Heinera wrote:I promised myself I wouldn't bother anymore, but weak willpower makes me try one more time to teach someone some elementary probability theory:
Promise yourself to learn some basic statistics before you speak next time. And before you respond to this thread any further, I strongly suggest you read post #1, very carefully
As clearly explained in post #1, the above is impossible. So again, go back to the first page and read the argument in post #1, and save yourself from further embarrassment. Make sure you do not miss the part where it is shown that the above is impossible. If for some reason you do not like me personally (evidently), such that you have a bias against valid arguments made by me, perhaps you may like to read a purely mathematics paper which pre-dates Bell, and shows exactly the same thing rigorously
http://www.panix.com/~jays/vorob.pdf. Do not be deceived that your naive "probability reasoning" is valid. Such arguments are made all the time by novices who do not understand a shred of probability theory. You can read some more examples in Chapter 15 of Jaynes Book, Probability Theory: The Logic of Science. (
http://www-biba.inrialpes.fr/Jaynes/cc15b.pdf)
In short, you have no clue what you are talking about. Just because you are friends with, and hang around a few old-school statisticians does not mean you understand probability theory.
Heinera wrote:The extra degrees of freedom is of no use to the modeler (or nature), since he/she can't make any use of them due to the random selection of settings.
Please also do yourself a favor and read-up on Bertrands paradox. Random sampling of "hidden variables" is an oxymoron. To randomly sample any variable you need to know ALL the parameters that influence its values and exactly how the values change. If you do not understand this, read this article, specifically related to Bell's inequality, in which a counterexample demonstrating this pitfall is presented
http://arxiv.org/abs/0907.0767