Re: The Future of Chess and Getting It "Unstuck"

In article
<a7a5edf4-e50e-4fe5-a62c-2490c2bd1464@[EMAIL PROTECTED]
>,
Rich Hutnik  <richardhutnik@[EMAIL PROTECTED]
> wrote:
>On Apr 17, 10:16 am, David Richerby <dav...@[EMAIL PROTECTED]
>
>wrote:
>> My take on Goedel's incompleteness theorems is that almost all
>> invocations of them are made by people who are ignorant of what they
>> mean.

	[I think this is at least slightly unfair!  But no matter.]

>>	  For the record, they refer to the use of systems of deduction
>> to reason about themselves.  Since chess is not a system of deduction,
>> incompleteness is totally irrelevant.
>You mean individuals like Steven Hawkings and Freeman John Dyson don't
>know a thing about Godel's Incompleteness Theorem?

	I doubt whether David did mean that, tho' he will no doubt
answer for himself.  "Almost all" is different from "all".

	SH and FJD are, in your quotes, talking about TOEs of physics.
In that context, it is largely a matter of philosophy and convention
whether we should regard typical theorems/conjectures of pure maths
to be part of physics or not.  If you do, then a TOE is manifestly not
possible;  if you don't, then Goedel's Theorems are irrelevant to
physics, except as a warning that logical deduction is not as obvious
a process as was thought a century or so ago.

[...]
>If one considers math to be the "language of everything" and rules
>relate to math in this regard, and is the means by which a game
>functions as a contained system, to say that, "No Godel's
>Incompleteness Theorem has NOTHING to do with game rules in any way",

	Luckily, that is not what David said, nor what he implied, nor
what he could reasonably be deduced to have intended.

>is to totally deny that math has anything to do with games, game
>rules, etc...  It is a shallow conclusion used to shut up
>conversation, rather than consider that maybe there is some overlap.

	Of course there is some overlap.  For example, Conway's
"Game of Life" includes initial configurations that can be set up
to emulate a universal Turing machine together with an arbitrary
initial tape.  So every interesting result of computability and
complexity [and hence lots of theorems relating to logic] has an
immediate relation to a result in "Life".  Many other games have
similar properties, including generalised [unbounded] variants of
chess and go.

>And to conclude on this is to totally ignore the issues involved with
>chess itself, and whether or it can hit an ultimate state of being
>solved or not.

	Um.  Well, many infinite/unbounded games have "issues".
But standard chess, and every reasonably similar game, is finite,
and Goedel's Theorems really do not have anything to say about
such games.  Everything you may plausibly want to know about a
chess position can be answered by a quite simple search process
consisting of a few hundred lines of code, a few kilobytes of
storage, and a bog-standard PC which runs without error for a
sufficiency of time.  The limitations of that are physical, not
mathematical.  Whether those limitations can be overcome is an
interesting question, but nothing at all to do with Goedel.

	[There are arbitrarily long games of chess -- if neither
player exercises the right to claim a draw -- and indeed an
uncountable infinity of different games, but only finitely many
different positions, so only a finite amount of analysis is needed
to determine the game-theoretic value of any given position.]

-- 
Andy Walker
Nottingham