I Am a Strange Loop

CHAPTER 3

The Causal Potency of Patterns

The Prime Mover

AS THE rest of this book depends on having a clear sense for the interrelationships between different levels of description of entities that think, I would like to introduce here a few concrete metaphors that have helped me a great deal in developing my intuitions on this elusive subject.

My first example involves the familiar notion of a chain of falling dominos. However, I’ll j azz up the standard image a bit by stipulating that each domino is spring-loaded in a clever fashion (details do not concern us) so that whenever it gets knocked down by its neighbor, after a short “refractory” period it flips back up to its vertical state, all set to be knocked down once more. With such a system, we can implement a mechanical computer that works by sending signals down stretches of dominos that can bifurcate or join together; thus signals can propagate in loops, jointly trigger other signals, and so forth. Relative timing, of course, will be of the essence, but once again, details do not concern us. The basic idea is just that we can imagine a network of precisely timed domino chains that amounts to a computer program for carrying out a particular computation, such as determining if a given input is a prime number or not. (John Searle, so fond of unusual substrates for computation, should like this “domino chainium” thought experiment!)

Let us thus imagine that we can give a specific numerical “input” to the chainium by taking any positive integer we are interested in — 641, say — and placing exactly that many dominos end to end in a “reserved” stretch of the network. Now, when we tip over the chainium’s first domino, a Rube Goldberg–type series of events will take place in which domino after domino will fall, including, shortly after the outset, all 641 of the dominos constituting our input stretch, and as a consequence various loops will be triggered, with some loop presumably testing the input number for divisibility by 2, another for divisibility by 3, and so forth. If ever a divisor is found, then a signal will be sent down one particular stretch — let’s call it the “divisor stretch” — and when we see that stretch falling, we will know that the input number has some divisor and thus is not prime. By contrast, if the input has no divisor, then the divisor stretch will never be triggered and we will know the input is prime.

Suppose an observer is standing by when the domino chainium is given 641 as input. The observer, who has not been told what the chainium was made for, watches keenly for while, then points at one of the dominos in the divisor stretch and asks with curiosity, “How come that domino there is never falling?”

Let me contrast two very different types of answer that someone might give. The first type of answer — myopic to the point of silliness — would be, “Because its predecessor never falls, you dummy!” To be sure, this is correct as far as it goes, but it doesn’t go very far. It just pushes the buck to a different domino, and thus begs the question.

The second type of answer would be, “Because 641 is prime.” Now this answer, while just as correct (indeed, in some sense it is far more on the mark), has the curious property of not talking about anything physical at all. Not only has the focus moved upwards to collective properties of the chainium, but those properties somehow transcend the physical and have to do with pure abstractions, such as primality.

The second answer bypasses all the physics of gravity and domino chains and makes reference only to concepts that belong to a completely different domain of discourse. The domain of prime numbers is as remote from the physics of toppling dominos as is the physics of quarks and gluons from the Cold War’s “domino theory” of how communism would inevitably topple country after neighboring country in Southeast Asia. In both cases, the two domains of discourse are many levels apart, and one is purely local and physical, while the other is global and organizational.

Before passing on to other metaphors, I’d just like to point out that although here, 641’s primality was used as an explanation for why a certain domino did not fall, it could equally well serve as the explanation for why a different domino did fall. In particular, in the domino chainium, there could be a stretch called the “prime stretch” whose dominos all topple when the set of potential divisors has been exhausted, which means that the input has been determined to be prime.

The point of this example is that 641’s primality is the best explanation, perhaps even the only explanation, for why certain dominos did fall and certain other ones did not fall. In a word, 641 is the prime mover. So I ask: Who shoves whom around inside the domino chainium?

The Causal Potency of Collective Phenomena

My next metaphor was dreamt up on an afternoon not long ago when I was caught in a horrendous traffic jam on some freeway out in the countryside, with several lanes of nearly touching cars all sitting stock still. For some reason I was reminded of big-city traffic jams where you often hear people honking angrily at each other, and I imagined myself suddenly starting to honk my horn over and over again at the car in front of me, as if to say, “Get out of my way, lunkhead!”

The thought of myself (or anyone) taking such an outrageously childish action made me smile, but when I considered it a bit longer, I saw that there might be a slim rationale for honking that way. After all, if the next car were magically to poof right out of existence, I could fill the gap and thus make one car-length’s worth of progress. Now a car poofing out of existence is not too terribly likely, and one car-length is not much progress, but somehow, through this image, the idea of honking became just barely comprehensible to me. And then I remembered my domino chainium and the silly superlocal answer, “That domino didn’t fall because its neighbor didn’t fall, you dummy!” This myopic answer and my fleeting thought of honking at the car just ahead of me seemed to be cut from the same cloth.

As I continued to sit in this traffic jam, twiddling my thumbs instead of honking, I let these thoughts continue, in their bully-like fashion, to push my helpless neurons around. I imagined a counterfactual situation in which the highway was shrouded in the densest pea-soup fog imaginable, so that I could barely make out the rear of the car ahead of me. In such a case, honking my horn wouldn’t be quite so blockheaded. For all I know, that car alone might well be the entire cause of my being stuck, and if only it would just get out of the way, I could go sailing down the highway!

If you’re totally fog-bound like that, or if you’re incredibly myopic, then you might think to yourself, “It’s all my neighbor’s fault!”, and there’s at least a small chance that you’re right. But if you have a larger field of view and can see hordes of immobilized cars on all sides, then honking at your immediate predecessor is an absurdity, for it’s obvious that the problem is not local. The root problem lies at some level of discourse other than that of cars. Though you may not know its nature, some higher-level, more abstract reason must lie behind this traffic jam.

Perhaps a very critical baseball game just finished three miles up the road. Perhaps it’s 7:30 on a weekday morning and you’re heading towards Silicon Valley. Perhaps there’s a huge blizzard ten miles ahead. Or it may be something else, but it’s surely some social or natural event of the type that induces large numbers of people all to do the same thing as one another. No amount of expertise in car mechanics will help you to grasp the essence of such a situation; what is needed is knowledge of the abstract forces that can act on freeways and traffic. Cars are just pawns in the bigger game and, aside from the fact that they can’t pass through each other and emerge intact post-crossing (as do ripples and other waves), their physical nature plays no significant role in traffic jams. We are in a situation analogous to that in which the global, abstract, math-level answer “641 is prime” is far superior to a local, physical, domino-level answer.

Neurons and Dominos

The foregoing down-to-earth images provide us with helpful metaphors for talking about the many levels of causality inside a human brain. Suppose it were possible to monitor any selected neuron in my brain. In that case, someone might ask, as I listened to some piece of music, “How come neuron #45826493842 never seems to fire?” A local, myopic answer might be, “Because the neurons that feed into it never fire jointly”, and this answer would be just as correct but also just as useless and uninformative as the myopic answers in the other situations. On the other hand, the global, organizational answer “Because Doug Hofstadter doesn’t care for the style of Fats Domino” would be much more on target.

Of course we should not fall into the trap of thinking that neuron #45826493842 is the sole neuron designated to fire whenever I resonate to some piece of music I’m listening to. It’s just one of many neurons that participate in the high-level process, like voters in a national election. Just as no special voter makes the decision, so no special neuron is privileged. As long as we avoid simplistic notions such as a privileged “grand-music neuron”, we can use the domino-chainium metaphor to think about brains, and especially to remind ourselves of how, for a given phenomenon in a brain, there can be vastly different explanations belonging to vastly different domains of discourse at vastly different levels of abstraction.

Patterns as Causes

I hope that in light of these images, Roger Sperry’s comments about “the population of causal forces” and “overall organizational forces and dynamic properties” in a complex system like the brain or the chainium have become clearer. For instance, let us try to answer the question, “Can the primality of 641 really play a causal role in a physical system?” Although 641’s primality is obviously not a physical force, the answer nonetheless has to be, “Yes, it does play a causal role, because the most efficient and most insight-affording explanation of the chainium’s behavior depends crucially on that notion.” Deep understanding of causality sometimes requires the understanding of very large patterns and their abstract relationships and interactions, not just the understanding of microscopic objects interacting in microscopic time intervals.

I have to emphasize that there’s no “extra” physical (or extra-physical) force here; the local, myopic laws of physics take care of everything on their own, but the global arrangement of the dominos is what determines what happens, and if you notice (and understand) that arrangement, then an insight-giving shortcut to the answer of the non-falling domino in the divisor stretch (as well as the falling domino in the prime stretch) is served to you on a silver platter. On the other hand, if you don’t pay attention to that arrangement, then you are doomed to taking the long way around, to understanding things only locally and without insight. In short, considering 641’s primality as a physical cause in our domino chainium is analogous to considering a gas’s temperature as a physical cause (e.g., of the amount of pressure it exerts against the walls of its container).

Indeed, let us think for a moment about such a gas — a gas in a cylinder with a movable piston. If the gas suddenly heats up (as occurs in any cylinder in your car engine when its spark plug fires), then its pressure suddenly increases and therefore (note the causal word) the piston is suddenly shoved outwards. Thus combustion engines can be built.

What I just told is the story at a gross (thermodynamic) level. Nobody who designs combustion engines worries about the fine-grained level — that of molecules. No engineer tries to figure out the exact trajectories of 1023 molecules banging into each other! The locations and velocities of individual molecules are simply irrelevant. All that matters is that they can be counted on to collectively push the piston out. Indeed, it doesn’t matter whether they are molecules of type X or type Y or type Z — pressure is pressure, and that’s all that matters. The explosion — a high-level event — will do its job in heating the gas, and the gas will do its job in pushing the piston. This high-level description of what happens is the only level of description that is relevant, because all the microdetails could be changed and exactly the same thing (at least from the human engineer’s point of view) would still happen.

The Strange Irrelevance of Lower Levels

This idea — that the bottom level, though 100 percent responsible for what is happening, is nonetheless irrelevant to what happens — sounds almost paradoxical, and yet it is an everyday truism. Since I want this to be crystal-clear, let me illustrate it with one more example.

Consider the day when, at age eight, I first heard the fourth étude of Chopin’s Opus 25 on my parents’ record player, and instantly fell in love with it. Now suppose that my mother had placed the needle in the groove a millisecond later. One thing for sure is that all the molecules in the room would have moved completely differently. If you had been one of those molecules, you would have had a wildly different life story. Thanks to that millisecond delay, you would have careened and bashed into completely different molecules in utterly different places, spun off in totally different directions, and on and on, ad infinitum. No matter which molecule you were in the room, your life story would have turned out unimaginably different. But would any of that have made an iota of difference to the life story of the kid listening to the music? No — not the teensiest, tiniest iota of difference. All that would have mattered was that Opus 25, number 4 got transmitted faithfully through the air, and that would most surely have happened. My life story would not have been changed in any way, shape, or form if my mother had put the needle down in the groove a millisecond earlier or later. Or a second earlier or later.

Although the air molecules were crucial mediating agents for a series of high-level events involving a certain kid and a certain piece of music, their precise behavior was not crucial. Indeed, saying it was “not crucial” is a ridiculous understatement. Those air molecules could have done exactly the same kid–music job in an astronomical number of different but humanly indistinguishable fashions. The lower-level laws of their collisions played a role only in that they gave rise to predictable high-level events (propagation of the notes in the Chopin étude to little Douggie’s ear). But the positions, speeds, directions, even the chemical identity of the molecules — all of this was changeable, and the high-level events would have been the same. It would have been the same music to my ears. One can even imagine that the microscopic laws of physics could have been different — what matters is not the detailed laws but merely the fact that they reliably give rise to stable statistical consequences.

Flip a quarter a million times and you’ll very reliably get within one percent of 500,000 heads. Flip a penny the same number of times, and the same statement holds. Use a different coin on every flip — dimes, quarters, new pennies, old pennies, buffalo nickels, silver dollars, you name it — and still you’ll get the same result. Shave your penny so that its outline is hexagonal instead of circular — no difference. Replace the hexagonal outline by an elephant shape. Dip the penny in apple butter before each flip. Bat the penny high into the air with a baseball bat instead of tossing it up. Flip the penny in helium gas instead of air. Do the experiment on Mars instead of Earth. These and countless other variations on the theme will not have any effect on the fact that out of a million tosses, within one percent of 500,000 will wind up heads. That high-level statistical outcome is robust and invariant against the details of the substrate and the microscopic laws governing the flips and bounces; the high-level outcome is insulated and sealed off from the microscopic level. It is a fact in its own right, at its own level.

That is what it means to say that although what happens on the lower level is responsible for what happens on the higher level, it is nonetheless irrelevant to the higher level. The higher level can blithely ignore the processes on the lower level. As I put it in Chapter 2, “Our existence as animals whose perception is limited to the world of everyday macroscopic objects forces us, quite obviously, to function without any reference to entities and processes at microscopic levels. No one really knew the slightest thing about atoms until only about a hundred years ago, and yet people got along perfectly well.”

A Hat-tip to the Spectrum of Unpredictability

I am not suggesting that the invisible, swarming, chaotic, microscopic level of the world can be totally swept under the rug and forgotten. Although in many circumstances we rely on the familiar macroworld to be completely predictable to us, there are many other circumstances where we are very aware of not being able to predict what will happen. Let me first, however, make a little list of some sample predictables that we rely on unthinkingly all the time.

When we turn our car’s steering wheel, we know for sure where our car will go; we don’t worry that a band of recalcitrant little molecules might mutiny and sabotage our turn. When we turn a burner to “high” under a saucepan filled with water, we know that the water will boil within a few minutes. We can’t predict the pattern of bubbles inside the boiling water, but we really don’t give a hoot about that. When we take a soup can down from the shelf in the grocery store and place it in our cart, we know for sure that it will not turn into a bag of potato chips, will not burn our hand, will not be so heavy that we cannot lift it, will not slip through the grill of the cart, will sit still if placed vertically, and so forth. To be sure, if we lay the soup can down horizontally and start wheeling the cart around the store, the can will roll about in the cart in ways that are not predictable to us, though they lie completely within the bounds of our expectations and have little interest or import to us, aside from being mildly annoying.

When we speak words, we know that they will reach the ears of our listeners without being changed by the intermediary pressure waves into other words, will even come through with the exact intonations that we impart to them. When we pour milk into a glass, we know just how far to tilt the milk container to get the desired amount of flow without spilling a drop. We control the milk and we get exactly the result we want.

There is no surprise in any of this! And I could extend this list forever, and it would soon grow very boring, because you know it all instinctively and take it totally for granted. Every day of our lives, we all depend in a million tacit ways on innumerable rock-solid predictabilities about how things happen in the visible, tangible world (the solidity of rocks being yet another of those countless rock-solid predictabilities).

On the other hand, there’s also plenty of unpredictability “up here” in the macroworld. How about a second list, giving typical unpredictables?

When we toss a basketball towards a basket, we don’t have any idea whether it will go through or not. It might bounce off the backboard and then teeter for a couple of seconds on the rim, keeping us in suspense and perhaps even holding an entire crowd in tremendous, tingling tension. A championship basketball game could go one way or the other, depending on a microscopic difference in the position of the pinky of the player who makes a desperate last-second shot.

When we begin to utter a thought, we have no idea what words we will wind up using nor which grammatical pathways we will wind up following, nor can we predict the speech errors or the facts about our unconscious mind that our little slips will reveal. Usually such revelations will make little difference, but once in a while — in a job interview, say — they can have huge repercussions. Think of how people jump on a politician whose unconscious mind chooses a word loaded with political undertones (e.g., “the crusade against terrorism”).

When we ski down a slope, we don’t know if we’re going to fall on our next turn or not. Every turn is a risk — slight for some, large for others. A broken bone can come from an event whose cause we will never fathom, because it is so deeply hidden in detailed interactions between the snow and our ski. And the tiniest detail about the manner in which we fall can make all the difference as to whether we suffer a life-changing multiple break or a just a trivial hairline fracture.

The macroscopic world as experienced by humans is, in short, an intimate mixture ranging from the most predictable events all the way to wildly unpredictable ones. Our first few years of life familiarize us with this spectrum, and the degree of predictability of most types of actions that we undertake becomes second nature to us. By the time we emerge from childhood, we have acquired a reflex-level intuition for where most of our everyday world’s loci of unpredictability lie, and the more unpredictable end of this spectrum simultaneously beckons to us and frightens us. We’re pulled by but fearful of risk-taking. That is the nature of life.

The Careenium

I now move to a somewhat more complex metaphor for thinking about the multiple levels of causality in our brains and minds (and eventually, if you will indulge me in this terminology, in our souls). Imagine an elaborate frictionless pool table with not just sixteen balls on it, but myriads of extremely tiny marbles, called “sims” (an acronym for “small interacting marbles”). These sims bash into each other and also bounce off the walls, careening about rather wildly in their perfectly flat world — and since it is frictionless, they just keep on careening and careening, never stopping.

So far our setup sounds like a two-dimensional ideal gas, but now we’ll posit a little extra complexity. The sims are also magnetic (so let’s switch to “simms”, with the extra “m” for “magnetic”), and when they hit each other at lowish velocities, they can stick together to form clusters, which I hope you will pardon me for calling “simmballs”. A simmball consists of a very large number of simms (a thousand, a million, I don’t care), and on its periphery it frequently loses a few simms while gaining others. There are thus two extremely different types of denizen of this system: tiny, light, zipping simms, and giant, ponderous, nearly-immobile simmballs.

The dynamics taking place on this pool table — hereinafter called the “careenium” — thus involves simms crashing into each other and also into simmballs. To be sure, the details of the physics involve transfers of momentum, angular momentum, kinetic energy, and rotational energy, just as in a standard gas, but we won’t even think about that, because this is just a thought experiment (in two senses of the term). All that matters for our purposes is that there are these collisions taking place all the time.

Simmballism

Why the corny pun on “symbol”? Because I now add a little more complexity to our system. The vertical walls that constitute the system’s boundaries react sensitively to outside events (e.g., someone touching the outside of the table, or even a breeze) by momentarily flexing inward a bit. This flexing, whose nature retains some traces of the external causing event, of course affects the motions of the simms that bounce internally off that section of wall, and indirectly this will be registered in the slow motions of the nearest simmballs as well, thus allowing the simmballs to internalize the event. We can posit that one particular simmball always reacts in some standard fashion to breezes, another to sharp blows, and so forth. Without going into details, we can even posit that the configurations of simmballs reflect the history of the impinging outer-world events. In short, for someone who looked at the simmballs and knew how to read their configuration, the simmballs would be symbolic, in the sense of encoding events. That’s why the corny pun.

Of course this image is far-fetched, but remember that the careenium is merely intended as a useful metaphor for understanding our brains, and the fact is that our brains, too, are rather far-fetched, in the sense that they too contain tiny events (neuron firings) and larger events (patterns of neuron firings), and the latter presumably somehow have representational qualities, allowing us to register and also to remember things that happen outside of our crania. Such internalization of the outer world in symbolic patterns in a brain is a pretty far-fetched idea, when you think about it, and yet we know it somehow came to exist, thanks to the pressures of evolution. If you wish, then, feel free to imagine that careenia, too, evolved. You can think of them as emerging as the end result of billions of more primitive systems fighting for survival in the world. But the evolutionary origins of our careenium need not concern us here. The key idea is that whereas no simm on its own encodes anything or plays a symbolic role, the simmballs, on their far more macroscopic level, do encode and are symbolic.

Taking the Reductionistic View of the Careenium

The first inclination of a modern physicist who heard this story might be reductionistic, in the sense of pooh-poohing the large simmballs as mere epiphenomena, meaning that although they are undeniably there, they are not essential to an understanding of the system, since they are composed of simms. Everything that happens in the careenium is explainable in terms of simms alone. And there’s no doubt that this is true. A volcano, too, is undeniably there, but who needs to talk about mountains and subterranean pressures and eruptions and lava and such things? We can dispense with such epiphenomenal concepts altogether by shifting to the deeper level of atoms or elementary particles. The bottom line, at least for our physicist, is that epiphenomena are just convenient shorthands that summarize a large number of deeper, lower-level phenomena; they are never essential to any explanation. Reductionism ho!

The only problem is the enormous escalation in complexity when we drop all macroscopic terms and ways of looking at things. If we refuse to use any language that involves epiphenomena, then we are condemned to seeing only untold myriads of particles, and that is certainly not a very welcoming thought. Moreover, when one perceives only myriads of particles, there are no natural sharp borders in the world. One cannot draw a line around the volcano and declare, “Only particles in this zone are involved”, because particles won’t respect any such macroscopic line — no more than ants respect the property lines carefully surveyed and precisely drawn by human beings. No fixed portion of the universe can be tightly fenced off from interacting with the rest — not even approximately. To a reductionist, the idea of carving the universe up into zones with inviolable macroscopic spatiotemporal boundary lines makes no sense.

Here is a striking example of the senselessness of local spatiotemporal boundaries. In November of 1993, I read several newspaper articles about a comet that was “slowly” making its way towards Jupiter. It was still some eight months from t-zero but astrophysicists had already predicted to the minute, if not to the second, when it would strike Jupiter, and where. This fact about some invisible comet that was billions of miles away from earth had already had enormous impacts on the surface of our planet, where teams of scientists were already calculating its Jovian arrival time, where newspapers and magazines were already printing front-page stories about it, and where millions of people like me were already reading about it. Some of these people were possibly missing planes because of being engrossed in the story, or possibly striking up a new friendship with someone because of a common interest in it, or possibly arriving at a traffic light one second later than otherwise because of having reread one phrase in the article, and so on. As t-zero approached and finally the comet hit Jupiter’s far side exactly as predicted, denizens of the Earth paid enormous attention to this remote cosmic event. There is no doubt that many months before the comet hit Jupiter, certain fender-benders took place on our planet that wouldn’t have taken place if the comet hadn’t been coming, certain babies were conceived that wouldn’t have been conceived otherwise, certain flies were swatted, certain coffee cups were chipped, and so on. All of this crazy stuff happening on our tiny planet was due to a comet coasting through silent space billions of miles away and nearly half a million minutes in advance of its encounter with the huge planet.

The point is that one gets into very hot water if one goes the fully reductionistic route; not only do all the objects in “the system” become microscopic and uncountably numerous, but also the system itself grows beyond bounds in space and time and becomes, in the end, the entire universe taken over all of time. There is no comprehensibility left, since everything is shattered into a trillion trillion trillion invisible pieces that are scattered hither and yon. Reductionism is merciless.

Taking a Higher-level View of the Careenium

If, on the other hand, there is a perceptible and comprehensible “logic” to events at the level of epiphenomena, then we humans are eager to jump to that level. In fact, we have no choice. And so we do talk of volcanoes and eruptions and lava and so forth. Likewise, we talk of bitten fingernails and rye bread and wry smiles and Jewish senses of humor rather than of cells and proteins, let alone of atoms and photons. After all, we ourselves are pretty big epiphenomena, and as I’ve already observed many times in this book, this fact dooms us to talking about the world in terms of other epiphenomena at about our size level (e.g., our mothers and fathers, our cats and cars and cakes, our sailboats and saxophones and sassafras trees).

Now let’s return to the careenium and talk about what happens in it. The way I’ve portrayed it so far focuses on the simms and their dashing and bashing. The simmballs are also present, but they serve a similar function to the walls — they are just big stationary objects off of which the simms bounce. In my mind’s eye, I often see the simms as acting like the silver marbles in a pinball machine, with the simmballs acting like the “pins” — that is, the larger stationary cylindrical objects which the marbles strike and ricochet off of as they roll down the sloped board of play.

But now I’m going to describe a different way of looking at the careenium, which is characterized by two perceptual shifts. First, we shift to time-lapse photography, meaning that imperceptibly slow motions get speeded up so as to become perceptible, while fast motions become so fast that they are not even seen as blurs — they become imperceptible, like the spinning blades of an electric fan. The second shift is that we spatially back away or zoom out, thus rendering simms too small to be seen, and so the simmballs alone necessarily become our focus of attention.

Now we see a completely different type of dynamics on the table. Instead of seeing simms bashing into what look like large stationary blobs, we realize that these blobs are not stationary at all but have a lively life of their own, moving back and forth across the table and interacting with each other, as if there were nothing else on the table but them. Of course we know that deep down, this is all happening thanks to the teeny-weeny simms’ bashing-about, but we cannot see the simms any more. In our new way of seeing things, their frenetic careening-about on the table forms nothing but a stationary gray background.

Think of how the water in a glass sitting on a table seems completely still to us. If our eyes could shift levels (think of the twist that zooms binoculars in or out) and allow us to peer at the water at the micro-level, we would realize that it is not peaceful at all, but a crazy tumult of bashings of water molecules. In fact, if colloidal particles are added to a glass of water, then it becomes a locus of Brownian motion, which is an incessant random jiggling of the colloidal particles, due to a myriad of imperceptible collisions with the water molecules, which are far tinier. (The colloidal particles here play the role of simmballs, and the water molecules play the role of simms.) The effect, which is visible under a microscope, was explained in great detail in 1905 by Albert Einstein using the theory of molecules, which at the time were only hypothetical entities, but Einstein’s explanation was so far-reaching (and, most crucially, consistent with experimental data) that it became one of the most important confirmations that molecules do exist.

Who Shoves Whom Around inside the Careenium?

And so we finally have come to the crux of the matter: Which of these two views of the careenium is the truth? Or, to echo the key question posed by Roger Sperry, Who shoves whom around in the population of causal forces that occupy the careenium? In one view, the meaningless tiny simms are the primary entities, zipping around like mad, and in so doing they very slowly push the heavy, passive simmballs about, hither and thither. In this view, it is the tiny simms that shove the big simmballs around, and that is all there is to it. In fact, in this view the simmballs are not even recognized as separate entities, since anything we might say about their actions is just a shorthand way of talking about what simms do. From this perspective, there are no simmballs, no symbols, no ideas, no thoughts going on — just a great deal of tumultuous, pointless careening-about of tiny, shiny, magnetic spheres.

In the other view, speeded up and zoomed out, all that is left of the shiny tiny simms is a featureless gray soup, and the interest resides solely in the simmballs, which give every appearance of richly interacting with each other. One sees groups of simmballs triggering other simmballs in a kind of “logic” that has nothing to do with the soup churning around them, except in the rather pedestrian sense that the simmballs derive their energy from that omnipresent soup. Indeed, the simmballs’ logic, not surprisingly, has to do with the concepts that the simmballs symbolize.

The Dance of the Simmballs

From our higher-level macroscopic vantage point as we hover above the table, we can see ideas giving rise to other ideas, we can see one symbolic event reminding the system of another symbolic event, we can see elaborate patterns of simmballs coming together and forming even larger patterns that constitute analogies — in short, we can visually eavesdrop on the logic of a thinking mind taking place in the patterned dance of the simmballs. And in this latter view, it is the simmballs that shove each other about, at their own isolated symbolic level.

The simms are still there, to be sure, but they are simply serving the simmballs’ dance, allowing it to happen, with the microdetails of their bashings being no more relevant to the ongoing process of cognition than the microdetails of the bashings of air molecules are relevant to the turning of the blades of a windmill. Any old air-molecule bashings will do — the windmill will turn no matter what, thanks to the aerodynamic nature of its blades. Likewise, any old simm-bashings will do — the “thoughtmill” will churn no matter what, thanks to the symbolic nature of its simmballs.

If any of this strikes you as too far-fetched to be plausible, just return to the human brain and consider what must be going on inside it in order to allow our thinking’s logic to take place. What else is going on inside every human cranium but some story like this?

Of course we have come back to the question that that long-agoshelved book’s title made me ask, and the question that Roger Sperry also asked: Who is shoving whom about in here? And the answer is that it all depends on what level you choose to focus on. Just as, on one level, the primality of 641 could legitimately be said to be shoving about dominos in the domino-chain network, so here there is a level on which the meanings attached to various simmballs can legitimately be said to be shoving other simmballs about. If this all seems topsy-turvy, it certainly is — but it is nonetheless completely consistent with the fundamental causality of the laws of physics.