Justo wrote:There is no way out of the irrelevance of the CFD assumption because even assuming it makes sense, you can completely ignore it and derive the inequality from physically meaningful assumptions, i.e., Local Causality(LC) and Statistical Independence(SI). The issue is so simple that even someone like me who does not know probability theory can do it. All you need to know is the intuitive meaning of probability as a relative frequency.
Actually, you can't. I just showed you that all derivations go through a 4xN spreadsheet. You either arrive at the spreadsheet through CFD as Gill does, or arrive at it through an assumption that the data from the experiment can be reordered and reduced. Bell's theorem is caught between a rock and a hard place. No escape.
Since Bell left all these trivialities implicit because he concentrated on the important points, I give a detailed explanation of how LC and SI naturally describe the Bell experiment without introducing metaphysics.
I think you are reading much more into Bell's thoughts and feelings beyond what is in his papers. It's like you want him to be right.
All you need is to count events, record them, and evaluate relative frequencies. That explains why the results of four different sets of experiments can be reduced under the same sum with equal hidden variables.
They can't be reduced. I've explained to you why they can't. And you understand it. Until you have a good argument against my explanation, it's not up-and-up to keep repeating the claim. It's a false claim. Saying we agree to disagree when you haven't explained anything to even be disagreed with is not up-and-up either.
If you say I am wrong then I guess you would agree with @minkwe. Basically, he says that I am wrong about the following: let us assume we have a great number of cards with 16 different values 1,2,...16 (for the sake of simplicity let us say the number of cards with different values is the same) My claim is that when you extract (with replacement) one card more than 16 times the values you choose will necessarily start to repeat and if you calculate the relative frequency of each extracted value after a great number of trials, the relative frequency of each extracted number should be approximately 1/16.
Are you serious, this is absolutely not what I'm saying. You are absolutely correct about the relative frequencies above. You need to go back and read the other thread. Pay particular attention to the repeated mention that the Fair Sampling assumption is granted. I assume you understand what that means.
Here is what I'm saying, using a similar analogy. We have two boxes of cards labelled "1", "2". Each box has the same distribution of card values. There are two methods of picking cards "a", "b", each method is biased in a different way. Obviously, using the same method to pick N pairs from the same box will yield samples that have a practically identical distribution of values if N is large.
Now perform an experiment with 4 couples. Each person is assigned a box and a method to use in picking cards. The couples pick pairs of cards with replacement each time. Each person always picks from the same assigned box using the same assigned method. The couple records their values in a 2xN spreadsheet.
The assigned boxes and methods for the couples in the experiment are
(a1,b1), (a1,b2), (a2,b1) and (a2,b2). Where a1 means picked from box "a" using method "1". Obviously, the distributions of values is the a1 columns are almost identical.
That is the Fair sampling assumption, absolutely not at issue. But the exact sequence of values in the a1 columns are different.
Now please go read my argument in the other thread. You should be able to complete the argument from this point.
What I'm saying is that the data from this experiment cannot be reordered and reduced from four independent 2xN spreadsheets into one 4xN spreadsheet. This is a simple exercise that anyone with Excel or OpenOffice can verify. The reordering is required in order for the derivation in your paper to proceed. It is an implicit assumption in the derivation, an assumption that turns out to be false.