Author: Michael Yee
Date: 18:41:47 01/12/05
Go up one level in this thread
On January 12, 2005 at 21:36:05, chandler yergin wrote: >On January 12, 2005 at 21:28:02, Michael Yee wrote: >>On January 12, 2005 at 21:07:42, chandler yergin wrote: >>>On January 12, 2005 at 21:03:54, Michael Yee wrote: [snip] >>>>What you just said is correct since you're talking about the *tree* of moves. >>>>But Uri and Dann are talking about the *set* of unique positions (many of which >>>>can arise through different move orders). So you and they are talking about >>>>different (mathematical) objects--trees (or paths in a tree) and graphs (or >>>>nodes in a graph). >>>> >>>>By the way, just because some quantity is large (or infinite) doesn't mean you >>>>can't prove something about it mathematically. For instance, you can prove that >>>>a geometric series (e.g., 1/2 + 1/4 + 1/8 + ...) convergences to a number even >>>>though their are an infinite number of terms. >>>> >>>>Michael >>> >>> >>>Yeah.. ya can compute Pi to a Billion or so digits... >>>I round off at 3.1416... >>>Close enough for me.. >>>So What? >>> >>>Ur missing the point. >> >>Actually, I don't think I'm missing your point. What you seem to be saying is >>this: >> >>(1) There are approx 10^120 chess positions in the *tree* of moves >>(2) There aren't even that many atoms in the universe >>(3) Therefore, it's impossible to "mathematically prove" anything about chess >>(i.e., solve it) >> >>And these are my points: >> >>(1) For solving chess, you only need to consider unique positions >>(2) You can prove things about infinite sets of things without having to "touch" >>each item. For example, we can even stay with your move tree and consider a K >>and Q versus K ending. Ignoring the 50-move rule, there are infinitely many >>move-paths (in your model) starting from some root position. By your thinking (I >>think), it would be impossible to prove that K+Q is a win because you couldn't >>possibly deal with an infinite number of move paths. But I think you would agree >>that it's easily shown to be a win. > > >End Game Tablebases Prove it... of course... > >What was the Topic? >Solving.. the Game of Chess. >Try reading with comprehension, and stick to the subject! >Too complicated for ya?? > I know the topic is solving chess. My point was that your logic/argument applied to even a simpler subproblem of chess goes haywire (and thus must be flawed). (That is, if my summary of your points was accurate.)
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