Author: Walter Faxon
Date: 05:46:33 05/10/05
Go up one level in this thread
On May 09, 2005 at 14:09:29, Werner Kraft wrote: >In computer chess , the method to find a move is based on " tree - searching " >>- you >>have a move ( 1.e4 ) - then the 20 reply moves for black . SO you build up >>trees - every variation move is a new branch on it. >>Now - as a complete analysis of a chess game involves 10-power 120 positions - >>you introduce evaluation system ... >> >>Was there ever another way of looking at that - may be from exotic branches of >>mathematics - topology e,g ? > >Try googling "surreal numbers". It's an entirely new number system by >mathematician John Conway (creater of the game of life) and is quite intresting. > It was developed specificly to analyze games, I believe he used it to analyze >the game of go. The entire theory is based on only two axioms - > > > comment " I did not understand even the axioms ... " > > > >I have looked it up on the internet - I found this chap very interesting - and I >want to read the book : How tow ex-students took up pure mathematics and >discovered ( eternal ?? ) happiness " > >I come back to you once I have read it . > >I mean I like people who work from a more poetic / intuitive level - the Polish >SciFi writer Lem is excellent at that. > >I had a chat at a campfire this weekend with a guy who studied physics and has >a Ph.D in Physiology ( now he does computer simulations of physiological >processes ). He thought there might be a link between chaos theory and making >predictions about the outcomes of a move in the longer term - at least in terms >of probability. > >I thought also about the concept of " mind tools " - creating sth like >geometrical figures , that represents chess sequences . > >I thought sth along the line of a Rubic cube - ones you have made all this turns >, it seems to be very hard to get back to unicolour surfaces - yet an >experienced player can do that in a few moves. >Now - think about a beatiful , geometric , multi-coloured objetc , that you can >turn and twist in your mind - > >( no, I am not talking about erotic fanatsies LOL ) > >- and that represent a complicated chess position. Just as a thought experiment >. Each manipulation helps you to solve a chess problem. All the rules of chess >are worked into the structure of this mind- object. >The outcome would be the perfect solution to your chess problem. >No chess computer could use it as an algorithm - because it is purely >geometrical. > >Wow - that would be cool !! > >I wish there is somewhere an intelligent and open-minded guy around , who has a >good back-ground in Mathematics , Theoretical Physics etc , and turn that all >into something real ... that would be cool. Hi, Werner. Viz. alternative methods of chess position evaluation, you might consider investigating the work of Ron Atkin on q-analysis, which regards mathematical relations between finite sets, and is most often applied to the social sciences. The first reference from a quick web search: http://www.laetusinpraesens.org/docs/missile.php Excerpt: ---------- The author who has perhaps best articulated the experiential cognitive relationship between simplicity and complexity is Ron Atkin (1977, 1981) in dealing with multidimensional conceptual spaces. The question is how to describe the experience of complexity within a framework of simplicity. And then how to describe the constraints on understanding when it becomes necessary to articulate complex insights into a simple framework -- and what gets lost in the process. (Note internal web reference) Ron Atkin. Combinatorial Connectivities in Social Systems: an application of simplicial complex structures to the study of large organizations. Basel, Birkhäuser, 1977 Ron Atkin. Multidimensional Man: Can man live in three dimensional space? London, Penguin, 1981 (see http://www.uia.org/strategy/141alt.htm) ---------- A computer chess group experimented with Atkin's ideas in the mid 1970s, as described in papers in some early volumes in the series of proceedings titled "Computer Chess N" (where N is a number from 1; these later became "Advances in Computer Chess N"). There is also a reference to an even earlier Atkin paper, "Multi Dimensional Structure in the Game of Chess" in the proceedings of the very first computer chess conference ever, held at the Atlas Computer Laboratory in 1973, but as of the late 1970s these proceedings were not available anywhere. Numbered in sequence with the others it would have been titled "Computer Chess 0". A review of Atkin's 1975 presentation of his paper for "Computer Chess 1": "The next paper by Ron Atkin, of Essex University, was more profound. Atkin has developed a mathematically valid approach to positional play in chess and also described a method of simulating the hierarchial method used by the chess master. His ideas have an intuitive appeal; one feels he must be right but the problem of implementing the ideas in a computer, are enormous and, as yet, unsolved." A later paper describes a program implementing Atkin's ideas. It was said to be able to "analyze better than Golombek" (a well-respected British IM and chess author). But that was the last I heard of it. Atkin's 1981 book mentions chess but doesn't go into details. The group may have abandoned the Atkin approach due to inadequate computer power, certainly less of a problem today. The (UK) Cybernetics Society (http://www.cybsoc.org/) recommends this primer and critique of Atkin's q-analysis: http://www.afscet.asso.fr/resSystemica/Crete02/Legrand.pdf Q-analysis originated with Atkin in 1972 but several researchers have studied it and its application at least through 2002. See http://www.geos.ed.ac.uk/homes/freitsma/qreferences.html Who knows, maybe the theory today has advanced so as to be even more useful for chess! Now, regarding your "I wish there is somewhere an intelligent and open-minded guy around , who has a good back-ground in Mathematics , Theoretical Physics etc , and turn that all into something real ... that would be cool." Yes, it would indeed be cool. But don't sit on the sidelines and expect anyone else to do it. If an idea intrigues you and you want to see it pursued, pursue it yourself: Learn all you can, get excited about it and try to get the brightest people you can find excited about it. Otherwise, decades may pass and nothing happen. Yes, decades. In your pursuit you're sure to learn a lot, even if a particular path eventually turns out to be a dead end. And you're sure to have some fun. Make sure you document your pursuit and findings for others. Science is a public activity. -- Walter
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