Author: Louis Fagliano
Date: 09:07:49 01/20/05
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On January 20, 2005 at 10:51:26, chandler yergin wrote: >Solving chess >From Wlog >According to Wikipedia (http://en.wikipedia.org/wiki/Chess) number of legal >positions in chess is estimated to be between 1043 and 1050. Also 1040 positions >has been mentioned. Lets assume 1043 positions and 1000 atoms for each position >in parallel computer for analysing and storing position. > >How big would that computer be? Avogadro's number number is approximately 6.022 >× 1023 . Asteroid mass can be as big as 9.445×1020 kg >(http://en.wikipedia.org/wiki/1_Ceres). Lets assume that one Avogadro's number >worth of atoms from Ceres has mass of 30g. This gives 9.445×1020 × 1000 × 6.022 >× 1023 / 30 / 1043 = 1900 atoms for each position. > >A bit related humor (http://www.enweirdenment.org/cgi-bin/topbot?list00317). > >So if assumptions are true, then biggest asteroid should have enough material to >solve chess. > >http://mathworld.wolfram.com/Chess.html > >In a game of 40 moves, the number of possible board positions is at least 10120 >according to Peterson (1996). > >Rex Stout's fictional detective Nero Wolfe quotes the number of possible games >after ten moves as follows: "Wolfe grunted. One hundred and sixty-nine million, >five hundred and eighteen thousand, eight hundred and twenty-nine followed by >twenty-one ciphers. The number of ways the first ten moves, both sides, may be >played" (Stout 1983). To be precise, the number of distinct chess positions >after n moves for n = 1, 2, ... are 20, 400, 5362, 71852, 809896?, 9132484?, ... >(Schwarzkopf 1994, Sloane's A019319). The number of chess games that end in >exactly n moves (including games that mate in fewer than n plies) for n = 1, 2, >3, ... are 20, 400, 8902, 197742, 4897256, 120921506, 3284294545, ... (K. >Thompson, Sloane's A006494). > > Regardless of the 'exact' numbers & error factor; >the number of molecules in the observable Universe is dwarfed by the number of >possible moves in a chess game of 40 moves. > >For the Programmers who think the Game will or can be 'solved' by Computers, >I say you are naive, & delusional, living in self deception & denial, & >disconnected from reality. > >Get some professional help, or find a new hobby that is less stressful. Ah, but you are assuming 1000 atoms for each position. Suppose we can get it down to one atom for each position. Then you would only need an asteroid that is the cube root of 1000 or ten times smaller than Ceres or only 80 miles in diameter! Suppose we can get it down to one quark for each position! Then, assuming a quark is about 1.5 billion times smaller than an atom, (and what the heck, lets throw out the Heisenberg Uncertainty Principle, too) we would only need an asteroid about the size of the cube root of 1.5 x 10^9 or 1150 times smaller than an asteroid 80 miles in diameter or 80/1150 = 0.07 miles or 370 feet, the size of a football field!
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