Re: computer-go: Mathematic Go

["Blue Thunder Somogyi" <blue@xxxxxxxxxxx>]

> I really like your way of thinking, Dan.

Same - Dan's comments resound with much of my go thinking

>   As to your "study empty board" suggestion, I don't feel there is
> much to research on. Mathemetically, it's a 19 x 19 matrix, and there is
> no much information on it. Maybe I am wrong.
> -- Mousheng Xu

On this I disagree with Mousheng - I've often felt the choice of a 19x19
board was significant (an echo of ancient wisdom), as when dissected, it is
really four 9x9 quadrants (the perfect learning board, and why 9x9 games can
be applied to larger games - don't care much for 13x13 myself, read on...),
which are in turn each composed of 5x5 boards - it may seem that the
symmetry breaks down at this point, but when each 5x5 board is examined,
each space on the board (not intersection, but space) can be seen
representing the 5x5 board itself, relative to the complete 19x19 board.
This replicating subdivision is innately fractal in nature, and to my mind,
leads towards realms of possibiltity of the study of the "fabric" of the
game, if you will.

Most of my work on go programming (I do not yet have a functioning prototype
yet, but it's been years in the making none-the-less :-) has been in the
area of game/stone representation (nesting structured representation - very
classically object oriented), compression techniques utilizing this property
of the game, and functions that operate at both a tactical & strategic level
(these are still mostly psuedo-code, but I feel the thinking within them is
sound).  One example is a method of representing stones on the board as
strings of base 4 digits.  When this method is compared with straight matrix
representation, each winds up taking the same number of binary bits (the
final representation in our silicon heros), but the quadrary string method
lends itself to a slew of efficient functions for juxtaposition and
amalgamation of game elements, as well as retaining more meaningful data
when undergoing truncation & concatanation (which BTW can achieve positional
translation across a board space more efficiently than using matrix
representation, but I'm not entirely sure of this - I haven't done a
in-depth study of this advantage, but that is my intuition)

The main advantages of these techniques, as I see it, are that game data can
be applied heuristically at various levels of abstraction.  It is my
postulation that the same principle that makes a particular joseki useful on
one corner of the board, could be applied as meta-data (to wit, a strategem,
or strategic overlay) to have a similar effect on the game as a whole.

Or maybe I've read one two many passages of the I Ching, and am now seeing
numbers within numbers within numbers - The real test will be proving the
viability of this "programatic ideology" on the board, something I'm quite
eager to do...

I hope I've at least painted a picture of my perspective, even if it is a
work in progress.
Blue Thunder Somogyi
blue@xxxxxxxxxxxxxxxxx

PS - I also am quite curious myself if any application of chaos theory
(strange attractors, etc) could be applied to the game, as Go itself is
nearly the definition (at least the commonly used scientific definition) of
chaos - "sensitive dependence on initial conditions"

> -----Original Message-----
> From: Compgo123@xxxxxxxxxxxxxxxxx [mailto:Compgo123@xxxxxxxxxxxxxxxxx]
> Sent: Sunday, October 24, 1999 11:34 AM
> To: computer-go@xxxxxxxxxxxxxxxxx
> Subject: computer-go: Mathematic Go
>
>
> Mathematic Go theory has achieved some quite interesting results
> regarding
> the end games. It demonstrated that in many end game situations, the
> best
> score can be calculated from the topological properties of the position
> alone
> and the look forward search is not needed. This success raise the hope
> of a
> 'magic formular' for winning Go games.
>
> However, the extension of these theories to the other parts of the game
> (such
> as the middle game) is met with difficulties. The reason is that there
> are
> just too many possible positions to be enumerated as required by
> existing
> mathematic Go thoery. I think there maybe one way to avoid this problem.
>
> Instead of studying the game positions, one may study the mathematical
> properties of the empty Go board. Since all possible game positions are
> completely pre-determined by the mathematical properties of the Go board
> and
> the set of Go rules. This becomes interesting that one may find the
> 'magic
> formular' by not studying the game, but ,instead, the empty Go board. It
>
> would be very interesting if someone can prove or disprove that such an
> approach is possible. One possible justification of this appraoch is
> that the
> Go boards can cost much more than the Go stones. A clear demonstration
> of the
> importance of the Go board.
>
>
> Dan Liu
>