Author: J. Wesley Cleveland
Date: 09:47:20 12/12/02
Go up one level in this thread
On December 11, 2002 at 16:46:21, Dann Corbit wrote: >On December 11, 2002 at 15:04:41, J. Wesley Cleveland wrote: > >>On December 10, 2002 at 18:28:08, Dann Corbit wrote: >> >>>On December 10, 2002 at 18:24:20, Uri Blass 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 ;-)] >>>> >>>>Most of the legal positions are irrelvant for solving chess because they can >>>>happen only after both sides play illogical moves. >>> >>>They are still fully relevant. You might throw away your queen and both rooks >>>and still win (in fact, it has been done). >>> >>>>I do not know the number of legal positions but I know no proof that there are >>>>more than 10^40 and I know no proof that the relevant legal positions to solve >>>>chess are more than 10^20 >>>> >>>>positions like 1.a4 a6 may be irrelevant to solve chess if you find that 1.a4 is >>>>losing against 1...e5 when 1.e4 is not losing. >>> >>>In order to prove that they are irrelevant, you will have to solve the tree. In >>>order to solve the tree you will have to compute and store it. >> >>Except he does not have to prove that they are irrelevant, you have to prove >>they are relevant. > >If he has not disproven them, then he has not demonstrated his point of a >suggested outcome. Either I am not communicating clearly or you do not >understand what I have said. You are the one that said you could prove that chess was not currently solvable, which means others can speculate and you have to prove them wrong. > >>>>in that case knowing the theoretic result after 1.a4 a6 is going to change >>>>nothing. >>>> >>>>Tree is only one way to prove things. >>>> >>>>It is possible to prove that KQ vs K without the 50 move rule win in n*n chess >>>>board for every dimension n. >>> >>>Believe it or not, you form a tree to solve it. You might have an alternate >>>formulation, but a tree solution will be perfectly equivalent and optimal. >> >>You are wrong here. You can prove by induction that KQ vs K is mate on a >>chessbord that is e.g. 10^17 by 10^17, while the tree is roughly the same size >>as the tree of chess. > >How many moves will the induction contain? > >The same as the tree. The proof takes only a few steps. Define king confined in a rectangle n,m as queen on square n+1,m+1, king in the rectangle not adjacent to the queen, and opposing king outside the rectangle n+1,m+1. Prove if the king is confined in a rectangle of 3,1 or 3,2, it is checkmate. Prove if the king is confined in a rectangle of n,1, you can force it to be confined in a rectangle of n-1,1. Prove if the king is confined in a rectangle of n,m, you can force it to be confined in a rectangle of n-1,m or n,m-1. Prove that you can confine the king in a rectangle. QED.
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