As we move our bodies in space, we often undergo head and body rotations about different axes - yaw, pitch, and roll. The order in which we rotate about these axes is an important factor in determining the final position of our bodies in space because rotations, unlike translations, do not commute. Does our brain keep track of the noncommutativity of rotations when computing changes in head and body orientation and then use this information when planning subsequent motor commands? We used a visuospatial updating task to investigate whether saccades to remembered visual targets are accurate after intervening, whole-body rotational sequences. The sequences were reversed, either yaw then roll or roll then yaw, such that the final required eye movements to reach the same space-fixed target were different in each case. While each subject performed consistently irrespective of target location and rotational combination, we found great intersubject variability in their capacity to update. The distance between the noncommutative endpoints was, on average, half of that predicted by perfect noncommutativity. Nevertheless, most subjects did make eye movements to distinct final endpoint locations and not to one unique location in space as predicted by a commutative model. In addition, their noncommutative performance significantly improved when their less than ideal updating performance was taken into account. Thus the brain can produce movements that are consistent with the processing of noncommutative rotations, although it is often poor in using internal estimates of rotation for updating.
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