Douglas Hofstadter - I Am a Strange Loop

SL #642: So it’s the fact that the system can watch itself that dooms it to this illusion.

SL #641: Not just that it can watch itself, but that it does watch itself, and does so all the time. That, plus the crucial fact that it has no choice but to radically simplify everything. Our categories are vast simplifications of patterns in the world, but the well-chosen categories are enormously efficient in allowing us to fathom and anticipate the behavior of the world around us.

SL #642: And why can’t we get rid of our hallucinations? Why can’t we attain that pure and selfless “I”-less state that the Zen people would aim for?

SL #641: We can try all we want, and it is an interesting exercise for a short while, but we can’t turn off our perception machinery and still survive in the world. We can’t make ourselves not perceive things like trees, flowers, dogs, and other people. We can play the game, can tell ourselves we’ve succeeded, can claim that we have “unperceived” them, but that’s just plain self-fooling. The fact is, we are macroscopic creatures, and so our perception and our categories are enormously coarse-grained relative to the fabric at which the true causality of the universe resides. We’re stuck at the level of radical simplification, for better or for worse.

SL #642: Is that a tragedy? You make it sound like a sad fate.

SL #641: Not at all — it’s our glory! It’s only those who take Zen and the Tao very seriously who consider this to be a condition to be fought against tooth and nail. They resent words, they resent breaking the world up into discrete chunks and giving them names. And so they give you recipes — such as their droll koans — to try to combat this universal built-in drive to use words. I myself have no desire to fight against the use of words in understanding the world’s mysteries — quite the reverse! But I admit that using words has one very major drawback.

SL #642: What is that?

SL #641: It is that we have to live with paradox, and live with it in the most intimate fashion. And the word “I” epitomizes all of that.

SL #642: I don’t see anything in the least paradoxical about the word “I”. In fact, I see no analogy at all between the commonplace, straightforward, down-to-earth notion of “I” and the esoteric, almost ungraspably elusive notion of a Gödelian strange loop.

SL #641: Well, consider this. On the one hand, “I” is an expression denoting a set of very high abstractions: a life story, a set of tastes, a bundle of hopes and fears, some talents and lacunas, a certain degree of wittiness, some other degree of absent-mindedness, and on and on. And yet on the other hand, “I” is an expression denoting a physical object made of trillions of cells, each of which is doing its own thing without the slightest regard for the supposed “whole” of which it is but an infinitesimal part. Put another way, “I” refers at one and the same time to a highly tangible and palpable biological substrate and also to a highly intangible and abstract psychological pattern. When you say “I am hungry”, which one of these levels are you referring to? And to which one are you referring when you declare, “I am happy”? And when you confess, “I can’t remember our old phone number”? And when you exult, “I love skiing”? And when you yawn, “I am sleepy”?

SL #642: Yes, now that you mention it, I do agree that what “I” stands for is a little hard to pin down. Sometimes its referent is concrete and physical, sometimes it’s abstract and mental. And yet when you come down to it, “I” is always both concrete and abstract at the same time.

SL #641: It is just one thing described in two phenomenally different ways, and that’s just the same as Gödel’s sentence. That’s why it is valid to say that it is both about numbers and about itself. Likewise, “I” is both about a myriad of separate physical objects and also about one abstract pattern — the very pattern causing the word to be said!

SL #642: It seems that this little pronoun is the nexus of all that makes our human existence mysterious and mystical. It’s so different from anything else around. The intrinsically self-pointing loop that the pronoun “I” involves — its indexicality, as philosophers would call it — is quintessentially different from all other structures in the universe.

SL #641: I don’t quite agree with that. Or rather, I don’t agree with it at all. The pronoun “I” doesn’t involve a stronger or deeper or more mysterious self-reference than the self-reference at the core of Gödel’s construction. Quite the contrary. It’s just that Gödel spelled out what “I” really means. He revealed that behind the scenes of so-called “indexicals”, there are merely codes and correspondences depending on stable, reliable systems of analogies. The thing we call “I” comes from that referential stability, and that’s all. There’s nothing more mystical about “I” than about any other word that refers. If anything, it is language that is so different from other structures in the universe.

SL #642: So for you, “I” is not mystical? Being is not mysterious?

SL #641: I didn’t say that. Being feels very mysterious to me, because, like everyone else, I’m finite and don’t have the ability to see deeply enough into my substrate to make my “I” poof out of existence. If I did, I guess life would be very uninteresting.

SL #642: I should think so!

SL #641: When we do look down at our fine-grained substrates through scientific experiments, we find small miracles just as Gödelian as is “I”.

SL #642: Ah, yes, to be sure — little microgödelinos! But… such as?

SL #641: I mean the self-reproduction of the double helix of DNA. The mechanism behind it all involves just the same abstract ideas as are implicated in Gödel’s type of self-reference. This is what John von Neumann unwittingly revealed when he designed a self-reproducing machine in the early 1950’s, and it had exactly the same abstract structure as Gödel’s self-referential trick did.

SL #642: Are you saying microgödelinos are self-replicating machines?

SL #641: Yes! It’s a subtle but beautiful analogy. The analogue of the Gödel number k is a particular blueprint. The “parent” machine examines this blueprint and follows its instructions exactly — that is, it builds what the blueprint depicts. To do that, it has to know what icons stand for what objects — a Gödelian kind of code, or mapping. The newly-built object is a machine that lacks one crucial part. To fill this lacuna, the parent machine then copies the blueprint and sticks the copy (which is the key missing part) into the new machine, and voilà ! — the new composite object is a “child” machine, identical to its parent.

SL #642: This reminds me of the Morton Salt logo. Would the “child machine” lacking the crucial part be like the “umbrella girl” standing there empty-handed? And the blueprint would be a little blue salt box?

SL #641: Right! Hand her the little blue box, and she’s off to the races! Infinity, ho! And amazingly, only a few years later molecular biologists found that von Neumann’s Gödelian mechanism was the same trick Nature had discovered for making self-reproducing physical entities. DNA is the blueprint, of course. It all hinges on the existence of stable mappings (in this case, the mapping called the “genetic code”) and the meanings that come from them. And look where that led — to all of life, as far as it has come, and wherever it’s still heading! Infinity, ho!

SL #642: So you claim that the sense of being a unique living thing, reflected in the magical indexicality of the elusive word “I”, is not a profound phenomenon, but just a mundane consequence of mappings?