Author: Dann Corbit
Date: 16:54:14 01/12/05
Go up one level in this thread
On January 12, 2005 at 19:27:05, chandler yergin wrote: >On January 12, 2005 at 19:11:12, Dann Corbit wrote: > >>On January 12, 2005 at 19:04:31, chandler yergin wrote: >> >>>So says Mark Twain.... >>> >>>You Programmers are spreading lies, misinformation, & disinformation. >>> >>>However I should not attribute to Malice, what can be explained by Ignorance! >>> >>>Computers will NEVER SOLVE CHESS! >>>Stop your Nonsense! >> >>If man were meant to fly, he'd have wings. >>Man will never fly faster than sound. >>Man will never go to the moon. >> >>Things that seem impossible quickly become possible. >> >>In this particular case, it is even obvious mathematically how it will come >>about. > >If you understood Mathmatics, you wouldn't say that! > >It IS Obvious, that it's an Impossibility! > >The Question of "whether or not God exists" is a Philosophical & Meataphysical >Question. >Would you agree? > >Some say.. "It can't be Proven". >With a Philosophical Question, there are NO 'right or wrong' answers... > >With Mathmatics, there ARE 'right & wrong' answers. > >Your perception is in error! > >THINK! > >"In a tree, from the Starting Position, there are 20 possible moves for white. >There are 20 * 20 = 400 possible moves for black, depending on what white does. >Then there are 400 * 20 = 8,000 for white. Then there are 8,000 * 20 = 160,000 >for black, and so on. If you were to fully develop the entire tree for all >possible chess moves, the total number of board positions is about >1,000,000,000,000,000,000,000,000, >000,000,000,000,000,000,000,000,000,000,000,000,000,000, >000,000,000,000,000,000,000,000,000,000,000,000,000,000, >000,000,000,000, or 10^120, give or take a few. That's a very big number. For >example, there have only been 10^26 nanoseconds since the Big Bang. There are >thought to be only 10^75 atoms in the entire universe. When you consider that >the Milky Way galaxy contains billions of suns, and there are billions of >galaxies, you can see that that's a whole lot of atoms. That number is dwarfed >by the number of possible chess moves. Chess is a pretty intricate game!" > >NOW, Do you want to "Disprove" this... >OR, >Re-think your position? > >HMMMMM? >Stop the Nonsense! You do not have to calculate all the games. You only have to calculate all the positions. There are about 10^43 of them: http://mathworld.wolfram.com/Chess.html KD has encoded chess positions into 162 bits, which gives an absolute upper maximum on the number of board positions as: 2^162 = 5846006549323611672814739330865132078623730171904 possible positions. (about 5.846e48) So, if we take that figure, then we would need a tree of sqrt(5.846e48) = 2417851639229258349412352 positions (which is less than one mole of them) to store a complete solution tree. This was proven by Knuth in 1972. There are some other things that the programmer would have to track (hmc and 3-way repeat, for instance) but that is trivial. My brother in law's father has a patent on a storage medium that will hold a terrabyte per square centimeter. So the storage for such a collection is already nearly possible. That would require 2417851639229 square centimeters, which is 241785163 square meters = 241 square kilometers. Since there are 230.4 acres per square kilometer, that means we would need a mere 55,430 acres of the stuff. If someone were to invest a few billion dollars, we could do it today. But we may as well wait 40 years, in which time it will cost a few pennies to do it.
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