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

["Hans F. Zschintzsch" <hfz@xxxxxxxxxxx>]

John Aspinall schrieb:

>   Problem: Find a metric for the space of go-board positions.  Show that
> your metric satisfies the triangle inequality ...

well, if  B = {b1,b2,...}  is "the" go board, and  f:B->{Free, Black,
White} 
is a coloring, then define

  |f,g| = |{b \in B, f(b)<>g(b)}|

[remark: The distance is just the number of points of the board, 
where the color is different]

Obviously |f,g|=0 if and only if f=g, and also |f,g| is symmetric 
because <> is.

For any three colorings f,g,h ge get the triangle inequality 

  |f,g| <= |f,h| + |h,g|

because at each point b \in B where f(b)<>g(b) also either
h(b)<>f(b) or h(b)<>g(b). 

So there is at least one metric a little bit more interesting
than just |f,g|=0 if f=g and |f,g|=1 otherwise. 

Hans

PS. I know nothing about "string-distance", however when 
having to decide about "similarity of words", i would probably
also count the number of matches.