Haptically perceiving size at a distance

Six experiments are reported on perceiving the sizes of gaps by probing with a hand-held rod. A collective parameter, lambda, is invariant over the time-varying dynamics of probing: lambda = sin(alpha/2)[1-(2a/b) + (a/p)] = sin(alpha/2) delta, where alpha is the angular excursion of the rod-plus-limb segment and a, b, and p are the distances, respectively, of the center of mass, point of contact, and the center of percussion from the axis of rotation. If perceived size is specific to lambda, then it should (a) be a single-valued function of lambda regardless of the muscles executing, and deformed by, the probing; (b) equal, underestimate, and overestimate actual size according to 2b/delta = 1, 2b/delta < 1, and 2b/delta > 1, respectively; and (c) change with actual size at a rate equal to (1/2b-a/b2 + a/2bp), the partial derivative of lambda with respect to size. The experimentally confirmed predictions are discussed in relation to hypotheses about the specificity of perception to information, and the tensorial nature of dynamic touch.