Cooperative Phenomena in Biological Motion

Abstract

The production of a “simple” utterance, such as the syllable /ba/, involves the cooperation of a large number of neuromuscular elements operating on different time scales, e.g., at respiratory, laryngeal, and supralaryngeal levels. Yet somehow, from this huge dimensionality, /ba/ emerges as a coherent and well-formed pattern. Similarly, were one to count the neurons, muscles, and joints that cooperate to produce the “simple” act of walking, literally thousands of degrees of freedom would be involved. Yet again, somehow walking emerges as a fundamentally low-dimensional cyclical pattern—in the language of dynamical systems, a periodic attractor. In physics, an infinite dimensional system, described by a complicated set of partial, nonlinear differential equations can be reduced—when probed experimentally or analyzed theoretically—to a low-dimensional description [1,2]. In all these cases, it seems, information about the system is compressed—from a microscopic basis of huge dimensionality—to a macroscopic basis of low dimensionality.

Research supported by ONR Contract N00014-83-C-0083, NINCDS Grant NS-13617, and BRSG Grant RR-05596. We are very grateful to Professor H. Haken for his continued interest and encouraging comments on this work, as well as his coworkers in Stuttgart (particularly G. Schöner and H. Bunz) for their helpful, informed discussions.