Symmetry groups-rules that connect different configurations of a given set of components-represent a compact means of coding for effects, a feature that is desirable in both model and theory-building. The present study was designed to compare the effects of spatial orientation differences with the various other asymmetries (e.g., timing differences, handedness preferences, the direction of attention) that are accommodated by current models of bimanual coordination. The authors used symmetry groups to predict specific patterns of results. In 2 experiments, participants (N = 13, Experiment 1; N = 9, Experiment 2) coordinated the movements of differently oriented (1 downward and 1 upward) pendulum pairs at a low (0.62 Hz) or high (0.82 Hz) movement frequency to establish an in-phase or antiphase pattern. Consistent with previous results (P. G. Amazeen, E. L. Amazeen, & M. T. Turvey, 1998a), the downward-oriented pendulum tended to lead slightly. In contrast to the effects of other bimanual asymmetries, the downward-oriented pendulum lead was amplified at low frequencies. Although the results contradicted the predictions of existing models of bimanual coordination, they were consistent with predictions from symmetry group theory. In the discussion, the authors focus on the application of symmetry groups to both bimanual coordination and other phenomena with more complex symmetric structures.

Abstract from:

Mulvey, G. M., Amazeen, P. G., & Riley, M. A. (2005). The use of (symmetry) group theory as a predictive tool for studying bimanual coordination. Journal of Motor Behavior, 37, 295-309.