Eigenvalues of the inertia tensor and exteroception by the “muscular sense”

Abstract

Muscle spindles and Golgi tendon organs constitute the receptor foundation to the “muscle sense”. Muscle sensitivity has long been assumed relevant to the non-visual perception of the positions and motions of the body's segments and of the properties of hand-held objects. Dynamic touch is the label given to the particular kind of tactile exteroperception that involves a non-spatial input from muscles and tendons. When a hand-held object is wielded, hefted, carried and so on, the hand movements, together with the physical properties of the object, produce torques and angular motions that change in time with the movement. There is, however, an unchanging quantity that relates the variable torques and angular motions, namely, the object's inertia for rotation about a fixed point in the wrist. Our research revealed that the non-visual perception of the length of a wielded object by dynamic touch is a function of muscular sensitivity to the principal moments or eigenvalues of the inertia tensor. Across four experiments, variations in object length were accompanied by variations in width, spatial and material heterogeneity, the relation of the tensorial components to mass, and geometric shape. Subjects had no foreknowledge of the variations in object dimensions. Perceived lengths of occluded objects were reported by adjusting a visible marker so that its position corresponded to the position of the felt end of the object. In each experiment, perceived length was closely related to actual length and uniquely constrained by the major and minor eigenvalues of the inertia tensor. The present results, in conjunction with previous research, suggest that the inertia tensor provides the domains for two sets of functions realized by the “muscular sense” one consisting of the principal moments of inertia or eigenvalues, which map on to perceived object magnitudes (e.g. length, weight), and one consisting of the principal directions or eigenvectors, which map on to perceived relations between hand and object (e.g. position of grasp). The significance of information-perception specificity over cognitive mechanisms is underlined and perspectives on dynamic touch and its underlying muscular sensitivity, including a general tensorial analysis, are discussed.