Abstract
In each of five experiments Ss made direct assessments of interpoint distances within a stimulus configuration. A multidimensional scaling method was applied to make explicit the form of the subjective configuration. The stimulus configurations consisted of small light points arranged in a two- or three-dimensional array in a dark room, and of real stars in the sky. All the data were adequately accounted for by a configuration constructed in Euclidean space of the appropriate dimensionality. That was true even in the situation where alley experiments with the same Ss gave the result that is usually regarded as evidence for a hyperbolic binocular space. The Euclidean interpretation entails a more complicated form of correspondence between physical and visual spaces than the hyperbolic interpretation.
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Blank, A. A. The Luneburg theory of binocular visual space.J. Opt. Soc. Amer., 1953, 43, 717–727.
Blank, A. A. The geometry of vision.Brit. J. physiol. Opt, 1957, 1–30.
Blank, A. A. Axiomatics of binocular vision. The foundation of metric geometry in relation to space perception.J. Opt. Soc. Amer., 1958a, 48, 328–334.
Blank, A. A. Analysis of experiments in binocular space perception.J. Opt. Soc. Amer., 1958b, 48, 911–925.
Hardy, L. H., Rand, G., Rittler, M. C, & Boeder, P.The geometry of binocular space perception. Knapp Memorial Laboratories, Institute of Ophthalmology, Columbia University College of Physicians and Surgeons, 1953.
Hyman, R., &Well, A. Judgments of similarity and spatial models.Percept. & Psychophys., 1967, 2, 233–248.
Indow, T. Two kinds of multidimensional scaling method as tools for investigating color space from the macroscopic point of view.Acta Chromatica, 1963, 1, 60–71.
Indow, T. Two interpretations of binocular visual space: Hyperbolic and Euclidean.Ann. Jap. Assoc. Philos. Sci., 1967, 3, 51–64.
Indow, T., Inoue, E., &Matsushima, K. An experimental study of the Luneburg theory of binocular space perception (1), The 3- and 4-point experiments.Jap. psychol. Res., 1962a, 4, 6–16.
Indow, T., Inoue, E., &Matsushima, K. An experimental study of the Luneburg theory of binocular space perception (2). The alley experiments.Jap. psychol. Res., 1962b, 4, 17–24.
Indow, T., Inoue, E., &Matsushima, K. An experimental study of the Luneburg theory of binocular space perception (3). The experiments in a spacious field.Jap. psychol. Res., 1963, 5, 10–27.
Indow, T., &Kanazawa, K. Multidimensional mapping of Munsell colors varying in hue, chroma, and value.J. exp. Psychol., 1960, 59, 330–336.
Indow, T., &Uchizono, T. Multidimensional mapping of Munsell colors varying in hue and chroma.J. exp. Psychol., 1960, 59, 321–329.
Kaufman, L., &Rock, I. The moon illusion, I.Science, 1962, 136, 953–961.
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 1964a, 29, 1–27.
Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method.Psychometrika, 1964b, 29, 115–129.
Luneburg, R. K.Mathematical analysis of binocular vision. Princeton, N. J.: Princeton University Press, 1947.
Luneburg, R. K. Metric methods in binocular visual perception. Studies and essays.Courant Anniversary Volume. 1948, 215–240.
Luneburg, R. K. The metric of binocular visual space.J. Opt. Soc. Amer., 1950, 40, 637–642.
Matsushima, K., &Noguchi, H. Multidimensional representation of binocular visual space.Jap. psychol. Res., 1967, 9, 85–94.
Rock, I., &Kaufman, L. The moon illusion, II.Science, 1962, 136, 1023–1031.
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function I.Psychometrika, 1962a, 27, 125–140.
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function II.Psychometrika, 1962b, 27, 219–246.
Torgerson, W. A. Multidimensional scaling: I. Theory and method.Psychometrika, 1952, 17, 401–419.
Torgerson, W. A.Theory and methods of scaling. New York: John Wiley, 1958.
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The author wishes to express his warmest gratitude to his collaborators who conducted the experiments and discussed the subject matter with the author. Thanks are also due to the staff member and students in the Psychological Laboratory in Keio University who participated in the experiments. Detailed reports on Experiments I to IV are being published by Matsushima and Noguchi (1967).
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Indow, T. Multidimensional mapping of visual space with real and simulated stars. Perception & Psychophysics 3, 45–53 (1968). https://doi.org/10.3758/BF03212711
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DOI: https://doi.org/10.3758/BF03212711