Douglas Hofstadter - I Am a Strange Loop

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.