computer-go: Chaos theory and Go

[Compgo123@xxxxxxx]

Because of the recent discussion about chaos theory, I cannot help but think 
about this subject. Well I'm not an expert in chaos theory. Following is some 
comments I came up.

In general, chaos theory studies a dynamic system. That is the evolvement of 
a function of time and space variables, or time and some other variables. Or 
in general, the evolvement of a function of some variables. The evolvement of 
this function is governed by it's intrinsic nature. This is usually in the 
form of a differential equation. To form a dynamic system, there must be 
interactions or driving forces. This drving force usually appears in the 
differential equation as one or several terms. Note that even the driving 
force equals to zero, the differential equation still exists. And the 
solution of this reduced equation are just plane waves or equivalent, which, 
apparently, are not chaotic.

Now let's go back to Go. To apply chaos theory to Go we immediately face 
several problems. First, what's the function that is to be evolved? What's 
the variables of this function? May be we can define a function or something 
silimlar as the sequence of moves. Let's assume the board position is the 
variable.  Even so we are confronted with other problems. What's the equation 
govern the evolvement of our function?  And what is the driving force? Well, 
we may say,  to get the maximum score at the end of the game is the driving 
force. Apparently, all these problems must be solved to achieve a successful 
theory. 

Even with above crude definitions, some interesting observations can be drawn.
1. From above definition, one can see that the function value itself becomes 
part of the variable for the future evolution of the function. This may 
indicate that the governing equation is nonlinear. If this is true, the 
system we defined is possible to be chaotic. Because we know chaotic system 
is usually governed by nonlinear equations.
2. What's the plane wave solutions of our equation? If without the drving 
force, we know we can play the game any way we want. Thus, the plane wave 
solutions of our equation is just any legal sequences of moves.
3. Because the move sequence has to be legal, the governing equation depends 
on the set of Go rules.
4. Then can our equation descibe a game between the theory and a human or a 
game between two humans? The answer is yes. All we need to do is just find 
the proper diving force terms. A human opponent will be represented by a 
force term. Since it's not plausible to find a term that can determine a 
human player exactly, our function becomes a function of random variables.
5. When our equation describe a game between two humans, the driving force is 
no longer to get the maximum score at the end of the game. Even though this 
is the goal for both players, due to non-perfection of human players, it 
becomes distorted.

Apparently, there are many flaws in my comment. As a Chinese proverb says 'if 
one person throw out stones, due to chain reaction, someone else may throw 
out gems and gold nuggets'. This is my purpose.
 

Dan Liu