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.     

Patterns of theorizing about chess skill – Commentary on Linhares and Freitas (2010) and Lane and Gobet (2011)

Although Linhares and Freitas (2010) have failed to characterize earlier experimental work in chess skill accurately, their conceptual approach of “experience-recognition”-driven problem solving points to the need to incorporate analogical reasoning mechanisms into explanations of how chess players choose the best move in chess. The Lane and Gobet (2011) commentary and the cognitive simulation models that they espouse consist of plausible mechanisms to support choosing a good move, but need additional development to incorporate abstract/semantic information. One possible avenue for future exploration will be to produce hybrid models that use both “piece-on-square” chunk and template representations and abstract high-level representations to guide search in chess.     

Recall of random and distorted chess positions: Implications for the theory of expertise

This paper explores the question, important to the theory of expert performance, of the nature and number of chunks that chess experts hold in memory. It examines how memory contents determine players’ abilities to reconstruct (1) positions from games, (2) positions distorted in various ways, and (3) random positions. Comparison of a computer simulation with a human experiment supports the usual estimate that chess Masters store some 50,000 chunks in memory. The observed impairment of recall when positions are modified by mirror image reflection implies that each chunk represents a specific pattern of pieces in a specific location. A good account of the results of the experiments is given by the template theory proposed by Gobet and Simon (in press) as an extension of Chase and Simon’s (1973b) initial chunking proposal, and in agreement with other recent proposals for modification of the chunking theory (Richman, Staszewski, & Simon, 1995) as applied to various recall tasks.     

The role of constraints in expert memory

A great deal of research has been devoted to developing process models of expert memory. However, K. J. Vicente and J. H. Wang (1998) proposed (a) that process theories do not provide an adequate account of expert recall in domains in which memory recall is a contrived task and (b) that a product theory, the constraint attunement hypothesis (CAH), has received a significant amount of empirical support. We compared 1 process theory (the template theory; TT; F. Gobet & H. A. Simon, 1996c) with the CAH in chess. Chess players (N=36) differing widely in skill levels were required to recall briefly presented chess positions that were randomized in various ways. Consistent with TT, but inconsistent with the CAH, there was a significant skill effect in a condition in which both the location and distribution of the pieces were randomized. These and other results suggest that process models such as TT can provide a viable account of expert memory in chess.     

Perception in chess and beyond: Commentary on Linhares and Freitas (2010)

Linhares and Freitas (2010; LF) argue that experts use analogical or semantic similarity, similarities that are not available from direct surface representations. LF make their case using a critique of Chase and Simon (1973b) and the presentation of a few chess positions and examples from other domains. Their conclusion is that models such as CHREST (Gobet et al., 2001) and theories such as the chunking theory (Chase & Simon, 1973b) and the template theory ( [Gobet and Simon, 1996a] and [Gobet and Simon, 1996b]) are inadequate for dealing with these issues. They propose an alternative paradigm, which they call “experience recognition.” Although we find this issue an interesting one, the separation between pattern recognition and problem solving is a lot more complex than LF portray. We instead suggest that a “revolution” in our to date successful modelling is not necessary. Especially in the chess domain, LF’s examples do not make the point they claim. Furthermore, their criticisms of CS are incorrect, and they have failed to mention a large number of experimental results that have supported the hypothesis of location-specific encodings. Although we agree that experts use semantic information and similarities, these ideas already possess analogues in CHREST, which can form the basis of further evolution of the theory.     

Recall or evaluation of chess positions revisited: the relationship between memory and evaluation in chess skill

We extend work by Holding and Reynolds (1982) on recall and problem solving with quasirandom chess positions. We tested 17 chess players on both quasirandom and structured chess positions. Consistent with the earlier study, initial recall of quasirandom chess positions is unrelated to chess skill level, and quality of the move selected in subsequent problem solving is related to skill level. However, recall following problem solving is related to chess skill level. These results support the view that pattern recognition processes underlie superior performance by skilled chess players, contrary to the conclusions of Holding and Reynolds (1982). Mechanisms such as long-term working memory retrieval structures (Ericsson & Kintsch, 1995) or templates (Gobet & Simon, 1996a) could explain the effective encoding of quasirandom positions during problem solving.     

Visualization,pattern recognition,and forward search: effects of playing speed and sight of the position on grandmaster chess errors

A new approach examined two aspects of chess skill, long a popular topic in cognitive science. A powerful computer‐chess program calculated the number and magnitude of blunders made by the same 23 grandmasters in hundreds of serious games of slow (“classical”) chess, regular “rapid” chess, and rapid “blindfold” chess, in which opponents transmit moves without ever seeing the actual position. Rapid chess led to substantially more and larger blunders than classical chess. Perhaps more surprisingly, the frequency and magnitude of blunders did not differ in rapid versus blindfold play, despite the additional memory and visualization load imposed by the latter. We discuss the involvement of various cognitive processes in human problem‐solving and expertise, especially with respect to chess. Prior opposing views about the basis of general chess skill have emphasized the dominance of either (a) swift pattern recognition or (b) analyzing ahead, but both seem important and the controversy appears currently unresolvable and perhaps fruitless.     

The impact of chess research on cognitive science

Summary Although chess research has not been a mainstream activity in cognitive science, it has had a significant impact on this field because of the experimental and theoretical tools it has provided. The two most-cited references in chess research, de Groot (1965) and Chase and Simon (1973 a), have accumulated over 250 citations each (SSCI andSCI sources summed), with the majority of citations coming a decade or more from their publication dates. Both works are frequently cited in contemporary cognitive-psychology textbooks. Chess playing provides a model task environment for the study of basic cognitive processes, such as perception, memory, and problem solving. It also offers a unique opportunity for the study of individual differences (chess expertise) because of Elo's (1965, 1978) development of a chess-skill rating scale. Chess has also enjoyed a privileged position in Artificial-Intelligence research as a model domain for exploring search and evaluation processes.     

When the Solution Is on the Doorstep: Better Solving Performance,but Diminished Aha! Experience for Chess Experts on the Mutilated Checkerboard Problem

Insight problems are difficult because the initially activated knowledge hinders successful solving. The crucial information needed for a solution is often so far removed that gaining access to it through restructuring leads to the subjective experience of “Aha!”. Although this assumption is shared by most insight theories, there is little empirical evidence for the connection between the necessity of restructuring an incorrect problem representation and the Aha! experience. Here, we demonstrate a rare case where previous knowledge facilitates the solving of insight problems but reduces the accompanying Aha! experience. Chess players were more successful than non‐chess players at solving the mutilated checkerboard insight problem, which requires retrieval of chess‐related information about the color of the squares. Their success came at a price, since they reported a diminished Aha! experience compared to controls. Chess players’ problem‐solving ability was confined to that particular problem, since they struggled to a similar degree to non‐chess players to solve another insight problem (the eight‐coin problem), which does not require chess‐related information for a solution. Here, chess players and non‐chess players experienced the same degree of insight.     

Planning abilities and chess: A comparison of chess and non‐chess players on the Tower of London task

Playing chess requires problem‐solving capacities in order to search through the chess problem space in an effective manner. Chess should thus require planning abilities for calculating many moves ahead. Therefore, we asked whether chess players are better problem solvers than non‐chess players in a complex planning task. We compared planning performance between chess (N=25) and non‐chess players (N=25) using a standard psychometric planning task, the Tower of London (ToL) test. We also assessed fluid intelligence (Raven Test), as well as verbal and visuospatial working memory. As expected, chess players showed better planning performance than non‐chess players, an effect most strongly expressed in difficult problems. On the other hand, they showed longer planning and movement execution times, especially for incorrectly solved trials. No differences in fluid intelligence and verbal/visuospatial working memory were found between both groups. These findings indicate that better performance in chess players is associated with disproportionally longer solution times, although it remains to be investigated whether motivational or strategic differences account for this result.     

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.     

In search of templates

This study reflects a recent shift towards the study of early stages of expert memory acquisition for chess positions. Over the course of 15 sessions, two subjects who knew virtually nothing about the game of chess were trained to memorise positions. Increase in recall performance and chunk size was captured by power functions, confirming predictions made by the template theory [Cogn. Psychol. 31 (1996) 1; Memory 6 (1998) 225; Cogn. Sci. 24 (2000) 651]. The human data were compared to that of a computer simulation run on CHREST (Chunk Hierarchy and REtrieval STructures), an implementation of the template theory. The model accounts for the pattern of results in the human data, although it underestimates the size of the largest chunks and the rate of learning. Evidence for the presence of templates in human subjects was found.     

Pattern recognition makes search possible: Comments on Holding (1992)

Chase and Simon's chunking theory of expert memory, which emphasizes the role of pattern recognition in problem solving, has attracted much attention in cognitive psychology. Holding advanced a series of criticisms that, taken together, purported to refute the theory. Two valid criticisms – that chunk size and LTM encoding were underestimated – are dealt with by a simple extension of the theory. The remainder of Holding's criticisms either are not empirically founded or are based on a misunderstanding of the chunking theory and its role in a comprehensive theory of skill. Holding's alternative SEEK theory, which emphasizes the role of search, lacks key mechanisms that could be implemented by the type of pattern recognition proposed by Chase and Simon. Received: 3 September 1997 / Accepted: 28 January 1998     

Visuospatial representations used by chess experts: A preliminary study

Blindfold chess is played without the players seeing either the pieces or the board. It is a skill‐related activity, and only very skilled players can construct the mental images required. This is why blindfold chess provides a good task with which to investigate the spatial memory and skilled mental images of expert players. In a PET investigation, we compared memory performance and problem solving in very experienced chess players with their performance in an attention task, in which the subjects classified the names of chess pieces. The memory task predominantly activated the temporal areas, whereas problem solving activated several frontal areas. The relevance of these findings to concepts such as general imagery, skilled imagery, apperception, and long‐term working memory are discussed.     

Five Seconds or Sixty? Presentation Time in Expert Memory

For many years, the game of chess has provided an invaluable task environment for research on cognition, in particular on the differences between novices and experts and the learning that removes these differences, and upon the structure of human memory and its paramaters. The template theory presented by Gobet and Simon based on the EPAM theory offers precise predictions on cognitive processes during the presentation and recall of chess positions. This article describes the behavior of CHREST, a computer implementation of the template theory, in a memory task when the presentation time is varied from one second to sixty, on the recall of game and random positions, and compares the model to human data. Strong players are better than weak players in both types of positions, especially with long presentation times, but even after brief presentations. CHREST predicts the data, both qualitatively and quantitatively. Strong players' superiority with random positions is explained by the large number of chunks they hold in LTM. Their excellent recall with short presentation times is explained by templates, a special class of chunks. CHREST is compared to other theories of chess skill, which either cannot account for the superiority of Masters in random positions or predict too strong a performance of Masters in such positions.     

Specialization effect and its influence on memory and problem solving in expert chess players

Expert chess players, specialized in different openings, recalled positions and solved problems within and outside their area of specialization. While their general expertise was at a similar level, players performed better with stimuli from their area of specialization. The effect of specialization on both recall and problem solving was strong enough to override general expertise—players remembering positions and solving problems from their area of specialization performed at around the level of players 1 standard deviation (SD) above them in general skill. Their problem-solving strategy also changed depending on whether the problem was within their area of specialization. When it was, they searched more in depth and less in breadth; with problems outside their area of specialization, the reverse. The knowledge that comes from familiarity with a problem area is more important than general purpose strategies in determining how an expert will tackle it. These results demonstrate the link in experts between problem solving and memory of specific experiences and indicate that the search for context-independent general purpose problem-solving strategies to teach to future experts is unlikely to be successful.     

Waves,streams, states,and self: An outline of an integral psychology 1

Abstract

Although far from unanimous, there seems to be a general consensus that neither mind nor brain can be reduced without remainder to the other. This essay argues that indeed both mind and brain need to be included in a nonreductionistic way in any genuinely integral theory of consciousness. In order to facilitate such integration, this essay presents the results of an extensive cross‐cultural literature search on the “mind” side of the equation, suggesting that the mental phenomena that need to be considered in any integral theory include developmental levels or waves of consciousness, developmental lines or streams of consciousness, states of consciousness, and the self (or self‐system). A “master template” of these various phenomena, culled from over one‐hundred psychological systems East and West, is presented. It is suggested that this master template represents a general summary of the “mind” side of the brain‐mind integration. The essay concludes with reflections on the “hard problem,” or how the mind‐side can be integrated with the brain‐side to generate a more integral theory of consciousness.     

A comparison of information processing and dynamical systems perspectives on problem solving

Abstract

This article compares the information processing and dynamical systems perspectives on problem solving. Key theoretical constructs of the information-processing perspective include “searching” a “problem space” by using “heuristics” that produce “incremental” changes such as reaching a “subgoal” to solve a puzzle. Key theoretical constructs of the dynamical-systems perspective include “positive attractors”, “negative attractors”, and “latent attractors” that can cause large “nonincremental” changes in the possibility of a solution through the “emergence” of new ideas and beliefs that can resolve a conflict. The proposed alignment maps dynamical-system constructs to information-processing constructs: state space to problem space, negative attractor to impasse, positive attractor to productive subgoal, latent attractor to implicit cognition, and nonincremental change to insight. The purpose of the mapping is to explore similarities and differences between these constructs. Research from cognitive and social psychology illustrates how using constructs from both perspectives is helpful. The concluding section on Future Directions recommends an agenda based on three objectives: (1) create ontologies to organise current knowledge, (2) conduct research to obtain new knowledge, and (3) provide education to inform students about this knowledge.     

Stimulus congruence and stimulus-response compatibility: Two variables disentangled in an auditory reaction time task

Abstract

Stimulus—response (S-R) compatibility was a tem fmt used by Wtts and Seeger (1953) to describe effcts observed on reaction time (RT) when the stimulus—response relationship was varied, as in the following instructions: “move to tbe right when the stimulus appears on the right” (compatible) or “move to the left when the stimulus appears on the right” (incompatible). This term was later employed in a broader sense (Simon & Rudell, 1967) with paradigms involving elaborate stimuli, such as the verbal command ‘RIGHT’ delivered to the right tar (compatible) or to the left ear (incompatible). In such paradigms. subjects respond faster when the response is delivered on the same side as the stimulus (the so-called “Simon effect”). It has been shown, however, that this effect could be reversed under some circumstanas in the visual domain. In this paper, we report data showing that it can also be reversed in the auditory domain when using the above-mentioned verbal commands. This brings further evidence that stimulus-response compatibility and the Simon effect difier in essence, with the latter effect reflecting the influence of stimulus congruence, the correspondence relationship borne by the two simultaneous characteristics of the stimulus. Stimulus congruence and stimulus-response compatibility had indeed independent influences on RT, which in a serially connected information-processing modcl would imply that they act upon independent stages.     

Cognitive determinants of the success of inventors: Complex problem solving and deliberate use of divergent and convergent thinking

With reference to Henderson's (2004) assumption that inventors are “expert problem solvers”, we studied the ability of inventors to solve complex problems (CPS) using a sample of 46 German inventors. The participants had to use FSYS 2.0, a computer-simulated microworld. Additionally, we assessed metacognition, in particular the participants' ability to make deliberate use of divergent and convergent thinking. This ability was expected to be an important skill involved in solving complex problems (Dörner, Kreuzig, Reither, & Stäudel, 1983). We assumed a positive correlation between the individual success of inventors (number of granted and marketed patents) and CPS abilities. Controllability of divergent and convergent thinking turned out to be a predictor of the success of inventors and allowed us to identify the top 10% performers. Oddly however, the best problem solvers were inventors with exactly one granted patent. Data from a posteriori conducted interviews help explaining the results.