Gödel Escher Bach

Douglas Hofstadter's Pulitzer Prize-winning exploration of self-reference, consciousness, and the nature of meaning — weaving together Gödel's incompleteness theorem, Escher's impossible drawings, and Bach's fugues.

Strange loops: self-referential systems that, in tangling levels, generate something new — consciousness as the strange loop that arises in sufficiently complex brains. Gödel's theorem as a strange loop: formal systems that are powerful enough to talk about themselves generate true statements that cannot be proved within the system. The analogy between Gödel, Escher, and Bach: all three create strange loops through self-reference. Meaning and isomorphism: meaning is an isomorphism between formal systems.