Happily, by the end of this chapter, we will see the choir coalesce into sections, each of which sings the complete song. Unlike the placements favored by choirmasters, the sopranos are not grouped together; it’s more like each section has one soprano, one alto, one bass, and so forth, each singing a different part. Each section is surrounded by neighbors, sections that are similarly diverse. You might think that this would make it difficult for a choirmaster — if one exists — to conduct, but remember that string quartets get along nicely without a conductor, and what I will describe here is a chorus of string quartets.

    In cortex, it looks as if one string-quartet section occupies a space that is hexagonal in shape and about 0.5 mm across. It could constitute the most elementary version of Hebb’s cell-assembly, one that could represent a word, a face, or a pronunciation. Cloning indeed clues us in, suggesting what the relevant code might be — that characteristic pattern needed for the first darwinian essential. To get there, however, we first need to consider a few more aspects of the geometry and its relevant neurophysiology.

    Anatomical connectivity (the fanout of the axon terminals, the width of dendritic trees) is usually far more widespread than physiological responsiveness (such as receptive field centers). Indeed, at a few removes, every neuron in the brain can potentially connect to every other neuron — but such extensive funneling rarely happens. Antagonistic surrounds serve to concentrate things. In the retina, for example, wide areas of the photoreceptor mosaic would seem to have paths to a second-order cell, but a bipolar cell usually has a far smaller receptive field center, thanks to flanking inhibition (or it has an inhibited center with flanking excitation, the other type of antagonistic center-surround arrangement commonly seen) except during dark adaptation.

    In addition to antagonistic arrangements, some axon terminals seem to have very weak synaptic strengths; indeed, we sometimes talk of “silent synapses.” Anatomically, they’re there; physiologically, they’re undetectable most of the time. An example of this second type of physiological focusing is the projection from a thalamic neuron, one specializing in just one finger tip, to the hand map in cerebral cortex. Its axon terminal branches seem to span much of the hand’s map, but, when you look at the cortical neurons they’re feeding, you find that they typically have small receptive fields, little larger than those of thalamic neurons. Another indicator of size: visual cortex cells at millimeter separations with similar orientation preference are interconnected, suggesting the possibility of hot spots that are as small as those 0.03 mm minicolumns.

    The superficial pyramidal neurons are not the only cells contacted by the intrinsic axon collaterals; about 20 percent of the axon terminals are onto smooth stellate neurons (that themselves produce GABAergic inhibition), presumably contributing to forms of flanking inhibition that reduce the size of the hot spot.

    It has, however, six neighbors that are all sending it synchronous inputs at the standard time in the cycle, thus tending to correct it (actually, it may have a dozen because the axons tend to have several terminal clusters 0.5 mm apart). The same argument applies if the idiosyncratic neuron attempts to omit a impulse. Similarly, early firings tend to be corrected the next time around if the neuron has any tendency to produce longer-than-average interimpulse intervals following an earlier-than-average impulse.

    Spatially, there is the aforementioned tendency to focus synchronous excitation on the center of the hot spot. What both tendencies mean is that, like a crystal forming, we might expect to see some standardization. One might almost think of it as error correction.

    Another force for standardization may be the minicolumn of association cortex (represented as a raised bump in many of my “tangential slice” illustrations), those hundred cells organized around a dendritic bundle. The well-studied orientation columns of primary visual cortex seem to prefer similar stimuli, and the superficial pyramidal neurons have many close-in axon collaterals before the silent gap that often excite near neighbors. These suggest that a number of the minicolumn’s 39 superficial pyramidal neurons may be synchronously activated. Because of this, I have not found it useful to distinguish between the individual superficial pyramidal neuron and all the superficial pyramidal neurons within a given minicolumn. The six neighbors could be as many as 39x6=234 superficial pyramidal neurons, speaking together to exact conformity.

    One may thus think of the “cells” and “nodes” as really work-alike minicolumns. This tendency to act as a group could eliminate the “holes” in the lattice that might otherwise result from the incomplete “polka-dot” annuli of an individual superficial pyramidal neuron, and give rise to the point-to-annulus property that I infer.

    Any one superficial pyramidal neuron’s annulus isn’t perfect, of course, because its terminal clusters do not provide full coverage. But when six minicolumn’s worth of them overlap at the same node (even more, actually, because of the tendency of the axon to continue across another silent gap to produce another cluster), there will be one point that will have more input than others, and this ought to help define the node more narrowly. Furthermore, the cells implementing surround inhibition in the superficial layers of neocortex, the large stellate cells, have axons that reach far enough (except in rats) — so six inhibitory point-to-area circles also help define a node via subtraction.

    As we shall see in the next chapter, some synaptic augmentation mechanisms, such as those at the NMDA synapses, are available for rewarding such convergence. The NMDA synapses have a remarkably imprecise notion of synchrony, so augmentation per se might not be sensitive to the equal conduction distances that define the triangle. Exact synchrony of synaptic potentials depends on identical conduction times, all else being equal. Yet ordinary spatial summation — one bump standing on the shoulder of another postsynaptic potential — can define synchrony with considerable precision if the threshold for impulse production can be exceeded only by the optimal overlap, peak atop peak. Higher thresholds will shrink the size of hot spots and, if the conduction speeds are equal, center them equidistant from their inputs.

    When looking at a banana, various types of feature detectors ought to be interested; let us say that the parents of one triangular array (A) are fans of the yellow color of the banana. Other superficial pyramidal neurons will likely be interested in one or another of the tangents to the banana’s profile, and so one might get another triangular array (B) forming up to specialize in horizonal line representation. This second horizontal array need not be synchronized with the yellow array (as a common form of the binding theory assumes) for present purposes.

    Furthermore, the horizontal-tangent’s array might start several millimeters away from where the yellow array starts. One can easily imagine a half-dozen separate features, each with its own triangular array, each starting from a different part of the cortical work space. Provided that each array starts up on the same slant (this assumption will become more reasonable once we discuss evoking memories via resonances), the various triangular arrays will be parallel to one another.

    No, because that ensemble isn’t the minimal cell-assembly that could contain the minimal information needed to reconstruct it. There is obviously lots of redundancy in such a repetitive set of triangular arrays. Let us imagine using an unusually capable microscope and increasing the magnification as we gaze down on the cortical surface. Fewer and fewer nodes of each triangular array will be included as we increase the mag, just as zooming in on a flashing Christmas tree will encompass fewer and fewer lights in sync.

    Eventually we will zoom a bit too far, so that one of the triangular arrays (say, yellow) will no longer have a representative in our field of view. We might notice this because there are no longer any synchronous spots. So we zoom back out a little and one member of the yellow chorus pops back into sight. It’s now about 0.5 mm across our field of view. We decrease the mag a little further and now we’re seeing several sets of synchronized spots.

    So is the minimal Hebbian cell-assembly contained within a 0.5 mm circle? No, it is actually a hexagon, one that is 0.5 mm between parallel sides. We can suppose that we have, lining an edge of such a hexagon, one representative from each of N triangular arrays. Move the Nth array (say, the yellow specialists) out a little and other yellow point will creep into the opposite side of our original hexagon. It’s just like screen wrap on your computer monitor, where a line “ends around.” While the Hebbian cell-assembly may not look like a hexagon, its spatial extent may not be any larger than a hexagon, thanks to The Wrap.