I Am a Strange Loop

What about a soccer ball zipping down a long, narrow roadside gutter having a U-shaped cross-section — is it seeking any goal? Such a ball, as it speeds along, will first roll up one side of the gutter and then fall back to the center, cross it and then roll up the other side, then again back down, and so forth, gradually converging from a sinusoidal pathway wavering about the gutter’s central groove to a straight pathway at the bottom of the gutter. Is there “feedback” here or not? Is this soccer ball “seeking” the gutter’s mid-line? Does it “want” to be rolling along the gutter’s valley? Well, as this example and the previous one of the ball rolling down a hill show, the presence or absence of feedback, goals, or desires is not a black-and-white matter; such things are judgment calls.

The Slippery Slope of Teleology

As we move to systems where the feedback is more sophisticated and its mechanisms are more hidden, our tendency to shift to teleological terms — first the language of goals and then the language of “wishing”, “desiring”, “trying” — becomes ever more seductive, ever harder to resist. The feedback doesn’t even need to be very sophisticated, as long as it is hidden.

In San Francisco’s Exploratorium museum, there is an enclosure where people can stand and watch a spot of red light dancing about on the walls and floor. If anyone tries to touch the little spot, it darts away at the last moment. In fact, it dances about in a way that seems to be teasing the people chasing it — sometimes stopping completely, taunting them, daring them to approach, and then flitting away just barely in time. However, despite appearances, there is no hidden person guiding it — just some simple feedback mechanisms in some circuitry monitoring the objects in the enclosure and controlling the light beam. But the red spot seems for all the world to have a personality, an impish desire to tease people, even a sense of humor! The Exploratorium’s red dot seems more alive than, say, a mosquito or a fly, both of which attempt to avoid being swatted but certainly don’t have any detectable sense of humor.

In the video called “Virtual Creatures” by Karl Sims, there are virtual objects made out of a few (virtual) tubes hinged together, and these objects can “flap” their limbs and thus locomote across a (virtual) flat plane. When they are given a rudimentary sort of perception and a simple feedback loop is set up that causes them to pursue certain kinds of resources, then the driven manner in which they pursue what looks like food and frantically struggle with “rivals” to reach this resource gives viewers an eerie sensation of witnessing primitive living creatures engaged in life-and-death battles.

On a more familiar level, there are plants — consider a sunflower or a growing vine — which, when observed at normal speed, seem as immobile as rocks and thus patently devoid of goals, but when observed in time-lapse photography, seem all of a sudden to be highly aware of their surroundings and to possess clear goals as well as strategies to reach them. The question is whether such systems, despite their lack of brains, are nonetheless imbued with goals and desires. Do they have hopes and aspirations? Do they have dreads and dreams? Beliefs and griefs?

The presence of a feedback loop, even a rather simple one, constitutes for us humans a strong pressure to shift levels of description from the goalless level of mechanics (in which forces make things move) to the goal-oriented level of cybernetics (in which, to put it very bluntly, desires make things move). The latter is, as I have stressed, nothing but a more efficient rewording of the former; nonetheless, with systems that possess increasingly subtle and sophisticated types of feedback loops, that shorthand’s efficiency becomes well-nigh irresistible. And eventually, not only does teleological language become indispensable, but we cease to realize that there could be any other perspective. At that point, it is locked into our worldview.

Feedback Loops and Exponential Growth

The type of feedback with which we are all most familiar, and probably the case that gave it its name, is audio feedback, which typically takes place in an auditorium when a microphone gets too close to a loudspeaker that is emitting, with amplification, the sounds picked up by the microphone. In goes some sound (any sound — it makes no difference), out it comes louder, then that sound goes back in, comes out yet louder, then back in again, and all of a sudden, almost out of nowhere, you have a loop, a vicious circle, producing a terrible high-pitched screech that makes the audience clap their hands over their ears.

This phenomenon is so familiar that it seems to need no comment, but in fact there are a couple of things worth pointing out. One is that each cycling-around of any input sound would theoretically amplify its volume by a fixed factor, say k — thus, two loops would amplify by a factor of k², three loops by k³, and so on. Well, we all know the power of exponential growth from hearing horror stories about exponential growth of the earth’s population or some such disaster. (In my childhood, the power of exponentials was more innocently but no less indelibly imprinted on me by the story of a sultan who commanded that on each square of a chessboard there be placed twice as many grains of rice as on the previous square — and after less than half the board was full, it was clear there was not nearly enough rice in the sultanate or even the whole world to get anywhere close to the end.) In theory, then, the softest whisper would soon grow to a roar, which would continue growing without limit, first rendering everyone in the auditorium deaf, shortly thereafter violently shaking the building’s rafters till it collapsed upon the now-deaf audience, and then, only a few loops later, vibrating the planet apart and finishing up by annihilating the entire universe. What is specious about this apocalyptic scenario?

Fallacy the First

The primary fallacy in this scenario is that we have not taken into account the actual device carrying out the exponential process — the sound system itself, and in particular the amplifier. To make my point in the most blatant manner, I need merely remind you that the moment the auditorium’s roof collapsed, it would land on the amplifier and smash it to bits, thus bringing the out-of-control feedback loop to a swift halt. The little system contains the seeds of its own destruction!

But there is something specious about this scenario, too, because as we all know, things never get that far. The auditorium never collapses, nor are the audience members deafened by the din. Something slows down the runaway process far earlier. What is that thing?

Fallacy the Second

The other fallacy in our reasoning also involves a type of self-destruction of the sound system, but it is subtler than being smashed to smithereens. It is that as the sound gets louder and louder, the amplifier stops amplifying with that constant factor of k. At a certain level it starts to fail. Just as a floored car will not continue accelerating at a constant rate (reaching 100 miles per hour, then 200, 300, 400, soon breaking the sound barrier, etc.) but eventually levels out at some peak velocity (which is a function of road friction, air resistance, the motor’s internal limits, and so forth), so an amplifier will not uniformly amplify sounds of any volume but will eventually saturate, giving less and less amplification until at some volume level the output sound has the same volume as the input sound, and that is where things stabilize. The volume at which the amplification factor becomes equal to 1 is that of the familiar screech that drives you mad but doesn’t deafen you, much less brings the auditorium crashing down on your head.

And why does it always give off that same high-pitched screeching sound? Why not a low roar? Why not the sound of a waterfall or a jet engine or long low thunder? This has to do with the natural resonance frequency of the system — an acoustic analogue of the natural oscillation frequency of a playground swing, roughly once every couple of seconds. An amplifier’s feedback loop has a natural oscillation frequency, too, and for reasons that need not concern us, it usually has a pitch close to that of a high-frequency scream. However, the system does not instantly settle down precisely on its final pitch. If you could drastically slow down the process, you would hear it homing in on that squealing pitch much as the rolling soccer ball seeks the bottom of the gutter — namely, by means of a very rapid series of back-and-forth swings in frequency, almost as if it “wanted” to reach that natural spot in the sonic spectrum.

What we have seen here is that even the simplest imaginable feedback loop has levels of subtlety and