Another Response to Richard Gill's 10,000 Euros Challenge

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 8:26 pm

FrediFizzx wrote:
gill1109 wrote:I take this answer to mean "yes". The two files contain a sequence number and the x and y coordinates of 7070 directions. I changed the headers to the two files accordingly. Yesterday at around 18:00 pm I uploaded them to the cloud, and my calculations are at http://rpubs.com/gill1109/christian-test.

Those are NOT the right files. I posted the correct direction files here on June 7th.

Sorry Fred, Joy told me yesterday at 18:00 to take the two files produced by the "write" statement in his script.

However I am happy to treat your files as a separate submission by you.

OK?
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby FrediFizzx » Tue Jun 10, 2014 8:36 pm

See above for the correct files.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 8:41 pm

FrediFizzx wrote:See above for the correct files.

OK Fred I am treating your submission as a separate one from Christian's but though it was submitted earlier, I'll give Christian the benefit of the doubt and process his first (it is now in the adjudication phase).

I evaluated your submission and found it legal. I consider it also a "pre June 11 submission" so you are going for the 10 000 Euro prize.

My findings are is that it does not win the challenge:
http://rpubs.com/gill1109/testFred
(I changed the name of your files and added a name of the first column in the header, but did not alter the body of the files).

Do you wish to go to adjudication? Warning: in that case, you will not be allowed later "re-tries".

This is an interesting new development: a challenge-team "forks" into two separate challenges. Yet another unforeseen eventuality.

Fred: I know that you think that the data files need to be processed using what you call 3-sphere geometry but I call Pearle's detection loophole model. The challenge unfortunately was to "win" using flatland geometry. I think you agree that interpreted flatlandishly it is impossible to win. In fact, because of my Nx4 spreadsheet theorem... This therefore concludes our FQXi debate, the one which led to you setting up this forum, even! It was a long slog but it was worth it.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 9:16 pm

[Link to derogatory comment removed]
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby FrediFizzx » Tue Jun 10, 2014 9:40 pm

gill1109 wrote:
FrediFizzx wrote:See above for the correct files.

OK Fred I am treating your submission as a separate one from Christian's but though it was submitted earlier, I'll give Christian the benefit of the doubt and process his first (it is now in the adjudication phase).

I evaluated your submission and found it legal. I consider it also a "pre June 11 submission" so you are going for the 10 000 Euro prize.

My findings are is that it does not win the challenge:
http://rpubs.com/gill1109/testFred
(I changed the name of your files and added a name of the first column in the header, but did not alter the body of the files).

Do you wish to go to adjudication? Warning: in that case, you will not be allowed later "re-tries".

This is an interesting new development: a challenge-team "forks" into two separate challenges. Yet another unforeseen eventuality.

Fred: I know that you think that the data files need to be processed using what you call 3-sphere geometry but I call Pearle's detection loophole model. The challenge unfortunately was to "win" using flatland geometry. I think you agree that interpreted flatlandishly it is impossible to win. In fact, because of my Nx4 spreadsheet theorem... This therefore concludes our FQXi debate, the one which led to you setting up this forum, even! It was a long slog but it was worth it.

LOL! Like you were ever going to cough up the 10K Euros anyways. :lol: I did not post those files to enter your challenge because I knew it was rigged from the start. I posted them along with the proper correlation calculations to show you how to do it correctly for 3-sphere geometry and that Joy's model can in fact be applied to the experiment. That was my point. And that was your point also with challenge to see if the experiment is viable.
Here is Joy's latest simulation with outputing the direction files and then reading them right back in. Works perfectly well. BAM! That is all I care about.
Code: Select all
## Richard Gill has offered 10,000 Euroes to anyone who can simulate the N
## directions of angular momentum vectors appearing in equation (16) of my
## experimental proposal: http://arxiv.org/abs/0806.3078. In this simulation
## I provide such N directions. They are given by the vectors 'u' in this
## simulation. He has also offered further 5,000 Euros to me if my proposed
## experiment is realized successfully. I am hopeful that that will happen
## some day. The details of these challanges by Richard Gill can be found
## here: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=52#p1898.
## While this is by no means the most perfect simulation of my model, it does
## meet all of the conditions set out by Richard Gill for his challenge.

## The theoretical description of the model can be found in this paper:
## http://arxiv.org/abs/1405.2355 (see also http://lccn.loc.gov/2013040705).

## Since after the explosion the angular momentum vectors 'u' moving along
## the z direction will be confined to the x-y plane, a 2D simulation is good
## enough for my proposed experiment.

set.seed(9875)

M <- 10^4  ## Sample size. Next, try 10^5, or even 10^6

angles <- seq(from = 0, to = 360, by = 10) * pi/180

K <- length(angles)
Ns <- numeric(K)  ## Container for number of states
corrs <- matrix(nrow = K, ncol = K, data = 0)  ## Container for correlations

r <- runif(M, 0, 2 * pi)
s <- runif(M, 0, pi)

x <- cos(r)
y <- sin(r)

w <- rbind(x, y)
write.csv(t(w), file = "AliceDirectionsu1.txt")
write.csv(t(-w), file = "BobDirectionsv1.txt")
ad <- read.csv("AliceDirectionsu1.txt")      # alice directions file
u <- rbind(ad$x, ad$y)           # just the x and y coordinates as a 2xN matrix
rownames(u) <- c("x", "y")
bd <- read.csv("BobDirectionsv1.txt")   # alice directions file
v <- rbind(bd$x, bd$y)           # just the x and y coordinates as a 2xN matrix
rownames(v) <- c("x", "y")

## 'u' and 'v' are 2xM matrix. The M columns of 'u' represent the x and y
## coordinates of points on a unit circle in the equatorial plane.

p <- 1.21 * (-1 + (2/(sqrt(1 + (3 * s/pi)))))

for (i in 1:K) {
    alpha <- angles[i]
    a <- c(cos(alpha), sin(alpha))
    for (j in 1:K) {
        beta <- angles[j]
        b <- c(cos(beta), sin(beta))
        ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
        cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
        good <- abs(ca) > p & abs(cb) > p  ## Sets the topology to that of S^3
        N <- sum(good)
        corrs[i, j] <- sum(sign(ca[good]) * sign(cb[good]))/N
        Ns[i] <- N
    }
}
(N)
par(mar = c(0, 0, 2, 0))
persp(x = angles, y = angles, z = corrs, zlim = c(-1, 1), col = "pink", theta = 135,
    phi = 30, scale = FALSE, xlab = "alpha", ylab = "beta")

 
alpha <- 0 * pi/180
beta <- 45 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
(E_0_45 <- sum(sign(ca) * sign(cb))/N)
## [1] -0.6993

alpha <- 0 * pi/180
beta <- 135 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
(E_0_135 <- sum(sign(ca) * sign(cb))/N)
## [1] 0.703

alpha <- 90 * pi/180
beta <- 45 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
(E_90_45 <- sum(sign(ca) * sign(cb))/N)
## [1] -0.699

alpha <- 90 * pi/180
beta <- 135 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
(E_90_135 <- sum(sign(ca) * sign(cb))/N)
## [1] -0.7276

## The Bell-CHSH inequality is violated:

abs(E_0_45 - E_0_135 + E_90_45 + E_90_135)
## [1] 2.829

And the results are,
Code: Select all
(N)
[1] 7070
> par(mar = c(0, 0, 2, 0))
> persp(x = angles, y = angles, z = corrs, zlim = c(-1, 1), col = "pink", theta = 135,
+     phi = 30, scale = FALSE, xlab = "alpha", ylab = "beta")
>

> alpha <- 0 * pi/180
> beta <- 45 * pi/180
> a <- c(cos(alpha), sin(alpha))
> b <- c(cos(beta), sin(beta))
> ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
> cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
> (E_0_45 <- sum(sign(ca) * sign(cb))/N)
[1] -0.6992928
> ## [1] -0.6993
>
> alpha <- 0 * pi/180
> beta <- 135 * pi/180
> a <- c(cos(alpha), sin(alpha))
> b <- c(cos(beta), sin(beta))
> ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
> cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
> (E_0_135 <- sum(sign(ca) * sign(cb))/N)
[1] 0.7029703
> ## [1] 0.703
>
> alpha <- 90 * pi/180
> beta <- 45 * pi/180
> a <- c(cos(alpha), sin(alpha))
> b <- c(cos(beta), sin(beta))
> ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
> cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
> (E_90_45 <- sum(sign(ca) * sign(cb))/N)
[1] -0.6990099
> ## [1] -0.699
>
> alpha <- 90 * pi/180
> beta <- 135 * pi/180
> a <- c(cos(alpha), sin(alpha))
> b <- c(cos(beta), sin(beta))
> ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
> cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
> (E_90_135 <- sum(sign(ca) * sign(cb))/N)
[1] -0.7275813
> ## [1] -0.7276
>
> ## The Bell-CHSH inequality is violated:
>
> abs(E_0_45 - E_0_135 + E_90_45 + E_90_135)
[1] 2.828854
> ## [1] 2.829
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 11:03 pm

FrediFizzx wrote:LOL! Like you were ever going to cough up the 10K Euros anyways. :lol: I did not post those files to enter your challenge because I knew it was rigged from the start. I posted them along with the proper correlation calculations to show you how to do it correctly for 3-sphere geometry and that Joy's model can in fact be applied to the experiment. That was my point. And that was your point also with challenge to see if the experiment is viable.
Here is Joy's latest simulation with outputing the direction files and then reading them right back in. Works perfectly well. BAM! That is all I care about.

Seems like we all successfully made our points. Indeed, I was never ever going to have to cough up 10K Euro: that was the whole point of the challenge. It's a Randi challenge. It has pedagogical purposes only, it cannot actually be won.

But there are some things I disagree with, in your summary, Fred. What you call "Joy's model", I call "Pearle's model". And Christian even needed Gill in order to be able to use it.

But what's in a name? Part of the challenge was to see if the Christian experiment as formulated in 2008 was viable. The answer is: no. We needed to discover Pearle's model, and Christian still has to figure out how to explain to the experimenters why they need to do some auxiliary randomization before they see the singlet correlations. I still do respectfully advise Christian to revise his experimental paper. Also Christian also still needs to derive Pearle's model from his 3-sphere ideas. He says he has done so in his latest arXiv paper but I beg to differ.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby FrediFizzx » Tue Jun 10, 2014 11:09 pm

gill1109 wrote:But what's in a name? Part of the challenge was to see if the Christian experiment as formulated in 2008 was viable. The answer is: no. We needed to discover Pearle's model, and Christian still has to figure out how to explain to the experimenters why they need to do some auxiliary randomization before they see the singlet correlations. I still do respectfully advise Christian to revise his experimental paper. Also Christian also still needs to derive Pearle's model from his 3-sphere ideas. He says he has done so in his latest arXiv paper but I beg to differ.

Joy does not need to revise his experimental paper. You seem to be having extreme trouble understanding the difference between a simulation where it is necessary to simulate what Nature might be doing and a real experiment. It is quite unbelievable that you don't even know what a hidden variable is after all this time.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Wed Jun 11, 2014 2:45 am

FrediFizzx wrote:
gill1109 wrote:But what's in a name? Part of the challenge was to see if the Christian experiment as formulated in 2008 was viable. The answer is: no. We needed to discover Pearle's model, and Christian still has to figure out how to explain to the experimenters why they need to do some auxiliary randomization before they see the singlet correlations. I still do respectfully advise Christian to revise his experimental paper. Also Christian also still needs to derive Pearle's model from his 3-sphere ideas. He says he has done so in his latest arXiv paper but I beg to differ.

Joy does not need to revise his experimental paper. You seem to be having extreme trouble understanding the difference between a simulation where it is necessary to simulate what Nature might be doing and a real experiment. It is quite unbelievable that you don't even know what a hidden variable is after all this time.

I thought we were talking about how experimenters are to analyse data coming out of an experiment described in a publication by Christian posted on arXiv in 2008 (page 4 of the experimental paper). The challenge does not ask you to simulate Nature, or to simulate Christian's model.

It simply asks you to invent in any way, whatever you like, an actual data set which, if it had been generated by Christian's experiment, and then processed according to his instructions, it would have confirmed his theory. Both you and Christian have failed to do this.

Hidden variables are hidden to experimenters, so I don't think anyone's understanding or misunderstanding of the concept has anything to do with this.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby menoma » Wed Jun 11, 2014 8:27 am

If it cannot be said what the data from Dr. Christian's proposed experiment ought to look like, could the correct data even be recognized were it to be generated? Isn't the experiment, as proposed, therefore incoherent?
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Wed Jun 11, 2014 8:42 am

menoma wrote:If it cannot be said what the data from Dr. Christian's proposed experiment ought to look like, could the correct data even be recognized were it to be generated? Isn't the experiment, as proposed, therefore incoherent?

If Christian's theory were correct, then the "correct data" would be instantly recognisable, because it would generate, when processed as Christian prescribes, the singlet correlations E(a, b) = - cos(a.b). Unfortunately it is a theorem that no data whatsoever can generate the singlet correlations when processed as Christian prescribes.

IMHO the experiment is incoherent and my purpose with my challenge was to make this clear to everyone.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Wed Jun 11, 2014 8:47 am

gill1109 wrote:[Link to derogatory comment removed]

Fred, could you tell me by a private message what comment you thought was derogatory? (I suppose that you were the one who edited that posting by me). Then I could re-write it so that it doesn't upset anyone. I have been talking all day to people at Växjö who agree with you and Christian that Bell was badly mistaken. No-one has complained about my slides. I have been very careful to be polite and diplomatic and focus on content.

There were requests to clarify some statements and so I will be updating those slides soon.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Wed Jun 11, 2014 9:19 am

menoma wrote:If it cannot be said what the data from Dr. Christian's proposed experiment ought to look like, could the correct data even be recognized were it to be generated? Isn't the experiment, as proposed, therefore incoherent?

The data from my proposed experiment looks exactly like the data from my proposed experiment. You can see that yourself in this simulation of the data.

Several people tried to show that, somehow, my proposed experiment is not viable. The above simulation of the data from my proposed experiment, together with all the other simulations I have produced to date, lend substantive support to my local-realistic model for the EPR-Bohm correlation.

Needless to say, the above comments by the QC Gill about my proposed experiment are untruthful. My proposed experiment is not only coherent and viable, but it is the only experiment that can truly test local realism, because it is the only experiment in which all the counterfactual results in an EPR-Bohm type scenario exist in a data set for all eternity.

There is another point that is worth stressing once again. It is that the QC Gill has quite a knack of constantly producing untruthful propaganda. I can't be bothered to correct his propaganda all the time, because in the end truth will prevail and his propaganda will be exposed for what it is. I will only make the following statement to counter his propaganda: My central hypothesis is that the EPR-Bohm type correlations are a result of the intrinsic geometry and topology of the physical space we live in, namely the geometry and topology of the parallelized 3-sphere. Now as a topological space the 3-sphere has several different representations. The latest paper of mine I have linked above brings out only one of these representations. It happens to coincide with the classic local-realistic model produced by Pearle some 45 years ago, but that should not be surprising to anyone. After all, the same mathematical structure can be represented in the physical world in several different ways.
Last edited by Joy Christian on Wed Jun 11, 2014 10:06 am, edited 1 time in total.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Rick Lockyer » Wed Jun 11, 2014 9:57 am

Fred, you still do not see the error of your ways. Joy does not want to look, his loss. The requirement is for the statements

a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a) ## Inner products of cols of 'u' with 'a'
cb <- colSums(v * b) ## Inner products of cols of 'v' with 'b'
E_alpha_beta <- sum(sign(ca) * sign(-cb))/N

to have ca and cb lengths = N, not something else. You have ca and cb lengths of 10000, but divide by the value 7070 = N in your program. How convenient! It is equivalent to rescaling the results by roughly a factor of sqrt(2), but quite out of bounds and has absolutely nothing to do with 3-sphere geometry. 7070 is nothing more than the last count of true "good"s in the nested for loops in what amounts to genning up a totally non-local method to match -cos(a-b), which it does quite well as can be seen by running the included program. This program includes the E_ calculations for the agreed on Alice and Bob directions and the final inequality abs() within the for loops such that every i,j pass is analyzed, not just the one with terminal i,j as you and Joy do in your R programs. Guess what? The inequality sum is always abs(-2) and -cos(a-b) is matched in a clearly non-local fashion roughly within +/- 0.03. So what does the program you and Joy are touting actually do? It demonstrates the well known fact you can beat Bell's Inequality if you give up locality. This is not Joy's position in his book or writings, so at best the program the two of you are promoting does not apply to his work. If the two of you can't see this, then you either have your heads in the sand or are beyond my ability to help.

Code: Select all
## Richard Gill has offered 10,000 Euroes to anyone who can simulate the N
## directions of angular momentum vectors appearing in equation (16) of my
## experimental proposal: http://arxiv.org/abs/0806.3078. In this simulation
## I provide such N directions. They are given by the vectors 'u' in this
## simulation. He has also offered further 5,000 Euros to me if my proposed
## experiment is realized successfully. I am hopeful that that will happen
## some day. The details of these challanges by Richard Gill can be found
## here: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=52#p1898.
## While this is by no means the most perfect simulation of my model, it does
## meet all of the conditions set out by Richard Gill for his challenge.

## The theoretical description of the model can be found in this paper:
## http://arxiv.org/abs/1405.2355 (see also http://lccn.loc.gov/2013040705).

## Since after the explosion the angular momentum vectors 'u' moving along
## the z direction will be confined to the x-y plane, a 2D simulation is good
## enough for my proposed experiment.

set.seed(9875)

M <- 10^4  ## Sample size. Next, try 10^5, or even 10^6

angles <- seq(from = 0, to = 360, by = 10) * pi/180

K <- length(angles)
Ns <- numeric(K)  ## Container for number of non-local states
corrs <- matrix(nrow = K, ncol = K, data = 0)  ## Container for non-local correlations
E_0_45 <- matrix(nrow = K, ncol = K, data = 0)
E_0_135 <- matrix(nrow = K, ncol = K, data = 0) 
E_90_45 <- matrix(nrow = K, ncol = K, data = 0) 
E_90_135 <- matrix(nrow = K, ncol = K, data = 0) 
ineq <- matrix(nrow = K, ncol = K, data = 0)   ## container for Bell's inequality for each non-local ensemble e
corrErrs <- matrix(nrow = K, ncol = K, data = 0)  ## Container for non-local correlation deviation from -cas(alph - bet)

r <- runif(M, 0, 2 * pi)
s <- runif(M, 0, pi)

x <- cos(r)
y <- sin(r)

u <- rbind(x, y)

## 'u' is a 2xM matrix. The M columns of 'u' represent the x and y
## coordinates of points on a unit circle in the equatorial plane.

p <- 1.21 * (-1 + (2/(sqrt(1 + (3 * s/pi)))))

minIneq = 10   ##values to force initial replacements
maxIneq = -10
minCorrErr = 10
maxCorrErr = -10

for (i in 1:K) {
    alph <- angles[i]
    ai <- c(cos(alph), sin(alph))
    for (j in 1:K) {
        bet <- angles[j]
        bj <- c(cos(bet), sin(bet))
        ca <- colSums(u * ai)  ## Inner products of cols of 'u' with i loop 'a'
        cb <- colSums(u * bj)  ## Inner products of cols of 'u' with j loop 'b'
        good <- abs(ca) > p & abs(cb) > p  ## Sets the topology to that of S^3??????
        N <- sum(good)
        corrs[i, j] <- sum(sign(ca[good]) * sign(-cb[good]))/N
        corrErrs[i, j] = corrs[i, j] + cos(alph-bet)

        if(corrErrs[i, j] > maxCorrErr) maxCorrErr <- corrErrs[i, j]
        if(corrErrs[i, j] < minCorrErr) minCorrErr <- corrErrs[i, j]

        Ns[i] <- N

        t <- x[good]
        w <- y[good]

        e <- rbind(t, w)

        alpha <- 0 * pi/180
        beta <- 45 * pi/180
        a <- c(cos(alpha), sin(alpha))
        b <- c(cos(beta), sin(beta))
        ca <- colSums(e * a)  ## Inner products of cols of 'e' with 'a'
        cb <- colSums(e * b)  ## Inner products of cols of 'e' with 'b'
        E_0_45[i, j] <- sum(sign(ca) * sign(-cb))/N

        alpha <- 0 * pi/180
        beta <- 135 * pi/180
        a <- c(cos(alpha), sin(alpha))
        b <- c(cos(beta), sin(beta))
        ca <- colSums(e * a)  ## Inner products of cols of 'e' with 'a'
        cb <- colSums(e * b)  ## Inner products of cols of 'e' with 'b'
        E_0_135[i, j] <- sum(sign(ca) * sign(-cb))/N

        alpha <- 90 * pi/180
        beta <- 45 * pi/180
        a <- c(cos(alpha), sin(alpha))
        b <- c(cos(beta), sin(beta))
        ca <- colSums(e * a)  ## Inner products of cols of 'e' with 'a'
        cb <- colSums(e * b)  ## Inner products of cols of 'e' with 'b'
        E_90_45[i, j] <- sum(sign(ca) * sign(-cb))/N

        alpha <- 90 * pi/180
        beta <- 135 * pi/180
        a <- c(cos(alpha), sin(alpha))
        b <- c(cos(beta), sin(beta))
        ca <- colSums(e * a)  ## Inner products of cols of 'e' with 'a'
        cb <- colSums(e * b)  ## Inner products of cols of 'e' with 'b'
        E_90_135[i, j] <- sum(sign(ca) * sign(-cb))/N
        ineq[i, j] <- abs(E_0_45[i, j] - E_0_135[i, j] + E_90_45[i, j] + E_90_135[i, j])

        if(ineq[i, j] > maxIneq) maxIneq <- ineq[i, j]
        if(ineq[i, j] < minIneq) minIneq <- ineq[i, j]

    }

}

maxCorrErr
minCorrErr
maxIneq
minIneq

par(mar = c(0, 0, 2, 0))
persp(x = angles, y = angles, z = corrErrs, zlim = c(-0.1, 0.1), col = "pink", theta = 135,
    phi = 30, scale = FALSE, xlab = "alpha", ylab = "beta")


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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Heinera » Wed Jun 11, 2014 10:13 am

Rick, you are completely correct in your analysis of this version of their model.

In other versions, the culprit has been cherry picking subsets of the data to suit the detector settings.

Since they have been producing a new model every 24 hours or so, it is hard to keep up unless one follows this thread as a livelihood.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Wed Jun 11, 2014 10:21 am

Rick Lockyer wrote:The requirement is for the statements ... to have ca and cb lengths = N, not something else.

Where does that say in the Gill challenge?

Are you trying to help Gill rewrite the rules of his challenge yet again, the Nth time?

And have you figured out yet what a "compete state" means in Bell's local realistic framework?

Perhaps it is worth repeating what I have said before about Gill's misinterpretation of my experiment: viewtopic.php?f=6&t=31&p=1651&hilit=replacement#p1651.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Rick Lockyer » Wed Jun 11, 2014 10:39 am

Come on Joy.

"Let's call the directions of angular momentum in Alice's file u_k, k=1,...,N, and in Bob's file v_k, k = 1, ..., N

If I pick measurement directions a and b,thinking now of directions as unit vectors in R^3, then according to the same paper the outcomes left and right are

A_k = sign(a . u_k) and B_k = sign(b . v_k),

and the estimated (observed, sample, experimental ...) correlation is

E(a, b) = 1/N sum_k A_k B_k "

Clearly here
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Wed Jun 11, 2014 10:44 am

Rick Lockyer wrote:Come on Joy.

"Let's call the directions of angular momentum in Alice's file u_k, k=1,...,N, and in Bob's file v_k, k = 1, ..., N

If I pick measurement directions a and b,thinking now of directions as unit vectors in R^3, then according to the same paper the outcomes left and right are

A_k = sign(a . u_k) and B_k = sign(b . v_k),

and the estimated (observed, sample, experimental ...) correlation is

E(a, b) = 1/N sum_k A_k B_k "

Clearly here


And how does this square with the condition that the four correlations must be computed separately as I pointed out here: viewtopic.php?f=6&t=31&p=1651&hilit=replacement#p1651?

After all, Gill's challenge is about my proposed experiment, isn't it? What does the opening sentence of his challenge say?
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Rick Lockyer » Wed Jun 11, 2014 11:19 am

Joy,

In your referenced post

"It is a matter of indifference whether N here is chosen to be the same or different for each of the four alternatives."

This is true as long as each N is large enough to minimize the non in the limit error. But it does NOT permit you to sum over M elements but divide by N not equal to M, which is precisely what you are doing without ANY real justification. Otherwise what I am doing in my faithful adaptation of your program, using the CLEAR requirements that M=N, meets your "separate" requirement. After all, you are on record saying it is what you wanted. You and Fred just screwed up by not using M=N.

Fred,

Bam?? More like thud.

Both,

No more BS please. Both of you are clearly wrong in stating you have beat Richard, you clearly (really clear) have not. I am done commenting on the bet and your conclusions on whether or not you won based on the requirements. DO NOT INTERPRET MY FAILURE TO ENGAGE ON ANY ADDITIONAL COMMENTS AS A SIGN I HAVE NO POSITION TO DISAGREE.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Wed Jun 11, 2014 11:30 am

Rick Lockyer wrote:DO NOT INTERPRET MY FAILURE TO ENGAGE ON ANY ADDITIONAL COMMENTS AS A SIGN I HAVE NO POSITION TO DISAGREE.

No, Rick. I won't. You can disagree as much as you like. :)

I remain unimpressed, however, by your comments, because you have failed to answer the basic question I asked you after you posted your first post in this thread.

PS: I just discovered that Rick was talking complete nonsense. Here are the results I found, the meaning of which should be obvious to anyone knowledgeable in R:

For the first correlation E_0_45:

(s1 <- sum(sign(ca) * sign(-cb)))
## [1] -4944

(s1a <- sum(sign(ca)))
## [1] 30

(s1b <- sum(sign(-cb)))
## [1] -114

(s1ca <- sum(ca))
## [1] 30.45

(s1cb <- sum(-cb))
## [1] -61.96

Note that, contrary to what Rick claimed, none of the above quantities is going anywhere near 10,000. So I don't know what Rick was going on about.
Last edited by Joy Christian on Wed Jun 11, 2014 1:17 pm, edited 4 times in total.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Wed Jun 11, 2014 12:26 pm

Perhaps it is worthwhile to point out that Rick is mistaken on several counts. Even without going into details it is fairly obvious from this simulation that manifestly local-realistic surface is produced---which of course exhibits ALL possible correlations not just the special four---with unambiguously standard formulae for the mean value and the measurement functions:

E(a, b) = 1/N sum_k A_k B_k ,

where A_k = sign(a . u_k[good]) and B_k = -sign(b . u_k[good]) are manifestly local and realistic functions of hidden variables and the measurement directions.

The results of these computations are spectacular, as can be appreciated from the correlation surface shown below.

What I am trying to say here is that comparing this surface with the predictions of the four correlations is more than sufficient by itself to recognize that the Gill challenge has been defeated. Of course, it helps if you also read this paper of mine to understand what is going on.

Image
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