Ben6993 wrote:Richard:
I think the Perle and ChaoticUnsharpeBall have similar 'corr-cos' charts (the last chart in the listings) but the former is better and only used 10^6 data pairs while the latter used 10^7. So the Perle is the winner at the moment?
The 'corr-cos' graphs are very roughly -0.002*sin(angle) and +0.0025*sin(angle), respectively. Don't those rough sine curves indicate that there is more pattern still to be extracted from the data as , ideally, there would only be random noise remaining?
Pearle is exact. Take the sample size bigger and bigger (and increase the numerical precision of your computer ...) and you will converge exactly to the cosine.
The same is true for Gisin and Gisin.
None of the others is exact.
Pearle's model *is* a particular chaotic unsharp ball model. It's one with a spot-on choice for the probability distribution of the radius of the circular caps.
From
Pearle's proof of this we can see that other choices are possible (his solution is not
unique). But his is very simple, and as I said, very very exact.
The rough sinusoidal shape of the error curves is because the *same* sample of 10^6 hidden variables is being used for all possible measurement angles. That saves a heap of time, but creates correlation. Which wouldn't be there, of course, if we used a new sample to calculate each separate point on the curve.
Multiply the sample size 10^6 by 100, and the simulation error will get 10 times smaller.