title: The dynamics of insight: mathematical discovery as a phase transition.
abstract: 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.
authors.affiliation: Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269-1020, USA. damian.stephen@uconn.edu
authors.forename: Damian G
authors.initials: DG
authors.lastname: Stephen
authors.forename: Rebecca A
authors.initials: RA
authors.lastname: Boncoddo
authors.forename: James S
authors.initials: JS
authors.lastname: Magnuson
authors.forename: James A
authors.initials: JA
authors.lastname: Dixon
mesh_terms: D000465:Algorithms; D001288:Attention; D001364:Awareness; D019277:Entropy; D005133:Eye Movements; D006801:Humans; D007092:Imagination; D008433:Mathematics; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D009949:Orientation; D010364:Pattern Recognition, Visual; D011340:Problem Solving; D011597:Psychomotor Performance; D011601:Psychophysics