I Am a Strange Loop

by Douglas R. Hofstadter

What kinds of categories, then, does a mosquito need to have? Something like “potential source of food” (a “goodie”, for short) and “potential place to land” (a “port”, for short) seem about as rich as I expect its category system to be. It may also be dimly aware of something that we humans would call a “potential threat” — a certain kind of rapidly moving shadow or visual contrast (a “baddie”, for short).

The key issue here is whether a mosquito has symbols for such categories, or could instead get away with a simpler type of machinery not involving any kind of perceptual cascade of signals that culminates in the triggering of symbols.

If you answered “no” to these questions, then imagine similarly unaware mechanisms inside a mosquito’s head, enabling it to find blood and to avoid getting bashed, yet to accomplish these feats without using any ideas.

Mosquito Selves Having considered mosquito symbols, we now inch closer to the core of our quest. What is the nature of a mosquito’s interiority? That is, what is a mosquito’s experience of “I”-ness?

I hope it doesn’t sound too blasphemous or crazy if I suggest that a mosquito’s “soul” might be roughly the same “size” as that of the little red spot of light that bounces around on the wall at the Exploratorium — let’s say, one ten-billionth of one huneker (i.e.., roughly one trillionth of a human soul).

The key point is much simpler and cruder: merely that there is some kind of creature to which essentially this level of complexity, and no greater level, would apply. If you disagree with my judgment, then I invite you to slide up or down the scale of various animal intellects until you feel you have hit the appropriate level.

An Interlude on Robot Vehicles

Valentino Braitenberg in his book Vehicles.)

Such successes give the lie to the tired dogma endlessly repeated by John Searle that computers are forever doomed to mere “simulation” of the processes of life.

Likewise, when a dog chases its tail, even though it is surely unaware of the loopy irony of the act, it must know that that tail is part of its own body. I am thus suggesting that a dog has some kind of rudimentary self-model, some kind of sense of itself.

In any case, the emergence of this kind of reflexive symbolic structure, at whatever level of sentience it first enters the picture, constitutes the central germ, the initial spark, of “I”-ness, the tiny core to which more complex senses of “I”-ness will then accrete over a lifetime, like the snowflake that grows around a tiny initial speck of dust.

How many hunekers would dogs have to have, on the average, for you to decide to organize a protest demonstration at an animal shelter?

A spectacular evolutionary gulf opened up at some point as human beings were gradually separating from other primates: their category systems became arbitrarily extensible. Into our mental lives there entered a dramatic quality of open-endedness, an essentially unlimited extensibility, as compared with a very palpable limitedness in other species.

In other words, concepts could nest inside each other hierarchically, and such nesting could go on to arbitrary degrees.

For instance, the phenomenon of having offspring gave rise to concepts such as “mother”, “father”, and “child”. These concepts gave rise to the nested concept of “parent” — nested because forming it depends upon having three prior concepts: “mother”, “father”, and the abstract idea of “either/or”. (Do dogs have the concept “either/or”? Do mosquitoes?)

In the collective human ideosphere, the buildup of concepts through such acts of composition started to snowball, and it turns out to know no limits.

Not all of these component concepts need be activated when we think about a grocery store checkout stand, to be sure — there is a central nucleus of concepts all of which are reliably activated, while many of these more peripheral components may not be activated — but all of the foregoing, and considerably more, is what constitutes the full concept in our minds.

Moreover, this concept, like every other one in our minds, is perfectly capable of being incorporated inside other concepts, such as “grocery store checkout stand romance” or “toy grocery store checkout stand”. You can invent your own variations on the theme.

Episodic ...

Episodes are concepts of a sort, but they take place over time and each one is presumably one-of-a-kind, a bit like a proper noun but lacking a name, and linked to a particular moment in time.

Little wonder, then, that when a human being, possessed of such a rich armamentarium of concepts and memories with which to work, turns its attention to itself, as it inevitably must, it produces a self-model that is extraordinarily deep and tangled. That deep and tangled self-model is what “I”-ness is all about.

As children and teenagers, we see directly, or we see on television, or we read about, or we are told about many things that supposedly exist, things that vie intensely with each other for our attention and for acceptance by our reality evaluators — for instance, God, Godzilla, Godiva, Godot, Gödel, gods, goddesses, ghosts, ghouls, goblins, gremlins, golems, golliwogs, griffins, gryphons, gluons, and grinches.

By “sorting out the reality of X”, I mean coming to a stable conclusion about how much you believe in X and whether you would feel comfortable relying on the notion of X in explaining things to yourself and others.

Another way of thinking about “how real X is to you” is how much you would trust a newspaper article that took for granted the existence of X (for example, a living dinosaur, a sighting of Hitler, insects discovered on Mars, a perpetual-motion machine, UFO abductions, God’s omniscience, out-of-body experiences, alternate universes, superstrings, quarks, Bigfoot, Big Brother, the Big Bang, Atlantis, the gold in Fort Knox, the South Pole, cold fusion, Einstein’s tongue, Holden Caulfield’s brain,

Some of these concepts, we are repeatedly told by authorities, are not real, and yet we hear about them over and over again in television shows, books, and newspapers, and so we are left with a curious blurry sense as to whether they do exist, or could exist, or might exist.

Why do I believe what certain people tell me more than I believe what others tell me? Why do I believe in (some) photos as evidence of reality? Why do I trust certain photos in certain books? Why do I trust certain newspapers, and why only up to a certain point? Why do I not trust all newspapers equally? Why do I not trust all book publishers equally? Why do I not trust all authors equally?

Inevitably, what seems realest to us is what gets activated most often.

We are all egocentric, and what is realest to each of us, in the end, is ourself. The realest things of all are my knee, my nose, my anger, my hunger, my toothache, my sideache, my sadness, my joy, my love for math, my abstraction ceiling, and so forth.

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 non-embryonic, 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.

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.

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.

(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.)

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.”

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.

Embarking on a Strange-Loop Safari

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

Strange loop definitiona

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.

In short, a strange loop is a paradoxical level-crossing feedback loop.

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.

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!

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?

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...

then we would all be illusions, and that would be a great shame. So it’s fortunate that some strange ...

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,...

In fact, the italicized phrase does not merely describe b “somehow”; it is b’s very definition! So the concept of b is nastily self-undermining. Something very strange is going on.