Movement-produced invariants in haptic explorations: An example of a self-organizing, information-driven, intentional system

Abstract Biological systems are the prototypes of self-organizing systems; systems that are self starting, self-driving, adaptive systems. A self-driving, adaptive system is one whose evolutionary behavior is governed by the descriptions of the system, the initial conditions, and the constraints imposed by its environment. Basically, a self-driving, adaptive system is a dynamical system. This article is on a dynamic model of a task-specific, intelligent-mechanism of the haptic system. The mechanisms of interest is the hand and its appendages in the act of discerning the length of a visually occluded hand-held rod. Empirical observations showed that people are extremely adept in these tasks and the perceived lengths, considered as outputs of the mechanisms — hand-muscles-joints haptic subsystems, matched almost perfectly the actual lengths of the rods, particularly, when the rods were of uniform density and mass distribution. These observations pose, to the theoretician, the onerous task of discovering both the descriptions of the system as well as the inputs to the system. On the basis of several investigations, Solomon (Solomon and Turvey 1988) proposed a Haptic Operator model for the intelligent-mechanism of the haptic subsystem. The model characterizes the subsystem as a self-starting, self-driving, adaptive system whose outputs are only the invariant properties of its own dynamics. Because it is self-starting, the mechanism is identified as an intentional system. In this article, intentionally is simply labeled as a selection operator without further elaborations on the nature of the operation of selection. Because it is self-driving and adaptive, the mechanism is identified as an information-driven dynamical system. To underscore the information-driven character of biological systems, the article begins by distinguishing three kinds of dynamical systems: energy-driven, signal-driven, and information- driven systems. Then, the concepts of transformations and invariants are introduced to motivate the concept of dynamical invariants and the emergence of operators as representations of these dynamical properties. The article concludes by drawing the parallel between the invariants of a dynamical system and the invariants of the geometry of the system's dynamics and identifying information with the geometric/kinematic invariants of a dynamical system.