Author: Robin Smith
Date: 12:09:28 01/12/01
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On January 11, 2001 at 21:41:45, Dann Corbit wrote: >When we are talking about qualities I agree with you. When we are talking about >PROOFS mathematics is THE ONLY WAY to accomplish that. Dan, I agree with many of the arguments you have been making in this thread, but in some cases it seems you go way over board. For example, the above is a rather extreme statement, don't you think? In a US criminal court of law, there is the concept of "proof beyond a reasonable doubt", and yet I doubt there are very many arguments that lawyers make which would be classified as mathematical proofs. I agree that a mathematical proof is the most formal and rigorous kind of proof, but it is certainly not "THE ONLY WAY" to prove something. Clearly the definition of "proof" that the lawyers had in mind is not the same definition of "proof" that you are using. Different people have different ideas of what constitutes proof. Yours is a mathematical definition, but that does not mean other definitions are invalid, just different. Mathematical proofs may be the least prone to error, but that does not make them the "only way", nor does it make them infallible. Even mathematical proofs are sometimes wrong. Also, if you want 100% mathematical certainty, a mathematical/statistically based argument can NEVER "prove" that someone is of "GM strength", even if they win 100% of the games they play against GM's and they play hundreds of games. The uncertainty in the claim that they are GM strength becomes very, very small .... but it never goes to zero. Mathematically there will always be a small, but non-zero, chance that they were very, very "lucky". Right now we can already say, statistically, Rebel IS GM strength. It is just the uncertainty in the validity of that statement that is still quite large. As more games are played and the uncertainty goes down, we will have more confidence that the assertion is true (or not, as subsequent data suggests). There is no magic number of games at which point we have suddenly "proved mathematically" that computers are (or are not) GM strength. Robin Smith
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