Douglas Hofstadter - I Am a Strange Loop

Of course my impression of seeing an infinite number of doorways was illusory, since the graininess of the TV screen and the speed of light set a limit as to how many nestings could occur. Nevertheless, peering down what looked like a magically endless corridor was much more enticing and provocative than merely peering down a mundanely truncated corridor.

My next set of experiments involved tilting the camera. When I did this, each screen obediently tilted at exactly the same angle with respect to its containing screen, which instantly gave rise to a receding helical corridor — a corridor that twisted like a corkscrew. Though quite attractive to the eye, this was not terribly surprising to the mind.

An unanticipated surprise, however, was that at certain angles of camera twist, instead of peering down a helical corridor punctuated by doorways, I seemed to be looking at a flat spiral resembling a galaxy as seen through a telescope. The edges of this spiral were smooth, continuous curves of light rather than jagged sets of straight lines (coming from the edges of the TV screen), and such smoothness mystified me; I saw no reason why a sudden jump from jagged corners to graceful curves should take place. I also noticed that at the very core of each “galaxy”, there was nearly always a beautiful circular “black hole”. (On our more recent video voyage, Bill and I were unable to reproduce this “black hole” phenomenon, to our puzzlement and chagrin, so you won’t see any black holes in the photos in the insert.)

Enigmatic, Emergent Reverberation

At some point during the session, I accidentally stuck my hand momentarily in front of the camera’s lens. Of course the screen went all dark, but when I removed my hand, the previous pattern did not just pop right back onto the screen, as I expected. Instead, I saw a different pattern on the screen, but this pattern, unlike anything I’d seen before, was not stationary. Instead, it was throbbing, like a heart! Its “pulse rate” was about one cycle per second, and over the course of each short “heartbeat”, the shapes before my eyes metamorphosed greatly. Where, then, had this mysterious periodic pulsation come from, given that there was nothing in the room that was moving?

Whoops — I’m sorry! What I just wrote is a patent falsity — there was something in the room that was moving. Do you know what it was, dear reader? Well, the image itself was moving. Now that may strike you as a fatuous, trivial, or smart-alecky answer, but since the image was of itself (albeit at a slight delay), it is in fact quite to the point. A faithful image of something changing will itself necessarily keep changing! In this case, motion begat motion endlessly because I was dealing with a cyclic setup — a loop. And the original motion that had set things going — the prime mover — had been my hand’s motion, of which this video reverberation now constituted a stable, self-sustaining visible memory trace!

This situation reminds me of another loopy phenomenon that I call “reverberant barking”, which one sometimes can hear in a neighborhood where many dogs live. If a jogger passes one house and triggers one dog’s bark, then neighbor dogs may pick up the barking and a chain reaction involving a dozen dogs may ensue. Soon the barking party has taken on a life of its own, and in the meantime its unwitting instigator has long since exited the neighborhood. If dogs were a bit more like robots and didn’t eventually grow tired of doing the same thing over and over again, their reverberant barking could become a stable, self-sustaining audible memory trace of the jogger’s fleeting passage through their street.

The dynamically pulsating patterns that I encountered in my video voyage were completely unlike the unwavering “steady-state universes” that I had observed up till then. Stable, periodic video reverberation was a strange and unanticipated phenomenon that I’d bumped into by accident while exploring the possibilities lurking in video feedback.

Even today, all these years later, the origins of such pulsation remain quite unclear, even mysterious, to me; for that reason, it is an emergent phenomenon, otherwise known as an epiphenomenon, as discussed in Chapter 3. In general, an emergent phenomenon somehow emerges quite naturally and automatically from rigid rules operating at a lower, more basic level, but exactly how that emergence happens is not at all clear to the observer.

I admit to feeling a little dense for not having fully fathomed what lies behind video reverberation, but at this point I am so accustomed to it that it “makes sense” to me. That is, I have a clear intuition for how to induce it on the screen, and I know that once it starts, it is a robust phenomenon that will continue unabated probably for hours, perhaps even forever, if I don’t interfere with it. Rather than trying to figure out how to account precisely for video reverberation in terms of phenomena at lower levels, I have come to just accept it as a fact, and I deal with it at as a phenomenon that exists at its own level. This should sound familiar to you, since it’s how we deal with almost everything in our physical and biological world.

Feeding “Content” to the Loop

As I mentioned at the outset, one lucky thing about the Stanford setup was the seemingly random metallic strip on one side of the television set I’d been given to use. That strip — a kind of interloper — added a key note of “spice” to the image that was being cycled round and round, and in that sense it was a crucial ingredient of Video Voyage I.

While Bill and I were conducting Video Voyage II, there were times, to our surprise, when the seas we were sailing seemed a bit too placid for our taste, and we longed for a bit more action, more visual excitement. This brought to my mind the crucial “spicy” role played by the interloping metal strip during Voyage I, so on a lark we decided to introduce something that would play an analogous role in our system. I picked up various objects around the room and dangled them in front of the camera without any idea of what would happen when the image was cycled round and round the video loop. Usually we got marvelous results that were (once again) unanticipatable. For instance, when I dangled a chain of beads in front of the screen, what emerged (the choice of verb is not accidental) was a random-looking swirl of pockmarked bluish-white globs that reminded me a bit of some kind of exotic cheese.

Of course each such interloping object opened up a whole new universe of possibilities, since we could vary its position as well as all the other standard variables (the amount of zoom, the angle of tilt, the direction of the camera, the brightness, the contrast, and others). I tried such things as a glass vase, a compact disk, and, eventually, my own hands. The results were quite fantastic, as you can see in the color insert, but alas, Bill and I didn’t have infinite amounts of time to explore the manifold universes we had uncovered and sampled. We played with the possibilities for perhaps a dozen hours and from that we got a 400-photo memory album, and that’s all. Like any excursion to a wondrous and exotic place, our trip had to end earlier than we would have preferred, but we were very glad to have taken it and to have savored it together.

A Mathematical Analogue

As might be expected, all the unexpected phenomena that I observed depended on the nesting of screens being (theoretically) infinite — that is, on the apparent corridor being endless, not truncated. This was the case because the most unpredictable of the visual phenomena always seemed to happen right in the vicinity of that central point where the infinite regress converges down to a magical dot.