Re: [computer-go] Search = Bad!

["Paul Tabor" <paul@xxxxxxxxx>]

Apart from issues over continuous/discrete functions, the problem I have with mapping Go to a fractal is that Go is essentially a finite game, whereas fractals are inherently infinite. Although large, the solution space for Go is finite, being described by a finite number of moves on a finite board. Unfortunately, the nature of the problem is such that it is apparently P-space hard as already noted, and for this reason most people have accepted that tackling it with a conventional tree-searching algorithm alone is doomed to failure (even though this would be a successful approach given more computing power than is likely to be practically available in the foreseeable future). Given the discrete nature of the problem, I wonder if we should be looking to number theory instead if we want to achieve a complete solution. In the meantime, if we're looking for an approximation, which might help in producing a seriously strong computer go player, using fractals may well be a useful technique to allow us to converge on the solution more quickly than we can do presently.

Paul

----- Original Message -----
From: "Paul Pogonyshev" <pogonyshev@xxxxxxxxxxxxxxxxx>
To: "computer-go" <computer-go@xxxxxxxxxxxxxxxxx>
Subject: Re: [computer-go] Search = Bad!
Date: Mon, 21 Feb 2005 13:06:56 +0200

> 
> Frank de Groot wrote:
> 
> > Go is 100% a fractal and the game has nothing to do with territory,
> > capturing, Ko etc. It is 100% a case of navigating fractal space.
> 
> You are either going to start a revolution in game theory or this
> idea will silently fade into oblivion.  I bet the chances are probably
> like 10e-10 for the former and the rest for the latter.
> 
> In all you have been saying here nothing was specific to Go.  You can
> say the very same replacing the word ``Go'' with ``chess'' and
> ``territory'', ``ko'', ``influence'' etc. with ``mobility'', ``check''
> and ``pawns''.  You can say that chess has nothing to do with capturing
> pieces and checkmating your opponent's king: it's all about navigating
> of fractal space.
> 
>  From your point of view, chess, Amazons and all other two-player
> deterministic board games with full knowledge should be solvable by
> ``pondering'' on fractals and deriving a ``magical'' mathematical
> formula that is easy to compute.  Somehow, I seriously doubt that's
> possible.
> 
> Paul
> 
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