From: hau4@ellis.uchicago.edu (sven  hauptfeld)
Subject: Re: Chess is not solvable
Reply-To: hau4@midway.uchicago.edu
Organization: University of Chicago Computing Organizations
Date: Sat, 26 Sep 1992 05:39:01 GMT

In article <gekeYe_2ATvu4hZUcE@pitt.edu> Teri A Meyers <tasst2+@pitt.edu> writes:
>
>In article 6997 Sven Hauptfeld chides me for my perspective as follows:
>
>Me: "Here are my thoughts on the matter, which come more from philosophy
>    than game theory".
>
>Him: "Game theory also comes from philosophy, but one that works."
>
>Me:  "I operate on the assumption that from the initial position neither
>     side can force a win."
>
>Him: "No, no!  That's not called philosophy, that's called religion.  And
>     what you call 'assumption' is called a dogma.  Philosophy must start
>     from much more general, abstract assumptions."
>
>Obviously, Sven has a very particular version of philosophy in mind here;
>certainly anyone versed in the history of philosophy will know that there
>are many other ways to approach it than deduction from abstract principles.

"Deduction from abstract principles" is quite different from what I said.
Anyway, starting from such a particular and arbitrary statement as "starting
position is a draw" is certainly contrary to the spirit of philosophy, math
or science.

>  All I wish to do in
>working from the assumption that the initial position is dynamically
>balanced (a "draw" to those who wish to assign a discrete value to my
>concept of 'dynamic balance'), is to begin my chess philosophizing from
>an experiential starting point (drawing on my background as a chess master),

You failed. There is no experimental evidence that the initial position is
ballanced, on the contrary, tournament results favor white by almost 6-4,
so from the experimental point of view (of which I am far more qualified to
speak than of the philosophical), the assumption you based your whole
philosophy on has a very high likelihood of being false.

BTW, one doesn't have to be a master to see that the initial position is only
*statically* ballanced, while *dynamically* white is a tempo up.

>then one can also point to certain absurdities that a purely deductive
>approach can lead one to; in this instance, the idea that the initial
>position in chess may turn out to be a win for Black.

The theorem around which this discussion developed says *nothing* of the kind.
It says that possibilities *other than* forced win for white, forced draw and
forced win for black (in other words, the infamous 'undeternined value' 
positions, which keep popping out in so many postings) are *not* possible.

>  Logically this is
>true, but experientially it is a canard.

I've just shown that this is irrelevant, but even 'experimentally' it is well
justified. Many games of the same class actually favor black. While this is
highly unlikely to be true for chess, that is just a particular example.

>"Your dogma might well be shown true (I bet it is!), but it must be shown,
>not postulated",
>
>then how will the game theorist account for it?  He can only say 'that's
>just how it turned out,' or something of the sort.  For him, it must be
>shown (empirically, I suppose, since Sven says not postulated); experience
>cannot count because it might be an illusion.

This is nonsense. Postulated means 'not derived'. There is no dogma in game
theory nor is there a 'postulate' that chess is solvable. It is a theorem, 
i.e. it is derived from more general statements. (Yes, eventually it is 
derived from postulates. But not postulates like "initial position is
ballanced" but those like "one is greather than zero". See the difference?)

>I am not saying that the game theory approach to chess is not useful or
>valid, I only wish to claim it is not the only useful and valid approach.

For the issues it addresses, it is. If you disagree, don't bug me, but 
construct a concurring theory. (Friendly advice: don't try.)

>Also, I disagree with some of its conclusions.  I agree there are a finite
>number of legal positions.  I disagree with the claim that a list of these
>positions constitutes a solution to chess.  Two people responded to this:

You are really obnoxious. This is not a 'conclusion' of the game theory, nor
has anybody stated anything like that in this discussion.

>Sven wrote "All positions are either a completed win for one side (ie. mate)
>or draw by rules or on a path leading to one of the previous cases.  Therefore
>a complete list of positions AND transitions (moves) from one position to 
>another already contains all evaluation information."   Well, a list of all
>games possible from the initial position will contain wins, losses, and draws.
>In order to separate the wheat from the chaff, you will have to make use of
>some type of evaluation process not contained in your list.

You only need 'evaluation' if you are not certain of the outcome. If you have
a graph of all paths among all positions, you can trivially evaluate every
path by inspection - does it end in 1, 1/2 or 0?

>but unless the
>machine can tell us everything there is to know about all the immortal
>games of chess it will not have "solved" chess in any complete sense.

First of all, you seem to impose an entirely different definition of "solved"
than the one being discussed (which had been clearly stated), which makes
your argument invalid. But even so, we *would* know everything there is to
know about all immortal games (as well as about not-so-immortal ones), i.e.
we would know exactly which moves were mistakes and which were exceptionally
good.

>Suppose (at the end of time) it finishes its analyses and tells us, Chess
>is a draw.  Would that be the 'solution'?  It would certainly answer the
>game theorist's question whether it is a win for white, black, or draw.
>For myself and those like me who want to know something about that 
>beautiful little world that stirs our emotions, it would be pale comfort.

What is your point? Let me use a loose - but illustrative - analogy: I *know*
that I'll die. Therefore, the final result of my life is 'solved'. Does that
make my life any less interesting?

	Sven

Xref: sparky rec.games.chess:8317 sci.math:12453