Re: computer-go: Go and chaos theory

[Henrik Rydberg <rydberg@xxxxxxxxxxxxxx>]

Ray,

If you define 'sensitive' as an
exponentially increasing 'error' as a function of
time, number of moves or whatever, that is definitely
applicable to a finite system. Pushing this argument
"in limes" adds no new fundamental behaviour.

Moreover, it's one of the fundamental differences between
a chaotic system and a non-chaotic (or stable) system that 
in the chaotic system, two neighboring initial states
*diverge*, whereas in a stable system, they *converge*.
Luyapunov exponents measures precisely this property, and
are indeed possible to retrieve for any finite system.
For some systems, they are all negative, implying a stable
system, whereas in others, some of them are positive,
implying a chaotic behavior. Hence, there is definitely
no implication saying that if one system is sensitive in
the above meaning, all systems have to be.

Go definitely satisfies the fundamental aspects of chaos.

Henrik

-- 
Henrik Rydberg (http://fy.chalmers.se/~rydberg),
Department of Applied Physics, Chalmers University of Technology.