Perceptual-Cognitive Universals as Reflections of the World

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Abstract
The Universality, invarinace, 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 bilogically significant objects and their properties. (1) {\it Positions} and {\it motions} of objects conserve their {\it 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) {\it Colors} of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is cancelled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) {it 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.
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