Sensorimotor optimization in higher dimensions

Most studies of neural control have looked at constrained tasks, with only a few degrees of freedom, but real sensorimotor systems are high dimensional--e.g. gaze-control systems that coordinate the head and two eyes have to work with 12 degrees of freedom in all. These extra degrees of freedom matter, because they bring with them new issues and questions, which make it hard to translate low-dimensional findings into theories of real neural control. Here I show that it is possible to predict high-dimensional behavior if we apply the optimization principles introduced by 19th-century neuroscientists like Helmholtz, Listing, and Wundt. Using three examples--the vestibulo-ocular reflex, saccadic eye movements, and depth vision--I show how simple optimization theories can predict complex, unexpected behaviors and reveal fundamental features of sensorimotor control, e.g. that neural circuits perform noncommutative algebra; that in rapid gaze shifts the eye controllers deliver commands with three degrees of freedom, not two; and that the eyes roll about their lines of sight in a way that may simplify stereopsis.