Developing Mathematics for Insight into Sensorimotor Neurobiology

This paper summarizes a research program to express the organization of sensorimotor control by specifying physiological states and the conditions for transitions among them. By a slight change in standard notation, conditional dynamics provides a moving spotlight, focussing on salient subspaces within a high-dimensional space. This mathematical approach serves as a window on the organization of sensorimotor neurobiology. The intertwined efforts to express the intrinsic organization of neurobiology and to clarify it mathematically are yielding a mathematical structure that is growing on fertile empirical ground.