James A. Dixon

Dynamics of representational change: entropy, action, and cognition.

Explaining how the cognitive system can create new structures has been a major challenge for cognitive science. Self-organization from the theory of nonlinear dynamics offers an account of this remarkable phenomenon. Two studies provide an initial test of the hypothesis that the emergence of new cognitive structure follows the same universal principles as emergence in other domains (e.g., fluids, lasers). In both studies, participants initially solved gear-system problems by manually tracing the force across a system of gears. Subsequently, they discovered that the gears form an alternating sequence, thereby demonstrating a new cognitive structure. In both studies, dynamical analyses of action during problem solving predicted the spontaneous emergence of the new cognitive structure. Study 1 showed that a peak in entropy, followed by negentropy, key indicators of self-organization, predicted discovery of alternation. Study 2 replicated these effects, and showed that increasing environmental entropy accelerated discovery, a classic prediction from dynamics. Additional analyses based on the relationship between phase transitions and power-law behavior provide converging evidence. The studies provide an initial demonstration of the emergence of cognitive structure through self-organization.

The Developmental Role of Intuitive Principles in Choosing Mathematical Strategies

This study investigated the relation between the development of understanding principles that govern a problem and the development ofmathematical strategies used to solve it. College students and 2nd, 5th, 8th, and I lth graders predicted the resulting temperature when 2 containers of water were combined. Students first estimated answers to the problems and then solved the problems using math. The pattern of estimated answers provided a measure of the intuitive understanding of task principles. Developmental differences in intuitive understanding were related to the type of math strategy students used. Analysis of individual data patterns showed that understanding an intuitive principle was necessary but not sufficient to generate a math strategy consistent with that principle. Implications for the development of problem solving are discussed. Current models of problem solving propose that a persons conceptual or intuitive understanding is an important factor in solving a problem with formal methods such as mathematics. Conceptual or intuitive understanding involves the qualitative representation of the relevant relations among variables in a task. We call this type of understanding intuitive, following Brunswik (1956) and Hammond (1982; Hammond, Harem,

The dynamics of insight: Mathematical discovery as a phase transition

In recent work in cognitive science, it has been proposed that cognition is a self-organizing, dynamical system. However, capturing the real-time dynamics of cognition has been a formidable challenge. Furthermore, it has been unclear whether dynamics could effectively address the emergence of abstract concepts (e.g., language, mathematics). Here, we provide evidence that a quintessentially cognitive phenomenon—the spontaneous discovery of a mathematical relation—emerges through self-organization. Participants solved a series of gear-system problems while we tracked their eye movements. They initially solved the problems by manually simulating the forces of the gears but then spontaneously discovered a mathematical solution. We show that the discovery of the mathematical relation was predicted by changes in entropy and changes in power-law behavior, two hallmarks of phase transitions. Thus, the present study demonstrates the emergence of higher order cognitive phenomena through the nonlinear dynamics of self-organization.

The link between statistical segmentation and word learning in adults

Many studies have shown that listeners can segment words from running speech based on conditional probabilities of syllable transitions, suggesting that this statistical learning could be a foundational component of language learning. However, few studies have shown a direct link between statistical segmentation and word learning. We examined this possible link in adults by following a statistical segmentation exposure phase with an artificial lexicon learning phase. Participants were able to learn all novel object-label pairings, but pairings were learned faster when labels contained high probability (word-like) or non-occurring syllable transitions from the statistical segmentation phase than when they contained low probability (boundary-straddling) syllable transitions. This suggests that, for adults, labels inconsistent with expectations based on statistical learning are harder to learn than consistent or neutral labels. In contrast, a previous study found that infants learn consistent labels, but not inconsistent or neutral labels.

A Tutorial on Multifractality, Cascades, and Interactivity for Empirical Time Series in Ecological Science

Interactivity is a central theme of ecological psychology. According to Gibsonian views, behavior is the emergent property of interactions between organism and environment. Hence, an important challenge for ecological psychology has been to identify physical principles that provide an empirical window into interactivity. We suspect that multifractality, a concept from statistical physics, may be helpful in this regard, and we offer this article as a tutorial on multifractality with 2 main goals. First, we aim to describe multifractality with a series of simple, concrete, but progressively more elaborate examples that will incrementally elucidate the relationship between multifractality and interactivity. Second, we aim to describe a direct estimation method for computing the multifractal spectrum (e.g., Chhabra & Jensen, 1989), presenting it as an alternative that avoids the pitfalls of more popular methods and that may address more appropriately the measurements traditionally taken by ecological psychologists. In sum, this tutorial aims to unpack the theoretical background for an analytical method allowing rigorous test of interactivity in a variety of empirical settings.

Multifractal dynamics in the emergence of cognitive structure.

The complex-systems approach to cognitive science seeks to move beyond the formalism of information exchange and to situate cognition within the broader formalism of energy flow. Changes in cognitive performance exhibit a fractal (i.e., power-law) relationship between size and time scale. These fractal fluctuations reflect the flow of energy at all scales governing cognition. Information transfer, as traditionally understood in the cognitive sciences, may be a subset of this multiscale energy flow. The cognitive system exhibits not just a single power-law relationship between fluctuation size and time scale but actually exhibits many power-law relationships, whether over time or space. This change in fractal scaling, that is, multifractality, provides new insights into changes in energy flow through the cognitive system. We survey recent findings demonstrating the role of multifractality in (a) understanding atypical developmental outcomes, and (b) predicting cognitive change. We propose that multifractality provides insights into energy flows driving the emergence of cognitive structure.

The Self-Organization of Insight: Entropy and Power Laws in Problem Solving

Explaining emergent structure remains a challenge for all areas of cognitive science, and problem solving is no exception. The modern study of insight has drawn attention to the issue of emergent cognitive structure in problem solving research. We propose that the explanation of insight is beyond the scope of conventional approaches to cognitive science in terms of symbolic representation. Cognition may be better described in terms of an open, nonlinear dynamical system. By this reasoning, insight would be the self-organization of novel structure. Self-organization is a well-studied phenomenon of dynamical systems theory, associated with specific trends in entropy and power-law behavior. We present work using nonlinear dynamics to capture these trends in entropy and power-law behavior and thus to predict the self-organization of novel cognitive structure in a problem-solving task. Future explorations of problem solving will benefit from considerations of the continuous nonlinear interactions among action, cognition, and the environment.

The prehistory of discovery: precursors of representational change in solving gear system problems.

Microgenetic research has identified 2 different types of processes that produce representational change: theory revision and redescription. Both processes have been implicated as important sources of developmental change, but their relative status across development has not been addressed. The current study investigated whether (a) the process of representational change undergoes developmental change itself or (b) different processes occupy different niches in the course of knowledge acquisition. College, 3rd-, and 6th-grade students solved gear system problems over 2 sessions. For all grades, discovery of the physical principles of the gear system was consistent with theory revision, but discovery of a more sophisticated strategy, based on the alternating sequence of gears, was consistent with redescription. The results suggest that these processes may occupy different niches in the course of acquiring knowledge and that the processes are developmentally invariant across a broad age range.

Redescription disembeds relations: Evidence from relational transfer and use in problem solving

How relational information becomes disembedded from its original context is an important issue for theories of cognition. Two experiments tested the hypothesis that a process calledredescription disembeds relations, resulting in abstract and, therefore, more transferable and robust representations. In Experiment 1, participants solved simple problems involving an alternating sequence. Participants who discovered the alternating-sequence relation through redescription transferred the relation to a second type of problem more quickly and used it more consistently than did participants who had been directly instructed on the alternating-sequence strategy. Experiment 2 showed similar effects for participants who discovered the alternating-sequence relation through redescription, as compared with participants who had discovered the relation through information available in the display. The present results converge with previous experimental and correlational evidence that suggests that redescription creates abstract representations of relations.

Accelerated Head and Body Growth in Infants Later Diagnosed With Autism Spectrum Disorders: A Comparative Study of Optimal Outcome Children:

Previous research has demonstrated accelerated head and body growth during infancy in children with autism spectrum disorders. No study has yet examined head growth in children who lose their autism spectrum disorder diagnoses. Head circumference, length, and weight growth during infancy for 24 children who maintained their diagnoses were compared with 15 children who lost their diagnoses, and to 37 typically developing controls. Results showed that head circumference and weight growth were significantly greater in both autism spectrum disorder groups compared with controls, with no significant differences between autism spectrum disorder groups. However, when length and weight were controlled for, accelerated head growth remained significant in the children who lost their diagnoses. Findings suggest that children who lose their autism spectrum disorder diagnoses and children who maintain their diagnoses show similar head circumference, length, and weight growth trajectories during infancy, although subtle differences in body growth between groups may exist.