I Am a Strange Loop

wildly discrepant viewpoints. Not all thinking creatures understand the careenium nearly as clearly or as fully as I described it in Chapter 3. The God’s-eye point of view is simply not available to all observers; indeed, the very fact that such a point of view might exist is utterly unsuspected by some careenium observers. I am in particular thinking of one very special and privileged careenium observer, and that is the careenium itself.

When the careenium grapples with its own nature, particularly when it is “growing up”, just beginning to know itself, long before it has become a scientist that studies mathematics and physics (and perhaps, eventually, the noble discipline of careeniology), all it is aware of is its simmballic activity, not its simm-level churnings. After all, as you and I both know (but it does not know), the careenium’s perceptions of all things are fantastically coarse-grained simplifications (small sets of simmballs that have been collectively triggered by a vast storm of impinging signals) — and its self-perceptions are no exception.

The innocent young careenium has no inkling that behind the scenes, way down on some hidden micro-scale, churning, seething, simm-level activities are taking place inside it. Not once has it ever suspected the existence, even in principle, of any alternative viewpoint concerning its nature and its behavior. Indeed, this young careenium reminds me of myself as an adolescent, just before I read the books on the human brain by Pfeiffer and by Penfield and Roberts, books that so troubled me and yet that so fired my imagination. This idealistic young careenium is much like the naive teen-aged Doug, just at the cusp, just before he began to glimpse the extraordinary eerieness of what goes on in total darkness, day and night, inside each and every human cranium.

And so, built as irrefutably as a granite marble into the careenium’s pre-scientific understanding of itself is the sense of being a creature driven entirely by thoughts and ideas; its self-image is infinitely far from that of being a vast mechanistic entity whose destiny is entirely determined by billions of invisibly careening, mutually bashing micro-objects. Instead, the naive careenium serenely asserts of itself, “I am driven solely by myself, not by any mere physical objects anywhere.”

What kind of thing, then, is this “I” that the careenium posits as driving its choices and its actions, and that human beings likewise posit as driving theirs? No one will be surprised at this point to hear me assert that it is a peculiar type of abstract, locked-in loop located inside the careenium or the cranium — in fact, a strange loop. And thus, in order to lay out clearly my claim about what constitutes “I”- ness, I need to spell out what I mean by “strange loop”. And since we’re just finishing Chapter 7 of I Am a Strange Loop, it’s about time!

CHAPTER 8

Embarking on a Strange-Loop Safari

Flap Loop, Lap Loop

I’VE already described, in Chapter 4, how enchanted I was as a child by the brazen act of closing a cardboard box by folding down its four flaps in a cyclic order. It always gave me a frisson of delight (and even today it still does a little bit) to perform that final verboten fold, and thus to feel I was flirting dangerously with paradoxicality. Needless to say, however, actual paradox was never achieved.

A close cousin to this “flap loop” is the “lap loop”, shown on the facing page. There I am with a big grin (I’ll call myself “A”), front and center in Anterselva di Mezzo, sitting on the lap of a young woman (“B”), also grinning, with B sitting on C’s lap, C on D’s lap, and so forth, until one complete lap has been made, with person K sitting on my lap. One lap with lots of laps but no collapse. If you’ve never played this game, I suggest you try it. One feels rather baffled about what on earth is holding the loop up.

Like the flap loop, this lap loop grazes paradoxicality, since each of its eleven lap-leaps is an upwards leap, but obviously, since a lap loop can be realized in the physical world, it cannot constitute a genuine paradox. Even so, when I played the “A” role in this lap loop, I felt as if I was sitting, albeit indirectly, on my own lap! This was a most strange sensation.

Seeking Strange Loopiness in Escher

And yet when I say “strange loop”, I have something else in mind — a less concrete, more elusive notion. What I mean by “strange loop” is — here goes a first stab, anyway — not a physical circuit but an abstract loop in which, in the series of stages that constitute the cycling-around, there is a shift from one level of abstraction (or structure) to another, which feels like an upwards movement in a hierarchy, and yet somehow the successive “upward” shifts turn out to give rise to a closed cycle. That is, despite one’s sense of departing ever further from one’s origin, one winds up, to one’s shock, exactly where one had started out. In short, a strange loop is a paradoxical level-crossing feedback loop.

One of the most canonical (and, I am sorry to say, now hackneyed) examples is M. C. Escher’s lithograph Drawing Hands (above), in which (depending on where one starts) one sees a right hand drawing a picture of a left hand (nothing paradoxical yet), and yet the left hand turns out to be drawing the right hand (all at once, it’s a deep paradox).

Here, the abstract shift in levels would be the upward leap from drawn to drawer (or equally, from image to artist), the latter level being intuitively “above” the former, in more senses than one. To begin with, a drawer is always a sentient, mobile being, whereas a drawn is a frozen, immobile image (possibly of an inanimate object, possibly of an animate entity, but in any case motionless). Secondly, whereas a drawer is three-dimensional, a drawn is two-dimensional. And thirdly, a drawer chooses what to draw, whereas a drawn has no say in the matter. In at least these three senses, then, the leap from a drawn to a drawer always has an “upwards” feel to it.

As we’ve just stated, there is by definition a sharp, clear, upwards jump from any drawn image to its drawer — and yet in Drawing Hands, this rule of upwardness has been sharply and cleanly violated, for each of the hands is hierarchically “above” the other! How is that possible? Well, the answer is obvious: the whole thing is merely a drawn image, merely a fantasy. But because it looks so real, because it sucks us so effectively into its paradoxical world, it fools us, at least briefly, into believing in its reality. And moreover, we delight in being taken in by the hoax, hence the picture’s popularity.

The abstract structure in Drawing Hands would constitute a perfect example of a genuine strange loop, were it not for that one little defect — what we think we see is not genuine; it’s fake! To be sure, it’s so impeccably drawn that we seem to be perceiving a full-fledged, true-blue, card-carrying paradox — but this conviction arises in us only thanks to our having suspended our disbelief and mentally slipped into Escher’s seductive world. We fall, at least momentarily, for an illusion.

Seeking Strange Loops in Feedback

Is there, then, any genuine strange loop — a paradoxical structure that nonetheless undeniably belongs to the world we live in — or are so-called strange loops always just illusions that merely graze paradox, always just fantasies that merely flirt with paradox, always just bewitching bubbles that inevitably pop when approached too closely?