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A book by
William H. Calvin
Thinking a Thought in the Mosaics of the Mind
MIT Press
copyright ©1996 by William H. Calvin


A Compressed Code Emerges

These self-re-exciting systems [cell-assemblies] could not consist of one circuit of two or three neurons, but must have a number of circuits. . . . I could assume that when a number of neurons in the cortex are excited by a given sensory input they tend to become interconnected, some of them at least forming a multicircuit closed system. . . . The idea then [1945] was that a percept consists of assemblies excited sensorily, a concept of assemblies excited centrally, by other assemblies.
Donald O. Hebb, 1980

Polyphonic music elaborated on chants by combining a number of independent but harmonizing melodies. The task of this chapter is considerably easier: we only have to combine notes, each from a different triangular array, into a simple melody (polyphony, as chapter 7 will show, is a useful analogy to what’s going on in category representations). While this chapter starts with some issues regarding the cortical landscape from which the choir sings, it soon progresses to an abstraction much like written music.

    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.

The “hot spot” could be sizeable, because of the width of those 0.25 mm clusters of terminals. But the history of neurophysiology suggests that, functionally speaking, the hot spot might be far smaller, perhaps as small as a minicolumn (0.03 mm diameter, and a small percent of the area). Before returning to the spatial extent of a triangular array, let us consider the size of its nodes (I’ll use node as a punctate theoretical term, with hot spot referring to physiologists measure, and axon terminal clusters referring to what anatomists see).

    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.

There should be a marked stability of the triangular arrays formed by the hot spots, even under various perturbations. Let us suppose that a triangular array is firing in a repeated cycle. And that one point in the midst of a triangular array tries to fire out of sync, later than its neighbors.

    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.

Does a hot spot form at precisely the location suggested by the node of a triangular array? It need not, of course, if other wiring principles override the triangular tendency; for example, making connections with other orientation columns of the same orientation angle might obscure triangular tendencies in primary visual cortex. But this is a theory for association cortex, not for the most specialized of cortical areas. Clustered recurrent excitatory terminals have indeed been found in many neocortical areas of many animal species.

    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.

Let us now consider the ensemble problem in the context of this tendency to recruit a triangular chorus. We don’t have just one triangular array, but multiple ones that interdigitate.

    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.

Is the Hebbian cell-assembly the whole collection of triangular arrays, each stretching over many millimeters, looking like those multiple strings of Christmas tree lights, out of sync with one another but flashing together within strings?

    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.

SUPPLEMENTARY MATERIAL: There are now animated illustrations for the spatiotemporal patterns.

What’s the relationship between hexagonal mosaics and the triangular arrays? There are some potential confusions, particularly because of the similarity in dimensions, each being about 0.5 mm (as are macrocolumns, which are areas with similar sources of distant inputs). The hexagon is a committee comprised of one member from each of a number of different triangular arrays.

    Because a hexagon is the largest nonredundant collection of points from a set of triangular arrays, the hexagon is a shorthand term that we must treat with care, lest we become overly concrete. For example, that the largest nonrepeating area is a hexagon does not tell us that it is a fixed hexagon. Our hexagonal-shaped viewing mask can be moved about (though not rotated) and still fulfill the requirement of containing only one element of each triangular array. If you try this exercise with your wallpaper, remember that checkerboards are the other common regular mosaic; we’re unlikely to encounter square mosaics here because there is no apparent copying mechanism for them.

    We might still see hexagons embedded in the anatomy if something in the underlying cortical circuitry tended to make some areas interact as groups. The immovable color blobs might serve as fixed anchors, as might the macrocolumns (ocular dominance columns also span about 0.5 mm). Perhaps the ABCD points tend to form an emergent rhythm that comes to be contained in the local connectivity. It, then, would have a territorial identity that would make some mask placements more meaningful than others — an anchored hexagon.

    The Wrap has an interesting consequence for the issue of what’s the unit pattern (still a problem in biology; see Helena Cronin’s answer in the glossary under “gene”): even if the feature detectors that were originally active were scattered over a few millimeters, we now have a more compact representation. We have compacted the presynchronization, premosaic Hebbian cell-assembly into a small standard space, presumably making it easier to restart the characteristic spatiotemporal firing pattern from a local cortical circuit; indeed, any of a number of similar hexagons could proceed to clone a whole population of the resurrected spatiotemporal pattern.

    Of course, we have a tendency to concentrate on only those cells that are firing in response to the banana. If you also consider what cells must remain silent to avoid fogging the characteristic pattern, the cerebral code for Banana occupies the full hexagon. In the musical analogy that opened this chapter, this hexagon corresponds to the string quartet. Its members, too, have to know when to keep quiet so as not to ruin the harmony.

    Another way to look at the unit-pattern problem is to ask what is the minimum cell-assembly needed to reignite this spatiotemporal pattern. That’s the minimal assembly of cells which can begin to generate a hexagonal mosaic, not necessarily all the individual “tiles” of the parent pattern stretching out laterally across a cortical work space, but at least a “starter” fraction of it. Because it takes two cells 0.5 mm apart to start generating a triangular array, the minimal Hebbian cell-assembly is two adjacent hexagons worth of the characteristic spatiotemporal pattern. Even if sensory input isn’t providing a subliminal fringe of almost-active inputs for triangular node recruitment to boost, the NMDA augmentation can still recruit a new node; it just takes longer than if sensory input was already pushing the nodal neurons into the subthreshold region. In chapter 5, I will elaborate on the reconstitution of spatiotemporal firing patterns from spatial-only connectivity patterns and revisit this point.

    For now, observe that our original collection of feature detectors, possibly scattered over some distance in cortex, has become rather like those hexagonal mosaics forming the floors of the Grecian steam baths 2,500 years ago. Looking down on the cortex with fine enough resolution won’t necessarily reveal the boundaries of even anchored hexagons — not any more than you can detect the boundaries of the unit pattern of wallpaper in the midst of the mosaic it forms. But looking down on the cortical surface ought to reveal a triangular array via its synchrony, and then another such triangular array offset somewhat in time. Perhaps we would see one triangular array, and then the others, recruit additional territory. It would be as if additional hexagonal tiles were being added to the unfinished floor. Later we might see the finished portion of the tiling retreat, fading out as if erased, or perhaps replaced by a competing string-quartet pattern, advancing from the other direction.

The recurrent excitation of the superficial layers of neocortex seems an excellent setup for cloning spatiotemporal patterns. Like the patches of bluegrass and crabgrass in my backyard, they could even compete for territory, though at the expense of losing their clonelike uniformity near the cerebral frontiers.

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