Clergyman's

A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization decays exponentially with this distance, and does so in accordance with one of two metrics, depending on the relation between the dimensions along which the stimuli vary. These empirical regularities are mathematically derivable from universal principles of natural kinds and probabilistic geometry that may, through evolutionary internalization, tend to govern the behaviors of all sentient organisms.
- Roger Shepard

In spite of some unresolved issues, the close match we have found between mental rotation and their counterparts in the physical world leads inevitably to speculations about the functions and origin of human spatial imagination. It may not be premature to propose that spatial imagination has evolved as a reflection of the physics and geometry of the external world. The rules that govern structures and motions in the physical world may, over evolutionary history, have been incorporated into human perceptual machinery, giving rise to demonstrable correspondences between mental imagery and its physical analogues.
- Roger Shepard

In spite of some unresolved issues, the close match we have found between mental rotation and their counterparts in the physical world leads inevitably to speculations about the functions and origin of human spatial imagination. It may not be premature to propose that spatial imagination has evolved as a reflection of the physics and geometry of the external world. The rules that govern structures and motions in the physical world may, over evolutionary history, have been incorporated into human perceptual machinery, giving rise to demonstrable correspondences between mental imagery and its physical analogues.
- Roger Shepard

The system of constraints that governs the projections and transformations of... bodies in space must long ago have become internalized as a powerful, though largely unconscious, part of our perceptual machinery.
- Roger Shepard

The system of constraints that governs the projections and transformations of... bodies in space must long ago have become internalized as a powerful, though largely unconscious, part of our perceptual machinery.
- Roger Shepard

The system of constraints that governs the projections and transformations of... bodies in space must long ago have become internalized as a powerful, though largely unconscious, part of our perceptual machinery.
- Roger Shepard

The system of constraints that governs the projections and transformations of... bodies in space must long ago have become internalized as a powerful, though largely unconscious, part of our perceptual machinery.
- Roger Shepard

Students of the human mind have long noted its ability to mimic internally the positive notions and transformations of objects in the external world. In the middle of the eighteenth century, the British empiricist David Hume wrote that to ""join incongruous shapes and appearances costs the imagination no more trouble than to conceive the most natural and familiar objects"" and that ""this creative power of the mind amounts to no more than the faculty of compounding, transposing, augmenting, or diminishing the materials afforded us by the senses and experience.
- Roger Shepard

I suggest that the psychophysical function that maps physical parameter space into a species' psychological space has been shaped over evolutionary history so that consequential regions for that species, although variously shaped, are not consistently elongated or flattened in particular directions.
- Roger Shepard

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. 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. 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. 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
- Roger Shepard