The Geometry of Visual Space

Abstract

In this paper I shall investigate the geometrical structure of phenomenal visual space. I shall assume at the outset that visual perception is indirect, and thus that we are never immediately aware of even the surfaces of physical objects. Instead I will hold that our immediate visual awareness consists of a phenomenal field of colors, visual space, whose geometrical and qualitative features are determined by causal connections with the physical objects being seen; that is by light rays reflected from these objects being focused on the retina, and the various subsequent neural events which take place in the brain. I have defended the causal theory of perception in detail elsewhere (French, 1987), but in order to keep this paper within manageable length, while still doing justice to the geometrical arguments involved, I shall not summarize those arguments here. While there may be various structural resemblances between portions of visual space and the corresponding physical objects being seen, many of which being given by the laws of projective geometry, it remains possible that both the topological and metric structure of visual space is quite different from that of physical space. Thus, an attitudinal shift is required here away from direct realism, which numerically equates the two, to a more neutral attitude where a geometrical analysis can be made of our visual experience in and of itself. I shall attempt to undertake such a geometrical analysis in this paper. Thus, I shall now turn to an investigation of the topology of visual space, to be followed by an investigation of its metric structure.