VOLUMETRIC SPACE IN FLAT CORTEX
The one remaining obstacle to completing the relation between phenomenology and physiology is that the cortex appears to be a two-dimensional space whereas perception is essentially spherical. How can this aspect of perception be accommodated in the physical structure of the brain? An answer to this question can be found by the principle of functional isomorphism, by applying topological distortions to the perceptual spherical space to flatten it out into a sheet, while preserving the interconnectivity between regions of the representation, thereby maintaining a functional isomorphism with the spherical space. Imagine the following topological operation performed on the sphere of perceptual space. First we insert a vector into the perceptual manifold from the rear, extending radially from the outer surface in to the center of the space, as suggested by the arrow in Fig. 7.5A. This hole is then widened into a cylindrical cavity, as suggested in Fig. 7.5B, but as the hole is widened, the perceptual tissue is pushed aside topologically, while preserving its functional connectivity, as suggested by the warped grid lines in Fig. 7.5B. The interior surface of this cylindrical cavity therefore now represents the radial vector at a single point at the back of the head, and the computations of collinear and coplanar completion follow the distorted lines of collinearity depicted in the figure, so as to proceed isomorphically as if performed in a geometrically continuous space. The cylindrical hole can be further expanded in this manner, eventually molding the entire perceptual sphere into a hollow bowl shape as suggested in Fig. 7.5C, like a "pinch pot" made out of a ball of clay by pressing a thumb into the center of the ball from one side. The entire rim of this bowl-shaped structure now represents the single point at the back of the head. The thickness of this concave disk of tissue represents the depth dimension of the visual world replicated in bas-relief, with the inner surface of the bowl representing the surface of the face, and the outer surface representing perceptual infinity. It is therefore perfectly conceivable that a geometrically flat surface of finite thickness, like the cortical surface, can be wired to be functionally isomorphic with a spherical perceptual space. Indeed, the discovery of binocular disparity-tuned cells arranged in a regular array of increasing disparity (Barlow, Blakemore, & Pettigrew, 1967) is consistent with this kind of representation.
Figure 7.5
I propose therefore that a section of cortical tissue from the primary visual cortex encodes the spatial structure of the visual world by spatial regions in the volume of the cortex, as suggested in Fig. 7.5D, in which the different colors in the figure represent volumetric regions of cortical tissue that are in different electrochemical states, corresponding to the subjective experience of opacity or transparency and perceived color currently represented in that visual space. The exact representation depicted in Fig. 7.5D is of course highly speculative, for it attempts to unite information from two disparate realms of knowledge, the phenomenological and the neurophysiological. However, unless we take the incredible position that phenomenology exists somehow independent of physiology, there must be some kind of neural substrate to the phenomenal experience, and that substrate must encode all of the information present in the subjective experience. In an epistemological sense, therefore, the most speculative component in Fig. 7.5D is the neurophysiological portion, for all of our scientific knowledge of the external world is indirect, built on inferences and indirect measurements that are all ultimately grounded in subjective experience. Therefore the regions of different colors in Fig. 7.5D are epistemologically more certain to exist in the brain in some form than the neurons and electrical signals postulated by neurophysiology. Those colors and structures are experienced directly, whereas neurons and electrical signals are detected only indirectly by specialized instruments, which in turn are viewed through the veil of conscious experience. All that remains uncertain is the neurophysiological form taken by those subjective components of experience in the physical brain. Figure 7.5D expresses the hypothesis that some physical quantity in the brain corresponding to those perceived colors is spatially distributed in the cortex in a pattern corresponding to the patterns of that experience.