Re: the Mathematics of Chess

T.H. Ray wrote:
[snip]

As I said, your reputation is unassailable by me and
requires no defense from you. I haven't misunderstood
you, however--you have been clear that you consider the
algorithmic limit to be the limit of mathematical
modeling. I respectfully disagree.

Feel free to. I only object about the generality of your statement:

Indeed, chess is related to mathematics in the same
way that music is.

For Chess, there is a well-defined (and finite) set of rules which have a
one-to-one correspondence with mathematical rules, the totality of which
ultimately translates into finite machine states, which are dealt with, with the
specific implementation called a "chess engine". For any chess board position
you give me, I can give you a "best move" candidate.

I am not denying that "music" (however you want to define it) can be "modeled"
using mathematics. ANYTHING can be modeled using mathematics. Even your and my
brain. Your thoughts and my thoughts are just sequences of binary numbers, upon
neurons firing. The entire universe is just streams of number sequences.

However, such "models" are impractical at best, tenuous at worst. It is one
thing to reduce/model "music" to wave pulses or dominant harmonics, and another
to try to construct a deterministic algorithm which "composes" good music,
similar to a Chess program which always picks a best move.

The difference I am trying to outline is that algorithmic complexity is a fairly
good indicator of the _practicality_ of creating a viable mathematical model for
various endeavours.

Heck, composers exist. By virtue of them being able to compose good music, one
deduces that deterministic algorithms do indeed exist, since the thought
processes of the composer's mind are indeed sequences of numbers.

In other words, your statement, although tenuously true, lacks a very important
qualification, which lingers in the limit and distinguishes what's is practical
and what's not.

Let's see if you like the following:

"Both Chess and music can be modeled using mathematics, but the former can be
_practically_ realized, whereas the latter cannot".

Do you object to that? I mean, if you do not consider algorithmic complexity to
be a reasonable mathematical modeling limit, can you propose a different limit
for a viable/practical mathematical model for music? And if you can, where do
you draw the line?
--
I.N. Galidakis

.

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