Author: Uri Blass
Date: 16:46:44 12/10/02
Go up one level in this thread
On December 10, 2002 at 18:31:38, Dann Corbit wrote: >On December 10, 2002 at 18:19:43, Ingo Lindam wrote: > >>On December 10, 2002 at 18:12:53, Dann Corbit wrote: >> >>>On December 10, 2002 at 17:55:51, Dann Corbit wrote: >>> >>>>On December 10, 2002 at 17:51:40, Ingo Lindam wrote: >>>> >>>>>On December 10, 2002 at 17:30:47, Dann Corbit wrote: >>>>> >>>>>>On December 10, 2002 at 13:42:36, Bernardo Wesler wrote: >>>>>>[snip] >>>>>>>THE ALGORITHM. A MATHEMATICAL FORMULA THAT , FOR EXAMPLE, ASSURE YOU THAT IF YOU >>>>>>>DO THE FIRST MOVE YOU ALWAYS WIN. >>>>>>>I MEAN TO THINK ABOUT DISCOVERING A CHESS ALGORITHM IS AN UTHOPY? >>>>>> >>>>>>Provably impossible on current hardware and software systems. >>>>>>Maybe in 100 years the game will be formally solved. Not in the near futre. >>>>> >>>>>provably impossible on current hardware...? >>>>>are you sure? >>>> >>>>Absolutely sure. >>>> >>>>To solve chess you must store at least the square root of nodes of the solution >>>>tree. Considering the half move clock and castle rights, it easily exhausts any >>>>possibility of solution. >>>> >>>>>without assuming anything about the kind of solution? >>>> >>>>No assumptions are necessary. We pick an adversary in the tree. It's just like >>>>how you would prove a sort works in O(f(n)). >>>> >>>>>atleast you are assuming the use of hardware... >>>>>(an assumtion I could live with because I wouldn't bet on find the solution >>>>>faster by using just a pencil and a sheet of paper :-)) >>>> >>>>I am assuming that if you turned the universe into silicon chips and devoted >>>>half of them to CPU's and the other half to memory storage that all the stars >>>>will go out before you find the answer. >>>> >>>>>me would like to see the proof for 'provably impossible' as much as I would like >>>>>to see the solution for chess >>> >>>10^48 formations * 100 states for half-move clock * 4 bits for castle state. >>>sqrt(1.5e+51) = 38729833462074168851792654 [64 moles of positions ;-)] >>> >>>Assume that you can access one position in one nanosecond -- better yet, we will >>>assume that we can correctly compute the value in one nanosecond, access the >>>relevant parts and save the result in one nanosecond. We will assume that our >>>algorithm is totally optimal and move ordering is perfect so that we can achieve >>>the square root of the tree factor. >>> >>>It would take 38729833462074169 seconds to fill the tree. That is 448261961366 >>>days and 1,228,114,962 years. >>> >>>This is an incredibly conservative estimate. It would probably take at least >>>one thousand times that long. >> >>yes, >>this IS an incredible conservative estimate of SOMETHING... >>BUT NOT... >>of the size/time of a proof/solution. >> >>the esitmation has completely nothing to do >>with the question whether chess is solvable in general or not... >> >>just try to get the point :-) > >Happy solving fellows. Don't say I didn't warn you. I do not believe that it is possible to solve it with the hardware of today so I am not going to try. It is not a proof that it is impossible to solve it. Uri
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