X-Message-Number: 223 From att!la.tis.com!fermat!r Wed Sep 12 21:12:01 1990 Return-Path: <att!la.tis.com!fermat!r> Received: from att.UUCP by whscad1.att.uucp (4.1/SMI-3.2) id AA01834; Wed, 12 Sep 90 21:12:00 EDT Received: by att.att.com; Wed Sep 12 18:52:25 1990 Received: by la.tis.com (4.1/SMI-DDN) id AA06345; Wed, 12 Sep 90 15:51:20 PDT Received: by rhmr.com (3.2/SMI-3.2) id AA16072; Wed, 12 Sep 90 15:31:40 PDT Date: Wed, 12 Sep 90 15:31:40 PDT From: fermat! (Richard Schroeppel) Message-Id: <> To: Subject: re: cryonics #222, chess You wrote > To understand why that may be, recall that the > game of chess theoretically can be solved > completely, but the combinatorial explosion in > the game tree renders a complete solution > impractical (within the anticipated lifetime > of this universe anyway). The number of possible chess positions is only around 10^40. The number of possible games has been estimated at 10^120. (Since there are many different ways of going between the various positions.) To actually solve chess, and prove the solution, only requires knowing the value of about 10^20 critical positions. (Most of the 10^40 possible positions are very unbalanced, with one side or the other clearly winning.) We routinely hear of computations that take 10^16 instructions: The recent factoring of F9 was estimated at ~100 computer years (distributed over a few hundred workstations); a 3Mips machine will execute 10^14 instructions/year. A 1Gips Cray would execute 10^16.5 ins/year. There is enough computer power already existing to solve chess in a decade or so. (Assumptions: Current capacity is 10^22 ins/year; 1000 instructions to process a position.) Of course, chess isn't an important enough problem to absorb all our computer resources. But our computers continue to get better every year. I suspect we will see chess solved long before we see anyone revived; say in 25 years. With any luck, the current universe should last that long. On the other hand, GO looks hard. (Picky, picky, picky ...) Rich Schroeppel [ Rich, thanks for the enlightening figures. The next time I need an example of an exceptionally combinatorially difficult problem, I will choose something other than chess. By the way, how hard is GO? ... - KQB ] Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=223