Physical Modeling Applies to Physiology, Too∗

A physical model was utilized to show that the neural system can memorize a target position and is able to cause motor and sensory events that move the arm to a target with more accuracy. However, this cannot indicate in which coordinates the necessary computations are carried out. Turning off the lights causes the error to increase which is accomplished by cutting off one feedback path. The geometrical properties of arm kinematics and the properties of the kinesthetic and visual sensorial systems should be better known before inferences about higher levels of processing can be drawn. An acceptable model for a physical system should be able to account for the observations in a wide range of situations and in a manner that does not depend on its own representation but only on that of the represented system. Coincidentally, this necessity is currently receiving a fair bit of attention in the robotics research, although, at least in the case of mechanical systems, the question was settled satisfactorily by the physicists and the mathematicians of the last century. Bruynincks (1991) has listed four types of invariance which are required to construct a theory with physical relevance. Although discussed in an engineering context, these invariances are also needed for physiological models. These are: invariance (1) to a change in reference frame, (2) to a change in physical units, (3) to a change in mathematical representation, and (4) to a change in arbitrary choices. It is unfortunate that the model proposed by Flanders et al. fails all four requirements. In other terms, one could construct uncountable variations of the proposed model that could equally explain the data. The question of reference frame invariance is of course of direct relevance to the subject matter since the essence of the proposed model is to deal with coordinate changes. In the study and in this commentary, the human arm is ∗in Behavioral Brain Sciences 1992 15(2):342–343, open peer commentary on Flanders, M., Tillery, S. I. H., Soechting, J. F. Early stages in a sensorimotor transformation. Behavioral Brain Sciences 1992 15(2):309–320. treated as three articulated rigid bodies: the torso used as the ground body, the arm and the forearm. Fig. 1 shows a cartoon version of the human arm kinematic arrangement in terms of two joints and three rigid links. For the sake of brevity, it will be discussed only intuitively. It can be readily observed that four coordinates are required to describe its position (and velocity). These coordinates can be chosen among many arbitrary possibilities. One fundamental reason from an engineering viewpoint, and most certainly, also from a physiological view point, for choosing one set rather than another is their respective computational advantages. From an engineering perspective, the reasons for making that choice are given by the computing hardware available to us. From a physiological perspective, the question cannot be so easily answered. The lack of detailed knowledge of how neural computations are carried out makes it difficult to speak of computational advantages other than in very general terms, if indeed it is a factor influencing Nature’s choice. The discussion about coordinates is important because it directly affects that of reference frames. What has just been discussed may be illustrated by an example. In the case of computer control, the set