I Am a Strange Loop

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.