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

Partitioning the Playfield

[The genes vs. bodies] genotype-phenotype duality of the living organism is the reason why it is not sufficient in biology to search for a single cause in the study of a phenomenon, as is often sufficient in the physical sciences.
Ernst Mayr, 1988

Hebb’s dual trace memory had long seemed to me to constitute a possible analog to the genes versus bodies distinction. Throughout the 1980s, I kept thinking about spatial-only long-term memory traces and contrasting them with spatiotemporal patterns for active memory (p. 17), hoping to see an analogy to genes somewhere.

    As it turns out, nothing in my hexagons theory is analogous to the “germ line,” the genes that are unaffected by feedback from the body (but whose chances of being successfully copied are dependent on the body). The biological two-levels tradition was, however, quite influential in how I came to see Hebb’s dual-trace-memory problem. Getting from there to here has depended on quite a few additional developments in science.

    John Z. Young kicked off the neural round of selectionist thinking with his 1964 book, A Model of the Brain, where he discussed tuning up the nervous system by weakening synapses. Richard Dawkins touched on the same theme in 1971, extending it to selective cell death; outside of prenatal development, neuronal death is not currently considered an important candidate. Dawkins’s real contribution has turned out to be on the copying side, not the selection side, of mental darwinism. In his 1976 book, The Selfish Gene, he extended the notion of copying genes to copying memes (cultural entities such as words and tunes). It took awhile before anyone realized its implications for copying inside a single brain.

    Jean-Pierre Changeux’s selective stabilization of developing synapses confirmed me in thinking that selecting among the possibilities, and letting self-organization adjust the connection strengths, made far more sense of the known neurobiology than other approaches. Then Gerald Edelman convinced me in the summer of 1977 that a selectionist approach to higher brain functions could be made from the level of pathways and synapses. It was a very liberating view, helping me make sense out of the fuzzy wiring of the brain, the extensive variability between individuals (such as a three-fold range in size of primary visual cortex among adults), and all of those “silent” synapses that we were discovering. Edelman emphasized that to the newborn animal, the world was an unlabeled place and that adaptive mechanisms in the brain had to partition the objects and events of the individual’s experience.

    When chaos theory came along (which, for me, is dated to Otto Rössler’s famous paper of 1983), it started to become evident how basins of attraction lived in the connectionists' networks. When complexity theory and artificial life came along on their heels, the possibilities of getting to the bottom of Hebb’s dual-trace memory seemed promising. Then in 1988, I spent more than two months digesting Edelman’s Neural Darwinism, thanks to a request from Science to write a book review that explained it all.

I said that Neural Darwinism was essential reading (and it still is) for anyone interested in brains and development, though it is an unnecessarily difficult book. What I didn’t see, in my reading of Edelman, was any role for the repeated copying of active spatiotemporal patterns, particularly as a prelude to the selection step. He seemed to have an intriguing analogy to evolutionary biology, but with the reproducing populations left out. The nature of analogies, of course, is that you always leave something out; the issue is whether what’s left out is central to the theme, potentially leaving you confused by a hollow or crippled analogy.

    Even if you are adding new synapses all the time, selection by itself is merely a carving process and, although it sometimes introduces interesting patterns, it has none of the power of the full darwinian process with its six essentials and various catalysts. Edelman’s “reentry,” in the sense of repeated interactions with other regions providing “differential amplification of particular variants in a population,” didn’t carry the connotation of repeatedly copying a spatiotemporal pattern, such as an ephemeral “fabric” with many cloned repeats of the unit spatiotemporal “swatch.”

    Most such confusions of darwinian concepts did not detract from the power of Edelman’s analysis. But some do, as when he says, “[This] is a population theory, that is, it claims that brains operate by selection upon variance at several levels. Such a process leads to differential modification of synapses and the selection of particular neuronal groups on the basis of individual experience in an open-ended world or environment.” All true, except something of a non sequitur. Populations — in ecology and evolutionary biology, and even in immunology — usually involve lots of individuals somehow making near copies of themselves, all present at the same time, interacting with one another and with the environment.

    I have a difficult time identifying either an individual unit or a copying mechanism in Edelman’s lots-of-neurons notion of a “population.” His differential amplification via re-entrant loops, although undoubtedly an important process, doesn’t really involve a population in the way the word is used elsewhere in biology. Francis Crick’s famous quip, that Neural Darwinism ought to be called “neural Edelmanism” instead, is supposed to remind us not to conflate selectionist carving with the darwinian algorithm, the bootstrapping process that makes quality products from crude beginnings.

    But even if Edelman’s selectionism and populations do not encompass the full-fledged darwinian process (the six essentials and those “catalysts,” p.21), his term “neural darwinism” did correspond to the popular notion of darwinism as a carving process, a notion shared by many scientists. If we are to blame anyone for the frequent confusion of selectionism with the full darwinian process, we would have to start with Charles Darwin himself, who named his theory for only one aspect of the six-part process: natural selection.

The road to wisdom?
Well, it’s plain and simple to express:
Err and err and err again
but less and less and less.

Piet Hein
Truly darwinian evolution requires populations of nearly identical individuals, with enough variation for selection to skew reproduction and enough climate fluctuations to pump the process. Could you get darwinian shaping merely from a loop between two cortical maps, the back-and-forth interactions between them serving to adjust both of them? That’s Edelman’s going-beyond-selectionism idea, though his terminology often has to be translated for the uninitiated.

    Edelman, quite properly, doesn’t like the control systems connotations of “feedback” (technically speaking, there’s a standard being compared to an erroneous version that needs correcting). But instead of using “loops” to avoid the error connotation, he used the term “reentry” — though not especially with the “sneaking behind the lines” connotation that the term has acquired in automata theory and cardiac physiology, thus adding to the confusion.


    I can imagine Edelman’s back and forth adjustment process between maps serving to implement a shaping-up process, just as subsequent versions of a marked-up manuscript show improvement. Indeed, the analogy to the editorial process suggests a useful (though somewhat shopworn) name: revisionism. It is surely slower, less amenable to the traditional darwinian multiple-species competitions, and less algorithmic than proper darwinism; most of the six essentials are hard to identify. However appropriate it may be for the days-to-years time scale that Edelman discusses, shaping up quality in milliseconds-to-minutes may require population-based darwinism, all the six essentials, most of the known catalysts, and perhaps even some unique-to-the-brain shortcuts based on them as well — just to keep us speedy enough to avoid avoir l’esprit de l’escalier.

    I like the Edelmanian interacting maps for other applications, one of the most important of which is embedding one-trial episodic memories into neocortical connectivity. The more usual skill-acquisition memories that involve many repeated trials have repeated opportunities to embed a new attractor. One-trial learning does exist, but episodic memories are the first to go if memory malfunctions from head injuries, aging, or simply loss of sleep (we tend to guess wrong, or confabulate, rather than realize that we don’t know). Eyewitness memories are notoriously unreliable — indeed, they are malleable, with subsequent errors in recall becoming memories themselves, more accessible than the truth.

    A rehearsal process during the consolidation of an episodic memory, to imitate repeated trials, is one obvious possibility. I like to think of hippocampus (actually entorhinal cortex, to which hippocampus is a subprocessorlike appendage) triggering the neocortex with the first few notes of the melody, perhaps during sleep or other idle periods, and the cortex responding with the whole line of “music” (or perhaps entorhinal sending the short “message digest” and the neocortex elaborating it into the full “text” of the episode).

    But rehearsal isn’t cloning either, not any more than reentry is.

Cloning was finally on my mind again by 1991. It wasn’t the first time. A decade earlier, I’d hypothesized cloning of cortical spatiotemporal patterns as a way of curing timing jitter, getting around the inherent noise of the neuron via an emergent property of a common neural circuit. I’d even taken my original notion of cloning movement commands and extended it to the hyperacuity problem in sensation. No thanks to me, clone had also become an everyday word in the 1980s. This time around, I was looking for cortical circuitry that could do the cloning job.

    In November 1991, while talking to my old friend Jennifer S. Lund at the neuroscience meetings in New Orleans, things clicked. She was explaining her monkey visual cortex poster to me when I asked about the intrinsic horizontal connection’s regularity that she mentioned in passing. Oh yes, Jenny said, that’s nothing new, we saw it about ten years ago in the cortex of the tree shrew. Earlier I’d been talking about synchronization of relaxation oscillators with some experts, finding out that entrainment was even more profound than I’d thought from my earlier work (it could be hard to avoid, given slight excitatory coupling). All of what has become chapter 2 began to hang together. On the airplane that night, and in a standing-room-only waiting room in the Miami airport en route to visiting my wife’s parents, I sketched out what in subsequent months became the hexagons theory. It probably helped that my in-law’s apartment had a hexagonal tile floor. I gave my first public lectures on the theory about two months later, to the Seattle neurophysiologists and to the Boston cognitive science community.

    I promptly discovered that I would need to explain niches and population thinking while I was at it.

Concepts from evolutionary biology and its “population thinking” are not well known among nervous system researchers or those who would mimic the brain via inventing artificial intelligences. I’d only learned about them myself in the 1980s when I’d volunteered to teach biology to honors-program undergraduates (I’d somehow missed taking introductory biology myself, so I’d had the problem of staying ahead of my bright students in some areas of biology). Population biology has some useful concepts to remember when venturing into the spatiotemporal aspects of a neocortical darwinism, as do the newer concepts of evolutionarily stable strategies, the applications of game theory to interacting populations.

    In some sense, it suffices to imagine a dynamically reforming patchwork quilt, each patch’s fabric pattern having lots of triangular arrays that, on closer inspection of swatches, constitute cloning hexagons. But population thinking requires more. It involves learning how to phrase the questions in population terms, so as to see both the individual and the population in the manner of seeing both the tree and the forest.

    There are, for example, barriers to populations such as mountains, deserts, and large bodies of water. They partition the playfield into parcels (they parcellate it), creating regionally isolated subpopulations (demes) that don’t often interbreed. Most importantly, barriers have gaps that function as gateways. Hikers call them passes while mariners call them passages, which is perhaps a better term for our mostly flat paving-the-park analogy. The neocortical version of a gateway is what encourages variant spatiotemporal patterns to form individuals that differ slightly from the clones that serve as their parents.

Escaping error correction involves keeping most of the six neighbors to a hexagon (p. 41) from ganging up on the variant. The simplest way to accomplish this is with patchy unresponsive areas, where triangular arrays are unable to recruit followers.

    Lack of excitation, the usual tendency of a lot of activity to produce surround inhibition a la Békésy and Hartline (and the recurrent connections of the layer 5-6 pyramidal neurons are a candidate), preoccupation with other activities — all could serve as a barrier that limited the spread of a mosaic. In paving-the-park, it would correspond to the mindless paver-layers running into a curb — or perhaps a ridge line thrown up by an enterprising gopher enlarging an underground tunnel.

    Wide gateways, like wide slits in the physicists’s particle-wave experiments, aren’t very interesting. Narrow ones, about the width of the local “0.5 mm” metric, stop annexation altogether. It takes activity in two adjacent hexagons to clone a third: just recall that lab coat campaign button that reads Don’t Clone Alone! But gateway widths between two and three times the metric provide a way to escape error correction.

    Just through the gateway, triangular array nodes are only subject to the two nodes occupying the gateway. For some of the multiple triangular arrays that constitute the hexagon’s spatiotemporal pattern, a failure to recruit might occur. Or a neuron will instead be recruited off to one side of the equilateral triangle, simply because of imprecise anatomy. It is perhaps only with six surrounding neighbors that the nodes are forced into the proper equilateral triangles, just as crystals may be imperfect near their natural edges.

    On the far side of the gateway, the imperfect hexagon’s triangular arrays will still be able to take part in producing another hexagon, acting in combination with one of the perfect hexagons in the narrow passage. If the imperfect pattern is again created, then there are two imperfect hexagons side by side, the essential setup for cloning a lot more of them.

    Although a sexually reproducing species can colonize a new island via just one pregnant female, the asexual cortical hexagons seem to require two to tango.

Competition with the parent pattern seems quite likely, particularly if the parent pattern simply does an end run around the barrier. Soon the variants will be contending for the no-mans-land (p. 59) that separates them from the parent clones.

    Thanks to concepts such as basins of attraction and how they might be biased by noncloning long-distance inputs, we can imagine why one pattern might succeed better than another in annexing no-mans-land. Indeed, we can ask about how this battlefront moves and stabilizes by considering a three-array spatiotemporal pattern called Bach meeting up with a four-array pattern such as Beethoven.

    Suppose that the undecided territory has shrunken to only one unfilled tile’s worth, and that it has three Bach neighbors trying to recruit it via annexing nodes in its three triangular arrays. But it also has the three Beethoven neighbors, also trying to recruit the four corresponding nodes of their arrays. The underlying resonances ought to make the difference in which wins: it’s the equivalent of a memorized environment biasing a darwinian copying competition. (They might merely superimpose, a topic I’ll save for Act II.)

    Boundaries seem more likely to form along an angle, however, such that all the hexagons on the border have four similar inputs but only two of the other pattern. Although a well-resonating pattern on the two-side might nonetheless invade the territory of a less resonant pattern, four-to-two probably creates a temporary stability in the midst of change.

Ambiguous perceptions provide a useful example of how copying competitions could perform a common mental task. When overlearned objects are sensed, there is likely no need for a copying competition to decide the issue: they probably immediately pop through to an appropriate attractor and “early decision” obviates the need for prolonged copying. But a lot of what we see is ambiguous, at least temporarily.

    Suppose that you see an object go whizzing past, which then disappears beneath something. You can’t take a closer look. But what was it? It was seemingly roundish, about the size of many kinds of balls and fruit. How do you guess what it was? Perhaps you use the cortical equivalent of the immune response.

    In terms of a cortical darwinian competition, the first task is to take the spatiotemporal pattern of the sensory input, good old “?” (hereafter called unknown), and make a territory of clones in a region of cortex that we might call the sensory buffer. A barrier with a gateway will then allow variants to be made on this original group of triangular arrays. A series of additional short end-runable barriers with gateways (not shown) can allow further variants from the original (the distorted ? in the figure). Finally one of the variant spatiotemporal patterns gets close enough to the lemon attractor to be captured by it: a few lemon clones form up in one part of the territory. About the same time, the baseball attractor has been similarly activated by a different variant, aided by the fact that you’re currently at a picnic (baseball and picnic perhaps have an association in your brain). In a third part of the cortical territory for handling ambiguous visual objects, apple has been fired up.

    It’s possible to simply have a stalemate between unknown and the three candidates. But background conditions change much more quickly than the weather — and so lemon takes over much of apple territory. Finally, baseball not only converts many of the remaining unknown variants but also the apple territory. Because having a number of clones in sync is a good way for long corticocortical paths to get the attention of premotor and language cortex (to be discussed in chapter 8), we get the decision: “It was a baseball.”

    It’s a very simple-minded example of how a perceptual task could get some help from a darwinian cloning competition when there’s too much ambiguity for a quick decision. First, variants are spawned. Second, attractors capture some variants and thus create standard spatiotemporal patterns for vocabulary items. Third, a cloning competition ensues, aided by some fluctuations in background excitability. Finally, a decision occurs when there are enough of one type singing in a chorus.

Just as climate fluctuations speed up biological evolution, so cortical excitability fluctuations might speed up hexagonal competitions. Some areas will be converted from prepared-for-pavers into barriers that partition the playfield.

The capacity to blunder slightly is the real marvel of DNA. Without this special attribute, we would still be anaerobic bacteria and there would be no music.
Lewis Thomas, 1979
    A raised threshold in a region (another way of saying reduced excitability or increased inhibition) can be envisaged as humps thrown up by that enterprising gopher. It’s not really a fence, in the sense of enclosure, but simply the equivalent of underbrush that’s easier to go around than through. Neither does it necessarily partition anything (think instead of those alcoves that open out into the more general-purpose parts of the park, p.56).

    Barriers help fragment reproducing populations so that they can go their own way, unconstrained by interactions with the other demes or the main population itself. The second consequence is, of course, that the narrower gaps between barriers permit reproduction of hexagonal spatiotemporal firing patterns without the usual error-correction. Thus we might expect fluctuating thresholds to both protect variants from correction and to actually generate more variants.

    Though recorded from the scalp, the electroencephalogram is a spatial average of much cortical electrical activity (especially synaptic potentials) in the superficial layers. While reminiscent of stochastic resonance, speeding up darwinian competitions could be done by excitability fluctuations, raising the question of whether some EEG component reflects the equivalent of a forcing function, analogous to climate change.

One might reasonably suppose that a bottleneck is my gateway in the hexagonal barrier, and that an empty niche is all that unrecruited territory that lies beyond, available for organization via creeping triangular arrays. A reasonable assumption, but nonetheless wrong. They are population-level terms in evolutionary biology, invented long ago and with well-established connotations, that may prove relevant to the dynamics of partitioning neocortex for hexagonal patterns.

    A bottleneck refers to small populations that were once large and diverse. Small populations have much less genetic diversity and inbreeding diminishes it further. Should this population somehow expand to a much larger population, as happened with the immigrants across the Bering Straits about 15,000 years ago who eventually colonized all of North and South America, its gene pool will also lack the diversity of the large original population. This is the founder effect — though the expansion itself may preserve any new recombination variants that happen via the boomtime survivals that would otherwise have been lost to juvenile mortality.

    A population of clones lacks the variations of most natural populations, what causes us to talk of gene frequencies. But an active hexagonal mosaic need not be uniform. Think of the barriers to annexation (and error correction) not as fences or curbs but as little ridge lines — in the park reverie, they might be created by that enterprising gopher burrowing along under the flat surface, so invitingly prepared for pavers. Even if they are flattened down again, they seem to pop up elsewhere. This makes possible an occasional gateway (a flat-enough area between ridgelines). And that produces an occasional variant by preventing error correction from operating. At any one point in time, the cerebral park’s paver population exhibits variation. You’d even expect its temporary alcoves to develop regional subspecies, just as a natural population of fruit flies in Hawaii tends to have somewhat different gene pools in different valleys.

    So, too, excitability declines in some regions of cortex will wipe out the local triangular array nodes and prevent new ones from forming — in effect, raising a barrier to further cloning. As long as this bumpy landscape keeps changing faster than the most efficient error correction can conform the entire population, there will always be some variation around. If error correction were to triumph everywhere, it would constitute a bottleneck as severe as that of the single pregnant female that finds an empty island, even if the cloned territory is large. Yes, variation will return shortly after some new barriers arise, but its base will be the standardized spatiotemporal pattern rather than that of the more diverse assemblage that preceded the bottlenecking uniformity.

    Even a uniform bottleneck hexagonal mosaic (say, Beethoven clones occupying hundreds of hexagons) can create variation as it tries to embed a new attractor in the underlying connectivities. Because hexagonal territories have stopped expanding at many different places in the past, the underlying connectivities vary over a mosaic’s current territory. To the extent that the old embedded attractors interact with the new one, regional variants will occur later, when the Beethoven spatiotemporal pattern is recreated from scratch.

Similarly, an empty niche is not just an unorganized region of cortex. Even busy areas could also have an empty niche — which brings us back once again to multifunctionality.

    Niche is an ecological term that refers to all of the resources, protection from predators, nesting sites, and other things that allow a population to reproduce itself; toads might not need waterholes all the time, but a return to the water’s edge is essential at egg-laying time and that makes waterholes a part-time but essential element of their niche. A niche is the “outward projection of the needs of an organism.”

    An empty niche is a term referring to a niche with significant resources that are going unused; lots may be going on in a cortical region but an additional hexagonal resonance is available that, if activated, would cause minimal impact on the other ongoing activities. Mayr describes one extracranial empty niche:

The tropical forests of Borneo and Sumatra, for instance, provide resources for 28 species of woodpeckers. By contrast there are no woodpeckers what-so-ever in the exceedingly similar forests of New Guinea, and on that island hardly any other species of birds make use of the woodpecker niche. The existence of insufficiently utilized resources is further documented by successful cases of colonization or invasion which do not result in a visible decline of any previously existing species.

Most species are relatively independent of one another, simply getting out of one another’s way like the proverbial two ships passing in the night — but without even the distant wave of a hand.

    So too, we might find that the different species of cortical spatiotemporal melodies can, if point-to-area inhibition is also low, occupy the same cortex without significant interaction: perhaps those competing Bach and Beethoven hexagons can overlap just as French and Dutch do in Belgium. Avoiding using the same minicolumns would presumably aid “bilingualism”; changing the slant of the triangular arrays, earlier discussed for the passive resonances (p. 73), may also be a possible method for active spatiotemporal patterns to avoid one another.

    As Mayr points out elsewhere, the “existence of such potential niche space explains, of course, why speciation is sometimes successful.” To make an economic analogy, we might say that there was an unfilled niche for spreadsheet software prior to 1980 and that the boom in spreadsheets was a speciation event as well as an invention. But the empty niche concept, per se, is more closely associated with deme extinctions (a regional subpopulation dies out, usually from climate change or infectious disease) where proven-in-the-past resources are now going unused. Subsequent pioneers to this territory may thereby enjoy a boom time.

    Some analogies to economics and politics may make this clearer. A classical hidden agenda is encouraging bankruptcies by predatory pricing; it’s a stage-setting strategy for a market takeover that establishes a monopoly. The political equivalent might be unrealistic promises of tax cuts, or denigrating all government accomplishments (“Can’t do anything right”). Although it seems paradoxical to hear aspiring politicians say this, the governing niche itself won’t be destroyed by this anarchistic maneuver. That’s because our society has become too complex to run without government services and, in a fast-moving world, the government pays for the long-term research that no corporation has the incentive to perform itself. But even a smaller pie may be very profitable for the supporters of such anarchist politicians, particularly when the benefits are largely disguised, usually by shifting the tax burden to others. (As the lawyers like to say, Cui bono? The more pointed journalistic version of “Who benefits?” is “Follow the money.”) One has to imagine such contractions of business or government as being temporary, likely followed by a re-expansion around a new base, refilling the niche — and ask what that base of expansion will center about (likely — though not inevitably — the well-situated survivors). So too, in this neocortical theory, we see the possibilities for establishing sizeable pluralities, both by direct competition and by better surviving environmental fluctuations.

    Here, even when a pattern falls temporarily silent, the ghostly blackboard of temporarily enhanced connectivity makes it possible for the pattern to again ignite. And perhaps booting up with a novel pattern, a composite of several patterns that had recently inhabited the territory — but never simultaneously. Although I doubt that it is the most elementary mechanism for category formation, overlain hexagons hold the promise of dealing with advanced levels of abstraction.