The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe – provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the (...) Euclidean group of three-dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is canceled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily-shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum-entropy priors. Key Words: apparent motion; Bayesian inference; cognition; color constancy; generalization; mental rotation; perception; psychological laws; psychological space; universal laws. (shrink)

Space can be understood through perception and language, but are the processes that represent spatial information the same in both cases? This paper reviews psychological evidence for the functional equivalence of spatial representations based on perceptual and linguistic inputs. It is proposed that spatial information is processed by a specialised spatial representation system (SRS) that creates geometric representations of space. The SRS receives inputs from perceptual and linguistic systems and uses these basic inputs to construct mental spatial models of the (...) observed or described environment. A mental spatial model is created by determining the coordinate locations of objects in the egocentric or allocentric frame of reference. The goal of the SRS is not to represent strictly what is perceived, but to model an environment that has an inherent three‐dimensional spatial structure. (shrink)