Space—an essential dimension of our life—is analyzable from different viewpoints, which often gives rise to contrasting conceptualizations. Perceptual analyses shed light on the intrinsic anisotropy and deformations of perceived space, raising the issue of which geometry may be able to represent perceptual space. Pictorial drawings and painting have been relevant sources of information about the nature of living and perceived space. Although the geometry of perceptual space is still in its infancy, contributions are beginning to appear. This special issue contributes (...) to the development of the geometry of perceptual space. (shrink)

The contribution deals with some key problems of cognitive science, whose plurality transcends the boundaries of the disciplines drawn by classical epistemology. In particular, it addresses the issues of mental images, spaces of representation, and the architecture of cognitive processes in vision theory. The thesis presented is that a proper treatment of vision within psychophysics entails an analysis of a series of interconnected spaces, objects and methodologies, from psychophysics to the many virtual realities of representation.

Following a previous article published in Biological Theory, in this study we present a mathematical theory for a science of qualities as directly perceived by living organisms, and based on morphological patterns. We address a range of qualitative phenomena as observables of a psychological system seen as an impredicative system. The starting point of our study is the notion that perceptual phenomena are projections of underlying invariants, objects that remain unchanged when transformations of a certain class under consideration are applied. (...) The study develops with the observables, the entailed total order and metric, whence the algebra and the geometry of such a science, presenting a formal phenomenological model for phenomena that are not rigidly Euclidean. We show how non-Euclidean perception can have many useful Euclidean formalizations, as well as locally-homeomorphic-to-Euclidean-space models. The mathematical models we provide are tested on the basis of results from experimental psychology, in particular from the field of color, time, and space perception. (shrink)