[Edgar Allan Poe’s Eureka] dismissed the methods of both Bacon and Aristotle as the paths to certain knowledge.... He argued for a third method to knowledge which he called imagination . . . . Imagination, or genius, or intuition, lets the classification start so that the successive iterations, back and forth between the empirical and the rational, hone the product until it finally conforms to nature. Only then is the dross of the classifier skimmed away and a true order in nature, if it exists, revealed. Allan Sandage, 1995

    How we carve up our world depends on what’s out there — and on the analogies we bring to bear. We often talk as if ideas and thoughts were objects, that words and sentences were containers for these objects, and that communication was simply a matter of finding the right object, packaging it up, and sending it to a recipient who unpacks it. We often talk of rational thought as if it were just the algorithmic manipulation of such symbols. We go looking for computational elements in the brain that could accomplish such logical operations with virtual objects. This, alas, leaves no room for guessing or imagination. Our inadequate container schemas have boxed us in.

    Without imagination, we have no mechanisms by which to use reflection to mold experience, to bring something new out of the old, or to sympathetically project ourselves into someone else’s shoes. There’s no room, either, in traditional categories from set theory, as they box us in with necessary and sufficient conditions rather than allowing for fuzzy edges.

    Most of us normally function at a level of description that regards a chair as an object rather than a collection of wood grains or molecules or atoms. We are comfortable talking about a chair, even if we are physicists. We’re also comfortable talking about a schematic level of representation such as furniture. We use such abstractions to make sense of the common features of diverse experiences. Our borrowing from the physical and social worlds often aids feeling our way around, within a different level of organization.

    If we are to have meaningful, connected experiences — ones that we can comprehend and reason about — we must be able to discern patterns to our actions, perceptions, and conceptions. Underlying our vast network of interrelated literal meanings (all of those words about objects and actions) are those imaginative structures of understanding such as schema and metaphor, such as the mental imagery that allows us to extrapolate a path, or zoom in on one part of the whole, or zoom out until the trees merge into a forest. Can such properties be represented by the aforementioned cerebral codes and darwinian processes?

    Schemas are often about one thing relative to another. They include the little words of grammar — only a few dozen in number — that position things or events relative to each other on a mental map: relative location (above, below, in, on, at, by, next to), relative direction (to, from, through, left, right, up, down), relative time (before, after, while, and the various indicators of tense such as -ed), relative number (many, few, some, the -s of plurality), relative possibility (can, may, might), relative contingency (unless, although, until, because), possession (of, the possessive version of -s, have), agency (by), purpose (for), necessity (must, have to), obligation (should, ought to), existence (be), nonexistence (no, none, not, un-), and more.

    Other common schemas are blockage, center-periphery, full-empty, more-less, near-far, splitting, attraction, balance, matching, removing a restraint, attracts, circles, part-whole, and the easy-to-misuse containment. Note that schemas tend to refer to movement, rather than static properties (they’re often structures of an activity, not attributes of an object such as wet or cold). Even more than abstracts, schemas are flexible enough to fit many similar situations with differing details. They’re few enough in number to be handled as special cases, just as the several hundred irregular verbs are handled as exceptions to the general rule for past tense, add -ed.

    As chapter 7 discussed, hexagonal cerebral codes allow for forming new spatiotemporal patterns from several sources. Note that superpositions need not keep all of the component attractors; the category Fruit can amalgamate some the attractors from Apple and Orange into a new strange attractor. The same thing can happen in going from features such as round and red to an object-level description such as Apple. We don’t have to amalgamate all the component’s features into the category. The test is whether one can selectively reactivate the object-level codes from the higher category, whether one can get back from Apple to red.

    There are two major ways in which categories could arise: from active superpositions of hexagonal codes and from linking them (as when the U-fibers copy a pattern into another cortical area with different attractors, as when recognition-only hashes or loose-fitting abstracts are elaborated into full-text spatiotemporal patterns). Both results are capable of representing dynamic aspects (spatiotemporal patterns can represent both static and dynamic things); both can accommodate malleable edges. They seem amenable to the fuzzy types of categories that we form up from prototypes, with less prototypical members at various distances from the category’s center.

    Prototypes (a good American English /i/ vowel, for example) may capture a lot of variants, from the high-pitched ones of children to the garbled ones uttered by those with laryngitis. In the speech and hearing sciences, this is called the “magnet effect” of the prototype. Given that its representation is some spatiotemporal pattern in cortex, one can think of this as simply the capture effect of the attractor in the cortical connectivity that produces that characteristic spatiotemporal firing pattern.

    Schemas are one kind of fuzzy category. Metaphors are another, and they build upon a foundation of schemas.

Metaphors and analogical reasoning are the central means by which we project structure across levels. We use schemas as source domains for constructing a metaphor, as when up-down is used in the metaphor more is up. When we say that the stock market is up, we refer back to our childhood experiences of stacking things in a pile, where more things make a higher pile.

     When we try to understand one domain of experience in terms of structures from a different domain, we usually strip some detail away from the donor. When we metaphorically speak of the electrons orbiting the atomic nucleus as being like planets orbiting the sun, we aren’t implying that the nucleus is hot and yellow, only that the geometry bears some resemblance. We’re making use of such schemas as massive, attracts, revolves around, and circles to help describe something too small to see; again, structures are more likely to be mapped than mere attributes.

     The power of metaphors, poetic similes, Aesop’s parables, analogies, maps, and economists’ models is that they permit us to carry out reasoning within a familiar domain and subsequently map our findings back to the domain of interest. The Macintosh desktop metaphor allowed people to operate in the familiar realm of folders, documents, and trash cans rather than having to think about those pesky directories, files, and deletions.

    If analogies map with enough points of correspondence, you can reason with some accuracy. You can solve electrical problems, for example, using the analogy to water flow [or, if you prefer, the analogy to moving crowds]. An object such as a wire maps to a pipe [or a sidewalk]. Properties map too: electrical current maps to flow rate [or the rate at which people pass a checkpoint]; voltage maps to water pressure [or to the push of the crowd]; resistance can be narrow pipes [or sidewalk cafes that obstruct]. Relations can be imported as well: we can connect wires much as we do pipes [or pathways].

    To serve as the source domain of a metaphor, a schema needs to be pervasive in our experience, well understood, and simply structured. Anyone who teaches is constantly on the lookout for useful metaphors, but most candidates have to be discarded because their source domain isn’t simply structured or isn’t familiar enough. More people can solve electrical circuit problems using the crowd-flow analogy, probably because few of us are sufficiently experienced with fluid dynamics for it to be a good source domain. With such an analogy, you can often guess the answer to parallel resistor and source impedance problems.

    Schemas constrain our meaning and understanding. If we take circle too literally in our quest for understanding orbiting electrons, we will miss out on elliptical paths. Metaphors similarly constrain our reasoning: more is up might blind us to enormous underground fungi. Mark Johnson’s analysis of Hans Selye’s work on stress emphasizes how the body as machine metaphor in medicine (breakdowns occur at specific points in the system, repair may involve replacement or mending, etc.) blinded physiologists for a long time because there was no locale for purpose in a machine. Switching to the homeostasis metaphor (up-regulating, down-regulating within components) allowed Selye to envisage a widely distributed system associated with response to stress and then predict some of its malfunctions.

    But constraints are also the strength of schemas and metaphors, in the sense of a channel, within which the mapping can wander with a loose fit. You can be more-or-less “in the groove.” This is reminiscent of basins of attraction, where many starting paths eventually “converge,” allowing us to imagine a relatively standard spatiotemporal pattern as the underpinning of a schema.

    Again, there would seem to be no problem with encoding a metaphor (even a gedankenexperiment) as a hexagonal spatiotemporal pattern, much as in the case of other categories. It would just tend to be recombinations of schema codes, rather than those of the more concrete mental images needed for making a schema code. Linkage would be even more important in implementing the metaphor, converting thought into action, but the unit hexagonal representation would be what competes with alternatives.

    Before tackling analogical reasoning, let us note that high level concepts involving relationships need not occupy any more space than low level ones for objects. Just as short words and long words can equally well refer to complex concepts, so they can probably all occupy a single pair of adjacent hexagons in cerebral cortex. It’s the linkages that must be followed before getting the action underway which may become more extensive at the more abstract levels.

    First of all, there is the relationship problem: what attributes are shared by A and B? Size, animate-inanimate, movement, color, or perhaps one of those exemplar schemas? Let us say that attracts and containment are prominent among AB associations, that blue and blockage are among CD’s, containment and circles are among CE’s, and that CF has no schema associations, only less common ones. On this basis, only the CE association containment is shared with those of AB.

    Although this would seem to require a staged series of hexagonal competitions, remember the lessons of plating rows of infectious material and columns of the different antibiotics in order to find matches in the matrix — and, hopefully, an antibiotic that will attack all the organisms involved. Finding rare higher-dimensional combinations in the “directed evolution” experiments of molecular biology can now be done by matching up fragments of DNA with RNA candidates. All we really need, after CD, CE, and CF territories are each formed up, is for them to override an AB territory, with its fading attractors in the short-term memory for attracts and containment. One then reduces the excitability until only the better resonances remain active; AB’s fading containment attractor will help keep CE going better than its competitors.

    One could match for several shared attractors simultaneously without additional staging, thanks to the short-term memory of AB biasing the competition. And one can always use successive layers of staging, as in the sashimi example, each fading with time. That gives some additional possibilities, analogous to generations of back-crossing of hybrids to the parent population.

    For coupling of thought to action, there will probably be two spatiotemporal patterns involved, a processed sensory stimulus such as Apple and a movement program such as Say “apple”. I will again use the butterfly attractor as an easily visualized example of how an association can be formed, as two separate attractors become one strange attractor for Apple, Say “apple”.

    The minimal set of attractors for cloning triangular arrays involves two adjacent hexagons. I will explore the duet case here and rephrase the question: How can a multiple-trial, spatially-extensive, territory of a sensory schema and a movement schema association become, on some future presentation, preemptive? Acting before a substantial territory forms? It depends on how output pathway gating mechanisms interpret “good enough.”

    Ordinarily, quite a few hexagonal candidates might be reporting at once, with no one set of voices clearly standing out from the crowd in the manner that Brian Eno called “nimble playing.” With plenty of time to await a coherent choir to emerge, an economistlike weighing-all-the-factors decision can then be made. But sometimes, you operate very quickly. Consider the rates at which you can comprehend the sentences on this page; surely shortcuts are used for the familiar words, and we only have darwinian competitions when we stumble — and, perhaps, for the highest levels of sentence meaning. Even there, good-enough hegemony may be more like the way committee decisions are informally taken, moving on to some other topic without a formal vote, yet without total agreement of all parties. Only on some occasions is it likely to be like an electoral plurality following a full day of voting.

    In the presence of some “hurry up” factor, several strong voices from a small choir, early in the competition period, might suffice for action to be gated in HurryUp Mode. How might this be done using a foundation of hexagonal cloning? On the assumption that shortcuts were originally formed via a history of large synchronous choirs, we can ask how that history might modify certain cortical hexagons within a typical territory to make them more successful on their own, during “hurry up” times.

    While one characteristic of a successful territory in ordinary competitive times is the size of the recruited choir, no one hexagonal Apple, Say “apple” tile of cortex knows how big the entire territory is. But there are core areas, ones that are always activated for Apple, Say “apple”, just as there are peripheral patches that are activated on some trials and not others. The core areas are more likely to have complete sets of triangular arrays. And in these core areas, the nodes of triangular arrays might be particularly well-defined, as error correction from crystallization tendencies are presumably at their best there. So these centrally-located hexagons might function particularly well together, seldom impeding neighbors with “off-key” notes.

    A perfectly synchronous duet could be easily detected with a sufficiently well-tuned NMDAlike synaptic arrangement in a neuron having a high threshold from an automatic gain control. Although all triangular arrays are approximately synchronous and approximately triangular, the ones repeatedly at the core of a repeatedly large territory might be more sharply defined and truly synchronous — even at startup, before a larger territory forms.

    A short but detailed Say “apple” melody would probably be needed for a fast track decision. So one can imagine the musical equivalent of a characteristic introductory phrase — say, Beethoven’s dit-dit-dit-dah — packed into a short period of time. An arpeggio might be a faster Say “apple” signature, as it would correspond to a half-dozen pairs of cells all firing in succession rather than the same cells having to fire again, as in the Beethoven example. Fastest of all would be an idiosyncratic chord coming simultaneously from two adjacent hexagons. As such, it would probably be a hash, good for getting the Say “apple” movement started but not actually constituting the full movement program; however, details of a movement could follow, after the Go decision was made.

    Such a preemptive scheme has its dangers. Whenever in HurryUp Mode, the organism would be at the mercy of millimeter-sized patches of cerebral cortex, trusting them not to get their act together too quickly, not to pop into the Apple, Say “apple” spatiotemporal pattern unless an apple were truly present and the situation appropriate. If Apple were even a little ambiguous, you’d want the Apple, Say “apple” linkage to be delayed long enough by competitors for other such strange attractors to get there first.

    As such, it becomes a reaction time problem, where it is very desirable to have short latencies for sure bets and longer latencies for the others. Longer latencies, in the hexagonal theory, result from having to clone more territory before synchrony, from crystallization tendencies that sharpen things up, and from linkage requirements.

    If evolution provides you with the neural machinery for doing one such task, maybe it can be used at other times for constructing the structures needed for language and planning ahead. Ape-to-human evolution during the last six million years may well have involved natural selection “for” all these skills at various times. A common neural substrate has an interesting implication. Improving one skill via enlargement might also improve the others, for example, selection for language skills could improve throwing accuracy (and vice versa, which I consider even more likely). Some uses of this common neural machinery for fancy structured sequences, such as music and dance and games, have probably been under little environmental selection for their own usefulness.

    Hexagonal cloning competitions seem possible for many cortical areas; they all, so far, have some version of the spatially patterned intrinsic horizontal connections in the superficial layers that, together with entrainment tendencies, provide the setup for synchronized triangular arrays. Language localization in cortex is highly variable among individuals, suggesting a widespread substrate of cortical areas that are capable of housing the particular attractors that form up to implement language during the preschool years. So too, planning and the ballistic skills might have a variable localization — and be able to borrow nonspecialist areas on occasion.

[T]he more consciousness one has, the more layers of processing divide one from the world. . . . Progressive distancing from the external world is simply the price that is paid for knowing anything about the world at all. The deeper and broader [our] consciousness of the world becomes, the more complex the layers of processing necessary to obtain that consciousness.

    The useful mental shortcut is also disintermediation. Sometimes it conflates several different levels of explanation (the results of mingling the levels can be either good or bad). Even more important than shortcuts may be consolidation, creating a firm footing which allows the exploration of new complexities. This Rube Goldberg tower of the quasi-stable is what Jacob Bronowski liked to call stratified stability.

    Stage-setting and warm-up exercises are probably an important preamble to operating in the metaphorical realm. With particularly good metaphorical stand-ins for the real world, we can even simulate courses of action before coming to closure, acting for real. A decision is usually a “good enough” judgment but it varies with the setting, Bingo on some perfect-fit occasions and “Let’s get on with it” when comparisons have exhausted themselves.

    Half of education seems, at times, to consist of cultivating a habit of mind that avoids premature closure — to do some comparison shopping, at least for long enough to involve some standard schemas such as before-after. When selecting a rental car at the airport counter, we invoke larger-smaller and so bring to mind some comfort considerations — and also the memory that many garages now have undersized parking spaces, meaning that small cars will fit into all of the empty spaces while the large car will need to pass up half of the candidates.

    Then the more-less schema brings up rental costs, and better-worse reminds us of considerations such as crash worthiness and poor design. Because there are a limited number of schemas, invoking them may eventually become “hardwired” in a way that fancier comparisons cannot. Indeed, schemas might not even require hexagonal cloning competitions, because they have become so routinized that ordinary weighing criteria suffice (and so, because the clock is ticking away, we pick the intermediate-sized rental car, once again).

    It’s meeting a high quality criterion that, in the end, makes a judgment emotionally satisfying, whether it is detecting complicated patterns or creating fancy maneuvers. In some areas, quality is judged against elaborate criteria, not just routine schemas. Whatever rationality consists of, its classy reputation is surely tied up with narrative structure, with our quest for narrative unity, and how well we satisfy it.