minkwe wrote:He did not. Here is what he did. Critics argued that he was using a single 3xN spreadsheet instead of 3 disjoint 2xN spreadsheets. He replied that he was using 3 disjoint 2xN spreadsheets. But based on his equations, that is false. He is using 2 2xN spreadsheets and from each of them he separates one column, recombines them to generate a third 2xN spreadsheet that is not independent of the other two in the same way the first two are independent from each other. While it appears to diffuse the criticism, it does not eliminate it. Perhaps he did not understand the root of the problem.

Michel, Bell does not use the idea of a spreadsheet. His first Bell inequality paper does not talk much about data. If you did do the experiment you would have data sets of various sizes for each of the setting pairs, as well as a data set testing the anti-correlation at equal settings.

The criticism is invalid. It has been adequately answered. But people will continue to misunderstand Bell’s arguments, that we can be sure of!

minkwe wrote: Why must the terms be cyclical? Why has nobody been able to "prove" Bell's theorem without relying on a cyclicity? What manner of "non-realism" or "non-locality" is this that only shows up when terms are cyclically related? I would have expected more curiosity from you on such topics.

There are numerous other ways to prove Bell’s theorem. Yes, I am very curious about this question. See Gull’s proof. https://arxiv.org/abs/2012.00719. No cyclicity. Fourier analysis and time series. Very elegant.

minkwe wrote: Oh so now you agree with me that it is very important to know "What" statistics converge to 2? You admit that there are local realistic statistics that converge to 2 and non-local statistics that do not converge to 2?

There are simulation experiments which give all kinds of answers. You wrote some yourself. I recall Joy Christian showing how you could get 2, 2 sqrt 2, or 4, by changing the value of a parameter in a simulation model which, he I think he said, was your simulation of his model, as improved by myself and others, done in R.

minkwe wrote: P(b,c) in the inequality is more restricted than P(a,b) and P(a,c) due to the cyclic nature of the terms. This is the core ingredient of all variants of Bell's theorem. They include a hidden reduction of independence that is simply ignored when comparing the results with experimental data where no such reduction in independence is present.

Proofs all exploit the *manifest* dependence of the various correlations, since they all depend on the same functions A, B and rho. In an experiment, each observed correlation could be anything from -1 to +1. But if Bell’s assumption is correct they will tend to converge to those integrals. And they will be related by Bell’s inequality.

You can test that yourself by writing your own simulation experiments! Dream up and A, B and rho satisfying the usual conditions. Take a number of independent, big, samples of lambda. Dream up a, b, c…