Gödel, Escher, Bach

A long book, subtitled 'An Eternal Golden Braid', that uses the logician Kurt Gödel, the artist M. C. Escher and the composer J. S. Bach to ask how meaning, self and consciousness can arise from meaningless parts. Chapters alternate with playful dialogues between Achilles and the Tortoise, characters borrowed from Lewis Carroll, whose forms often imitate Bach's canons and fugues. Hofstadter introduces formal systems through puzzles such as the MU puzzle, explains recursion and isomorphism, and builds a simple formal system of arithmetic in order to give a careful, step-by-step account of Gödel's incompleteness theorem. His central idea is the strange loop: a system that, by moving through levels, ends up referring to itself, as in Escher's drawings of hands drawing each other or Gödel's sentence that says of itself that it cannot be proved. Later chapters apply this to the brain, symbols, artificial intelligence and the nature of the 'I', arguing that a self is a strange loop arising in the patterns of a brain.

It is the most inventive popular book on logic, computation and mind, and it explains Gödel's theorem better than most textbooks while asking what a self is.