This paper outlines the functional capacities of a novel scheme for cognitive representation and computation, and it explores the possible implementation of this scheme in the massively parallel organization of the empirical brain. The suggestion is that the brain represents reality by means of positions in suitably constitutes phase spaces; and the brain performs computations on these representations by means of coordinate transformations from one phase space to another. This scheme may be implemented in the brain in two distinct forms: (1) as a
phase-space sandwich
, which may explain certain laminar structures, such as cerebral cortex and the superior colliculus; and (2) as a
neural matrix
, which may explain other structures, such as the beautifully orthogonal architecture of the cerebellum.
Keywords Representation - computation - cortex - sensorimotor coordination - coordinate transformation
Special thanks to Patricia Churchland, who originally set me the problem of coordinating the schematic crab; and to Jeff Foss, whose scepticism concerning the computational power of neurally-embodied matrices provoked my construction of the phase-space sandwich. Thanks also to Larry Jordan, Bruce Bolster, Rodolfo Llinas, Andras Pellionisz, Francis Crick, and the Cognitive Mechanisms Group at the University of California, San Diego. This research was supported by a grant from the Institute for Advanced Study, by the Social Sciences and Humanities Research Council of Canada, grant no. 451-83-3050, by a sabbatical leave from the University of Manitoba, and by the University of California, San Diego.