In chapter 5, entitled 'Empiricism and the geometry of visual space' of his book Philosophical Problems of Space and Time, 1 Professor Griinbaum deals with K. Luneburg's theory of binocular visual perception. At the time of his writing, experimental psychology was providing some good support for Luneburg's theory that visual space has a constant negative curvature. Accordingly most psychologists accepted the assumption that visual geometry belongs to the Lobachevskian hyperbolic type.
Griinbaum's fundamental epistemological question about Luneburg's theory was stated thus: "How do human beings manage to get about so easily in a Euclidean physical environment even though the geometry of visual space is presumably hyperbolic?" (op. cit., p. 155) or, in other words: "How is man able to arrive at an approximately correct apprehension of the Euclidean metric relations of his environment by the use of a psychological instrument whose deliverances are claimed to be non-Euclidean?" (op. cit., p. 155-156). As Griinbaum says "the need to answer these questions becomes even greater, if we assume that our ideas concerning the geometry of our immediate physical environment are formed, in the first instance, not by the physical geometry of yardsticks or by the formal study of Euclidean geometry but rather by the psychometry of our visual sense data" (op. cit., p. 156).
Griinbaum submitted these and other related questions to A. A. Blank, an authority in Luneburg's theory, and received back, among others, the following two suggestions that we consider central to our discussion: (i) People "learn the significance of ever changing patterns of visual sensations for the metric of physical space by discounting much of the psychometry of visual sensations" (op. cit., p. 156); (ii) "There are certain small two-dimensional elements of visual space Synthese 35 (1977) 423-429.