From: gilmozzi@stsci.edu (Roberto Gilmozzi)
Subject: Chess Solvability is a true but meaningless statement
Originator: gilmozzi@lucifer.stsci.edu
Organization: Space Telescope Science Institute
Date: Sat, 26 Sep 1992 05:45:41 GMT

Summary (for the wary reader): A parallel with classical mechanics.
Unmanageability of great numbers (in physics as well as in game
solving). Pruning not allowed for final solution. Solvability is a true
but meaningless statement. Final conclusion: who cares?

This thread about chess solvability reminds me of a similar diatribe
going on during the golden age of determinism in classical physics: it
was believed that it would be possible, IN PRINCIPLE, to write down a
complete set of equations describing every and each particle in the
universe.  Together with an equal number of boundary conditions one
would have then "solved" the universe...  Of course everybody realized
that in practice this was pure gibberish (considering only the dynamical
aspect of the problem you need to write about 10^80 equations and 10^80
boundary conditions, THEN if you need to predict the state of the
universe at epoch T you would have to solve simultaneously _all_ of
them!).  For this reason they invented thermodynamics, which deals with
"moles" (chunks of 10^23 particles or so) and predicts their behaviour
in a statistical sense only.  But the point is that eighteen century
physicists thought that in principle the universe was solvable...  until
(enter quantum mechanics and relativity and Heisenberg principle etc)
even the principle got thrown away. 

I am not saying chess is not solvable: the proof is trivial and --
unlike classical mechanics which is an earlier set of deterministic
rules _invented_ to describe the universe and which proved not to be
adequate (nor indeed deterministic at all) -- the rules of chess are a
given of the problem.  What remains is that the task is unmanageable
from the practical point of view (try to store a complete board position
in each hydrogen atom by playing with its excitation states and you
still do not have enough memory available in the entire universe, let
alone the problem of sending a packet of information to some atom 10
billion light years distant...).  And i am afraid pruning algorithms are
not allowed to solve the game (by definition of solvability you must try
out every and each branch: i can imagine the supercomputer declaring
after 1.Na3!!, "mate in 178 moves" and some epigon of Kasparov finding a
line apparently so far from "best" play that it was discarded by the
"decision" routine as an obvious early win for white but that, after you
give up Q,R,R,B,B,N,N and 5 pawns ends in a forced stalemate at move
92...)

So, solvability of chess enters the category of statements which are
true but meaningless [had i wings, i could fly -- maybe ;-) ].  This is
not to say that a powerful computer, with a strong pruning algorithm and
fast enough to "see" 10 or 15 plies ahead, cannot become stronger than
humans at chess.  But this has nothing whatsoever to do with the
solvability problem, nor with the way humans "solve" each and every
game: intuition, feeling, experience, the pleasing aestethics of some
moves and very, very few look-ahead "computations"... 

Conclusion: attach an electronic piano to a computer and you will have
flawless renditions of any piece ever written. Does it prevent you from
trying to play it? Even if your version is nowhere near that level of
"perfection"? Do you indeed care?

Roberto