We call this our "ice cube model" of the cortex. It illustrates how the cortex is divided, at one and the same time, into two kinds of slabs, one set for ocular dominance (left and right) and one set for orientation. The model should not be taken literally: Neither set is as regular as this, and the orientation slabs especially are far from parallel or straight. Moreover, they do not seem to intersect in any particular angle—
certainly they are not orthogonal, as shown here.
UNITS OF FUNCTION IN THE CORTEX
We must conclude that any piece of primary visual cortex about 2 millimeters by 2 millimeters in surface area must have the machinery to deal completely with some particular area of visual field—an area of visual field that is small in or near the fovea and large in the periphery. A piece of cortex receiving input from perhaps a few tens of thousands of fibers from the geniculate first operates on the information and then supplies an output carried by fibers sensitive to orientation, movement, and so on, combining the information from the two eyes: each such piece does roughly the same set of operations on about the same number of incoming fibers. It takes in information, highly detailed over a small visual-field terrain for fovea but coarser and covering a larger visual-field terrain for points outside the fovea, and it emits an output—without knowing or caring about the degree of detail or the size of the visual field it subserves. The machinery is everywhere much the same.
That explains the uniformity observed in the gross and microscopic anatomy.
The fact that covering a 2-millimeter span of cortex is just enough to move you into a completely new area of retina means that whatever local operations are to be done by the cortex must all be done within this 2 millimeter by 2 millimeter chunk. A smaller piece of cortex is evidently not adequate to deal with a correspondingly smaller retinal terrain, since the rest of the 2-millimeter piece is also contributing to the analysis of that region. This much is obvious simply from a consideration of receptive-field positions and sizes, but the point can be amplified by asking in more detail what is meant by analysis and operation. We can start by considering line orientation. For any region in the visual field, however small, all orientations must be taken care of. If in analyzing a piece of retina, a 2-millimeter piece of cortex fails to take care of the orientation +45 degrees, no other part of the cortex can make up the deficit, because other parts are dealing with other parts of the visual field. By great good luck, however, the widths of the orientation stripes in the cortex, 0.05 millimeter, are just small enough that with 180 degrees to look after in 10degree steps, all orientations can be covered comfortably, more than twice over, in 2 millimeters. The same holds for eye dominance: each eye requires 0.5 millimeter, so that 2 millimeters is more than enough. In a 2-millimeter block, the cortex seems to possess, as indeed it must, a complete set of machinery.
Let me hasten to add that the 2-millimeter distance is a property not so much of area 17 as of layer 3 in area 17. In layers 5 and 6, the fields and the scatter are twice the size, so that a block roughly 4 millimeters by 4 millimeters would presumably be needed to do everything layers 5 and 6 do, such as constructing big complex fields with rather special properties. At the other extreme, in layer 4C, fields and scatter are far smaller, and the corresponding distance in the cortex is more like 0.1 to 0.2 millimeter. But the general argument remains the same, unaffected by the fact that several local sets of operations are made on any given region of visual field in several different layers—that is, despite the fact that the cortex is several machines in one.
All this may help us to understand why the columns are not far more coarse.
Enough has to be packed into a 2 millimeter by 2 millimeter block to include all the values of the variables it deals with, orientation and eye preference being the ones we have talked about so far. What the cortex does is map not just two but many variables on its two-dimensional surface. It does this by selecting as the basic parameters the two variables that specify the visual field coordinates (distance out and up or down from the fovea), and on this map it engrafts other variables, such as orientation and eye preference, by finer subdivisions.
We call the 2 millimeter by 2 millimeter piece of cortex a module. To me, the word seems not totally suitable, partly because it is too concrete: it calls up an image of a rectangular tin box containing electronic parts that can be plugged into a rack beside a hundred other such boxes. To some extent that is indeed what we want the word to convey, but in a rather loose sense. First, our units clearly can start and end anywhere we like, in the orientation domain. They can go from vertical to vertical or -85 to +95 degrees, as long as we include all orientations at least once. The same applies to eye preference: we can start at a left-eye, right-eye border or at the middle of a column, as long as we include two columns, one for each eye. Second, as mentioned earlier, the size of the module we are talking about will depend on the layer we are considering.
Nevertheless, the term does convey the impression of some 500 to 1000 small machines, any of which can be substituted for any other, provided we are ready to wire up 10,000 or so incoming wires and perhaps 50,000 outgoing ones!
Let me quickly add that no one would suppose that the cortex is completely uniform from fovea to far periphery. Vision varies with visual-field position in several ways other than acuity. Our color abilities fall off with distance, although perhaps not very steeply if we compensate for magnification by making the object we are viewing bigger with increasing distance from the fovea.
Movement is probably better detected in the periphery, as are very dim lights.
Functions related to binocular vision must obviously fall off because beyond 20 degrees and up to 80 degrees, ipsilateral-eye columns get progressively narrower and contralateral ones get broader; beyond 80 degrees the ipsilateral ones disappear entirely and the cortex becomes monocular. There must be differences in circuits to reflect these and doubtless other differences in our capabilities. So modules are probably not all exactly alike.
DEFORMATION OF THE CORTEX
We can get a deeper understanding of the geometry of the cortex by comparing it with the retina. The eye is a sphere, and that is consequently the shape of the retina, for purely optical reasons. A camera film can be flat because the angle taken in by the system is, for an average lens, about 30 degrees.
A fish-eye camera lens encompasses a wider angle, but it distorts at the periphery. Of course, bowl-shaped photographs would be awkward—flat ones are enough of a pain to store. For the eye, a spherical shape is ideal, since a sphere is compact and can rotate in a socket, something that a cube does with difficulty! With a spherical eye, retinal magnification is constant: the number of degrees of visual field per millimeter of retina is the same throughout the retina—3.5 degrees per millimeter in human eyes. I have already mentioned that ganglion-cell receptive-field centers are small in and near the fovea and grow in size as distance from fovea increases, and accordingly we should not be surprised to learn that many more ganglion cells are needed in a millimeter of retina near the fovea than are needed far out. Indeed, near the fovea, ganglion cells are piled many cells high, whereas the cells farther out are spread too thin to make even one continuous layer, as the photographs on the facing page show. Because the retina has to be spherical, its layers cannot be uniform.
Perhaps that is part of the reason for the retina's not doing more information processing than it does. The layers near the fovea would have to be much too thick.
The cortex has more options. Unlike the retina, it does not have to be spherical; it is allowed simply to expand in its foveal part, relative to the periphery. It presumably expands enough so that the thickness—and incidentally the column widths and everything else—remains the same throughout