Re: computer-go: Go and chaos theory

[Avijit Ghosh <aghosh@xxxxxxxxxxxxxxxxx>]

On Tue, 26 Oct 1999, Ray Easton wrote:
> > - it just says that the state one arrives at after
> > some interval (be it real time, number moves, whatever) is highly dependent on
> > the initial state down to it's final detail.
> 
> Then, according to your definition, *every* determinsitic system is chaotic!

	A potential that looks like a funnel would be non-chaotic
obviously and its deterministic and doesn't fall under his definition
(i.e. not highly dependent on initial conditions)

> > have dramatic effects on the result of the game.  I would say go is a highly
> > chaotic system.
> 
> In the loose sense of the term you employ here, perhaps so.  But it will be diffcult
> to apply the results of chaos theory to Go -- an idea I find somewhat bizarre in any
> case -- when Go does not satisfy the standard definition of a chaotic system.

	Obviously go is aperiodic as there is a defined beginning and an
end and most of the time we try and make sure we don't get stuck in
loops.. Your other problem is discretization..  Just because
a system is discrete doesn't mean that it can't be chaotic.. According
to that theory every computer model of 'chaotic' systems are themselves
not chaotic as all computers have an ennumerable number of states. 
Obviously there is a question of scale, if it is beyond
'typical' enumeration i.e. number of states is 10^30 in comparision to the
time evolution of states i.e. trajectory lengths that are for instance 
10^3 then you can call it effectively chaotic when appropriate and in fact
they do this.  Incidentally the *real* world, as in a closed system w/
your normal garden variety conservation laws,
classically  (or not) is *periodic*, it is just 'effectively' aperiodic
because non of us have the patience to wait that long (and a closed
quantum system is also *discrete*). My only protest here is that if we
take this definition of chaos, you are going to have to start claiming
that systems such as 10^23 gas particles interacting closely in a closed
box as being non-chaotic which is umm problematic ! 


	-avi