Re: Go rules and Spectral equivalence

[Henrik Rydberg <rydberg@xxxxxxxxxxxxxx>]

Mousheng,

I was so inspired by your discussion with Rich, so I decided
to put forward this thing, more as another thread in the very
exciting world of fundamental concepts we all struggle with
to make better Go programs, than as a comment on patterns.
I of course agree that patterns are useful, and as you two, 
discussing the fundamental models of solution to such problems,
is in my opinion what carries the goal forward.

I was thinking of continuum models of Go. Just as patterns help 
evaulating positions, suggesting
moves or more generally defining relations, a set of coupled
non-linear differential equations could do the job of measuring
the status of a particular board situation. But this would not be
meningful unless: 

a) One knew the equation was modelling some particular rule-set, 
   preferably Go :)

b) Equations (often) have (numerical) solutions, which then means
   a solution to some problem related to Go.

I don't have the slightest idea of how to transfer the rules of Go
onto a such a mathematical model, but I like to think about it. :)
Maybe patterns could be used for that purpose as well, I don't know.

Henrik