Author: Roger D Davis
Date: 00:43:21 01/13/05
Go up one level in this thread
On January 13, 2005 at 00:41:05, chandler yergin wrote: >On January 12, 2005 at 21:56:52, Jason Kent wrote: > >>On January 12, 2005 at 21:47:23, chandler yergin wrote: >> >>>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 > >YOU GOT IT! >Thank You! > > There are, however, more numbers than there are atoms---infinitely more---and yet we have many proofs about numbers. Roger
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