On Fri, 2007-01-12 at 15:43 -0600, Nick Apperson wrote: > yeah, there are upper limits placed on computation rate by > thermodynamics. 19x19 is way beyond those as Dave pointed out. But, > even if you believe that technology will improve and the most > revolutionary change yet will come to understanding of physics and > that change will give us signifigantly more computational power and > time etc... You can always make a bigger board. If life comes to a > point where go could be solved for any size board, you will no longer > be in this world and solving things such as "is go solvable?" will > have no meaning.
Yes, you can always make a bigger problem by making a bigger go board but that doesn't change the theoretical properties of the game. The game will always be solvable. The game might be trivially solvable even now to a being not confined to our 3 physical dimensions. I hate to get philosophical like this, but there are theories of other dimensions that (if true) say we live in a multi-dimensional universe. There may be much more here than we can sense and that we can perhaps take advantage of. But it doesn't matter. When Chris said 1 billion years you should have instantly realized that he didn't mean this literally, he just meant a correct procedure exists for solving the game. Since no one has proved how long the universe will last, I don't think you can even prove that in a practical sense it's unsolvable. If you lack imagination you can simply say it's not solvable because you believe it can't be done in your lifetime - as if science and math cares about how long we live or even the universe. If the universe will die in 10 trillion years does that mean the number 20 trillion is an impossible number? The concept of infinity is important in mathematics. It's even useful, but I suppose that it really should be considered meaningless since we all die after 70 or 80 years. - Don _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
