I Am a Strange Loop

by Douglas R. Hofstadter

Take the adjective “nondescript”, for instance. If I say, “Their house is so nondescript”, you will certainly get some sort of visual image from my phrase — even though (or rather,

Russell did his best to deflect the paradox’s sting by claiming that it was an illusion arising from a naïve misuse of the word “describable” in the context of mathematics. That notion, claimed Russell, had to be parceled out into an infinite hierarchy of different types of describability — descriptions at level 0, which could refer only to notions of pure arithmetic; descriptions at level 1, which could use arithmetic but could also refer to descriptions at level 0; descriptions at level 2, which could refer to arithmetic and also to descriptions at levels 0 and 1; and so forth and so on.

using computer programs instead of English-language descriptions, and this clever shift turned out to yield a radically new proof of, and perspective on, Gödel’s 1931 theorem. From there, Chaitin and others went on to develop an important new branch of mathematics known as “algorithmic information theory”.

This woman, in a well-meaning gesture, had strictly banned all toy guns from her household.

In short, plunging deeply into the new wave of paradoxes seemed to be a useful if not indispensable activity for anyone working on the foundations of mathematics, for the new paradoxes were opening up profound questions concerning the nature of reasoning — and thus concerning the elusive nature of thinking — and thus concerning the mysterious nature of the human mind itself.

But the other half of my intense curiosity was my sense that what was really being explored by Gödel, as well as by many people he had inspired, was the mystery of the human mind and the mechanisms of human thinking.

They were dense, almost impenetrably so — but I kept on thinking that if only someday, some grand day, I could finally read them and fully fathom them, then at last I would have penetrated to the core of the mysteries of thinking, meaning, creativity, and consciousness.

What drove all this — my core inner passion — was a burning desire to see unveiled the secrets of human mentation, to come to understand how it could be that trillions of silent, synchronized scintillations taking place every second inside a human skull enable a person to think, to perceive, to remember, to imagine, to create, and to feel.

course of the next couple of decades I lost essentially all of my faith in the notion that these disciplines contained (even implicitly) the answers to all these questions, one thing I never lost was my intuitive hunch that around the core of the eternal riddle “What am I?”, there swirled the ethereal vortex of Gödel’s elaborately constructed loop.

IN THE early twentieth century, Bertrand Russell, spurred by the maxim “Find and study paradoxes; design and build great ramparts to keep them out!” (my words, not his),

At this juncture, I feel compelled to point out a distinction not between two classes of numbers, but between two classes of people. There are those who will immediately be drawn to the idea of pattern-seeking, and there are those who

will find it of no appeal, perhaps even distasteful. The former are, in essence, those who are mathematically inclined, and the latter are those who are not. Mathematicians are people who at their deepest core are drawn on — indeed, are easily seduced — by the urge to find patterns where initially there would seem to be none. The passionate quest after order in an apparent disorder is what lights their fires and fires their souls.

You probably have seen Euclid’s proof of the infinitude of the primes somewhere, but if not, you have missed out on one of the most crucial pillars of human knowledge that ever have been found.