Let us consider first the exquisite design of the cerebellar cortex as a laminated rectangular lattice, a structure built with a precision only exceeded in biology by the insect eye and its connectivities. A theory of the cerebellar cortex has to incorporate this design as a key feature, and moreover has to account for the convergence onto each Purkinje cell of two quite distinctive inputs, that from the mossy-fiber input with the immense divergence (8,000) and convergence (100,000) and that from the climbing fibers where the divergence number is about 10 and the convergence number is 1. This extraordinary double innervation has been maintained through all the exigencies of evolution from primitive cerebella to the great efflorescence in mammals and birds. It is particularly remarkable that, when the cerebellar hemispheres were developed in step with the cerebral hemispheres, the inferior olive hypertrophied also. The cerebral efferents had to travel down to the medulla oblongata to excite the newly developed inferior olivary neurons for the essential climbing fiber input to the cerebellar hemispheres.