Representations in Distributed Cognitive Tasks

In this article we propose a theoretical framework of distributed representations and a methodology of representational analysis for the study of distributed cognitive tasks—tasks that require the processing of information distributed across the internal mind and the external environment. The basic principle of distributed representations Is that the representational system of a distributed cognitive task is a set of internal and external representations, which together represent the abstract structure of the task. The basic strategy of representational analysis is to decompose the representation of a hierarchical task into its component levels so that the representational properties at each level can be independently examined. The theoretical framework and the methodology are used to analyze the hierarchical structure of the Tower of Hanoi problem. Based on this analysis, four experiments are designed to examine the representational properties of the Tower of Hanoi. Finally, the nature of external representations is discussed.     

The effect of external representations on numeric tasks

This article explores the effect of external representations on numeric tasks. Through several minor modifications on the previously reported two-digit number comparison task, we obtained different results. Rather than holistic comparison, we found parallel comparison. We argue that this difference was a reflection of different representational forms: The comparison was based on internal representations in previous studies but on external representations in our present study. This representational effect is discussed under a framework of distributed number representations. We propose that in numerical tasks involving external representations, numbers should be considered as distributed representations, and the behaviour in these tasks should be considered as the interactive processing of internal and external information through the interplay of perceptual and cognitive processes. We suggest that theories of number representations and process models of numerical cognition should consider external representations as an essential component.     

The Nature of External Representations in Problem Solving

This article proposes a theoretical framework for external representation based problem solving. The Tic-Tac-Toe and its isomorphs are used to illustrate the procedures of the framework as a methodology and test the predictions of the framework as a functional model. Experimental results show that the behavior in the Tic-Tac-Toe is determined by the directly available information in external and internal representations in terms of perceptual and cognitive biases, regardless of whether the biases are consistent with, inconsistent with, or irrelevant to the task. It is shown that external representations are not merely inputs and stimuli to the internal mind and that they have much more important functions than mere memory aids. A representational determinism is suggested—the form of a representation determines what information can be perceived, what processes can be activated, and what structures can be discovered from the specific representation.     

Mental evolution and development: evidence for secondary representation in children, great ages, and other animals

Recent interest in the development and evolution of theory of mind has provided a wealth of information about representational skills in both children and animals. According to J. Perner (1991), children begin to entertain secondary representations in the 2nd year of life. This advance manifests in their passing hidden displacement tasks, engaging in pretense and means-ends reasoning, interpreting external representations, displaying mirror self-recognition and empathic behavior, and showing an early understanding of "mind" and imitation. New data show a cluster of mental accomplishments in great apes that is very similar to that observed in 2-year-old humans. It is suggested that it is most parsimonious to assume that this cognitive profile is of homologous origin and that great apes possess secondary representational capacity. Evidence from animals other than apes is scant. This analysis leads to a number of predictions for future research.     

Representing task context: proposals based on a connectionist model of action

Representations of task context play a crucial role in shaping human behavior. While the nature of these representations remains poorly understood, existing theories share a number of basic assumptions. One of these is that task representations are discrete, independent, and non-overlapping. We present here an alternative view, according to which task representations are instead viewed as graded, distributed patterns occupying a shared, continuous representational space. In recent work, we have implemented this view in a computational model of routine sequential action. In the present article, we focus specifically on this model's implications for understanding task representation, considering the implications of the account for two influential concepts: (1) cognitive underspecification, the idea that task representations may be imprecise or vague, especially in contexts where errors occur, and (2) information-sharing, the idea that closely related operations rely on common sets of internal representations.     

Basing Categorization on Individuals and Events

Exemplar, prototype, and connectionist models typically assume that events constitute the basic unit of learning and representation in categorization. In these models, each learning event updates a statistical representation of a category independently of other learning events. An implication is that events involving the same individual affect learning independently and are not integrated into a single structure that represents the individual in an internal model of the world. A series of experiments demonstrates that human subjects track individuals across events, establish representations of them, and use these representations in categorization. These findings are consistent with “representationalism,” the view that an internal model of the world constitutes a physical level of representation in the brain, and that the brain does not simply capture the statistical properties of events in an undifferentiated dynamical system. Although categorization is an inherently statistical process that produces generalization, pattern completion, frequency effects, and adaptive learning, it is also an inherently representational process that establishes an internal model of the world. As a result, representational structures evolve in memory to track the histories of individuals, accumulate information about them, and simulate them in events.     

From parallel to serial processing: a computational study of visual search

A novel computational model of a preattentive system performing visual search is presented. The model processes displays of lines, reproduced from Wolfe, Friedman-Hill, Stewart, and O'Connell's (1992) and Treisman and Sato's (1990) visual-search experiments. The response times measured in these experiments suggest that some of the displays are searched serially, whereas others are scanned in parallel. Our neural network model operates in two phases. First, the visual displays are compressed via standard methods (principal component analysis), to overcome assumed biological capacity limitations. Second, the compressed representations are further processed to identify a target in the display. The model succeeds in fast detection of targets in experimentally labeled parallel displays, but fails with serial ones. Analysis of the compressed internal representations reveals that compressed parallel displays contain global information that enables instantaneous target detection. However, in representations of serial displays, this global information is obscure, and hence, a target detection system should resort to a serial, attentional scan of local features across the display. Our analysis provides a numerical criterion that is strongly correlated with the experimental response time slopes and enables us to reformulate Duncan and Humphreys's (1989) search surface, using precise quantitative measures. Our findings provide further insight into the important debate concerning the dichotomous versus continuous views of parallel/serial visual search.     

Identifying Representational Competence With Multi-Representational Displays

Increasingly, multi-representational educational technologies are being deployed in science classrooms to support science learning and the development of representational competence. Several studies have indicated that students experience significant challenges working with these multi-representational displays and prefer to use only one representation while problem solving. Here, we examine the use of one such display, a multi-representational molecular mechanics animation, by organic chemistry undergraduates in a problem-solving interview. Using both protocol analysis and eye fixation data, our analysis indicates that students rely mainly on two visual–spatial representations in the display and do not make use of two accompanying mathematical representations. Moreover, we explore how eye fixation data complement verbal protocols by providing information about how students allocate their attention to different locations of a multi-representational display with and without concurrent verbal utterances. Our analysis indicates that verbal protocols and eye movement data are highly correlated, suggesting that eye fixations and verbalizations reflect similar cognitive processes in such studies.     

How a Cockpit Remembers Its Speeds

Cognitive science normally takes the individual agent as its unit of analysis. In many human endeavors, however, the outcomes of interest are not determined entirely by the information processing properties of individuals. Nor can they be inferred from the properties of the individual agents, alone, no matter how detailed the knowledge of the properties of those individuals may be. In commercial aviation, for example, the successful completion of a flight is produced by a system that typically includes two or more pilots interacting with each other and with a suite of technological devices. This article presents a theoretical framework that takes a distributed, socio-technical system rather than an individual mind as its primary unit of analysis. This framework is explicitly cognitive in that it is concerned with how information is represented and how representations are transformed and propagated in the performance of tasks. An analysis of a memory task in the cockpit of a commercial airliner shows how the cognitive properties of such distributed systems can differ radically from the cognitive properties of the individuals who inhabit them.     

A Cognitive Theory of Graphical and Linguistic Reasoning: Logic and Implementation

We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form, and (b) the implementational differences that affect facility of inference. Our theory proposes that graphical representation limit abstraction and thereby aid “processibility”. We discuss the ideas of specificity and abstraction, and their cognitive relevance. Empirical support both comes from tasks which involve the manipulation of external graphics and tasks that do not. For the former, we take Euler's (1772) circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals and with Johnson-Laird's (1983) mental models representations. We demonstrate equivalence of the graphical Euler system, and the nongraphical mental models system. For tasks not involving manipulation of external graphics, we discuss text comprehension, and the mental performance of syllogisms. By positing an internal system with the same specificity as Euler's circles, we cover the mental models data, and generate new empirical predictions. Finally, we consider how the architecture of working memory explains why such specific representations are relatively easy to store.     

Fantasy,defense, and the representational world

This paper discusses the manipulation of mental representations, particularly in relation to the psychoanalytic concepts of conscious or unconscious fantasy. A distinction is made between the unconscious phenomenal (experiential) aspect of representations and the nonexperiential, quasi-structural aspect. The concept of the representational world is described and elaborated, and its development is seen as a consequence of the infant's interaction with itself and the external world. Processes such as identification and projection can be seen in terms of changes in self and object representations, and the same is true for all the mechanisms of defense. The content of unconscious wishes is transformed, by use of such mechanisms, into representations that are acceptable to consciousness. Major transformations of unconscious representational content occur in the process of creating unconscious (preconscious) fantasy, and further transformations are frequently needed before such (preconscious) fantasies are permitted access to consciousness. The concept of projective identification is considered in the light of the ideas put forward in the paper.     

The perception/cognition distincton: Challenging the representational account

A central goal for cognitive science and philosophy of mind is to distinguish between perception and cognition. The representational approach has emerged as a prominent candidate to draw such a distinction. The idea is that perception and cognition differ in the content and the format in which the information is represented —just as perceptual representations are nonconceptual in content and iconic in format, cognitive representations are conceptual in content and discursive in format. This paper argues against this view. I argue that both perception and cognition can use conceptual and nonconceptual contents and be vehiculated in iconic and discursive formats. If correct, the representational strategy to distinguish perception from cognition fails.     

The impact of external representation in a rule discovery task

The 2-4-6 rule discovery task introduced by Wason (1960) elicits generally poor hypothesis-testing behaviour as reflected by the underwhelming effort and creativity participants invest in the process before announcing their “best” guess. The traditional task departs from real-world hypothesis testing in a significant respect: Reasoners proceed to discover the rule solely from an internal representation of the problem space. Two studies reported here examined representational effects in the 2-4-6 task by developing task isomorphs that offered external, physically manipulable, representations of the dimensions of the problem space. These isomorphs led to a significantly higher incidence of successful rule discovery, driven by significantly greater diligence and creative exploration of the problem space, compared to other task isomorphs that did not offer such an external representation. These results confirm the fruitfulness of a research programme that explores the contextual determinants of sound hypothesis testing.     

Husserl on Meaning,Grammar, and the Structure of Content

Husserl’s Logical Grammar is intended to explain how complex expressions can be constructed out of simple ones so that their meaning turns out to be determined by the meanings of their constituent parts and the way they are put together. Meanings are thus understood as structured contents and classified into formal categories to the effect that the logical properties of expressions reflect their grammatical properties. As long as linguistic meaning reduces to the intentional content of pre-linguistic representations, however, it is not trivial to account for how semantics relates to syntax in this context. In this paper, I analyze Husserl’s Logical Grammar as a system of recursive rules operating on representations and suggest that the syntactic form of representations (both mental and linguistic) contributes to their semantics because it carries information about semantic role. I further discuss Husserl’s syntactic account of the unity of propositions and argue that, on this  account, logical form supervenes on syntactic form. In the last section I draw some implications for the phenomenology of thought and conjecture that the structural features it displays are likely to convey the syntactic structures of an underlying language-like representational system.     

Apraxia in corticobasal degeneration.

Corticobasal degeneration (CBD) is a degenerative disease that often presents with an asymmetric progressive ideomotor limb apraxia. Some apraxic subjects may fail to perform skilled purposive movements on command because they have lost the memories or representations that specify how these movements should be performed (representational deficit). In contrast, other apraxic subjects may have the movement representations but are unable to utilize the information contained in them to execute skilled purposive movements (production-execution deficit). To learn if the apraxic deficit in CBD is induced by a representational or a production-execution deficit, we tested three nondemented subjects with CBD on tasks requiring production of meaningful or meaningless gestures to command, gesture imitation, gesture discrimination, and novel gesture learning. A fourth subject with incomplete data also is presented. The results suggest that the apraxia associated with CBD is initially induced by a production-execution defect with relative sparing of the movement representations.     

A dynamic context model of interactive behavior

A dynamic context model of interactive behavior was developed to explain results from two experiments that tested the effects of interaction costs on encoding strategies, cognitive representations, and response selection processes in a decision-making and a judgment task. The model assumes that the dynamic context defined by the mixes of internal and external representations and processes are sensitive to the interaction cost imposed by the task environment. The model predicts that changes in the dynamic context may lead to systematic biases in cognitive representations and processes that eventually influence decision-making and judgment outcomes. Consistent with the predictions by the model, results from the experiments showed that as interaction costs increased, encoding strategies and cognitive representations shifted from perception-based to memory-based. Memory-based comparisons of the stimuli enhanced the similarity and dominance effects, and led to stronger systematic biases in response outcomes in a choice task. However, in a judgment task, memory-based representations enhanced only the dominance effects. Results suggested that systematic response biases in the dominance context were caused by biases in the cognitive representations of the stimuli, but response biases in the similarity context were caused by biases in the comparison process induced by the choice task. Results suggest that changes in interaction costs not only change whether information was assessed from the external world or from memory but also introduce systematic biases in the cognitive representation of the information, which act as biased inputs to the subsequent decision-making and judgment processes. Results are consistent with the idea of interactive cognition, which proposes that representations and processes are contingent on the dynamic context defined by the information flow between the external task environment and internal cognition.     

Discrete internal pattern representations and visual detection of small changes in pattern shape

A scheme is proposed that relates the internal representation of pattern stimuli to visual pattern discrimination performance. The main assumptions of the scheme are: (1) internal representations are assigned to patterns probabilistically; (2) internal representations are discrete; (3) visual discriminability of two patterns is determined by the differences in the assignment probabilities of their internal representations. It is suggested that the internal representations associated with a pattern may be analyzed by measuring the visual detectability of small changes in pattern shape at points along a continuum of shapes. This continuum is generated by a group of transformations smoothly parameterized by a single variable. In two experiments designed to test this approach, subjects discriminated pattern displays containing combinations of three-dot subpatterns. Under the hypothesis that there were just two relevant internal representations, specifying dot collinearity and dot noncollinearity, the qualitative characteristics of the discrimination performance were correctly predicted.     

Factors affecting the onset and magnitude of linear vection

The role of central and peripheral vision in the production of linear vection was assessed by using displays in which flow structure and sources of internal and external depth information were manipulated. Radial optical flow was more effective for inducing self-motion in both central and peripheral visual fields than was lamellar flow in displays of the same size. The presence of external occlusion information was necessary to induce linear vection when small displays were composed of lamellar flow, whereas the effectiveness of small radial displays did not depend on the availability of occlusion edges.     

Similar but not the same: A comparison of the utility of directly rated and feature-based similarity measures for generating spatial models of conceptual data

Spatial models are employed to represent conceptual data in a wide range of fields within psychological research. In order to generate spatial models, it is necessary to first obtain empirical similarity data. A number of methods are available for collecting these data, but little effort has been made to compare their relative utility. In this article, we compare directly rated and five feature-based similarity data types in regard to their ability to be adequately represented by a spatial model (representational goodness of fit), and the ability of the representations to predict three external empirical variables (predictive validity). The results indicate that the representational goodness of fit of the feature-based similarities is noticeably superior to the directly rated similarities, and that the predictions of representations derived from common feature similarity data are substantially more likely than the predictions of all of the alternative representations. It is suggested that these findings are highly relevant to researchers employing spatial models to represent conceptual data, given that direct pairwise ratings have generally been considered the “gold standard” means of obtaining empirical similarities.