Roger Shepard: General

“We generalize from one situation to another not because we cannot tell the difference between the two situations but because we judge that they are likely to belong to a set of situations having the same consequence.”

Roger Shepard

Source: "Toward a universal law of generalization for psychological science," 1987, p. 1322

“The subject detects the presence and interrelationships of the basic components of one of the two-dimensional drawings - particularly, the variously oriented straight lines, the several types of vertices by which they are connected and, presumably, something of the structural relationships among these components within the two-dimensional pattern. Then, on the basis of some higher-level processing of these extracted features and their interrelationships, an internal representation, code, or verbal description is generated for each picture separately that captures the intrinsic structure of the three-dimensional object in a form that is independent of the particular orientation in which that object happens to be displayed.”

Roger Shepard

Source: Mental images and their transformations. 1982, p. 64; as cited in: Keith K. Niall, "‘Mental rotation’, pictured rotation, and tandem rotation in depth." Acta psychologica 95.1 (1997): 31-83.

Drawing

“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 (i) decays exponentially with this distance, and (ii) 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

Source: "Toward a universal law of generalization for psychological science," 1987, p. 1317

Behavior , Mathematics , Nature , Learning

“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 cancelled 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”

Roger Shepard

R. N. Shepard, (1994). "Perceptual-cognitive universals as reflections of the world." Psychonomic Bulletin and Review, 1, 2–28.

Color , Way , Optimism , Support