A systems theory of movement control in animals is presented in this article and applied to explaining the controlled behaviour of the single-celled Paramecium caudatum in an electric field. The theory—General Tau Theory—is founded on three basic principles: (i) all purposive movement entails prospectively controlling the closure of action-gaps (e.g. a distance gap when reaching, or an angle gap when steering); (ii) the sole informational variable required for controlling gaps is the relative rate of change of the gap (the time derivative of the gap size divided by the size), which can be directly sensed; and (iii) a coordinated movement is achieved by keeping the relative rates of change of gaps in a constant ratio. The theory is supported by studies of controlled movement in mammals, birds and insects. We now show for the first time that it is also supported by single-celled paramecia steering to the cathode in a bi-polar electric field. General Tau Theory is deployed to explain this guided steering by the cell. This article presents the first computational model of prospective perceptual control in a non-neural, single-celled system.