ABSTRACT
An experimental procedure to investigate the soft-construction of the pendular, clocking mode is described. In this procedure a person swings hand-held pendulums at the wrists, comfortably and rhythmically. This wrist-pendular, clocking mode can be assembled with one wrist-pendulum system (a pendulum held in either the left or right hand) or it can be assembled with two wrist-pendulum systems (one pendulum held in the left hand and another pendulum held simultaneously in the right hand). In the latter case the person's task is to swing the two pendulums comfortably together, at a common tempo and at a fixed phase relation. Several experiments using this procedure are reported in due course. The present chapter reports on one experiment, the main experiment on which much of the discussion in the book focuses.
The comfortable periodic times onto which a person settles vary with the magnitudes of the hand-held pendulums. The question posed is whether or not it is possible to describe the magnitudes of single wrist-pendulum systems and double (that is, coupled) wrist-pendulum systems in the same way through the same single quantities. To do so would lay the foundations for a general law-based account of wrist-pendular periodic motion.
A single wrist-pendulum system consists of three concentrations of mass— 130 those of the pendulum shaft, the added weights, and the hand—at different distances from a common axis of rotation. It is a compound pendulum. Through the method introduced by Huygens in the seventeenth century a compound wrist-pendulum system can be redescribed as a simple pendulum—that is, as a single concentration of mass at a single distance from the point of rotation—whose periodic timing is the same as that of the compound wrist-pendulum system. A double wrist-pendulum system is similarly conceivable as a common pendulum, albeit one in which mechanical forces are only partially responsible for the connections among the various masses. Neural processes, rather than mechanical forces, connect the total mass of the left wrist-pendulum system with that of the right wrist-pendulum system.
It is assumed herein that "Huygens' law" applies equally to single and double wrist-pendulum systems and that both, therefore, are describable through single quantities of mass, length, and time. The implication is that a double wrist-pendulum system can be characterized, in a principled manner, as a virtual single wrist-pendulum system. The means by which this characterization is achieved, namely, Huygens' law, is a conservation based symmetry operation. In general terms, the operation transforms a system into a considerably simpler version of itself, leaving invariant the behavioral property of periodic timing.
This physical notion of a virtual single system (or unitary process) assembled through the conservations pertains to very general aspects of the problem of how movements are coordinated and controlled. It is of particular relevance to the intuitive idea that in a coordinated activity such as locomotion, two or more biokinematic degrees of freedom are constrained to act as a single functional unit. As will become evident, the strategy of physically interpreting the behavior of two or more isochronous pendular systems as that of a (virtual) single system is fundamental to the analysis of the data and to the development of a law-based account of rhythmic movement.
