I Am a Strange Loop

by Douglas R. Hofstadter

  And yet, it’s undeniable that the phrase “it felt just like a marble” gets across my experience far more clearly to my readers than if I had written, “I experienced the collective effect of the precise alignment of a hundred triple layers of paper and a hundred layers of glue.” It is only because I called it a “marble” that you have a clear impression of how it felt to me. If I hadn’t used the word “marble”, would you have been able to predict that a thick pack of envelopes would give rise, in its middle, to something (some thing?) that felt perfectly spherical, felt like it had a size, felt extremely solid — in short, that this collective effect would feel like a very simple, very familiar physical object? I strongly doubt it. And thus there is something to be gained by not rejecting the term “marble”, even if there is no real marble in the box. There is something that feels remarkably like a marble, and that fact is crucial to my portraying and to your grasping of the situation, just as the concepts of “corridor”, “galaxy”, and “black hole” were crucial in allowing me to perceive and describe the phenomena on the screen of the self-watching television — even if, strictly speaking, no corridor, no galaxy, and no black hole were there to be seen.

  Where the Buck Seems to Stop

  I have recounted the story of the half-real, half-unreal marble inside the box of envelopes to suggest a metaphor for the type of reality that applies to our undeniable feeling that something “solid” or “real” resides at the core of ourselves, a powerful feeling that makes the pronoun “I” indispensable and central to our existence. The thesis of this book is that in a nonembryonic, non-infantile human brain, there is a special type of abstract structure or pattern that plays the same role as does that precise alignment of layers of paper and glue — an abstract pattern that gives rise to what feels like a self. I intend to talk a great deal about the nature of that abstract pattern, but before I do so, I have to say what I mean by the term “a self ”, or perhaps more specifically, why we seem to need a notion of that sort.

  Each living being, no matter how simple, has a set of innate goals embedded in it, thanks to the feedback loops that evolved over time and that characterize its species. These feedback loops are the familiar, almost clichéd activities of life, such as seeking certain types of food, seeking a certain temperature range, seeking a mate, and so forth. Some creatures additionally develop their own individual goals, such as playing certain pieces of music or visiting certain museums or owning certain types of cars. Whatever a creature’s goals are, we are used to saying that it pursues those goals, and — at least if it is sufficiently complicated or sophisticated — we often add that it does so because it wants certain things.

  “Why did you ride your bike to that building?” “I wanted to practice the piano.” “And why did you want to practice the piano?” “Because I want to learn that piece by Bach.” “And why do you want to learn that piece?” “I don’t know, I just do — it’s beautiful.” “But what is it about this particular piece that is so beautiful?” “I can’t say, exactly — it just hits me in some special way.”

  This creature ascribes its behavior to things it refers to as its desires or its wants, but it can’t say exactly why it has those desires. At a certain point there is no further possibility of analysis or articulation; those desires simply are there, and to the creature, they seem to be the root causes for its decisions, actions, motions. And always, inside the sentences that express why it does what it does, there is the pronoun “I” (or its cousins “me”, “my”, etc.). It seems that the buck stops there — with the so-called “I”.

  The Prime Mover, Redux

  Late one autumn afternoon, the red, orange, and yellow leaves are so alluring, and the fall weather so mild, compared to the just-finished muggy summer, that I decide to take a good long run. I go into my bedroom, search around for my running shorts and shoes and T-shirt, change my clothes in eagerness, and soon enough, my body finds itself out on the pavement, with my feet pounding the ground and my heart beginning to thump away. Before I know it, I’ve taken a hundred steps, and moments later it’s been three hundred. Then it’s been a thousand, then three thousand, and I’m still charging on, breathing hard, sweating, and thinking to myself, “Why do I always tell myself that I like running? I hate it!” And yet my body doesn’t stop for a split second, and no matter how tired my muscles are, my self just says to them, like a sadistic drill sergeant sneering at a bunch of new recruits, “Don’t be quitters!” — and lo and behold, my poor, huffing, heaving, protesting body unquestioningly obeys my self, even charging up steep hills against its will. In shorts, my rebelling physical body is being quite mercilessly pushed around by my intangible I’s equally intangible determination to take this autumn run.

  So who is pushing whom around here? Where are the particles of physics in this picture of what makes us do things? They are invisible, and even if you remember that they exist, they seem to be just secondary players. It is this “I”, a coherent collection of desires and beliefs, that sets everything in motion. It is this “I” that is the prime mover, the mysterious entity that lies behind, and that launches, all the creature’s behaviors. If I want something to happen, I just will it to happen, and unless it is out of my control, it generally does happen. The body’s molecules, whether in the fingers, the arm, the legs, the throat, the tongue, or wherever, obediently follow the supreme bidding of the Grand “I” on high.

  Thus it is that I push various pedals down and sure enough, my one-ton automobile obediently goes right where I want it to go. The ethereal “I” has pushed this huge physical object around. I twiddle my chopsticks and sure enough, the string beans obediently jump on board and I receive the sensory joy that I covet and the nourishment I need. I push certain keys on my Macintosh’s keyboard and sure enough, sentences obediently emerge on its screen, and they pretty much express the thoughts that the ethereal “I” hoped to express. And in all of this, where are the particles? Nowhere to be seen. All there seems to be is this “I” making it all happen.

  Well then, if this “I” thing is causing everything that a creature does, if this “I” thing is responsible for the creature’s decisions and plans and actions and movements, then surely this “I” thing must at least exist. How could it be so all-powerful and yet not exist?

  God’s Eye versus the Careenium’s Eye

  I’d like to return, at this point, to the image of the careenium. At the heart of my discussion of the tiny zipping simms and the far larger, more sluggish simmballs in the careenium was the fact that this system can be seen on two very distant levels, yielding widely discrepant interpretations.

  From the higher-level “thinkodynamics” viewpoint, there is symbolic activity in which simmballs interact with each other, taking advantage of the “heat energy” provided by the churning soup of invisible simms. From this viewpoint, what causes any simmballic event we see is a set of other simmballic events, even if the details of the causation are often tricky or too blurry to pin down precisely. (We are very familiar with this type of blurriness of causality in daily life — for instance, if I just barely miss a free throw in basketball, we know that it was my fault and that I did something a bit wrong, but we don’t know exactly what it was. If I throw a die and it comes up ‘6’, we aren’t in the least surprised, but we still don’t know why it came up ‘6’ — nor do we give the question the least thought.)

  Contrariwise, from the lower-level “statistical mentalics” viewpoint, there are just simms and simms alone, interacting through the fundamental dynamics of careening, bashing simms — and from this viewpoint, there is never the least vagueness or doubt about causality, because everything is governed by sharp, precise, hard-edged mathematical laws. (If we could zoom in arbitrarily closely on my arms and hands and fingers and also on the basketball and the backboard and the rim, or on the die and the table, and watch everything in slow motion of any desired slowness, we could discover exactly what gave rise to the missed free throw or the ‘6’. This might
require a descent all the way down to the level of atoms, but that’s all right — eventually, the reason would emerge into the clear.)

  If one understands the careenium well, it would seem that both points of view are valid, although the latter one, leaving out no details, might seem to be the more fundamental one (we could call it the “God’s eye” point of view), while the former, being a highly compressed simplification in which vast amounts of information are thrown away, might seem to be the more useful one for us mortals, as it is so much more efficient (even though some things then seem to happen “for no reason” — that’s the tradeoff ).

  I Am Not God

  But not all observers of the careenium enjoy the luxury of being able to flip back and forth between these two 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 naïve 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 naïve 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?

  Well, what about our old friend video feedback as a candidate for strange loopiness? Unfortunately, although this modern phenomenon is very loopy and flirts wi
th infinity, it has nothing in the least paradoxical to it — no more than does its simpler and older cousin, audio feedback. To be sure, if one points the TV camera straight at the screen (or brings the microphone right up to the loudspeaker) one gets that strange feeling of playing with fire, not only by violating a natural-seeming hierarchy but also by seeming to create a true infinite regress — but when one thinks about it, one realizes that there was no ironclad hierarchy to begin with, and the suggested infinity is never reached; then the bubble just pops. So although feedback loops of this sort are indisputably loops, and although they feel a bit strange, they are not members of the category “strange loop”.

  Seeking Strange Loops in the Russellian Gloom

  Fortunately, there do exist strange loops that are not illusions. I say “fortunately” because the thesis of this book is that we ourselves — not our bodies, but our selves — are strange loops, and so if all strange loops were illusions, then we would all be illusions, and that would be a great shame. So it’s fortunate that some strange loops exist in the real world.

  On the other hand, it is not a piece of cake to exhibit one for all to see. Strange loops are shy creatures, and they tend to avoid the light of day. The quintessential example of this phenomenon, in fact, was only discovered in 1930 by Kurt Gödel, and he found it lurking in, of all places, the gloomy, austere, supposedly paradox-proof castle of Bertrand Russell’s theory of types.