I Am a Strange Loop

by Douglas R. Hofstadter

Kurt Gödel was the first person to realize and exploit the fact that the positive integers, though they might superficially seem to be very austere and isolated, in fact constitute a profoundly rich representational medium. They can mimic or mirror any kind of pattern. Like any human language, where nouns and verbs (etc.) can engage in unlimitedly complex dancing, the natural numbers too, can engage in unlimitedly complex additive and multiplicative (etc.) dancing, and can thereby “talk”, via code or analogy, about events of any sort, numerical or non-numerical. This is what I meant when I wrote, in Chapter 9, that the seeds of PM’s destruction were already hinted at by the seemingly innocent fact that PM had enough power to talk about arbitrarily subtle properties of whole numbers.