Author: Randall Shane
Date: 11:59:00 01/20/05
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On January 20, 2005 at 12:55:37, chandler yergin wrote: > >To 'solve' Chess cannot be proven, until the Chess Tree of all Possible >moves in an average game of chess have been examined. This has been shown to >be 10^120th Power. Far exceeding the number of molecules in the observable >universe. > >Would you agree? No. What does the number of molecules in the observable universe have to do with whether chess has a solution? Nothing -- it's an irrelevant rhetorical trick, argument by misdirection. A hypothetical computer that can play perfect chess (i.e., can always search deep enough to resolve the actual value of the search tree as Win, Lose, or Draw) doesn't have to record every position it looks at -- it only needs to know the positions in its current search path. it can back up, go forward, all without probably having to record more than about 1000 positions at any one time. It may have to examine 10^120 positions along the way, but it doesn't have to memorize them. The entire chess tree does not have to be kept around at all. The tree is well defined and pieces of it can be generated in arbitrary repeatable order as needed. Simple minimax search is all that's needed, with a fairly small memory requirement. And, this can be mathematically proven. Admittedly, the computer may not finish its first move before the heat death of the universe, but that doesn't change the ironclad proof of chess's solvability. For all practical purposes, we aren't going to see a solution during my lifetime, but the theory is right. Chess is solvable. I have extremely strong doubts that it will be solved, but it does have a solution. > >From the "Practical Standpoint" Humans, with the aid of Computers, >may indeed reach a point where, for Practical prposes, the search depth >may go to 50 moves for any reasonable Opening, as we understand it, and >'prove' that with perfect play for both sides, Chess is indeed a draw. > >Would you agree? No. 50 moves probably isn't enough to give a reasonable guess, but that's just my intuition -- it's not something which can be mathematically proved one way or the other. A 'proof' in scare quotes usually means no proof at all, and that's what it would be. Will computers eventually play better than the best humans -- i.e., be able to consistently win matches and tournaments against the top grandmasters? I feel it's inevitable, as search depth eventually will go high enough to compensate for the top humans' analysis and intuition. Will computers still make occasional blunders? Yeah -- but top grandmasters make blunders too. But, overall, the mantle of superiority in chess will eventually pass to computers. Will that mean that those chess computers will be smarter than humans? No, it will be jsut a demonstration that while using human intelligence to play chess is possible, brute calculation is better suited than intelligence to winning chess games. And when computers pass humans for good in chess, it won't mean that chess is solved -- but chess as a game is still solvable.
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