Author: José Carlos
Date: 16:54:55 01/16/05
Go up one level in this thread
On January 16, 2005 at 18:48:10, Ricardo Gibert wrote: >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? Of course not. You miss a part of the scientific method I summarized: experiment. No experiment was possible to prove/refute the statment you proposed, so it's not relevant. But think carefully about science: it's all made of induction. Deductive reasoning is a tool to "prove" induction. For example: hypotesis: "light is made of particles" -> deduction: it must remove electrons in an specific rate -> experiment: electromagnetic effect -> it works! -> hypotesis not refuted, it passed the test so far. >> 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. I had a quick look. I see no explanation of the algorithm. If I don't see the algorithm, I hardly can believe they found a perfect solution for so many cities. I've seen impressive programs that "solve" that problem using genetic algorithms, but those solutions are not optimal, only "good enough" according to some criterium. Then again, I don't know if there exists a method to solve chess, but I can't imagine it. Exploring the whole graph (well, the relevant part if a mate is found) is the only way I can think of, and that's not doable IMO. José C.
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