Still no file of directions received. It is now more than 12 hours after dr. Christian's claim that he has won the bet he made with me.
For the time being, here is my answer to Christian:
http://rpubs.com/gill1109/Fail
It is a little R script proving that his claim is false. If he wants this result adjudicated by our board of adjudicators, he is welcome, but we can only bother them once on this particular challenge. So it would be his one and only chance for the 10 000 Euro jackpot.
Other alternatives: he tries again another day; he gives up; ...
My open one-sided offer does remain offer to anyone, up to June 11. After that it is reduced to 5 000.
Claims have to be submitted to me by email. For the time being I have had enough of discussions with dr. Christian. Submissions do not consist of some computer code drawing some pretty pictures. They consist of a link to a text file, posted on internet, containing N directions of angular momentum observed by Alice, and N directions of angular momentum observed by Bob. I will compute the "usual" four correlations E(0, 45), E(0, 135), E(90, 45), E(90, 135) according to the formulas agreed by Joy and myself which can be found here:
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=46
If any of them is off by 0.2 or more from the target values - 0.7071, 0.7071, - 0.7071, - 0.7071 the claim has failed. If all four are within tolerance, the claim has succeeded and will be honoured by me.
In case of dispute as to whether or not a particular submission is valid or has / has not won the bet, we will jointly approach three wise men Andrei Khrennikov, Hans de Raedt, and Gregor Weihs, and they may adjudicate. I haven't asked them if they are prepared to do this job, so if they are unavailable, we will have to come up with another adjudication procedure. In any case, we are only going to resort to adjudication once, so after one false claim, you are no longer eligible for new tries (unless of course you actually immediately convince me on your n'th submission that you finally got it right).
Any questions about this procedure are to be submitted to me by email. I am happy to give any further necessary clarification. If an issue is raised of general concern I will add a posting here, addressing it.
Here is the R code referred to above:
## My response to Christian's claim to my prize.
## First I delete all lines from his code except those generating
## the set of directions "e"
set.seed(9875)
N = 10^5
s = runif(N, 0, pi)
t = runif(N, 0, pi)
x = cos(s)/1.28
y = -1 (2/(sqrt(1 (3 * t/pi))))
e = rbind(x, y) ## 2 x N matrix; N columns of e represent the
## x and y coordinates of points on a circle:
## Alice's observed directions of angular momentum.
## Bob's observed directions are -e.
## Now I separately compute four correlations according to the
## formulas agreed by Christian
alpha = 0 * pi / 180
beta = 45 * pi / 180
a = c(cos(alpha), sin(alpha))
b = c(cos(beta), sin(beta))
(E_0_45 = mean(sign(colSums(e * a)) * -sign(colSums(e * b))))
alpha = 0 * pi / 180
beta = 135 * pi / 180
a = c(cos(alpha), sin(alpha))
b = c(cos(beta), sin(beta))
(E_0_135 = mean(sign(colSums(e * a)) * -sign(colSums(e * b))))
alpha = 90 * pi / 180
beta = 45 * pi / 180
a = c(cos(alpha), sin(alpha))
b = c(cos(beta), sin(beta))
(E_90_45 = mean(sign(colSums(e * a)) * -sign(colSums(e * b))))
alpha = 90 * pi / 180
beta = 135 * pi / 180
a = c(cos(alpha), sin(alpha))
b = c(cos(beta), sin(beta))
(E_90_135 = mean(sign(colSums(e * a)) * -sign(colSums(e * b))))
## Just for fun
- E_0_45 E_0_135 - E_90_45 - E_90_135
Here are the numerical results which I obtained:
[1] -0.68418
[1] 0.68382
[1] -0.31326
[1] -0.31874
[1] 2
I am now going on a short vacation but will be reading my email from time to time.