Author: Ricardo Gibert
Date: 15:48:10 01/16/05
Go up one level in this thread
On January 16, 2005 at 16:30:55, José Carlos wrote: >On January 16, 2005 at 09:19:03, Ricardo Gibert wrote: > >>On January 16, 2005 at 08:54:31, Mike Hood wrote: >> >>>On January 16, 2005 at 08:25:31, Ricardo Gibert wrote: >>> >>>>On January 16, 2005 at 08:09:14, Uri Blass wrote: >>>> >>>>>On January 16, 2005 at 07:34:01, Ricardo Gibert wrote: >>>>> >>>>>>On January 16, 2005 at 05:29:36, Uri Blass wrote: >>>>>> >>>>>>>On January 16, 2005 at 03:16:27, Bruce Moreland wrote: >>>>>>> >>>>>>>>To solve a game is to prove the result with best play for both sides. It's a >>>>>>>>term with precise meaning. >>>>>>> >>>>>>>What if there is no formal proof of the result with perfect play but every game >>>>>>>between top programs ends in a draw? >>>>>> >>>>>>It probably means that if a win exists, they cannot search deeply enough to find >>>>>>it. What else could it mean? I don't like the idea of trying to understand a >>>>>>problem with fanciful probabilies like this. It can be misleading. >>>>> >>>>>By the same logic you can say that maybe white does not win the following >>>>>position and black has a defence or even a win that programs cannot search deep >>>>>enough to see. >>>>> >>>>>[D]1nb1kbn1/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w - - 0 1 >>>>> >>>>> >>>>>> >>>>>>I used to think that calling chess a likely draw was a reasonable thing to say, >>>>>>but I've learned the hard way that the really right answer is to simply say we >>>>>>do not know. >>>>> >>>>>What about the more obvious assumption that white does not lose. >>>>> >>>>>I think that there are things that we can say that we know inspite of the fact >>>>>that we are unable to prove them. >>>> >>>>You want to say you *know* the above position to be a win for white, but why not >>>>simply say the truth? That you believe it to be a win even though you do not >>>>know it? Why the need to make a statement that is stronger than the one we are >>>>able to back up with the commensurate facts? >>>> >>> >>>Knowledge vs. Belief? >>> >>>We're wandering into the domain of metaphysics now :) >> >>Nothing metaphysical about it. He believes it to be a win, but does not know it, >>because he cannot prove it. It's as simple as that. > > But I think Uri's idea is interesting. I've thought about it also in the past. >It's pretty much like physics work. You observe, make a theory, try to refute it >by observation and experiment. If you fail to refute it, you accept it. So if a hundred years ago, if someone had proposed the moon were made of cheese and of course nobody could refute it, you would have accepted it? > It's not >the final and definitive truth, but in physics it has worked so well so far as >to allow us to talk about it in something called internet. > BTW, I personally think chess is not solvable because of the huge graph you >need to explore. For something bigger, check out the link I gave about the traveling salesman problem. For N cities, there are (N - 1)! possible paths. With N = 24978, 24977! = 3.87e98992 completely dwarfs the number of possible positions in chess. Finding an optimal solution for N = 24978 is truly mind boggling, but they did it. > > José C.
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