Abstract
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 andmotions of objects conserve theirshapes 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.
References
Anderson, I. R. (1991). The adaptive nature of human categorization.Psychological Review,98, 409–429.
Attneaye, F., &Block, G. (1973). Apparent movement in tridimensional space.Perception & Psychophysics,13, 301–307.
Balzano, G. J. (1980) A group-theoretic description of twelvefold and microtonal pitch systems.Computer Music Journal,4, 66–84.
Bethell-Fox, C., &Shepard, R. N. (1988). Mental rotation: Effects of stimulus complexity and familiarity.Journal of Experimental Psychology Human Perception & Performance,14, 12–23.
Brill, M. H. (1978). A device for performing illummant-invarant assesstnent of chromatic relations.Journal of Theoretical Biology,78, 473–478.
Buchsbaum, G. (1980). A spatial processor model for object color perception.Journal of the Franklin Institution,310, 1–26.
Bundesen, C., Larsen, A., &Farrell, J. E. (1983) Visual apparent movement: Transformations of size and orientation.Perception,12, 549–558.
Carlton, E. H., &Shepard, R. N. (1990a). Psychologically simple motions as geodesic paths: I. Asymmetric objects.Journal of Mathematical Psychology,34, 127–188.
Carlton, E. H., &Shepard, R. N. (1990b). Psychologically simple motions as geodesic paths II. Symmetric objects.Journal of Mathematical Psychology,34, 189–228
Carroll, J. D., &Chang, J.-J. (1970) Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition.Psychometrika,35, 283–319.
Chasles, M. (1830). Note sur les propertiétés génerales du système de deux corpes semblables entrèeux et placés d’une manièr quelconque dans l’espaces; et sur le déplacement fini ou infiniment pent d’un corps solide libre [A note on the general properties of a system of two similar bodies arbitrarily positioned in space; and on the finite or infinitely small displacement of an unconstrained solid body].Bulletin des Sciences Mathématiques, Férussac,14, 321–326.
Cooper, L. A. (1975). Mental rotation of random two-dimensional shapes.Cognitive Psychology,7, 20–43.
Cooper, L. A. (1976). Demonstrations of a mental analog of an external rotation.Perception & Psychophysics,19, 296–302.
Cooper, L. A., &Shepard, R. N. (1984, December). Turning something over in the mindScientific American, pp 106–114.
Corbin, H. H. (1942)The perception of grouping and apparent movement in visual depth (Archives of Psychology, No. 273). New York.
Curtis, D. W., Paulos, M. A., &Rule, S. J. (1973). Relation between disjunctive reaction time and stimulus difference.Journal of Experimental Psychology,99, 167–173.
Ekman, G. (1954). Dimensions of color vision.Journal of Psychology,38, 467–474.
Enright, J. T. (1972) A virtuoso isopod: Circa-lunar rhythms and their tidal fine structure.Journal of Comparative Physiology,77, 141–162.
Farrell, J. E. (1983). Visual transformations underlying apparent movement.Perception & Psychophysics,33, 85–92
Farrell, J. E., &Shepard, R. N. (1981). Shape, orientation, and apparent rotational motion.Journal of Experimental Psychology: Human Perception & Performance,7, 477–486.
Foster, D. H. (1975). Visual apparent motion of some preferred paths in the rotation group SO(3).Biological Cybernetics,18, 81–89.
Freyd, J. J. (1987). Dynamic mental representations.Psychological Review,94, 427438.
Freyd, J. J., &Jones, K. T. (in press). Representational momentum for a spiral path.Journal of Experimental Psychology Learning, Memory, & Cognition.
Garner, W. R. (1974).The processing of information and structure. Hillsdale, NJ: Erlbaum.
Gibson, J. J. (1979).The ecological approach to visual perception. Boston: Houghton Mifflin.
Gluck, M. A. (1991) Stimulus generalization and representation in adaptive network models of category learning.Psychological Science,2, 50–55.
Green, B. F. Jr. (1961). Figure coherence in the kinetic depth effect.Journal of Experimental Psychology,62, 272–282.
Guttman, L., &Kalish, H. I. (1956). Discriminability and stimulus generalization.Journal of Experimental Psychology,51, 79–88.
Hering, E. (1964).Outlines of a theory of the light sense (M. Hurvich & D. Jameson, Trans.). Cambridge, MA: Harvard University Press. (Original work published 1887)
Hurvich, L. M., &Jameson, D. (1957). An opponent-process theory of color vision.Psychological Review,64, 384–404.
James, W. (1950)The principles of psychology. New York: Dover. (Original edition published 1890)
Jaynes, E. T. (1978). Where do we stand on maximum entropy? In R. D. Levine & M. Tribus (Eds.),The maximum entraps formalism (pp 15–118). Cambridge, MA: MIT Press.
Judd, D. B., McAdam, D. L., &Wyszecki, G. (1964) Spectral distribution of typical daylight as a function of correlated color temperature.Journal of the Optical Society of America,54, 1031–1040.
Koffka, K. (1931). Die Wahrnehmung von Bewegung. In A. Bethe, et al. (Eds.),Handbook der normalen und pathologische Physiologie (Vol. 12: Pt 2, pp 1166–1214) Berlin: Springer-Verlag
Koffka, K. (1935)Principles of Gestalt psychology. New York: Harcourt Brace.
Kolers, P. A., &Powerantz, J. R. (1971) Figurai change in apparent motion.Journal of Experimental Psychology,87, 99–108.
Korte, A. (1915) Kinematoskopische Untersuchungen.Zettschrift für Psychologie,72, 193–296.
Krantz, D. H. (1975a). Color measurement and color theory: I. Representation theorem for Grassmann structures.Journal of Mathematical Psychology,12, 283–303.
Krantz, D. H. (1975b). Color measurement and color theory: II Opponent-colors theory.Journal of Mathematical Psychology,12, 304–327
Krumhansl, C. L., &Kessler, F. J. (1982). Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys.Psychological Review,89, 334–368.
Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrtka,29, 1–27.
Land, E. H., &McCann, J. J. (1971). Lightness and retinex theory.Journal of the Optical Society of America,61, 1–11.
Leyton, M. (1992).Symmetry, causality, mand. Cambridge, MA: MTT Press/Bradford Books.
Lockhead, G. R. (1966). Effects of dimensional redundancy on visual discrimination.Journal of Experimental Psychology,72, 95–104.
Maloney, L. T. (1986) Evaluation of linear models of surface spectral reflectance with small numbers of parameters.Journal of the Optical Society of America A,3, 1673–1683.
Maloney, L. T. &Wandell, B. A. (1986). Color constancy. A method for recovering surface spectral reflectance.Journal of the Optical Society of America A,3, 29–33.
Marimont, D. H., &Wandell, B. A. (1992). Linear models of surface and illuminant spectra.Journal of the Optical Society of America A,9, 1905–1913.
McBeath, M. K., &Shepard, R. N. (1989). Apparent motion between shapes differing in location and orientation. A window technique for estimating path curvature.Perception & Psychophysics,46, 333–337.
McClosky, M. (1983, April). Intuitive physics.Scientific American, pp. 122–130.
Metzler, J., &Shepard, R. N. (1974) Transformational studies of the internal representation of three-dimensional objects. In R. Solso (Ed.),Theories of cognitive psychology: The Loyola Symposium (pp. 147–201). Potomac, MD: Erlbaum.
Miller, G. F., &Shepard, R. N. (1993). An objective criterion for apparent motion based on phase discrimination. Journal of Experimental Psychology: Human Perception &Performance,19, 48–62.
Myung, I. J. (in press). Maximum entropy interpretation of decision bound and context models of categorization.Journal of Mathematical Psychology.
Noll, A. M. (1965). Computer-generated three-dimensional movies.Computers & Animation,14, 20–23.
Nosofsky, R. M. (1987). Attention and learning processes in the identification and categorization of integral stimuli.Journal of Experimental Psychology: Learning, Memory, & Cognition,13, 87–108.
Nosofsky, R. M. (1992). Similarity scaling and cognitive process models.Annual Review of Psychology,43, 25–53.
Nosofsky, R. M.,Gluck, M A.,Palmeri, T J , McKinlev, S. C , & Glauthier, P. (in press). Comparing models of rule-based classification learning; A replication and extension of Shepard, Hovland, and Jenkins (1961).Memory & Cognition.
Nosofsky, R. M., Kruschke, J. K., &McKinley, S. (1992) Combining exemplar-based category representations and connectionist learning rules.Journal of Experimental Psychology: Learning, Memory, & Cognition,18, 211–233.
Ogasawara, J. (1936). Effect of apparent separation on apparent movement.Japanese Journal of Psychology,11, 109–122.
Profeitt, D. R., &Gilden, D. L. (1989). Understanding natural dynamics.Journal of Experimental Psychology: Human Perception & Performance,15, 384–393.
Proffitt, D. R., Gilden, D. L., Kaiser, M. K., &Whelan, S. M. (1988) The effect of configurai orientation on perceived trajectory in apparent motion.Perception & Psychophysics,43, 465–474.
Proffitt, D. R., Kaiser, M. K., &Whelan, S. (1990). Understanding wheel dynamics.Cognitive Psychology,22, 342–373.
Robins, C., &Shepard, R. N. (1977) Spatio-temporal probing of apparent rotational movement.Perception & Psychophysics,22, 12–18.
Rock, I., Wheeler, D., &Tudor, L. (1989). Can we imagine how objects look from other viewpoints?Cognitive Psychology,21, 185–210.
Rosch, E., Mervis, C. B., Gray, W. D., Johnson, D. M., &Boyes-Braem, P. (1976). Basic objects in natural categories.Cognitive Psychology,8, 382–439.
Russell, S. (1988). Analogy by similarity. In D. H. Helman (Ed.),Analogical reasoning (pp. 251–269). New York: Kluwcr Academic Publishers.
Sälström, P. (1973). Colour and physics: Some remarks concerning the physical aspects of human color vision.Institute of Physics Report 73-09.
Shannon, C. E. (1948). A mathematical theory of communication.Bell System Technical Journal,27, 379–423. 623–655. Reprinted in C. E. Shannon, & W. Weaver (Eds.) (1949).The mathematical theory of communication. Urbana, IL: University of Illinois Press.
Shepard, R. N. (1962a). The analysis of proximities: Multidimensional scaling with an unknown distance function. I.Psychometrika,27, 125–140.
Shepard, R. N. (1962b). The analysis of proximities: Multidimensional scaling with an unknown distance function. II.Psychometrika,27, 219–246.
Shepard, R. N. (1964a). Attention and the metric structure of the stimulus space.Journal of Mathematical Psychology,1, 54–87.
Shepard, R. N. (1964b). Circularity m judgments of relative pitch.Journal of the Acoustical Society of America,6, 2346–2353.
Shepard, R. N. (1965). Approximation to uniform gradients of generalization by monotone transformations of scale. In D. I. Mostofsky (Ed.),Stimulus generalization (pp 94–110). Stanford, CA: Stanford University Press.
Shepard, R. N. (1978). The circumplex and related topological manifolds in the study of perception. In S. Shye (Ed.),Theory construction and data analysis in the behavioral sciences (pp. 29–80) San Francisco: Jossey-Bass.
Shepard, R. N. (1980). Multidimensional scahng, tree-fitting, and clustering.Science,210, 390–398.
Shepard, R. N. (1981a, August).Discrimination and classification: A search for psychological laws. Presidential address to the Division of Experimental Psychology of the American Psychological Association, Los Angeles.
Shepard, R. N. (1981b). Psychophysical complementarity. In M. Kubovy & J. Pomerantz (Eds.),Perceptual organization (pp. 279–341). Hillsdale, NJ: Erlbaum.
Shepard, R. N. (1982) Geometrical approximations to the structure of musical pitch.Psychological Review,89, 305–333.
Shepard, R. N. (1983). Demonstrations of circular components of pitch.Journal of the Audio Engineering Society,31, 641–649.
Shepard, R. N. (1984) Ecological constraints on internal representation: Resonant kinematics of perceiving, imagining, thinking, and dreaming.Psychological Review,91, 417–447.
Shepard, R. N. (1987a). Evolution of a mesh between principles of the mind and regularities of the world. In J. Dupré (Ed.),The latest on the best: Essays on evolution and optimality (pp. 251–275). Cambridge, MA: MIT Press/Bradford Books.
Shepard, R. N. (1987b). Toward a universal law of generalization for psychological science.Science,237, 1317–1323.
Shepard, R. N. (1988). The role of transformation in spatial cognition. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.),Spatial cognition: Brain bases and development (pp. 81–110). Hillsdale, NJ: Erlbaum.
Shepard, R. N. (1989, August).A law of generalization and connectionist learning. Plenary address to the Cognitive Science Society, Ann Arbor, MI.
Shepard, R. N. (1990). A possible evolutionary basis for trichromacy. InProceedings of the SPIE/SPSE Symposium on Electronic Imaging: Science and technology, 1250. Perceiving, measuring, and using color (pp. 301–309). Bellingham, WA: SPIE.
Shepard, R. N. (1991). Integrality versus separability of stimulus dimensions: From art early convergence of evidence to a proposed theoretical basis. In G. R. Lockhead & J. R. Pomerantz (Eds.),Perception of structure (pp. 57–71). Washington, DC: American Psychological Association.
Shepard, R. N. (1992). The perceptual organization of colors: An adaptation to the regularities of the terrestrial world? In J. Barkow, L. Cosmides, & J. Tooby (Eds.),The adapted mind. Evolutionary psychology and the generation of culture (pp. 495–532). New York: Oxford University Press.
Shepard, R. N. (1993). On the physical basis, linguistic representation, and conscious experience of colors. In G. Harman (Ed.),Con ceptions of the mind (pp. 217–245). Hillsdale, NJ: Erlbaum.
Shepard, R. N., &Carroll, J. D. (1966). Parametric representation of nonlinear data structures. In P. R. Krishnaiah (Ed.),Multivariate analysis (pp. 561–592). New York: Academic Press.
Shepard, R. N., &Chang, J. J. (1963). Stimulus generalization in the learning of classifications.Journal of Experimental Psychology,65, 94–102.
Shepard, R. N., &Cooper, L. A. (1982).Mental images and their transformations. Cambridge, MA: MIT Press/Bradford Books.
Shepard, R. N., &Cooper, L. A. (1992). Representation of colors m the blind, color blind, and normally sighted.Psychological Science,3, 97–104.
Shepard, R. N., &Farrell, J. E. (1985). Representation of the orientations of shapes.Acta Psychologica,59, 104–121.
Shepard, R. N.,Hovland, C. I , &Jenkins, H. M. (1961) Learning and memorization of classifications.Psychological Monographs,75 (13, Whole No. 517).
Shepard, R. N., &Judd, S. A. (1976). Perceptual illusion of rotation of three-dimensional objects.Science,191, 952–954.
Shepard, R. N., &Kannappan, S. (1991). Toward a connectionist implementation of a theory of generalization.Advances in Neural Information Processing Systems,3, 665–671.
Shepard, R. N., Kilpatrick, D. W., &Cunningham, J. P. (1975). The internal representation of numbers.Cognitive Psychology,7, 82–138.
Shepard, R. N., &Metzler, J. (1971). Mental rotation of three-dimensional objects.Science,171, 701–703.
Shepard, R. N., &Tenenbaum, J. (1991, November).Connectionist modeling of multidimensional generalization. Paper presented at the meeting of the Psychonomic Society, San Francisco.
Shepard, R. N., &Zare, S. (1983). Path-guided apparent motion.Science,220, 632–634.
Shepard, S., &Metzler, D. (1988). Mental rotation: Effects of dimensionality of objects and type of task.Journal of Experimental Psychology: Human Perception & Performance,14, 3–11.
Shiffrar, M., &Shepard, R. N. (1990). Comparison of cube rotations about axes inclined relative to the environment or to the cube.Journal of Experimental Psychology: Human Perception & Performance,7, 44–54.
Sinha, P., &Adelson, E. H. (1993). Recovering reflectance and illumination in a world of painted polyhedra. InProceedings of the Fourth International Conference on Computer Vision (pp.156–163). Los Alamitos, CA: IEEE Computer Society Press.
Spelke, E. (1991). Physical knowledge in infancy. In S. Carey & R. Gelman (Eds.),The epigenesis of mind: Essays on biology and cognition (pp. 133–169). Hillsdale, NJ: Erlbaum.
Todd, P. M., &Miller, G. F. (1991). On the sympatric origin of species: Mercurial mating in the quicksilver model. In R. K. Belew & L. B. Booker (Eds.),Proceedings of the Fourth International Conference on Genetic Algorithms (pp. 547–554) San Mateo, CA: Morgan Kaufmann.
Tominaga, S., &Wandell, B. (1989). Standard surface-reflectance model and illuminant estimation.Journal of the Optical Society of America A,6, 576–584.
Wertheimer, M. (1912). Experimentelle Studien uber des Sehen von Bewegung.Zeitschrift für Psychologie,61, 161–265 Translated in part in T. Shipley (Ed.) (1961),Classics in psychology (pp. 1032–1089). New York: Philosophical Library
Wiener, N. (1948).Cybernetics, or control and communication in the animal and the machine. New York: Wiley.
Winfree, A. T. (1980).The geometry of biological time. New York: Springer-Verlag.
Author information
Authors and Affiliations
Additional information
Successive approximations to this paper have been presented in three invited talks: (1) “How the mind reflects the world,” D. O. Hebb lecture, McGill University, September 29, 1989; (2) “Can natural selection yield universal principles of mind?” in the symposium Evolution of Cognitive Functions in Ecological-Cultural Context, Annual Meeting of the American Association for the Advancement of Science, Washington, D.C., February 18, 1991; and (3) “How the mind reflects the world,” Annual Meeting of the American Psychological Society, Chicago, June 27, 1993. The research and the drafting of this article were supported by National Science Foundation Grant DBS-9021648. Final revisions were supported, as well, by the Santa Fe Institute, and benefited significantly from interdisciplinary discussions with many scientists there, as well as from the expert editorial assistance of my Stanford secretary Kim Saccio. Other colleagues who have especially contributed to or influenced the particular work reviewed here include Eloise Carlton, Lynn Cooper, Leda Cosmides, Joyce Farrell, Jennifer Freyd. Sherryl Judd. Laurence Maloney, Michael McBeath, Jacqueline Meteler, Geoffrey Miller, In Jae Myung, Robert Nosofsky, Margaret Shiffrar, Joshua Tenenbuam, Brian Wandell, and Susan Zare.
Rights and permissions
About this article
Cite this article
Shepard, R.N. Perceptual-cognitive universals as reflections of the world. Psychonomic Bulletin & Review 1, 2–28 (1994). https://doi.org/10.3758/BF03200759
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03200759
Keywords
- Mental Rotation
- Apparent Motion
- Rigid Motion
- Color Constancy
- Rigid Transformation