Chess Masters Research Articles

The mind's eye in blindfold chess

Visual imagery plays an important role in problem solving, and research into blindfold chess has provided a wealth of empirical data on this question. We show how a recent theory of expert memory (the template theory; Gobet & Simon, 1996b, 2000) accounts for most of these data. However, how the mind's eye filters out relevant from irrelevant information is still underspecified in the theory. We describe two experiments addressing this question, in which chess games are presented visually, move by move, on a board that contains irrelevant information (static positions, semistatic positions, and positions changing every move). The results show that irrelevant information affects chess masters only when it changes during the presentation of the target game. This suggests that novelty information is used by the mind's eye to select incoming visual information and separate “figure” and “ground”. Mechanisms already present in the template theory can be used to account for this novelty effect.

Chunks in expert memory: Evidence for the magical number four … or is it two?

This study aims to test the divergent predictions of the chunking theory (Chase & Simon, 1973) and template theory (Gobet & Simon, 1996a, 2000) with respect to the number of chunks held in visual short-term memory and the size of chunks used by experts. We presented game and random chessboards in both a copy and a recall task. In a within-subject design, the stimuli were displayed using two presentation media: (a) physical board and pieces, as in Chase and Simon's (1973) study; and (b) a computer display, as in Gobet and Simon's (1998) study. Results show that, in most cases, no more than three chunks were replaced in the recall task, as predicted by template theory. In addition, with game positions in the computer condition, chess Masters replaced very large chunks (up to 15 pieces), again in line with template theory. Overall, the results suggest that the original chunking theory overestimated short-term memory capacity and underestimated the size of chunks used, in particular with Masters. They also suggest that Cowan's (2001) proposal that STM holds four chunks may be an overestimate.

Common sense, intuition, and theory in personality and social psychology.

Theoretical work in personality and social psychology benefits from a well-developed understanding of the prior empirical and theoretical work on a problem and from informed intuitions. Intuitions develop about a subject matter through years of study, investigation, and problem solving, just as chess masters develop a sophisticated set of cognitive structures that change the very appearance of the chess board. In part because the subject matter is so personal, students new to personality and social psychology arrive with many intuitions, prior beliefs, and naive theories about social processes and behavior based on unsystematic experiences and observations. These intuitions can hinder or foster theoretical progress. The role of mentors, critiques, and empirical tests in minimizing the deleterious effects of these entry biases is discussed. Refined scientific intuitions are also subject to error, however, so means of minimizing these errors are also discussed.

Chaucer's Knowledge of Chess

Chaucer's Knowledge of Chess Mark N. Taylor Among the aristocracy in the later Middle Ages, according to the authoritative H. J. R. Murray, "chess attained to a popularity in Western Europe which has never been excelled, and probably never equalled at any later date."1 Judging by the extant literature, its "conquest of the leisured classes" was complete, "while a knowledge of chess had spread downwards from the inmates of castle and monastery to the wealthier burgesses and merchants of the towns. It was widely played by the Jews in the Ghettoes. It was an essential portion of the equipment of the . . . minstrel."2 If the romances, chansons d'aventure, and occasional legal documents are any indication, aristocratic women also played chess and sometimes excelled: the board was regarded as one acceptable point of contact between sexes.3 Allusions to chess in medieval literature are numerous, from inclusions in lists of courtly pastimes, to accounts of chess masters, to legal briefs, to technical treatises, to a full-blown allegorical romance. On the technical side, medieval experimentation with the rules developed the slower Persian game into the seemingly perfected version played today. Given the high interest in chess in Chaucer's day, it is worth exploring the extent of the poet's knowledge of chess for the light it sheds on him as homo ludens and on his references to the game, notably the famous passage in the Book of the Duchess. Despite two articles in the 1940s on Chaucer and chess and two more in the past decade, the question has never been fully addressed, and Chaucer's references remain problematic. Among the recent treatments, Margaret Connolly assumes that Chaucer's knowledge of chess came only through the Roman de la Rose and so his handling of it was confused and ineffective.4 Guillemette Bolens and Paul B. Taylor exonerate Chaucer by assigning the poor application of the chess metaphor to a deliberate rhetorical strategy.5 Both readings are somewhat labored and their accuracy compromised by a failure to directly consult Murray's authoritative reference, which dispels some of the difficulties inherent in their understandings.6 In this article I argue that Chaucer used the chess metaphor in the Book of the Duchess to express, in the conventional terms of the day, the depths of the Knight's love for his late wife, and also that the poet's knowledge of chess was adequate to this purpose. [End Page 299] In Chaucer's works there are three references to chess that go beyond the metaphorical use of "mate" or "Chek mat!" (TC II, 754) for one who has been defeated.7 One passage in the Franklin's Tale merely includes the game as a typical aristocratic pastime (V 900) and does not warrant further consideration here. Of the other two references, both appear in the Book of the Duchess, and the more extensive one has attracted continued critical attention because of difficulties in its presentation, that is, how it may contribute to our understanding of the narrator and grieving Knight and how it reflects Chaucer's handling of loss as a theme. Using the metaphor of a chess game, the Knight blames his opponent Lady Fortune for the death of his beloved wife Blanche: "At the ches with me she gan to pleye;With hir false draughtes dyversShe staal on me, and tok my fers.And whan I sawgh my fers awaye,Allas, I kouthe no lenger playe,But seyde, 'Farewel, swete, ywys,And farewel al that ever ther ys!' "Therwith Fortune seyde, 'Chek her,'And mat in the myd poynt of the chekker,8With a poun errant. Allas,Ful craftier to pley she wasThan Athalus, that made the gameFirst of the ches, so was hys name.But God wolde I had oones or twyesYkoud and knowe the jeupardyesThat kowde the Grek Pictagores!I shulde have pleyd the bet at chesAnd kept my fers the bet therby.And thogh wherto? For trewelyI holde that wyssh nat worth a stree!Hyt had be never the bet for me,For Fortune kan so many a wyleTher be but fewe kan hir begile...

Data Mining Of Chess Chunks: A Novel Distance-based Structure

What can the disciplines of artificial intelligence and the cognitive sciences obtain from the application of data mining methodology? There is a great chasm between traditional artificial intelligence methods and real human cognition. The notorious game of chess is a good example, having been traditionally modeled by search engines with advanced pruning techniques. There is, however, considerable psychological evidence that points to the view that human players do not carry out such types of processes. A more suitable alternative view seems to be that chess masters are carrying out a form of mining, carefully categorizing each chunk perceived in a position and gradually building a complex dynamic structure to represent the pressures embedded in each position. This is not only a new application area for data mining, but it is also of utmost importance to psychological theories to model the chess game as a mining process. But what type of data preparation is required? In this paper a chess representation structure, referred to as a distance graph, is presented and discussed. This representation seems to account for numerous characteristics of human player's psychology, such as: (i) the movement of eye saccades between related pieces, (ii) the carefully counting of movement combinations in selected strategic points in the game, (iii) the presence of empty spaces in chess player's chunks and (iv) a much more selective search than the classical exhaustive tree model. The psychological plausibility of the computational model opens a new avenue of research for data mining methodology as applied to the cognitive sciences and to testing new theories of artificial intelligence.

Reproducing board game positions: Western Chess and African Bao

Cognitive experimental research on experts has been dominated by research on Chess masters. De Groot’s work on Chess masters ( de Groot 1946/1965 ) started a tradition of Chess research concentrating on perception, memory and problem-solving expertise (e.g. Chase & Simon, 1973 ; de Groot & Gobet, 1996 ; Newell & Simon, 1972 ). In later years, this research was replicated by research on board games other than Chess. Experiments on players of Gomoku, Go ( Eisenstadt & Kareev, 1977 ; Reitman, 1976 ) and Othello ( Billman & Shaman, 1990 ; Wolff, Mitchell, & Frey, 1984 ) largely confirmed the findings on Chess masters. In board games research the effect of “cultural” variables has not been studied or even considered. Despite the presence of Japanese, Russian, Dutch and recently African players or games, the results of the experiments have been compared as if there is one “board game culture”. As long as the results of the experiments do not upset the results of Chess research, one could claim that this cultural background is irrelevant and that cognitive experiments on experts concern a level of thinking which is universal in humans. However, recent research on Bao experts - a board game played in East Africa - contradicted some of the results in Chess ( de Voogt, 1995 ). In this instance, the role of “culture” became an issue in two ways. Is the difference between Bao and Chess players related to the differences in playing context or are the experiments designed for Chess not comparable or not applicable to Bao?

Visual Span in Expert Chess Players: Evidence From Eye Movements

The reported research extends classic findings that after briefly viewing structured, but not random, chess positions, chess masters reproduce these positions much more accurately than less-skilled players. Using a combination of the gaze-contingent window paradigm and the change blindness flicker paradigm, we documented dramatically larger visual spans for experts while processing structured, but not random, chess positions. In addition, in a check-detection task, a minimized 3 x 3 chessboard containing a King and potentially checking pieces was displayed. In this task, experts made fewer fixations per trial than less-skilled players, and had a greater proportion of fixations between individual pieces, rather than on pieces. Our results provide strong evidence for a perceptual encoding advantage for experts attributable to chess experience, rather than to a general perceptual or memory superiority.

Crescendo of the Virtuoso: Spectacle, Skill, and Self-Promotion in Paris during the Age of Revolution

During the Age of Revolution, Paris came alive with wildly popular virtuoso performances. Whether the performers were musicians or chefs, chess players or detectives, these virtuosos tranformed their technical skills into dramatic spectacles, presenting the marvellous and the outre for spellbound audiences. Who these characters were, how they attained their fame, and why Paris became the focal point of their activities is the subject of this study. Covering the years 1775 to 1850, Metzner describes the careers of a handful of virtuosos: chess masters who played several games at once; a chef who sculpted hundreds of four-foot-tall architectural fantasies in sugar; the first police detective, whose memoirs inspired the invention of the detective story; a violinist who played whole pieces on a single string. He examines these virtuosos as a group in the context of the society that was then the capital of Western civilization.

PAL: A Pattern-Based First-Order Inductive System

It has been argued that much of human intelligence can be viewed as the process of matching stored patterns. In particular, it is believed that chess masters use a pattern–based knowledge to analyze a position, followed by a pattern–based controlled search to verify or correct the analysis. In this paper, a first–order system, called PAL, that can learn patterns in the form of Horn clauses from simple example descriptions and general purpose knowledge is described. The learning model is based on (i) a constrained least general generalization algorithm to structure the hypothesis space and guide the learning process, and (ii) a pattern–based representation knowledge to constrain the construction of hypothesis. It is shown how PAL can learn chess patterns which are beyond the learning capabilities of current inductive systems. The same pattern–based approach is used to learn qualitative models of simple dynamic systems and counterpoint rules for two–voice musical pieces. Limitations of PAL in particular, and first–order systems in general, are exposed in domains where a large number of background definitions may be required for induction. Conclusions and future research directions are given.

LEARNING PLAYING STRATEGIES IN CHESS

It is believed that chess masters use pattern‐based knowledge to analyze a position, followed by a pattern‐based controlled search to verify or correct the analysis. This paper describes a first‐order system called PAL that can learn patterns in the form of Horn clauses from simple example descriptions and general purpose knowledge. It is shown how PAL can leam chess patterns that are beyond the learning capabilities of current inductive systems. The patterns learned by PAL can be used for analysis of positions and for the construction of playing strategies. By taking the learned patterns as attributes for describing examples, a set of rules which decide whether a Pawn can safely be promoted without moving the King in a King and Pawn vs King endgame, is automatically constructed with a similarity‐based learning algorithm. Similarly, a playing strategy for the King and Rook vs King endgame is automatically constructed with a simple learning algorithm by following traces of games and using the patterns learned by PAL. Limitations of first‐order systems, PAL imparticularly, are exposed in domains where a large number of background definitions may be required for induction. Conclusions and future research directions are given.

Expertise and hierarchical knowledge representation in chess

In two experiments the structure of knowledge representation in chess experts and average players was examined. Pattern-recognition theory explains expertise through the existence of many small, unrelated knowledge units. Recent research stresses the structure of knowledge representations. However, the standard paradigm does not allow for the detection of relations between chunks; the theoretical shift has to be accompanied by a methodological shift. In Experiment 1, by means of a partitioning task, evidence was provided for a hierarchical representation of chess positions. Chess masters formed larger and more complex knowledge units than average players. In Experiment 2, the typicality of the positions was varied. The more typical the positions were, the larger and more coherent the constructed knowledge units were. The greatest differences between both groups occurred in more typical positions. This reflects the experts' ability to relate several knowledge units with one another.

Modern Art and the Invention of Postmodern Capital

The contact and habit of Trl'n have disintegrated this world. Enchanted by its rigor, humanity forgets over and again that it is a rigor of chess masters, not of angels. Already the schools have been invaded by the (conjectural) primitive language of Tlon; already the teaching of its harmonious history (filled with moving episodes) has wiped out the one which governed in my childhood; already a fictitious past occupies in our memories the place of another, a past of which we know nothing with certainty-not even that it is false. -Jorge Luis Borges, Tion, Uqbar, Orbis Tertius, trans. James E. Irby

Using patterns and plans in chess

The purpose of this research is to investigate the extent to which knowledge can replace and support search in selecting a chess move and to delineate the issues involved. This has been carried out by constructing a program, PARADISE (PAttern Recognition Applied to DIrecting SEarch), which finds the best move in tactically sharp middle game positions from the games of chess masters. It encodes a large body of knowledge in the form of production rules. The actions of the rules post concepts in the data base while the conditions match patterns in the chess position and data base. The program uses the knowledge base to discover plans during static analysis and to guide a small tree search which confirms that a particular plan is best. The search is “small” in the sense that the size of the search tree is of the same order of magnitude as a human master's search tree (tens and hundreds of nodes, not thousands to hundreds of thousands as in many computer chess programs). Once a plan is formulated, it guides the tree search for several ply and expensive static analyses (needed to analyze a new position) are done infrequently. PARADISE avoids placing a depth limit on the search (or any other artificial effort limit). By using a global view of the search tree, information gathered during the search, and the analysis provided by the knowledge base, the program produces enough terminations to force convergence of the search. PARADISE has found combinations as deep as 19 ply.

The B∗ tree search algorithm: A best-first proof procedure

In this paper we present a new algorithm for searching trees. The algorithm, which we have named B∗, finds a proof that an arc at the root of a search tree is better than any other. It does this by attempting to find both the best arc at the root and the simplest proof, in best-first fashion. This strategy determines the order of node expansion. Any node that is expanded is assigned two values: an upper (or optimistic) bound and a lower (or pessimistic) bound. During the course of a search, these bounds at a node tend to converge, producing natural termination of the search. As long as all nodal bounds in a sub-tree are valid, B∗ will select the best arc at the root of that sub-tree. We present experimental and analytic evidence that B∗ is much more effective than present methods of searching adversary trees. The B∗ method assigns a greater responsibility for guiding the search to the evaluation functions that compute the bounds than has been done before. In this way knowledge, rather than a set of arbitrary predefined limits can be used to terminate the search itself. It is interesting to note that the evaluation functions may measure any properties of the domain, thus resulting in selecting the arc that leads to the greatest quantity of whatever is being measured. We conjecture that this method is that used by chess masters in analyzing chess trees.

Chunking in recall of symbolic drawings.

Three experiments explored memory for symbolic circuit drawings using skilled electronics technicians and novice subjects. In the first experiment a skilled technician reconstructed circuit diagrams from memory. Recall showed marked “chunking”, or grouping, by functional units similar to Chess Masters’ recall of chess positions. In the second experiment skilled technicians were able to recall more than were novice subjects following a brief exposure of the drawings. This advantage did not hold for randomly arranged symbols. In the third experiment the size of chunks retrieved systematically increased with additional study time. Supplementary analyses suggested that the chunking by skilled subjects was not an artifact of spatial proximity and chunk statistics, and that severe constraints are placed on any explanation of the data based on guessing. It is proposed that skilled subjects identify the conceptual category for an entire drawing, and retrieve elements using a generate-and-test process.

Non-Transitive Dominance

The design of generalized dice in which A beats B, B beats C, and C beats A.

Multi-dimensional structure in the game of chess

This paper is an immediate follow-up of the author's previous “From Cohomology in Physics to q -connectivity in Social Science”, published in the previous issue of this journal. It is an illustration of the theory of structure contained in the first paper, being an application to the game of chess. The relations which exist between the chess-men and the squares of the chessboard, together with the rules of the game, are used to define mathematical relations Γ W and Γ B . The connectivity patterns in multi-dimensional spaces, which these relations define, are then obtained by the use of computer programs written in Basys. The accepted theories of positional chess are traced out and expressed in terms of the structure in Q -space; in particular, checkmate can be defined precisely in terms of the intersection of appropriate simplicial complexes. Finally, a detailed analysis of the so-called Immortal Game (that between Anderssen and Kieseritsky—London, 1851) is given in terms of connectivity patterns: the subordination of tactical play to positional judgement (the structure in Q -space) is illustrated by the variation of the Structure Vector. If chess masters base their profound positional judgements on an unconscious appraisal of the connectivity structure in Q -space—as the author believes—then this analysis holds out the prospect of a chess-playing computer using the same methods of assessment in its play.

Does Age Affect Master Chess?

SUMMARY Data of World Championship chess matches and of the personal tournament performances of certain chess masters have been examined from the point of view of the players' ages. The author concludes that these data do not indicate that the mental capabilities of chess players are adversely affected by advancing age. Interpretations of the data are suggested and other considerations are mentioned. 1. THE PROBLEM THE effect of age on the capabilities of the physical sportsman is well known. Forty is an effective ceiling in most physical sports and the year by year progress of over-40 athletes is followed with interest everywhere in the world. The effect of age on the capabilities of the mental sportsman is less clear, and opinions differ as to whether the physical effects of ageing in any way affect a man's mental prowess, and if so, how. One mental sport well worth examination is When a chess player reaches a certain well-recognized, excellent standard of play, he is called a in the chess world. The data we shall present below in examining the question raised come from the world of master chess. In the or baseball world the equivalent standard would be professional soccer or professional baseball. We shall consider two types of data: (a) the results of all matches played by the World Chess Champions against challengers 1858-1961, and the ages of the participants; (b) the performances of recognized masters, including World Champions, in tournaments throughout their lives. A portion of these data previously appeared elsewhere (Rubin, 1960). The subsequent analysis, however, like the portion of data, appears inadequate.