computer-go: Go and chaos/complexity/dynamical-systems theory

[John Aspinall <jga@xxxxxxx>]

I think the fundamental issue under discussion here can be characterized by
the following two extreme positions.  (Note, most real people don't fall
out at these extremes, the extremes are for emphasis.)

[A]  It's about language.  If we don't agree what a word (or phrase) means,
then using that word will lead to confusion.  A word like "chaos" has been
totally debased by popularization.  You can't say "chaos" and expect that
everyone will understand it to mean the same thing.  Therefore if you use
the word "chaos", you should explain whether you mean math-chaos (i.e.
dynamical systems theory, Lyapunov exponents, etc.) or pop-chaos (i.e.
butterfly flapping its wings in South America, Jeff Goldblum in Jurassic
Park, etc.).  Fruitful discussions can only take place if we speak the same
language.

[B] It's about analogy.  Even if all the mathematical prerequisites haven't
been satisfied, there are enough parallels between Go and the theory of
chaotic systems that we ought to explore them further.  Mathematical rigor
will stifle discussion at this early stage.

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OK, now having previously staked out my position as far towards the A end
of the spectrum, I'll add two things.

Firstly, I agree with Dave Fotland.  We ought to be talking more about
representations (what to represent, how to represent it, what to compute on
it).   IMHO it's the key problem here, and its the big disappointment of
this list that we spend such a small fraction of the traffic on it.

Secondly, for those of you still high on math: a challenge.  If you're
going to employ any of the tools of dynamical systems, you need a metric
for the space of go games.  You can't talk about two game trajectories
diverging from each other unless you can measure that distance.  So...

  Problem: Find a metric for the space of go-board positions.  Show that
your metric satisfies the triangle inequality, and other standards of
reasonableness.  Hint: for all I know, this may be as simple as using
string-distance, like you do for sequence matching.  But let's see
something more than handwaving.