Space-time representation in the brain. the cerebellum as a predictive space-time metric tensor.

The concept of space-time representation in the brain is redefined using tensor network theory. We make the following suggestions. (a) In order to deal with the external world, the brain embeds the external space-time continuum into a high dimensional internal space. External space-time events are represented within the CNS in overcomplete, inherently oblique, reference frames where space and time information is detected as a continuum over each coordinate axis. (b) The central nervous system may be seen as imposing a geometry on this internal hyperspace in such manner that neuronal networks transform inputs in a metric tensor-like manner. (c) In order to coordinate movements the cerebellum acts as a predictive motor space-time metric which allows the establishment of coincidences of goal-directed movements of limbs in space-time with external targets.