Human odometry verifies the symmetry perspective on bipedal gaits

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary gaits are characterized by dihedral symmetry, whereas secondary gaits are characterized by a lower, cyclic symmetry. This fact was used in a test of human odometry. Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. Lessons are drawn from modeling the dynamics of behaviors executed in parallel (e.g., interlimb coordination) to model the dynamics of human odometry, in which the behaviors are executed sequentially. The major observations are characterized in terms of a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of that dynamic.