Author: chandler yergin
Date: 18:47:23 01/12/05
Go up one level in this thread
On January 12, 2005 at 21:41:47, Michael Yee wrote: >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.) Refute the Mathmatics! I have Posted them... Otherwise.. Opinion doesn't count.
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