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PHAT
06-02-2004, 02:26 PM
I'm waiting for the follow up book, "Refuting Mathematics". When local chess wunderkinder Sarfati takes on the cloistered mathematics crowd and shows complex numbers, eigenvalues and fourier transforms to be nothing more than the work of the devil. I believe he also provides proof that transcendentals are part of a world-wide conspiracy and pi is in fact exactly 22/7. :lol:


A little while back I was reading a book on "mind". It occured to me that something similar to the way the brain works are eigen values. If this is so, I wonder if anyone has given time to writing chess algorithms, based on eigen values of all positions held in our vast chess data bases. These algorithms might be the "intuition that the bots do not yet possess. They could run parallel to the number crunching, guiding it down the routes that humans tread but getting further down that route, faster. Maybe getting up towards 20-30 ply by avoiding "understood nonsence".


That's an interesting idea. I assume you are talking about representing chess positions as 8x8 square arrays in some way, and then perform Eigen decomposition on these arrays.

Give the huge number of transformations that could occur on these positions and other constraints - which make two very similar positions have a widely varying chess value, and the lack of applicability of dot or cross products (in particular) to these chess matrices - I can't see how eigenvalues will help evaluate positions. Or even if doing so is even computationally more efficient than existing (more prosaic perhaps) position evaluation algorithms.

It could be the eigenvalue link was more analogous and cannot be implemented in practice. Although perhaps Shaun has some thoughts on this or knows of some work in this area.

Better be careful or we may need to move this to the Chess Area. :eek:


I was thinking more along the lines of maybe:

Allocating a "degree of control" value to each square (the matrix) and seeing how each move effects the control of squares around the king (or queen). This sounds a bit like looking for a "mating net".

What I wonder is, is there a typical series of eigenvalues that precede a mate. This sounds like "preparation".

I s'pose I am thinking also, that good players look at a board and before they have time to properly analyse it, they may say, "Looks good for white." What are they seeing. are they recalling patterns piece placement or patterns of control.

Now if they are seeing patterns of control, they are seeing things that are not there in a physical sence - they are seeing forces. Surely they are not doing a 6 ply Fritz analysis at a glance. A question might be then , "Is intuition an unconscious application of eigenvalues?" If it is, then we might have a new way to guide chess engines down more promising lines. so that they can go deeper, faster.