I Am a Strange Loop (12 page)

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.