[FOM] Checkers is a draw
joeshipman at aol.com
Sat Jul 28 13:14:20 EDT 2007
The context of my remark was establishing the power of takebacks. It is
a form of handicap which allows me to get a very clear idea of exactly
how strong a computer program is. My claim was that the same process
would allow a strong grandmaster to, by interacting with a "perfect"
player, form a justified conviction about the mathematical value of the
game (a draw in the case of checkers, probably a draw in the case of
chess if a perfect player is ever developed or encountered).
The reason I think that this is possible is that a strong grandmaster
is probably within a few hundred rating points of "perfect", and I
think the power of takebacks is at least this large based on my own
experiences with very stong programs.
The metamathematical point I am ultimately making here is that the kind
of certainty so attained ought to count as "knowledge" even though it
is obtained neither by a formal mathematical proof, nor by an
"interactive proof" of the kind recognized by computation theorists
(Adi Shamir showed that PSPACE is the set of languages recognizable by
this type of interactive proof).
This kind of certainty could only be obtained by someone of grandmaster
strength, but exactly the same epistemological situation occurs for the
game-theoretically easier question of whether Black wins the intial
position of chess if you remove White's Queen Knight. Any reasonably
good chessplayer KNOWS this to be true, but there is no hope of a
If you are only a weak chessplayer, you still probably have enough
experience to "know" that removing White's Queen from the initial
position ensures a Black win (in this case, a mathematical proof is
conceivable within a decade or two making reasonable assumptions about
the development of computers, but the knowledge of chessplayers
concerning this fact would not be made much more certain by such a
From: Randall R Schulz <rschulz at sonic.net>
On Thursday 26 July 2007 08:30, joeshipman at aol.com wrote:
> I have a master's rating, and I own several Grandmaster-level chess
> engines. I rarely beat them when playing "straight", but I find it
> quite easy to beat any of them when I am allowed to use the "move
> takeback" option repeatedly.
Well, that's not chess as its rules define it, is it? It's chess with
time-travel into one's own past (while carrying back information from
the future, of course). It really tells us nothing about you or
these "engines," does it?
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