Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269-1020, USA.
Mem Cognit. 2009 Dec;37(8):1132-49. doi: 10.3758/MC.37.8.1132.
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.
在认知科学的近期研究中，有人提出认知是一个自组织、动力系统。然而，捕捉认知的实时动态一直是一个艰巨的挑战。此外，目前还不清楚动态是否能够有效地解决抽象概念（如语言、数学）的出现问题。在这里，我们提供的证据表明，一个典型的认知现象——自发发现数学关系——通过自组织而出现。参与者在解决一系列齿轮系统问题的同时，我们跟踪他们的眼球运动。他们最初通过手动模拟齿轮的力来解决问题，但随后自发地发现了一个数学解决方案。我们表明，熵的变化和幂律行为变化可以预测数学关系的发现，这两个都是相变的标志。因此，本研究通过自组织的非线性动力学证明了更高阶认知现象的出现。
