Zen wrote:Thanks, Heinera! You're right. I thought we were given the whole spreadsheet initially, and not just the first four columns. My mistake. I will fix it and post my analysis of Gill's proof asap.

In the mathematical sense, there is "given" an Nx4 array of numbers +/-1. Alice and Bob then toss coins. From each row of the array, Alice gets to see the entry from column A1 (S = heads) or from column A2 (S = tails). Similarly for Bob. Alice and Bob then get together to calculate four correlations each based on a different (disjoint) subset of rows.

We start with an Nx4 array with the numbers A1, A2, B1, B2. From now on it is fixed, given. Independently of this we do independent fair coin tosses, S, T; think of them as filling another Nx2 table. The two tables are combined (and reduced) to a new table with columns S, T, A_obs, B_obs. The four correlations are calculated from the third table: correlations between A_obs and B_obs for each combination of values of S and T.

I hope this is slowly getting crystal clear! Improvements to my notation and presentation are surely possible. My aim is to tell a story which science journalists, and high school students, and your grandmum and granddad, can *all* understand.

The link to Bell is that A1, A2, B1, B2 stand for (local functions of) the local hidden variables. S and T stand for Alice and Bob's freely chosen settings. A(obs) and B(obs) are the actually observed outcomes of Alice and Bob's measurements. Because of local realism, or because of local hidden variables, the experiment is "as if" Alice and Bob just randomly pick a predetermined outcome from one of two "preexisting" values. Note the "as if". I'm not saying it really is that way. I'm saying that the final results - what we finally get to see - is mathematically indistinguishable from the final results described here.

We can later discuss why this "as if" is certainly valid for computer simulations like Michel Fodje's "epr-simple". And once one has got the idea, one can extend further to e.g. "epr-clocked". But first I want to see if there is agreement on this little bit of elementary mathematics about randomly picking rows from a spreadsheet.

Think of it as "creating facts on the ground". But in fact, they are not being created by force - they already exist. It seems that Michel and Joy don't want to see them, but they are there, all right.