From: hau4@ellis.uchicago.edu (sven  hauptfeld)
Newsgroups: rec.games.chess
Subject: Re: Chess Solvability is a true but meaningless statement
Date: 26 Sep 92 08:32:54 GMT
Reply-To: hau4@midway.uchicago.edu
Organization: University of Chicago Computing Organizations

In article <1992Sep26.054541.15992@stsci.edu> gilmozzi@stsci.edu (Roberto Gilmozzi) writes:
>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?

Summary of my response: what you say is very good, but you missed a few things.

>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...

I have considered this analogy, too. But it falls short. Even under (of
course wrong) assumption that classical mechanics is *the* truth, and that
initial conditions can be known, the universe would still not be solvable.

This is because in mechanics we deal with continuous quantities, i.e. with
real numbers. Thus, initial conditions cannot, even in principle, be known
exactly, but only to a certain approximation. (I am assuming that you can, 
*in principle*, store any finite, however huge, information, like all chess 
positions or a list of all atoms in a 'classical mechanical universe', but 
you cannot, even in principle, store *infinite* information, like all digits
of an irrational number, e.g. pi.) But the equations are sensitive to small
perturbations in initial conditions, and if enough time is allowed, two
universes with slightly different initial conditions will look sufficiently
different.

Chess, as a finite system with discrete (i.e. integer) states, doesn't suffer
from such problems.
 
>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. 

This is a common misconception, even among physicists, that quantum mechanics
is somehow "less solvable" than classical mechanics. The truth is, it is less
solvable in variables of classical mechanics (position and momentum); however,
classical mechanics is not solvable at all in quantum mechanical objects 
(state vector or wave function), so by consistent pursuit of this reasoning
we should conclude that classical mechanics is less solvable. Of course, in
their own objects, both are perfectly solvable.

>                                 (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...).

This is a great overestimate of the number of positions, especially legal
ones. A recent thread on that issue settled somewhere around the order 10^21,
if my memory serves me well. And there are classes of positions that are
trivially equivalent (like all positions without sufficient mating material,
all positions with an impenetrable wall of pawns separating the two sides...)
and you don't have to store all positions at all times,... so I'd be more
cautious about feasibility of this project. I know I won't live long enough
to see chess solved (my doctors agree that I'll be dead by mid-21th century :-)
but who can say what the computers of 25th century will be like (provided we
don't destroy ourselves in the meantime)...

>So, solvability of chess enters the category of statements which are
>true but meaningless [had i wings, i could fly -- maybe ;-) ].

This is going too far. 

>Conclusion: attach an electronic piano to a computer and you will have
>flawless renditions of any piece ever written.

Gee, no electronic piano can still match a 'real' one. And it is absolutely
sure that computers will need a much longer time to compete with best human
pianists than with best human chess players.


Again, I generally liked your posting. The points I argued against are
certainly minor.

	Sven