So that the actual math question in all this is not lost, here it is: In R^3 is it possible to color the lines through the origin B or W so that in every orthogonal triple of lines exactly one is B? The answer is "no", and you demonstrate it by finding a finite set of lines on which the coloring constraint leads to a contradiction. The first proof by Kochen and Specker used 117 lines. Peres then found a symmetrical configuration with only 33 lines. Conway and Kochen found an even smaller set, with 31 lines, but it is less symmetrical and requires more work to prove the result. Veit On Mar 21, 2009, at 5:46 PM, Dan Asimov wrote:
I don't know what I think of the existence of free will per se, but just on heuristic grounds, this *implication* is not surprising.
I.e., if determinism applied to all sufficiently small regions of the universe, then it would seem to necessarily apply to larger regions.
So if the latter fails, the former must, too.
--Dan
Ray wrote:
<< http://science.slashdot.org/article.pl?sid=09/03/20/1229233
snahgle writes "Mathematicians John Conway (inventor of the Game of Life) and Simon Kochen of Princeton University have proven that if human experimenters demonstrate 'free will' in choosing what measurements to take on a particle, then the axioms of quantum mechanics require that <http://arxiv.org/abs/quant-ph/0604079>the free will property be available to the particles measured, or to the universe as a whole. . . .
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