Ramachandran’s The Tell-Tale Brain recounts the properties of the visual cortex, especially the edge detector area. Some of the early visual system seems to operate in parallel, in particular where it makes sense to speak of ‘peripheral vision’. A field of randomly placed small vertical line segments of the same length is immediately recognized as such. Any segment out of alignment is immediately evident. I conclude parallel processing done by a somewhat homogeneous 2D array of neurons in the visual cortex which is indeed physically laid out in a topologically continuous map of the ‘real visual field’. A stronger mathematical mechanism is evident as well—an affine connection. We immediately sense that two lines are parallel and about the same length even when they are not nearby. We seem to sense this even without motion of the eyeball. This is a difficult trick and any solution thereto is almost by definition an affine connection. Even presuming that the line segments were represented in the cortex by parallel sets or neurons, which seems unlikely, would not make the task easier.

Some neurons in the visual cortex are permanently associated with a particular point, or small neighborhood, in the visual field. Others are not. I call the former LV here.

I presume a neuron state (or local pattern of neuron states) that arises in LV when an edge with a particular orientation at a particular place in the visual field had been detected. When two of these are stimulated in different parts of the visual field we must wonder where the parallel relation between these two is noted. That is presumably not an LV neuron. I consider two places because that is the simplest mathematically. Nature may not have chosen the simplest way as math would have it. In any case edgeness is signaled by the edge detectors and such signals are somehow gathered together in a place situated to note that the detected edges are parallel.

Perhaps there is a delocalized signal for many vertical edges. Subsequent saccades suffice then to examine exceptions and corroborate our illusion that we saw all details simultaneously. It remains to say how a particular LV contributor knows that his edge is vertical.

Somewhere I have read a plausible hypothesis of how the visual cortex detects straightness of lines. It depends on the significant fact that certain eye motions leave the lines, or portions thereof, unchanged. I supposed at the time, and still do, that the cortex learned relations between places in the visual field such as betweenness, wherein point y is between x and z when y in on the line segment from x to z. This need not be long term learning; my suspicion is that we might even learn it again every day. (This is an easily tested hypothesis, or at least you don’t have to open the head to do it.)

Such a mechanism would not suffice to produce the affine connections, but similar mechanisms might. The cortex ‘knows’ when a portion of visual field which was presented to one part of the cortex, is later presented to some other particular part. Output from the first earlier portion must somehow be made to conform to the output of the later second portion. I can imagine a uniform evolved set of neurons that do this conformation and that these neurons, or other neurons produced in part by the same genes, do such conformation to other sorts of visual data at higher levels of processing. Higher levels of visual processing are no longer arranged in a continuous map and my mathematical tools dissolve. Perhaps there is no parallel processing at higher levels, or at least at the ‘per pixel’ level.

The same sorts of conformation could perhaps explain the conundrum that I saw in the synesthete’s ability to see the 2’s in a scattered set of 5’s. Such mechanisms can in effect cause learned signal detection (such as learning the figure 2) to be spread to the low level parallel processing cortex areas. It is also plausible that the synesthete may have an advantage here.

More Math

While we invoke math concepts we might go further. We sense roundness for which affine connection does not suffice. We know that there is something special about circles among ellipses. We detect circles unless some part of the brain adjusts for parallax. This immediately suggests an experiment: Does the sensing of parallel line segments depend on a head-on view of the field, or does the brain process as well when the visual field is distorted by a projective transformation? Not having done the experiment I conjecture that the projected parallel line segments, which are thus not parallel in the visual field, are not as readily processed for variation. Perhaps I will write some programs to make some pictures.
After a few days the following mechanism comes to mind.
Some neurons within the edge detector processing area, but allocated to peripheral areas, take note of a pattern they discern even while the eyeball moves so that the foveal area looks at the scene that had occupied said neurons moments before. I postulate that information from the neurons from the foveal goes to the brain part that seeks examples of learned patterns such as numerals. If there is a match a broadcast signal goes out to all the edge detectors saying, you just found something interesting; don’t forget it! Only the one edge detector neighborhood pays attention to that signal because it knew that the central pattern matcher was examining the small field it had just observed. Such mechanisms would explain both the affine learning above and the ability of the synesthetes.