The Gesture as an Autonomous Nonlinear Dynamical System

ABSTRACT

We propose a theory of how the speech gesture determines change in a functionally relevant variable of vocal tract state (e.g., constriction degree). A core postulate of the theory is that the gesture determines how the variable evolves in time independent of any executive timekeeper. That is, the theory involves intrinsic timing of speech gestures. We compare the theory against others in which an executive timekeeper determines change in vocal tract state. Theories that employ an executive timekeeper have been proposed to correct for disparities between theoretically predicted and experimentally observed velocity profiles. Such theories of extrinsic timing make the gesture a nonautonomous dynamical system. For a nonautonomous dynamical system, the change in state depends not just on the state but also on time. We show that this nonautonomous extension makes surprisingly weak kinematic predictions both qualitatively and quantitatively. We propose instead that the gesture is a theoretically simpler nonlinear autonomous dynamical system. For the proposed nonlinear autonomous dynamical system, the change in state depends nonlinearly on the state and does not depend on time. This new theory provides formal expression to the notion of intrinsic timing. Furthermore, it predicts experimentally observed relations among kinematic variables.