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

On Apr 17, 6:59 pm, a...@[EMAIL PROTECTED]
 (Andy Walker) wrote:

>         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.

Godel's Incompleteness Theorem says that there are true statements in
a mathematical system that cannot be proved from within that
mathematical system.

Since trying to prove mathematical systems from within themselves
requires clumsy machinery like Godel-numbering, at first some
mathematicians wondered if Godel's theorem was even relevant to
mathematics. But now that people use computers to do algebra, and not
just arithmetic, its significance becomes clearer.

Since physics uses mathematics - mathematics can predict the behavior
of physical systems, and physical systems can calculate mathematical
functions or otherwise do mathematics - statements about mathematics
can impinge on the physical world.

Chess, too, can be played mathematically - in a sense, any computer
chess program does exactly that.

Godel's theorem might impinge on chess by making unavailable some
infinite mathematical theorem that would be a simpler way to make a
statement about chess than a calculation applying only to one finite
form of chess. So even if it could not affect our _possible_ knowledge
about a finite game, it could affect the knowledge that is
_conveniently_ available about it.

(sci.math pulled back in: it will take people from there to comment on
this one!)

John Savard