Neural geometry: the need of researching association of covariant and contravariant coordinates that organizes a cognitive space by relating multisensory-multimotor representations

The research program whose initiation is reported starts with a subtle yet significant deviation from Euclidean geometries (spun by Cartesian coordinates) by exploiting the use of generalized coordinates. The first step is to investigate how covariant and contravariant expressions can be connected by association. Mathematically, it is evident that setting up relationships of such generalized vectors defines a metric, which establishes the non-Euclidean geometry of the cognitive space that connects (multi)sensory and (multi)motor systems. This line of research relies on complementing the proposed theoretical concepts and formalisms by quantitatively elaborated models of specific cases of sensorimotor transformations. Particular attention is on vestibulo-colic, oculomotor, and other gaze reflexes that are the basic mechanisms of sensorimotor mapping of the external world into an internal representation in a cognitive space.<>