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Joy Christian wrote:

gill1109 wrote:PS no escrow account is needed with 10 000 already placed in it, since it is certain that no one will win the challenge. This follows from the famous Nx4 spreadsheet theorem which we discussed here many times. However, I am a man of my word, so, in a counterfactual universe where the elementary rules of logic are different from ours and some-one did come up with a successful challenge, I would pay up (though it is doubtful I would ever have set the challenge in that alternative, impossible, universe ... so this is doubly counterfactual. Probably an example where a double negative is a positive).

No challenge can be defeated if one of the rules of the challenge says that the rules of the challenge will be altered, modified, abandoned, or changed beyond recognition every time someone defeats the so-called challenge. Your money is safe. But, please, stop calling yourself a gentleman: viewtopic.php?f=6&t=57.

And please stop insulting me by endlessly repeating the lie that we drew up the rules of the challenge together. We didn't. You only imagined that we did.

The rules have never been altered, modified, abandoned, or changed beyond recognition; they have only been refined, i.e., from time to time we became aware of ambiguities and each time we clarified the ambiguities. It's always been a matter of open negotation. If at any stage we can't agree, then the bet c.q. challenge obviously has to be cancelled.

One cannot make a bet under terms which keep changing ... but one also cannot make a bet under terms which are ambiguous. If ambiguity arises it needs to be resolved. If it can be resolved, we go ahead, if not, we abort. No harm done. After all, we are both gentlemen, right?

For instance, recently it turned out that you have a rather different idea about what is meant by a "set of directions", and about the representation of a set of directions in computer files, than I did. As far as I can see your ideas were rather novel, they did not already exist written down in your papers, so I think I may be excused from objecting. Tell me if I'm wrong.

So, do I understand that you do not accept my most recent proposed dis-ambiguation (concerning the interpretation of a, b, u_k, v_k, dot product, sign, and multiplication?) We are talking about how to interpret page 4 of your "experimental paper". If you think that it should be interpreted in a different way from how I interpreted it so far, then please go ahead and clarify.

A. Do you have an alternative proposal?

B. Or do you wish to let the adjudicators decide on your latest submission, to be evaluated under the rules then in force?

C. Or do you want to forget the whole thing?

I am happy, either way.

As far as new submissions are concerned, the old challenge with the newest disambiguation remains open.

All this also applies to Hugh's submission.

gill1109 wrote:PS no escrow account is needed with 10 000 already placed in it, since it is certain that no one will win the challenge. This follows from the famous Nx4 spreadsheet theorem which we discussed here many times. However, I am a man of my word, so, in a counterfactual universe where the elementary rules of logic are different from ours and some-one did come up with a successful challenge, I would pay up (though it is doubtful I would ever have set the challenge in that alternative, impossible, universe ... so this is doubly counterfactual. Probably an example where a double negative is a positive).

No challenge can be defeated if one of the rules of the challenge says that the rules of the challenge will be altered, modified, abandoned, or changed beyond recognition every time someone defeats the so-called challenge. Your money is safe. But, please, stop calling yourself a gentleman: viewtopic.php?f=6&t=57.

And please stop insulting me by endlessly repeating the lie that we drew up the rules of the challenge together. We didn't. You only imagined that we did.

PS no escrow account is needed with 10 000 already placed in it, since it is certain that no one will win the challenge. This follows from the famous Nx4 spreadsheet theorem which we discussed here many times. However, I am a man of my word, so, in a counterfactual universe where the elementary rules of logic are different from ours and some-one did come up with a successful challenge, I would pay up (though it is doubtful I would ever have set the challenge in that alternative, impossible, universe ... so this is doubly counterfactual. Probably an example where a double negative is a positive).

FrediFizzx wrote:

gill1109 wrote:My challenge is withdrawn till such time as a revision of the experimental paper is posted on arXiv.

No one is going to take the challenge serious unless you put the 10K Euros in an escrow account.

Sorry Fred, you are right, I did say the challenge was withdrawn!

I hereby withdraw that withdrawal.

The challenge
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=52#p1898
remains standing exactly as formulated, but with the following clarifications:

The formulas

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

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

should be interpreted as follows:

a, b, u_k, and v_k are non-zero vectors in R^3, represented with Cartesian coordinates (x, y, z);

"." is the ordinary scalar or dot product

"sign" is the ordinary sign function

multiplication, additions, and division are all done by ordinary arithmetic of real numbers

N is a non-negative integer, not larger than 100 000; but N = 10 000 should be perfectly adequate for purpose.

Data files may also be submitted by submission of a short computer script using a pseudo-random number generator with a pre-set seed, and containing two "write" statements which create the files.

Fred: you are still welcome to write a Mathematica script with an alternative interpretation of page 4 of Christian's experimental paper, if you think that a different interpretation is needed than the one which Christian and I earlier agreed to.

gill1109 wrote:My challenge is withdrawn till such time as a revision of the experimental paper is posted on arXiv.

No one is going to take the challenge serious unless you put the 10K Euros in an escrow account.

FrediFizzx wrote:

gill1109 wrote:If you can do this before June 11, and if Christian will resubmit two files of directions u_k and v_k before that date, then he can still win his 10 000 Euro. Proof of principle will have been supplied that his experiment can be successful. I will announce my capitulation at the Vaxjo conference. My talk is at 9:00 a.am. on Wednesday morning June 11.

Oh, so now you are NOT withdrawing the challenge? Pehaps you should put that 10K Euros into an escrow account where the adjudicators have control of it. That will let us all know that you are really serious about it. Otherwise, I am not wasting my time with it. Joy has already won anyways.

I never withdrew the challenge.

Joy is welcome to make a valid submission, so are you, so is Hugh.

If I say that a submission is invalid and the submitter disagrees, then we can try to recruit adjudicators.

Joy made a submission with two sets of directions for Alice and two sets for Bob. He has to tell me which one he wants me to use. I am not going to let him give Bob a different data-set deoending on Alice's setting. That is called action-at-a-distance, or perhaps "conspiracy".

Please help Joy create a legal submission on time.

While you are at it, write a Mathematica program for doing the calculation 1/N sum sign a.u sign b.v according to the principles of geometric algebra. So far Joy always used the ordinary dot product and sign function in his R scripts ... which originally were written by me. No wonder they don't work.

gill1109 wrote:If you can do this before June 11, and if Christian will resubmit two files of directions u_k and v_k before that date, then he can still win his 10 000 Euro. Proof of principle will have been supplied that his experiment can be successful. I will announce my capitulation at the Vaxjo conference. My talk is at 9:00 a.am. on Wednesday morning June 11.

Oh, so now you are NOT withdrawing the challenge? Pehaps you should put that 10K Euros into an escrow account where the adjudicators have control of it. That will let us all know that you are really serious about it. Otherwise, I am not wasting my time with it. Joy has already won anyways.

Please will *anyone* who wants to help Joy and Fred

write a piece of computer code which

(a) reads two files each containing N directions u_k and v_k,

(b) accepts as inputs from the user two directions a and b, and

(c) calculates E(a, b) = 1/N sum_k {sign(a . u_k)} {sign(b . v_k)}

treating of course, the product A_k B_k here as a geometric product, whatever that means. Isn't the product of two numbers +/-1 the same whether or not we think of the product as geometric? Possibly Fred is thinking of the dot product between real three-dimensional vectors a and u (and similarly b and v) as being some other new product? If that is the case, please define the mappings ".", "sign", and the product between A_k and B_k.

All directions to be specified by vectors in R^3, represented by Cartesian coordinates (x, y, z).

Earlier, I wrote an R program which did this task. Other people supplied Perl, Python, Excel, Mathematica. No one complained about those programs. They have all been tested and give the same output on the same inputs. However they were not written by experts on Joy's model and apparently there is something badly wrong with all of them.

PS: in case that the N u_k's are a large random sample from the uniform distribution on S^2, and a and b are vectors of unit length, and for each k, v_k = - u_k, we want E(a, b) to approximately equal - a . b (ordinary dot product).

PPS: since the u_k, v_k, a and b all specify directions of classical angular momentum of classical massive spinning rigid bodies in classical three dimensional space (zero gravity, vacuum), they all should be non-zero when represented as vectors in R^3. The lengths of the vectors (provided they are positive) should be irrelevant. For simplicity all vector-directions could be taken to have unit length.

Hi Everyone,

I have written another version of the second of the above two simulations: http://rpubs.com/jjc/18915.

Both versions of the simulation can be understood as respecting the parity change intrinsic to my 3-sphere model for the EPR-Bohm correlation.

The vectors for Alice and for Bob are now defined by the ordered sets



and

.

Note the differences in the definitions. The last two of the four correlations in the simulation are now calculated using left-handed basis for the spins instead of right-handed basis . Not surprisingly, all four correlations once again match exactly with the corresponding quantum mechanical predictions.

FrediFizzx wrote:Hello! A_k B_k has ALWAYS been a geometric product in Joy's model. And the experiment IS about Joy's model. So what you guys are missing or don't understand is that,

{sign(a . u_k)}{sign(b . v_k)}

Is a geometric product. And since it is a geometric product, it is easy to find that,

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

As Joy's simulations have shown. Can we move on now?

Please help us moving on, Fred, by writing a piece of Mathematica code which

(a) reads two files each containing N directions u_k and v_k,

(b) accepts as inputs from the user two directions a and b, and

(c) calculates E(a, b) = 1/N sum_k {sign(a . u_k)} {sign(b . v_k)}.

I suggest that all directions are specified in Cartesian coordinates (x, y, z).

Joy's simulation of my re-writing of Pearle's detection loophole model does not do this, as far as I can see. Maybe I am not good enough at understanding Joy's R code.

Joy's own script for analysing his submission to my challenge does not do this. Maybe I am not good enough at understanding Joy's R code.

As far as I could see, Joy's original theoretical derivation of the miraculous formula E(a, b) = - a . b (ordinary dot product here) in his one page paper was wrong. Maybe I am too algebraically challenged, being a mere third rate statistician myself.

Hugh Matlock's submission rejects many of the runs, replaces 1/N by something smaller, and introduces auxiliary randomization. He is effectively simulating Pearle's model but we all already know how to do that.

But perhaps you can do a better job than me, at writing this little piece of crucial computer code. Or perhaps Michel Fodje can help. Python would also be fine. R is fine.

If you can do this before June 11, and if Christian will resubmit two files of directions u_k and v_k before that date, then he can still win his 10 000 Euro. Proof of principle will have been supplied that his experiment can be successful. I will announce my capitulation at the Vaxjo conference. My talk is at 9:00 a.am. on Wednesday morning June 11.

Hello! A_k B_k has ALWAYS been a geometric product in Joy's model. And the experiment IS about Joy's model. So what you guys are missing or don't understand is that,

{sign(a . u_k)}{sign(b . v_k)}

Is a geometric product. And since it is a geometric product, it is easy to find that,

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

As Joy's simulations have shown. Can we move on now?

Hugh Matlock wrote:Dr. Gill,

You have written that my submission to the Gill Challenge was "legal but unfortunately unsuccessful". You indicated that I did not win because I used the "wrong dot product" in my analysis. You have also described the text of the Gill Challenge as ambiguous, and others have discussed alternative interpretations of the text.

But at the point where you depart from the rules of the Gill Challenge, the text is not ambiguous at all. When Richard announced his challenge (e.g., in the (original) Usenet group sci.physics.foundations), he wrote

R. Gill wrote:If I pick measurement directions a and b, then according to Christian's
experimental 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 = ( N(++) + N(--) - N(+-) - N(-+) ) / (
N(++) + N(--) + N(+-) + N(-+) )

in the obvious notation.

"In the obvious notation," the dot product clearly means the century old notation introduced by Gibbs & Wilson that we have been using ever since. If you out of the blue want to redefine established notation to something completely new and ad hoc, then do that. But you can't thereby claim the original notation was "ambiguous" and expect to win any bet that way.

OK so please provide a correct script which experimenters are supposed to use in order to calculate E(a, b). Publish it here. Let's move on. Science is a collaborative enterprise. It is driven by ego's, sure; but we have to communicate. Science is science by virtue of being reproducible. Inter-subjective.

This particular job is a crucial "finer detail of the experiment". No one will do the experiment if there is no "proof of concept" that it can be succesful. It has to be reproducible too.

Several people responded to my R script. John Reed did a mathematica version. Zen did Perl and Python. Heinera did Excel. (Maybe my memory is not quite correct).

Fred Diether did not respond. Joy Christian did not respond. Muchel Fodje did not respond (except to warn Joy against accepting the presently formulated challenge: he said Christian would certainly lose, and told Christian how to modify the rules. However Christian stuck by the description in his experimental paper).

So the current status is that my R script is presently accepted, there is nothing else on the table, Christian's supporters have had months of time in order to come up with a counter-proposal.

In fact for quite a few weeks, Christian has been even using my R code in his own attempts to win the challenge. You may recall that he has crowed victory about three or four times already, with three or four different submissions (sorry, I lose count).

So let's move on. Time to clarify details of the famous experiment. Time to clarify the post-processing of the data.

Ok, I guess we are NOT moving on. No one responded to your R script most likely because it was wrong. And that must be the case. The correlation of course must be done using A_k B_k as a geometric product. What Joy has presented clearly works for the experiment so we should be done with this phase. Now we should be working on finer details of how to actually do the experiment so as to better prep the experimenters that will do it.

Dear Hugh

Yes I will certainly reconsider your submission. I have also been reconsidering my statement that perhaps the wording of the challenge was ambiguous. I now believe that was not the case, certainly not when it is viewed in context. For a long time Christian and I were discussing a bet around his future experiment. The bet about the experiment (one-on-one, Joy and I each 5 000 Euro on the table) later evolved into a open challenge (the world can submit to me, no costs to the world, the first winner wins). The challenge involves creating data sets such as would be produced in the experiment, such that the final stage of the data-processing would give the results which Christian expects.

It is important that bets are very carefully worded so that no-one can later accuse the other of trickery. Therefore (back in the bet preparation days) I wrote out an R script which would be the basis for the data-processing part. Some contributors here provided versions in Excel and in Perl. They have been verified to give the same results on the same data. The code was published here. The directions are encoded as real 3-vectors, the dot product is the dot product, the sign function is the sign function. I asked Joy and his supporters to verify these codings and to provide their own alternative versions e.g. Python and Mathematica (I was thinking of Christian supporters Michel Fodje and Fred Diether respectively). There was never any response. No one objected to my R code or the Perl or Excel translations. No one supplied a Mathematica or Python version. (I think later Zen also wrote a Python version, but no one from the other camp tested it or complained about it).

So perhaps the challenge is ambiguous to you since you have not been party to all these many exchanges, but I think it is clearly not ambiguous to all long time active supporters of Joy Christian on this forum and others.

Now the text was written by myself but it was the result of a long and open conversation with Joy during which we both of us ironed out several ambiguities as they occurred, or added provisos for as yet unforseen scenarios.

By the way, week after week Christian was making new attempts, all of them using the dot product and the sign function... only just recently has he come up with a new trick, namely each of Alice's and Bob's directions comes in two pairs called u and v, and when we compute the correlation, we use Bob's u or v depending on whether Alice's measurement direction is a or a'. This is quite an extraordinary transparent action-at-a-distance. Christian says that both u and v represent the same direction, and I say: OK please choose one and I will work with it.

It is an as yet unforseen scenario on my part, that a new challenger comes up quite out of the blue with an alternative interpretation of the formula sign(a . u) sign(b . v) in the context of the written challenge, which explicitly refers to directions of angular momentum of macroscopic objects whose motion was captured on video camera. It has been said time and time again that the two files can be dreamed up in any way you like - you do not have to simulate Christian's model. You can get data from wherever you like, or you can just dream up numbers out of your head.

By the way Christian again and again stated explicitly that no "particles" are lost, there are no zero outcomes. There is no mention anywhere of any further randomization in the calculation of empirical correlations.

So also when I am back from my vacation I will reconsider your submission, give you my considered conclusion, and if you disagree with it, we will try to recruit some neutral and sufficiently knowledgable adjudicators. The draft letter to the adjudicators can be found somewhere in this forum, and there are some obvious candidate persons we can ask.

I also plan to post a revised disambiguated version of the challenge. I was too kind to Christian, to give him the option to choose between Cartesian coordinates or spherical coordinates or something else. I will write explicitly that the dot is the dot product and the sign is the sign function. I should also impose a practical limit on N and on the size of the files.

Richard

Dr. Gill,

You have written that my submission to the Gill Challenge was "legal but unfortunately unsuccessful". You indicated that I did not win because I used the "wrong dot product" in my analysis. You have also described the text of the Gill Challenge as ambiguous, and others have discussed alternative interpretations of the text.

I would like to bring your attention to a longstanding provision of law called "contra proferentum" under which ambiguous language is to be interpreted in favor of the party that did not draft the text.
http://en.wikipedia.org/wiki/Contra_proferentum

In light of this, I would ask that you reconsider my submission.

I will be away from the Internet for a few days (loading a moving truck, driving 1000 miles, unloading...) but I should be able to get back on at the weekend.

After due consideration, I hope you agree with my position; if not... well, luckily there is an adjudication provision in the challenge.

Aloha,
Hugh

gill1109 wrote:In the meantime: please do close this thread.

This thread was started by Hugh Matlock. It would be unfair to close it without his vote. We all know why Gill wants to close every thread that is inconvenient for him.

Fred, you are a man after my own heart. Let's move on.

Some time ago we were discussing how the data from Joy's experiment should be analyzed. I put forward an R script. Zen wrote a Perl script and an Excel spreadsheet. We were waiting for feedback "from the other side". For Python code from Fodje, Mathematica code from Diether. None came. No objections were raised. And where are we now? Stand-off. Exactly what I expected.

I am waiting either for legal data files from Christian (legal according to the rules he agreed to), or a rewrite of page 4 of his experimental paper abolishing all possible ambiguities for ever.

Either Joy wins the old challenge fair and square according to the previously agreed rules, or we rewrite the rules together.

In the meantime: please do close this thread.

gill1109 wrote:The challenge explicitly specified that u, v, a and b are real three-vectors; a.u and b.v are the ordinary scalar products; and "sign" is the usual sign function. Moreover for quite a few weeks Christian was turning out one failed simulation after another which made use of those same conventions. However at last light has begun to dawn.

Nope, it is you that failed to realize that A_k B_k is a geometric product. Please learn about this as it is essential to understanding Joy's model. Thanks.

There is no problem with the rest as far as what the vectors represent. The final result is that A_k B_k is a geometric product. Bang! Joy's model works for the experiment. Let's move on.

gill1109 wrote:Problem is, it seems Christian can't read. I have for a long time been suspecting dyslexia.

Can you read yourself, Richard?

Joy Christian wrote:Page 4 of my experimental paper contains only two unambiguous equations:



Here it is important to recall that

gill1109 wrote:
The experimental paper, page 4, states that we then calculate 1/N sum_j sign(a . lambda_j ) sign(b . -lambda_j).

...the vectors a, b, lambda_j, -lambda_j [are] unit vectors in R^3, the dot signified the usual scalar product, and sign [means] sign.

Note: There is only one correlation function, E(a, b), in equation (16), not four.

An introductory paragraph of the paper exposes the ambiguity in Bell's observables:



The following statement on my blog spells out the resolution of the Gill challenge:

Joy Christian wrote:
In addition to these simulations, I have recently won the 10,000 Euros offered by Richard Gill for theoretically producing the 2n angular momentum vectors, and , appearing in the equation (16) of my proposed experiment (see also this page). He had claimed that it was mathematically impossible to produce such 2n vectors and had challenged me to produce them as a "proof of concept" for my proposed experiment. I defeated his challenge on the 3rd of May 2014 by explicitly producing the 2n vectors in these two simulations.

It is very important to note that in the second simulation above I have used vectors defined by the ordered set



for calculating the first two of the four correlations in the simulation,

and vectors defined by the ordered set



for calculating the last two of the four correlations in the simulation.

Richard Gill claims that these sets of vectors specify different sets of directions in the physical space. But evidently they specify exactly the same set of directions in the physical space. They both define a unique distribution of points on a circle of radius . This should be quite easy for any mathematician to see, by

simply noting that .

and are thus different names of one and the same spin direction (say ) in the physical space.