Geometrical-optical illusions
When an illusion involves properties that fall within the purview of geometry it is geometrical–optical, a term given to it in the first scientific paper devoted to the topic by J.J. Oppel, a German high-school teacher, in 1854.
Before invoking concepts of apparent distance and size constancy, it helps to be sure that the retinal image hasn't changed much when the moon looks larger as it descends to the horizon.
[5] To illustrate: Instead of interpreting them as just a pair the sloping lines within which one feature is seen smaller than an identical one nearer to the point of convergence, the Ponzo pattern may be taken for a railroad track rendered as a perspective drawing.
A scientific study will include the recognition that a representation of the visual word is embodied in the state of the organism's nervous system at the time the illusion is experienced.
In the discipline of experimental neuroscience, a top-down influence has the meaning that signals originating in higher neural centers, repository of memory traces, innate patterns and decision operations, travel down to lower neuronal circuits where they cause a shift of the excitation balance in the deviated direction.
Top-down neural signaling would be a fitting implementation of the gestalt concept enunciated by Max Wertheimer[6] 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,[7] that map them on each other.
Application of differential geometry has so far not been notably successful [1] Archived 2012-03-25 at the Wayback Machine; 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.
