Poised midway between the unvisualizable cosmic vastness of curved spacetime and the dubious shadowy flickerings of charged quanta, we human beings, … - Douglas Hofstadter

But finally I realized that to me, Godel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to construct the central object, and came up with this book.

I had presented a “tower of power” — that is, an infinitely tall tower of separate Lisp definitions, one for each power, connecting it to the preceding power.

Thus our categories keep us well informed at all times, allowing us to bypass the need for direct observation. If we didn’t constantly extrapolate our knowledge into new situations — if we refrained from making inferences — then we would be conceptually blind. We would be unable to think or act, doomed to permanent uncertainty and to eternal groping in the dark. In short, in order to perceive the world around us, we depend just as much on categorization through analogy as we do on our eyes or our ears.