Affiliations: Department of Mathematics, Colby College, Waterville, ME 04901 USA.
Tel.: +1 207 872 3202; Fax: +1 207 872 3555; E-mail: jeholly@colby.edu
Abstract: The laws of physics explain many human misperceptions of whole-body passive self-motion. One classic misperception occurs in a rotating chair in the dark: If the chair is decelerated to a stop after a period of counterclockwise rotation, then a subject will typically perceive clockwise rotation. The laws of physics show that, indeed, a clockwise rotation would be perceived even by a perfect processor of angular acceleration information, assuming that the processor is initialized (prior to the deceleration) with a typical subject's initial perception – of no rotation in this case. The motion perceived by a perfect acceleration processor serves as a baseline by which to judge human self-motion perception; this baseline makes a rough prediction and also forms a basis for comparison, with uniquely physiological properties of perception showing up as deviations from the baseline. These same principles, using the motion perceived by a perfect acceleration processor as a baseline, are used in the present paper to investigate complex motions that involve simultaneous linear and angular accelerations with a changing axis of rotation. Baselines – motions that would be perceived by a perfect acceleration processor, given the same initial perception (prior to the motion of interest) as that of a typical subject – are computed for the acceleration and deceleration stages of centrifuge runs in which the human carriage tilts along with the vector resultant of the centripetal and gravity vectors. The computations generate a three-dimensional picture of the motion perceived by a perfect acceleration processor, by simultaneously using all six interacting degrees of freedom (three angular and three linear) and taking into account the non-commutativity of rotations in three dimensions. The resulting three-dimensional baselines predict stronger perceptual effects during deceleration than during acceleration, despite the equal magnitudes (with opposite direction) of forces on the subject during acceleration and deceleration. For a centrifuge run with the subject facing tangentially in the direction of motion, the deceleration baseline shows a perception of forward tumble (pitch rotation) beginning with ascent from the earth, while the acceleration baseline does not have analogous pitch and vertical motion. These results give a three-dimensional explanation for certain puzzling acceleration-deceleration perceptual differences observed experimentally by Guedry, Rupert, McGrath, and Oman (Journal of Vestibular Research, 1992 (2).). The present analysis is consistent with, and expands upon, previous analyses of individual components of motion.
