New research in neuro-engineering is beginning to suggest how the nervous system may perform the basic computations of calculus: Differentiation and Integration to facilitate the control of body movement. Computer models of cerebral and cerebellar control that solve large numbers of differential equations simultaneously enable lifelike simulation of sensorimotor neural control. Subsequent analysis by engineers using, for example, Laplace Transform techniques can suggest how important "long loop" reflexes are stabilized with respect to time delays. These compensated reflexes appear to enable the brain to control dynamically challenging tasks such as human walking much more simply than thought previously. Mathematical models of central nervous system function may soon enable us to construct artificial humanoids.