The dynamics of insight: Mathematical discovery as a phase transition |
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Authors: | Damian G Stephen Rebecca A Boncoddo James S Magnuson James A Dixon |
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Institution: | 1.Department of Psychology,University of Connecticut,Storrs;2.Haskins Laboratories,New Haven |
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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. |
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