox cases. He managed to fix the old phone (sorta) and we gave our old phones to the kiddos to play games. All went well until I scooped one up with bedding & threw it in the washing machine. We realized it almost immediately, but the damage was done.
The Otterbox Commuter cases were OK, and their customer service was great in replacing both of our cases when they cracked in the same place. I didn't open my replacement, figuring I'd wait until I really had to replace it, since I was coming to the end of the warranty. The Lifeproof cases were a lot more expensive than the Otterbox, but I thought about how much money we spent on replacement screens (and the paperweight that was our drowned iPhone3) and figured it was worth it.
They are pretty similar in size and thickness, though the Lifeproof is a bit longer since it has a bigger area at the bottom.
The cases come with a 90 day warranty, and if you register your case, it's extended to 1 year. Make sure you register your case FIRST before you install it. You will need serial #s on both sides of the case. You have to complete a quiz (which proves you read the instructions) and enter these #s. We didn't do this first, and still haven't brought ourselves to take them apart & get the #s. So save yourself the time and do it first!!
The cases are designed to be completely water-tight if installed correctly, and have a built in screen protector.
The case comes with a plug for the headphone jack, as well as an extender and an extra plug (hooks to the extender for safe keeping) which I didn't immediately realize when I was looking at the site.
I didn't realize how non-air, dirt etc. tight the Otterbox was until I took it off to install the Lifeproof. Fortunately, the Lifeproof also comes with a cleaning cloth!!
After you follow all of the instructions, including performing the water test (without the phone), you are ready to install. It's super easy.
The case has tons of extra features that you may not notice at first, like protecting the volume buttons.
It's pretty slick looking when it's on, and the edge has just enough grip, while the rest of the case slides in & out of pockets easily.
The iPhone headphones work fine, while you might need to use the extender for thicker headphone jacks. The standard iPhone charger works perfectly as well (there is a flap to make it waterproof when not being charged.) There is an optional extender to make the case work with speaker docking stations etc.
The phone works perfectly, with no change to the touch screen or sound.
Bonus, we put the cardboard iPhone screen in our old Otterbox cases and our kids are having a blast playing with them!
Get 15% off all orders at LifeProof.com with coupon code LUCKY through 3/18/13!
I purchased the pictured items myself. Post contains affiliate links however, I was not compensated for this post, and all opinions are my own.
Although you have a pretty thorough review I'd like to add my input. I bought my Lifeproof case a little over a year ago for my iPhone5 and it very "baby proof", just not "life proof". Although it's designed to withstand water, mine was slightly under water for a fraction of a second and has caused major malfunction to my phone which they will not cover under their "warranty". Actually they take no responsibility for any of it.
Also, talking on the phone is almost pointless due to the speakers being covered. Anyone I've known who owns this case claims they have the same problem. You're muffled and sound distant to whom you talk to and almost have to tell into the phone. A pleasant conversation is out of the question though.
Oh no! I haven't gotten mine wet thankfully but we had bought a Lifeproof case for my son's iPad. He immediately lost all the rubber pieces for it, then intentionally poured water on it "to see." (sigh) The microphone no longer works & the sound/headphone jack is wonky but it otherwise works. I'll have to be really careful with mine.
There are actual baby cases made for iphones/itouch. I just discovered them at Target last night. $15 or less I think. I can't remember the brand.
This review is fantastic! Thank you for sharing!
I need to look into one of these…my youngest thinks my phone is a teething toy.


Provinciehuis Antwerpen is the new landmark of Antwerp, a carbon neutral office building with the ambition of achieving a Breeam Excellent score.
Because the current county home in Antwerp no longer meets the standards of a modern office building, the Province of Antwerp wants to completely rebuild and adapt it to a modern and ecological building surrounded by a public park.
The site is part of a broader vision of using green space in the city: all existing trees are preserved, the green quality and soil permeability are increased. The building itself is very compact, it is north-south oriented so that the solar load can be reduced and the potential for natural ventilation maximized. To meet the required E-level, façade perforations are limited to 40%, but daylight is still optimized by the shape of the windows, and of the same quality for each employee. The workstations are also adaptable and flexible because of the open plan and raised floors. Group functions such as a restaurant and a library are strategically integrated into the complex.
In addition to the Project Management, Bopro performs the BREEAM International Assessment for this project, with the ambition of achieving an Excellent score.


? Please leave a opinion for us, hopefully we are able to present further helpful information and facts for future articles.
photo has submitted by godong , in category for this post: Black Hairstyles, section.


text:
Das Fassatal (kurz Fassa, veraltet Eves, italienisch Val di Fassa, ladinisch Val de Fascia []) ist ein zu zwei Dritteln ladinischsprachiges Tal in den Dolomiten. Es liegt im Trentino in Italien und wird zu Ladinien gezählt. Das Fassatal liegt am Oberlauf des Avisio, dessen untere Talabschnitte Fleimstal und Cembratal genannt werden. Die Gemeinden des Tals gehören zur Talgemeinschaft Comun General de Fascia. Diese ist mit der 2006 aufgelösten Bezirksgemeinschaft Ladino di Fassa deckungsgleich. Das Tal ist Teil des Wintersportgebietes Dolomiti Superski.

Für den Kraftverkehr erschlossen ist das Tal in erster Linie durch die SS 48.

Geographie

Im Fassatal befinden sich folgende Gemeinden:
 Campitello di Fassa (ladinisch Ciampedèl, deutsch historisch Kampidel im Fassatal)
 Canazei (ladinisch Cianacèi, deutsch historisch Kanzenei)
 Mazzin (ladinisch Mazin, deutsch historisch Matzin)
 Moena (ladinisch Moena, deutsch historisch Moyen)
 San Giovanni di Fassa (ladinisch Sèn Jan)
 Soraga di Fassa (ladinisch Soraga, deutsch historisch Überwasser)

Südlich von Moena wird das Tal des Avisio Fleimstal genannt. Die Ursache dieser unterschiedlichen Benennung des Tales liegt auch in den Besitzverhältnissen im Mittelalter, als das Fassatal zum Bistum Brixen gehörte und das Fleimstal zum Bistum Trient.

Sage und Geschichte

Die Geschichte des Fassatales liegt teilweise in sagenhaftem Dunkel. Vor den ersten schriftlichen Dokumenten soll es der Sage nach sieben Gemeinden, die "Regoles" (deutsch "Riegel"), im Fassatal gegeben haben. Das Fassatal war dabei immer wieder räuberischen Angriffen aus dem Osten über den Fedaia-Pass aus der "Marca Trevignana" (Hauptstadt Treviso) ausgesetzt. Daher ranken sich zahlreiche Sagen um das Fassatal über ständige Kämpfe mit den "Trevisanern" oder meist "Trusanern".

Die Gemeinden schlossen einen Schutzbund und heuerten eine Söldnertruppe an, die sogenannten "Arimannen" (Heermänner), die von "Sorastantes" (Über-Stehern) geleitet wurden. Der germanische Ausdruck Arimanne deutet auf langobardischen Einfluss. Die Trusaner wurden von den Arimannen entscheidend geschlagen, indem einer der ihren sich den Trusanern als Führer anbot, in Wirklichkeit sie aber in einen Hinterhalt lockte und dies mit seinem Leben bezahlte. Dieser Schlachtplatz liegt rechter Hand, wenn man von Canazei an Penia vorbei Richtung Fedaia fährt. Er heißt heute noch "Pian Trevisan" oder "Cian Trujan".

Die Arimannen bewachten in Holztürmen (ciasteles, vgl. Kastell) die Grenzen des Tales und meldeten gegebenenfalls mit Leuchtfeuern von eins bis drei verschiedene Alarmstufen in das Tal. Da die Arimannen sich aber auch selbst in längeren Friedenszeiten räuberisch verhielten, wurden sie auch Latrones (Räuber) genannt, was sie dann auch als Ehrentitel verwendeten.

Mit dem frühmittelalterlichen Anschluss des Tales an das Fürstbistum Brixen war die Einrichtung der Arimannen überflüssig geworden. Der Sage nach wurden danach noch einmal "die letzten der Latrones" von den Trusanern unterhalb des Fedaia-Passes überfallen und vernichtet. Zwar konnten die Arimannen noch ein Leuchtfeuer entfachen, das aber im Tal nicht mehr gesehen wurde. Seitdem sieht man oben in den Bergen noch heute bisweilen das "lum de morc", das Todeslicht.

Der Sagenforscher Karl Felix Wolff aus Südtirol bezeugt, ein frühmittelalterliches Dokument gesehen zu haben, das auf eine vorherige Existenz der Arimannen Bezug nimmt. Da dieses Dokument jedoch verschollen ist, gibt es derzeit keine schriftlichen Belege.

Weblinks

 Tourismusverband Fassatal

Tal in Europa
Tal im Trentino
Ladinia
Comun General de Fascia


text:
Change city Frankfurt (en)
Things to do Attractions Restaurants Bars Hotels
Time Out Frankfurt
Things to do Attractions Restaurants Bars Hotels More
Worldwide icon-chevron-right Europe icon-chevron-right Germany icon-chevron-right Frankfurt icon-chevron-right The 10 most beautiful buildings in Frankfurt
The 10 most beautiful buildings in Frankfurt
Take in the grandeur of Frankfurt's most stunning buildings—a mix of obscure modern designs and historic reconstructions
By Mairi Beautyman | Posted: Sunday March 25 2018
There is only one place in the world where half-timbered buildings seeped in old world charm are an eight-minute walk from Germany's highest tower: Frankfurt. The architecture in Germany's financial capital is as varied as it comes—it's undeniable that two world wars had an impact. However, a careful reconstruction effort combined with rich creativity tapped from a pool of talented architects mean a cityscape as strikingly diverse as its populous—a quarter of which have foreign citizenship. From a greenhouse formed as a cluster of flowers to a contemporary mall that sucks visitors in through a vortex, as well as one of the oldest churches in Germany, here are the ten most beautiful buildings in Frankfurt.
Most beautiful buildings in Frankfurt
Photograph: Courtesy CC/Wikimedia Commons/Daderot
The Tropicarium Greenhouse at PalmenGarten
Picture a cluster of flowers rendered in glass and you'll be visualizing the stunning Tropicarium greenhouse at Frankfurt's 140-year-old botanical garden, PalmenGarten, home to 13,000 subtropical and tropical species. Designed by Gustav Schoser, Tropicarium consists of seven large and six small greenhouse units which reflect the waterlilies in a nearby pond. Ten different tropical climatic-vegetation zones divide plants into groups according to their natural habitats, from arid to humid tropics. While tickets to PalmenGarten are seven euros for adults, you'll want to drop another 1.50 to hop on board the Palmen-Express, an electric train that runs April through October.
Photograph: Courtesy CC/Flickr/chaouki
Commerzbank tower
Is it beautiful? Well, it's undeniably tall. A feat of engineering constructed of steel rather than the more cost-friendly concrete, the Commerzbank tower, designed by Norman Foster, was completed in 1997 and was once the tallest building in Europe. Now owned by electronics giant Samsung, it remains the tallest building in Frankfurt—and in Germany. A striking contribution to Frankfurt's skyline and the city's financial district, the Commerzbank tower stretches 259 meters high (300 meters with its antenna) and includes a 160-meter-high atrium and nine tiered 'sky gardens' which have garnered the building several awards for sustainability. Unfortunately, public access is limited. Tours, while free of charge, need four-months of preparation, are exclusively on the last Saturday of the month and only available to a minimum of eight and a maximum of 18 people. If that doesn't fit your needs, head to the south side of the River Main before sunset, and watch the sky darken and the tower's lights flicker on—then it truly is beautiful.
Photograph: Courtesy CC/Wikimedia Commons/Epizentrum
Haus Wertheim
Talk about lucky. Haus Wertheim (Wertheim House) was the only timber-framed building in Frankfurt's old town to survive two wars. Located opposite the Historical Museum, the house was not particularly significant until it became the only one left—and representative of Frankfurt's architectural style. Built during the Renaissance around 1600, the house was restored for the first time in 1926, when the plaster was removed from the half-timber framing. At the cafe and restaurant on the ground floor, where antique porcelain and memorabilia cover walls, try a Frankfurter classic like eggs and parsley potatoes swimming in the traditional Frankfurter grüne Sosse (a creamy herb sauce).
Photograph: Courtesy CC/Wikimedia Commons/Sith Cookie
IG Farben Haus
A sprawling example of modernist architecture designed by Hans Poelzig, the IG Farben Haus in Frankfurt's Westend district was once the largest office building in Europe and the headquarters for Germany's largest chemical company—which supplied the deadly agent used in concentration camp Auschwitz's gas chambers. Built in 1930, it has six square wings connected by a gently curving 250-meter-long corridor. After the war, when it became known as "the Pentagon of Europe," the building was used by Allied forces, and then the U.S. government, which turned it back over to Germany in 1995. The building—still called IG Farben Haus by locals—is now the Westend Campus of the Goethe University Frankfurt. Stop by for a budget-friendly lunch in the University's cafeteria.
Photograph: Courtesy CC/Wikimedia Commons/I, Dontworry
Museum für Kommunikation Frankfurt
Perhaps the most beautiful of the museums along the south bank of the Main River, Frankfurt's Museum of Communication reopened in 1990 with a new building by German architecture firm Behnisch Architekten. To preserve a park and old-growth trees, the architects hid the main exhibition level of the modern glass and aluminum structure—which has won numerous
architecture awards—mostly underground. Transparency and openness reign inside, where visitors find a striking glass atrium and a wealth of information on the history of communication—extending back to the traditional African bush drum. The museum's former home is also worth a look; a historic sandstone mansion, it now houses administration offices and the library. Admission is four euros, age 16 and up.
Photograph: Courtesy CC/Wikimedia Commons/Felix König
The Alte Oper Frankfurt
In its prime, the original Alte Oper Frankfurt was one of the most significant opera houses in the world, premiering operas by Richard Wagner and with Giacomo Puccini and Richard Strauss among the leading performers. While the 1880 building designed by Berlin architect Richard Lucae skated through World War I with only superficial damage, World War II left it a ruin. It wasn't until August 1981, thanks to a major fundraising effort by the city's citizens and world-famous artists and intellectuals, that the Alte Oper once again opened its doors. The extensive reconstruction included the restoration of many of the original decorations, reliefs, medallions, frescoes, tiles and mosaics. Today, the historic façade—complete with its original Pegasus statue centered on a tiered roof—hides a state-of-the-art concert venue drawing some 475,000 visitors to around 450 cultural events a year.
Photograph: Courtesy CC/Wikimedia Commons/ArcCan
The Römer City Hall
With sections dating to the middle ages, the Römer is a three-story building complex that has served as Frankfurt's main city hall for 600 years. The complex consists of nine houses wrapping six courtyards—namesake Haus Römer is actually the middle building in a set of three facing the cobblestoned Römerberg square (home to the Frankfurt Christmas Market starting late November). At six centuries old, the oldest remaining rooms—the Römerhalle and Schwanenhalle—are located on the ground floor. The building complex is situated in the heart of Frankfurt's scenic 'new' old town on the Northern Main River bank. The old town reconstruction project revitalizes a 75,000-square-foot area that was more than 90 percent destroyed between Cathedral Square and the Römer.
Roman architect Massimiliano Fuksas based the fluid shape of the mostly transparent shell of the MyZeil shopping mall on a river, which flows to form an undulating roof and plunges to draw natural light into all six levels. With a gigantic curved glass-and-steel facade housing 77,000 square meters of retail space, the mall opened in 2009 in the center of Frankfurt. Head
down the Zeil, Frankfurt's main shopping street, and look for a vortex—that marks the entrance. The mall is part of the Palais Quartier development project, which also includes two hi-rise buildings and the reconstructed Palais Thurn und Taxis, a palace from 1793.
Photograph: Courtesy CC/Wikimedia Commons/Anja Jahn
Star-architect Richard Meier successfully integrated a 19th-century Neo-classicist family villa into a modernist building complex to form the Museum Angewandte Kunst (Museum of Applied Arts). Unveiled in 1985, the three cube-like new buildings—recalling the shape of the villa—are placed in an L-formation. United with the villa, they form a square and enclose a leafy green courtyard. The museum offers changing exhibitions focusing on contemporary art as well as a small permanent collection. Unless you go on the last Saturday of the month when admission is free, the ticket price is a rather hefty 12 euros for adults. However, the museum is included in the 18-euro Museum Embankment Ticket, which gives access to 34 museums over a two-day period.
Photograph: Courtesy CC/Wikimedia Commons/kgberger
Justinuskirche
An extremely rare, nearly complete example of a Medieval church—one of the few surviving today—the Justinuskirche (Saint Justin's Church) in the historic Höchst district is the oldest building in Frankfurt and one of the oldest churches in Germany; it's also an extremely popular wedding venue. Constructed beginning in 830, the church's three-aisle basilica is nearly 1200 years old. The interior gained a choir area and an additional northern aisle around 1443. Guided tours are available, if you don't want to join one of the Catholic services held every week. From May through September, and around Christmas, the church hosts regular organ concerts on an organ dating to 1740. Unless it is summer—when the church gardens are a scenic stroll—dress warmly, as heating is limited.
Time Out Frankfurt Site map


I was pleased to find a wide variety of antiques of all kinds on my visit to this shop. The prices were reasonable and the items were displayed and labelled. This shop has a great old time store feel.
I was pleased to find a wide variety of antiques of all kinds on my visit to this shop. The prices were reasonable and the items were displayed and labelled clearly. It's fun to shop in Bouckville!
At one time I was a patient of Dr. Van Wyk. Since my insurance changed and I sought a dentist closer to my home I no longer go. His office is located in the basement of a home in Irondequoit. The staff are pleasant and helpful. I feel I received adequate dental care at the time.
We have been pleased to have Dr. Attardo as a dentist. He is very pleasant and easy to talk to . He explains things thoroughly and performs the necessary treatment well.
I have never consigned an item here but have browsed and shopped here. The store has nice quality clothing name and designer brands in a wide selection of styles and sizes. The store has good organization and items are clearly marked.
After a brief visit to this shop I would certainly tell any friends or family about it. It looks like they could take care of any of you guitar needs. I stopped there to see if they purchase used electric guitars. They do and when I can I will consider them as an option. They were informative and friendly.
This Rubinos offers their delicious subs but also has a selection of Italian foods and ingredients for sale. The shop is somewhat like a small market. The employees were helpful and friendly.
I love to go to DiBellas for subs...for lunch or on my way home on a busy soccer night. The aroma of fresh baked rolls is the first thing you notice as you enter. The employees are eager and pleased to wait on you. You can select a from a wide variety of sandwich choices...they will make it to your specifications!!! The cookies are a must for dessert.
A small farm market that is open most of the spring, summer and fall. They have local fresh produce and products for sale. They are right on Ridge Road near West Webster. A convenient stop on your way down Ridge Rd or Empire Blvd.


A new neurological patient experience survey is open, to collect vital information about the experiences of treatment and care, social care and welfare received by people affected by neurological conditions. The survey aims to collect enough data to positively influence future neurology services.
The survey is by The Neurological Alliance – an organisation that brings together organisations working to make life better for millions of people in England with a neurological condition. Through the patient experience survey, The Neurological Alliance aims to positively influence the future quality of neuro health and social care services. Too often services fall below the standard expected. This survey aims to help change that.
We fully support the Neurological Alliance in its ambitions. We welcome the survey as an important tool in gathering shared insights across neurological conditions. The neurology community is strong when it stands together.
What will happen with the results?
The Neurological Alliance will publish the results in a report in summer 2019. This report will set out a comprehensive picture of what is happening in relation to neurological services and make recommendations about how care can be improved.
Made the case for continued national leadership for neurology. National Neuro Advisory Group set up.
Getting the National Neuro Advisory Group to prioritise care planning and communication with patients. Fed into NHS long term plan.
Developed a programme of work on mental health and neurology, report published.
Influenced the development of NICE guidance on suspected neurological conditions.
Raised the profile of neurology through media work.
How do I complete it?
The survey is open from 17th October 2018 to 22nd March 2019. It is for anyone with a neurological condition living in England. Carers can help complete the survey as needed.
The survey may take around 25 minutes to complete. Please be aware that you cannot save your answers and come back later. Your responses are completely confidential and anonymous.
Please click here to complete the survey.
Thank you – each response makes a difference.


On Wednesday 21st September Neil met Theo at the station to discuss Network Rail's refurbishment plans with their representative Karen Davidson. Karen was extremely helpful as she explained that the work would cover repair and repainting of the Canopy and the resurfacing of the entire platform including the installation of a tactile edge. Some time was spent looking at windows - The Railway Heritage Trust has recently awarded a grant to Northern to replace two modern windows with the historically correct design of sash windows. Neil pointed out to Karen that two futher windows (currently boarded up) could be brough back to life in a similar manner. The Network Rail work is scheduled to begin in October and will last for at least 3 months. FOGS is delighted that further investment is taking place!


Sir, – The fashion statement called "ripped jeans" has been with us for sometime now. Often the rips are no more than slits. However, I notice that in many instances the rips are so wide, that there is nearly as much leg, knee and thigh on show as there is trouser material.
Considering this, it struck me that not so long ago in this country, not to have an arse in your trousers would have been regarded as distinctly "uncool".


text:
Does Kim Really Run North Korea? Find Out with Military Diplomacy
By Van Jackson
Recent rumors of Kim Jong-un's whereabouts and whether a coup had occurred put our ignorance about what goes on in North Korea on full display. Speculation is natural when it comes to palace intrigue in a post-totalitarian state; of course inquiring minds want to know. But even the most sagacious Korea experts have done little more than speculate. Many find solace in reports of Kim Jong-un's appearance as confirming the status quo, forgetting that the status quo was rife with uncertainty – the very reason rumors swirled at the first sign of Kim Jong-un's absence.
Read the full op-ed at The Diplomat.
How the Defense Budget Could Actually Increase (Slightly)
Once all is said and done, it is more likely that defense spending will end up growing rather than shrinking....
By Diem Salmon
INKSTICK
The idea that presidents are able to use nuclear weapons in any way they personally desire is not correct....
By Tom Shugart
Navigating the Deepening Russia-China Partnership
In virtually every dimension of their relationship, cooperation between Beijing and Moscow has increased....
By Andrea Kendall-Taylor & David Shullman
Harnessing Multilateralism for Digital Development
Uneven access to digital technology is magnifying societal inequities around the world....
By Kristen A. Cordell & Kristine Lee


text:
Seriously impertinent
Revue DANSER / 2002
Unusual artist, a tad provocative, a bit iconoclast, Michel Schweizer, familiar to performance, invited an uncategorizable show programmed at îles de danses 2002. Uncategorizable and generous, he debunks misconceptions.
The idea for « Kings » started with the meeting of a young boy so enthused by boxer Mike Tyson that the channel Canal+ brought him to England to interview his idol. "I offered him to tell this story onstage. I started working on our relation in an introspective and respectful manner around the idea that it is useful to plunge people into a face to face without shadows onstage." With him come an ex-dancer fro Regine Chopinot, a hip-hop dancer, a tap dancer, a dog trainer… Slices of the lives of "kings" of a night, "Kings" diverts the principle of reality show by transposing it to the performance system. The project was selected based on an application file for Bagnolet. Michel then prepared a half an hour show and found himself – strange memory he says – at gymnase Maurice-Bacquet with a new UFO – a deliberately unidentifiable object that received support and gained new partners. The content is an exhibition with autobiographical material, but "Kings" is tightly written, negotiated with the people and built to please. Mixing reality with performance on different degrees is troubling also for the performers;" In short, a cultural object that, to this extent has a market value.
Introduce a new way of looking at things
Michel hired then a dog trainer to watch it, "according to a very simple partition, a precise stroll, until the dog bites a corner of the dance mat, scandalizing some audience members. Skillfully paced in time and space, it's a disruption element that galvanize tension."
Our iconoclast intends to make fun of "the relation stakes between art, politics and economics". He hopes that by troubling the audience member, he will introduce a new way of looking at things, free from the prejudices about boxers.
Bernadette Bonis