Steve, You mentioned three proofs relating to go... could you post the links to the papers?
> it makes no sense to ask if there is a mathematical proof > of anything related to humans. I didn't ask for a mathematical proof saying if a computer can beat a human. I asked in a roundabout way if this algorithm (or any known algorithm) has a proven complexity that is somehow tractable or useful to beat humans. Just by throwing human in does not mean you are out of the realms of math. What about statistics? The object of many statistical models is a group of people. So please don't say it makes no sense to ask about mathematical proofs of anything related to humans. A mathematical proof can have a result that affects humans. If it was proven tomorrow that there is a set of algorithms that can solve the game in poly time.. we could draw relevant conclusions with regards to beating a human being. Relating humans to math does not destroy the accuracy of the relation. whether or not computers can beat humans at go on a 19x19 board in a reasonable amount of time is unrelated to mathematics. Why? Let's say you can prove that the game is solvable so that black wins. Let's say that you can prove that it is solvable in linear time. You can then infer that we could build a machine to play the solved game and beat a human unconditionally. Why can't you use the math here to make a statement about beating humans?
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