FOM: chess contest
Harvey Friedman
friedman at math.ohio-state.edu
Thu Mar 19 22:00:04 EST 1998
Shipman 11:43PM 3/19/98 writes:
>Harvey, I would not regard the intuition that the initial position is a
>draw as
>anything close to either a chess "theorem" or a chess "axiom". However, the
>intuition of a Grandmaster about White's winning when Black's Queen is removed
>is strongly justified in a technical sense--any GM (indeed any master) could
>win this every time within 200 moves against all of the world's computers and
>GMs collectively ... Further, the winning
>technique can be explained in terms of chess strategy. If you are willing to
>accept as "axioms" statements that certain chess advantages suffice to win,
>then everything from there on is just like math.
Firstly, what do you think of the statement "the original chess position is
a win when black removes his queen" is not decidable
in ZFC using at most 2^100 symbols, even if ZFC is augmented in standard
ways to support abbreviations (which is required in order to make ZFC
capable of actual formalization)? I think it would be interesting to try to
give an upper bound on the number of symbols needed in ZFC with
abbreviations, to prove the original chess position is a win when black
removes his queen. In fact, it would be interesting to give an upper bound
on the number of symbols needed in ZFC with abbreviations to prove the
original position is a draw assuming that it is a draw; or needed to decide
the game value of any given chess position.
Naturally, the best one can expect to do with this now is to relate such
bounds to a bound on the size of the game tree from these initial
positions, or any given position, where the size of the game tree is
measured in some appropriate way for this kind of problem.
Do the upper bounds that one can get differ by much between the full
initial chess position and the initial chess position without black's
queen? Or the sizes of the game trees? Even here one might have the
frustrating situation that one cannot even get a substantial difference in
this kind of theory between the two cases!
Secondly, how are you going to give some interesting "axioms" of this kind
in order to prove that the initial position is a win with black's queen
removed? Of course, if you assume that under certain conditions if you are
a queen ahead, then it is immediate. Can you give an interesting sufficient
condition for winning if you are a queen ahead that you believe in?
Thirdly, let me state a contest. The winner is one who has a proof,
possibly computer-aided, that white has a win in the initial position where
black removes a number of pawns and/or pieces (not the king!), where the
total value of the removed items is smallest. Here pawns = 1, knights =
bishops = 3, rooks = 5, queen = 9. This should lead to some interesting
developments.
>On Thu, 19 Mar 1998 22:24:20 +0100, Harvey Friedman wrote:
>| The chess professionals are not turning these conjectures into chess
>| theorems merely by playing (even absolutely) correct moves against
>| particular defenses, unless you mean something unusual by "chess theorems."
Cabillon 1:45AM 3/20/98 writes:
>"chess theorems" = "winning positions".
Earlier, Cabillon wrote:
>These professionals are capable of showing
>how these conjectures can be turned into chess theorems just
>actually playing the proper moves against any defense chosen.
Under your definition of chess theorems, you are asserting that "these
chess professionals are capable of showing how these chess conjectures can
be turned into winning positions by playing the proper moves against any
defense chosen." But this doesn't make any sense to me.
I know that I may be wasting your time with word games here. But there may
be a point in talking this through. I don't quite know how you want to
describe what the chess professionals are doing when they play chess.
>Incidentally, "the original chess position is a draw" is not a "plausible
>conjecture".
Not **plausible**? Why not? I do understand why it is not "obvious."
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