Author: Ingo Lindam
Date: 15:19:43 12/10/02
Go up one level in this thread
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 :-) ingo
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