Ron Atkin

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Ronald Harry (Ron) Atkin, (born 1926)
a British mathematician and emeritus from University of Essex, whose research interests covers systems theory, algebraic topology, and structural properties. In writing a language of structure in algebraic topology, Atkin has generated a methodological approach of deep significance in all the human sciences. He has been strongly influenced by the concern for ethics and language exemplified by Ludwig Wittgenstein, although he was not a formal student of the philosopher during his undergraduate days at Cambridge [1]. In the 70s, Ron Atkin introduced the Q-analysis [2], a mathematical framework to describe and analyze structures in various systems and networks.


In applying Q-analysis to chess, Atkin, and Atkin along with Ian H. Witten [3], represents a model to evaluate chess positions based on connectivity of pieces and squares. Squares, attacked by a particular piece are labeled a simplex, and simplexes are composed into complexes, both subject of further analysis yielding in move predictions [4].


Multi Dimensional Structure

Excerpt from: The Machine Plays Chess? by Alex Bell [5]:

Even more mysterious was a paper Multi Dimensional Structure in the Game of Chess by Ron Atkin, a maths lecturer at Essex University. Up to this point all chess programs had evaluation functions which were decidedly ad hoc, the programmers had a feeling in their water that certain features, material, mobility, control of the centre, king safety, pawn structure, etc., were the most important and accordingly stuck them in the program with very little idea of their precise effect. Now here was a mathematician who, with lots of squiggly things, appeared to have a precise mathematical evaluation function. Unfortunately neither John nor I could understand the paper - so why not get Atkin to talk about it. There were a few other new ideas I did not understand - a new, knowledge approach to solving end games and some psychological theories about how chess players think - so why not have a conference? If nothing else I might get some idea of what was going on. 

Positional Play

From Alex Bell's report on Advances in Computer Chess 1 in Computer Weekly, April 10, 1975, Techniques for playing the end game [6]:

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 hierarchical 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. Another problem was that not a single person in the audience was sufficiently competent to stand up and say, "This is all very well but your approach will not handle this situation in a chess game, a tactic which often shoots down the simple minded crunch programs". 

Mathematical Structure

Excerpt from the Mathematical Structure in the Human Sciences, Pennsylvania State University, conference proposal by Waldo R. Tobler, University of Michigan, October 04, 1976 [7]:

This proposal for a two-day conference on Mathematical Structure in the Human Sciences represents a second attempt to convene a small and diverse group of scholars to discuss the major and innovative "language of structure" developed over the past ten years by Dr. Ronald H. Atkin of the Department of Mathematics, University of Essex. After extensive informal discussions, and immediately prior to the formal submission of the proposal in the Fall of 1975, Atkin suffered a severe heart attack. 
He has not only fully recovered, but is in a position to lead the proposed conference once again. It should be noted that the conference has been coordinated with Atkin' s proposed attendance at a second meeting sponsored by the Committee for Mathematics in the Social Sciences. It is for this reason that only funds for internal transportation are requested. 
In writing a language of structure in algebraic topology, Dr. Atkin has generated a methodological approach of deep significance in all the human sciences. Starting from his earlier work in algebras, he first began his research on the formation of a structural language in the field of physics. In an early paper he demonstrated that modern algebraic concepts are compatible with models in physics, and that within a definition of an abstract physics the deeper structure of "ordinary physics" could be analyzed. Later work provided a quite novel and fruitful approach in quantum mechanics, and it was from his studies of cohomologies in these areas that he perceived some remarkable similarities to problems in the Social Sciences.
The perception of such similarities was not fortuitous: Atkin has been strongly influenced by the concern for ethics and language exemplified by Wittgenstein, although he was not a formal student of the philosopher during his undergraduate days at Cambridge. In addition, wide reading in the social sciences and humanities forced a singular, and now obvious, fact upon his attention: that virtually every field of human thought and endeavor employs the word structure, yet seldom is a satisfactory or fruitful definition encountered. From the shallow handling of such a vital and ubiquitous concept in human affairs, he has developed an algebraic topological language capable of describing and illuminating structural questions in an extraordinarily diverse number of fields. His language is based simply upon set membership, but from the simplicial complexes generated he has obtained insights of such richness that some of his work represents a major extension of thought in artificial and prosthetic intelligence.
The diversity of his applications is worth emphasizing in summary form, for he represents that rare scholar in the Social Sciences who combines mathematical depth to the point of originality with a considerable ability to communicate the results of his applications to a wide, even popular, audience. In brief, he had demonstrated his ability to communicate with men and women who lack mathematical expertise, while being prepared to discuss with professional specialists deep areas of algebra.
Many of his applications stem from two research projects supported by the Social Science Research Council of the United Kingdom. The first of seven publications reported an analysis of architectural structure in a Tudor village of Essex, and demonstrated that the visual and aesthetic complexity of an urban landscape could be explored using the concept of a simplex. He has also analyzed the historical structure of a village in 1600, and other elements of his work may eventually change the way time is handled in the social, behavioral and historical sciences. Later reports outlined the mathematics of  Q-analysis, and reported upon a comparative study of urban structure for an English coastal town between 1900 and 1970. It was at this time that the University of Essex itself ran into grave difficulties, with considerable conflict between students, faculty and administration. An extensive analysis by Atkin of the structural relations characterizing the university pinpointed a number of areas where, the sheer physical and administrative organization was preventing communication. In addition, Q-holes (holes in the geometry), were found in the complex which acted as traffic generators and inhibitors of free communication, since such gaps in the backcloth do not allow anything to move through them.
During the same period, Atkin extended his earlier analysis of the game of chess - a game subject to intense scrutiny in the area of artificial intelligence. Realizing the ultimate combinatorial futility of  tree-searching methods, characteristic of virtually all computer algorithms devised during the past twenty years, he used his language of structure to describe, in essence, the micro "human" geography of a chessboard. With one of  England's International Grand Masters as his research assistant, he has achieved a description of the game at the N+l, or positional, level more closely akin to the thought processes characterizing Master play, rather than the N, or tactical, level typical of now-archaic tree-searching approaches.
Today his computer algorithm is printing out reasons for making a move which few people, and occasionally any person, understand(s). His analysis of some classical games of chess demonstrate clearly the structural integrity and dominance of one player, and conversely the relational disarray of the opponent and ultimate loser, well before the point of actual resignation. Atkin's basic thesis in this area of research is simply that there are many areas of human life where the complexity of structure and relations overwhelms the human brain. He is looking fifty years ahead to the common use of prosthetic intelligence once the problems have been described in a language appropriate to them.
Other applications stemming from his SSRC (UK) project include an analysis of the work of  Piet Mondrian, the black humor of a literary work such as Catch 22, and a Shakespearian sonnet. At the same time, he has been generous in helping medical colleagues, and his language has been fruitfully applied in the design of therapeutic facilities for braindamaged elderly patients (Gedye [8]), structural relationships of the brain recorded by drug residues found upon autopsy (Gedye) , and daily consulting work in clinical psychology (Mulhall). He has also noted, almost in passing, that conventional statistical techniques, such as regression analysis, destroy much structural information in a data set by replacing a relation X by a mapping, so that a is simply regarded as a collection of disconnected O-simplices. Unlike the common correlation coefficient (r), his structure coefficient (h), is a true measure of structural dependence, rather than conventional "linearity." 

Selected Publications

[9] [10] [11] [12]

External Links


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