Top-down neural signaling would be a fitting implementation of the gestalt concept enunciated by Max Wertheimer  that the "properties of any of the parts are determined by the intrinsic structural laws of the whole." When objects and associated percepts, in their respective spaces, correspond to each other albeit with deformations describable in terms of geometry, the mathematically inclined are tempted to search for transformations, perhaps non-Euclidean, that map them on each other. Application of differential geometry has so far not been notably successful ; the variety and complexity of the phenomena, significant differences between individuals and dependence on context, previous experience and instruction set a high bar for satisfying formulations.