Douglas Hofstadter - I Am a Strange Loop

The preceding sentence is totally different from this one, in that the words “preceding” and “following” have been exchanged, as have the words “in” and “except”, and the phrases “different from” and “identical with”.

This analogy is like lifting yourself up by your own bootstraps.

Thit sentence it not self-referential because “thit” it not a word.

If wishes were horses, the antecedent clause in this conditional sentence would be true.

This sentence every third, but it still comprehensible.

If you think this sentence is confusing, then change one pig.

How come this noun phrase doesn’t denote the same thing as this noun phrase does?

I eee oai o ooa a e ooi eee o oe.

Ths sntnc cntns n vwls nd th prcdng sntnc n cnsnnts.

This pangram tallies five a’s, one b, one c, two d’s, twenty-eight e’s, eight f’s, six g’s, eight h’s, thirteen i’s, one j, one k, three l’s, two m’s, eighteen n’s, fifteen o’s, two p’s, one q, seven r’s, twenty-five s’s, twenty-two t’s, four u’s, four v’s, nine w’s, two x’s, four y’s, and one z.

Although I received from readers a good deal of positive feedback (if you’ll excuse the term), I also received some extremely negative feedback concerning what certain readers considered sheer frivolity in an otherwise respectable journal. One of the most vehement objectors was a professor of education at the University of Delaware, who quoted the famous behavioral psychologist B. F. Skinner on the topic of self-referring sentences:

Perhaps there is no harm in playing with sentences in this way or in analyzing the kinds of transformations which do or do not make sentences acceptable to the ordinary reader, but it is still a waste of time, particularly when the sentences thus generated could not have been emitted as verbal behavior. A classical example is a paradox, such as “This sentence is false”, which appears to be true if false and false if true. The important thing to consider is that no one could ever have emitted the sentence as verbal behavior. A sentence must be in existence before a speaker can say, “This sentence is false”, and the response itself will not serve, since it did not exist until it was emitted.

This kind of knee-jerk reaction against even the possibility that someone might meaningfully utter a self-referential sentence was new to me, and caught me off guard. I reflected long and hard on the education professor’s lament, and for the next issue of the magazine I wrote a lengthy reply to it, citing case after case of flagrant and often useful, even indispensable, self-reference in ordinary human communication as well as in humor, art, literature, psychotherapy, mathematics, computer science, and so forth. I have no idea how he or other objectors to self-reference took it. What remained with me, however, was the realization that some highly educated and otherwise sensible people are irrationally allergic to the idea of self-reference, or of structures or systems that fold back upon themselves.

I suspect that such people’s allergy stems, in the final analysis, from a deep-seated fear of paradox or of the universe exploding (metaphorically), something like the panic that the television sales clerk evinced when I threatened to point the video camera at the TV screen. The contrast between my lifelong savoring of such loops and the allergic recoiling from them on the part of such people as Bertrand Russell, B. F. Skinner, this education professor, and the TV salesperson taught me a lifelong lesson in the “theory of types” — namely, that there are indeed “two types” of people in this world.

CHAPTER 5

On Video Feedback

Two Video Voyages, Three Decades Apart

THE loop of video feedback is rich, as I found out in my first explorations with our family’s new video camera in the mid-1970s. A few months later, my appreciation of the phenomenon deepened considerably when I decided to explore it in detail as a visual study for my book Gödel, Escher, Bach. I made an appointment at the Stanford University television studios, and upon arriving I found that the very friendly fellow there had already set up a TV and a camera on a tripod for me to play around with. It was a piece of cake to point the camera at the screen, zoom in and out, tilt the camera, change angles, regulate brightness and contrast, and so on. He told me I was free to use the system as long as I wanted, and so I spent several hours that afternoon navigating around in the ocean of “taboo” possibilities opened up by this video loop. Like any curious tourist, I snapped dozens of photos (just black-and-white stills) during my exotic trip, and later I selected twelve of my favorites to use in one of GEB ’s dialogues.

Since that first adventure in video feedback, three decades have passed and technology has advanced a bit, so for my new book I decided to give it another shot. This time I was aided and abetted by Bill Frucht, who, because of (or in spite of) being my editor at Basic Books for a dozen years or so, has become a good friend, and who flew in from New York just for this purpose. Together in my kids’ old “playroom”, Bill and I spent many delightful hours sailing the same old seas but in a somewhat newer craft, and we wound up with several hundred color snapshots that archived our voyage superbly. Aside from the cover illustration, sixteen of my favorites, covering a wide range, can be found in the color insert.

Although both video voyages were vivid and variegated, I decided for this chapter to write up a “diary” of the earlier one, undertaken long ago at Stanford, since that’s when I first explored the phenomenon and learned about it step by step. So the story below involves a different television, a different TV camera, and in general an older technology than was used in making this book’s color insert. Nonetheless, as you will see, much of the old diary still pertains to the newer voyage, though there are a few small discrepancies that I’ll mention when I come to them.

Diary of a Video Trip

There happened to be a shiny metallic strip running down the right side of the TV set I was given, and the presence of this random object had the fortuitous effect of making the various layers of screens-within-screens easily distinguishable. The first thing I discovered, then, was that there was a critical angle that determined whether the regress of nested screens was finite or infinite. If I pointed the camera at the metal strip instead of the center of the screen, this gave me what looked like a snapshot of the right wall of a long corridor, showing a few evenly spaced “doorways” (which actually were images of that metal strip), moving away from where I was “standing”. But I was not able to peer all the way down to the end of this “corridor”. I’ll therefore call what was visible on the screen in such a case a truncated corridor.

If I slowly panned the camera leftwards, thus towards the center of the screen and perforce further down the apparent corridor, more and more doorways would come into view along the right wall, smaller and smaller and farther and farther away — and all of a sudden, at a critical moment, there was a wonderful, dizzying sense of infinity as I would find myself peering all the way down the corridor toward a gaping emptiness, stretching arbitrarily far away toward a single point of convergence (the “vanishing point”, as it is called in the theory of perspective). I’ll call this an endless corridor. (Note that essentially this same kind of corridor is also visible in the photo of the self-reflecting mirrors in Chapter 4.)