Godel, Escher, Bach

Hofstadter constructs an argument about how consciousness could arise from non-conscious components, using Godel's incompleteness theorems, Escher's self-referential images and Bach's canons and fugues as parallel examples of what he calls strange loops. A strange loop occurs when moving through a hierarchical system returns you to where you started, and Hofstadter argues that a sufficiently complex formal system capable of referring to itself produces this structure.

The technical core is Godel's proof. Hofstadter builds the reader up to it through formal systems, showing how a system of symbols with rules can be assigned meaning, how numbers can encode statements about numbers, and how this permits a statement that asserts its own unprovability. The consequence is that any consistent formal system strong enough to describe arithmetic contains true statements it cannot prove.

Hofstadter's larger claim is that the self is a strange loop of this kind: a pattern in the brain that models itself, producing an apparently causal entity that has no separate physical existence. He applies this to artificial intelligence, to molecular biology where DNA both encodes and is manipulated by proteins, and to the question of whether meaning is intrinsic. The book alternates chapters with dialogues between Achilles and the Tortoise that illustrate the concepts structurally, imitating Bach forms.

It is long, difficult and demands active work. Many people start it and few finish. Hofstadter has said repeatedly that readers misunderstand it as a book about mathematics, music and art when it is a book about how selves arise from matter. The artificial intelligence material predates modern machine learning entirely and its predictions about what would be hard have not held.