The Geometry of Visibles

Abstract

The thesis I wish to defend is this: the geometry which precisely and naturally fits the actual configurations of the visual field is a non-Euclidean, two-dimensional, elliptical geometry. In substance, this thesis was advanced by Thomas Reid in 1764, although, since this preceded non-Euclidean geometries by 65 to 90 years, no mention was made of them.2 The thesis conflicts now, as in Reid's time, with the view held by most psychologists and philosophers that the actual two-dimensional configurations of the visual field are Euclidean. It also appears to conflict with the recent theory of Luneburg [8] that the geometry of binocular space perception is, though non-Euclidean, hyperbolic rather than elliptical; but we shall see that this latter difference is merely apparent-Luneburg's theory deals with a different problem. To grasp the import of our thesis it is important to distinguish at the outset: