Author: Robert Hyatt
Date: 08:18:03 10/23/02
Go up one level in this thread
On October 23, 2002 at 04:01:37, Tony Werten wrote: >On October 22, 2002 at 23:25:36, Robert Hyatt wrote: > >>On October 22, 2002 at 22:45:44, stuart taylor wrote: >> >>>On October 22, 2002 at 16:21:40, Robert Hyatt wrote: >>> >>>>On October 22, 2002 at 14:53:21, stuart taylor wrote: >>>> >>>>>On October 22, 2002 at 11:40:40, Robert Hyatt wrote: >>>>> >>>>>>On October 22, 2002 at 01:13:43, Timothy J. Frohlick wrote: >>>>>> >>>>>>>Sandia Labs is just down the street from me on Kirtland Air Force Base. >>>>>>>I lived about 1 kilometer from the labs when I lived on base. This "Red >>>>>>>Storm" machine will do 40,000,000,000,000 operations per second. Put Fritz X >>>>>>>on that and smoke it. >>>>>>> >>>>>> >>>>>>Put fritz on that and it will use exactly one cpu. That machine is pure >>>>>>message-passing. >>>>> >>>>>If it would use all, I think it should solve chess. >>>> >>>>Chess is exponential. Even if it had 16,000 X 16,000 processors, it would not >>>>be anywhere near enough. >>> >>>I know that required speed would be extremely great. But there must be a limit >>>at which chess would actually be solved, even if impossible to arrange. >>> And with the application of enough intelligence, that amount of speed could be >>>reduced significantly to still get the playing strength to a level that will >>>never lose any game to any machine or man. >>> I'm not speaking about if it is possible to arrange that in existing levels of >>>hardware in a PC of today. >>>S.Taylor >>>> >> >>The math is not so hard. If we take the relatively low estimate of 2^168 total >>possible >>positions, which ignores repetition issues and the like, then alpha/beta needs >>to search >>roughly 2^84 positions. that turns into 10^25 nodes. If you search 1M nodes >>per second, >>you need 10^19 seconds. If you go 1B nodes per second, 10^16 seconds. One >>trillion nodes >>per second, 10^13 seconds. >> >>10^13 seconds is 318,000 years. A _long_ time. even at 1 trillion nodes per >>second, which >>is actually doable should someone like Hsu decide to build a new DB-3 machine... > >If the math is correct. Suppose the goal of chess was not to checkmate but to >get a pawn on e4. The amount of possible positions would be the same except that >it would be trivial to solve. > >Unfortunately we can only tell this when chess is actually solved. If somebody >finds the 42 ply winning sequence for white then we can say how much positions >had to be searched. > >Tony This is like the "decidability issue" in computing theory. If the answer to a question is yes or no, then one of the answers might be computable while the other is not. For example, your case above comes to mind. It might well be that there is a forced mate in 30 plies. And if there is, when we can search 30 plies deep we will see the mate and know the game is a win for that side. But if there is no forced mate for 80 plies, we will have to search 80 plies to prove that, and that is going to take a _long_ time. My "math" was based on the premise that we don't know the outcome and that we will probably have to search every last possible position, if it turns out that the game is not a forced win... > >> >> >>>> >>>>> >>>>>S.Taylor >>>>>> >>>>>> >>>>>>> >>>>>>>TJF >>>>>>> >>>>>>>On October 22, 2002 at 00:06:51, Sally Weltrop wrote: >>>>>>> >>>>>>>>http://www.theregister.co.uk/content/3/27718.html
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