Damian G. Stephen: Publications


Stephen, D. G., Boncoddo, R. A., Magnuson, J. S., & Dixon, J. A. (2009). The dynamics of insight: Mathematical discovery as a phase transition. Memory & Cognition, 37, 1132-1149. [pdf]
Recent work in cognitive science has proposed that cognition is a self-organizing, dynamical system. However, capturing the real-time dynamics of cognition has been a formidable challenge. Further, 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 systematic changes in system entropy and power-law behavior, two hallmarks of phase transitions. Thus, the current study demonstrates the emergence of higher-order cognitive phenomena through the nonlinear dynamics of self-organization.  

Stephen, D. G., & Arzamarski, R. (2009). Self-training in dynamic touch: Striking improves judgment by wielding. Attention, Perception & Psychophysics, 71, 1717-1723. [pdf]
In traditional theories of perceptual learning, sensory modalities support one another. A good example comes from research on dynamic touch, the wielding of an unseen object to perceive its properties. Wielding provides the haptic system with mechanical information related to the length of the object. Visual feedback can improve the accuracy of subsequent length judgments: visual perception supports haptic perception. Such cross-modal support is not the only route to perceptual learning. We present a dynamic touch task in which we have replaced visual feedback with the instruction to strike the unseen object against an unseen surface following length judgment. This additional mechanical information improves subsequent length judgments. We propose a self-organizing perspective in which a single modality trains itself.
Keywords: dynamic touch, perceptual learning, feedback, growth curve modeling

Stephen, D. G., Mirman, D., Magnuson, J. S., & Dixon, J. A. (2009). Lévy-like diffusion in eye movements during spoken-language comprehension. Physical Review E, 79, 056114. [pdf]
This study explores the diffusive properties of human eye movements during a language comprehension task. In this task, adults are given auditory instructions to locate named objects on a computer screen. Although it has been convention to model visual search as standard Brownian diffusion, we find evidence that eye movements are hyperdiffusive. Specifically, we use comparisons of maximum likelihood fit as well as standard deviation analysis and diffusion entropy analysis to show that visual search during language comprehension exhibits Lévy-like rather than Gaussian diffusion.
PACS numbers: 89.75.Da, 05.40.Fb, 05.45.Tp, 87.19.lv
Blau, J. J. C., Stephen, D. G., Carello, C., & Turvey, M. T. (2009). Prism adaptation of underhand throwing: Rotational inertia and the primary and latent aftereffect. Neuroscience Letters, 456, 54-58. [pdf]
The effect of prism adaptation on movement is typically reduced when movement at test (with prisms removed) is different from movement at training.  Previous research suggests, however, that some adaptation is latent and only revealed through further testing in which the movement at training is fully reinstated. Movement in their training trials was throwing overhand to a vertical target with a mass attached to the arm. The critical test trials involved the same act initially without the attached mass and then with the attached mass. In replication, we studied throwing underhand to a horizontal target with left shifting prisms and a dissociation of the throwing arm’s mass and moment of inertia. The two main results were that the observed latent aftereffect (a) depended on the similarity of training and test moments of inertia, and (b) combined with the primary aftereffect to yield a condition-independent sum. Discussion focused on a parallel between prism adaptation and principles governing recall highlighted in investigations of implicit memory: Whether given training (study) conditions lead to good or poor persistence of adaptation (memory performance) at test depends on the conditions at test relative to the conditions at training (study).


Stephen, D. G., & Dixon, J. A. (2009). The self-organization of insight: Entropy and power laws in problem solving. Journal of Problem Solving, 2, 72-101. (Invited review). [pdf]
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 selforganization 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.
Keywords: problem solving, insight, emergence, self-organization, entropy, power law


Stephen, D. G., Dixon, J. A., & Isenhower, R. W. (in press). Dynamics of representational change: Entropy, action, and cognition. Journal of Experimental Psychology: Human Perception & Performance. [pdf of uncorrected proofs]
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 from the same universal priniciples 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.
Keywords: representation, cognition, dynamic systems, embodiment, entropy


Stephen, D. G., Stepp, N., Dixon, J. A., & Turvey, M. T. (2008). Strong anticipation: Long-range correlations in synchronization behaviors. Physica A, 387, 5271-5278. [pdf]
Strong anticipation has emerged as a new framework for studying prospective control. According to earlier theories of prediction, anticipatory behavior rests on temporally local predictions from internal models. Strong anticipation eschews internal models and draws on the embedding of an organism in its environment. In this formulation, behavior is sensitive to the non-local temporal structure of the environment. We present initial evidence for strong anticipation in a synchronization task with tapping as the behavior. Participants were instructed to synchronize, to the best of their abilities, with a (unpredictable) chaotic signal. Our data suggest a close relationship between the long-range correlations of the chaotic signal and the long-range correlations of the synchronization behavior.
Keywords: strong anticipation, synchronization, tapping, detrended fluctuation analysis (DFA)