This prelude is dialogue between the Tortoise, the Crab, Achilles, and a new character—the Anteater. Achilles and the Tortoise visit the Crab at his home to meet his friend. The Tortoise gifts the Crab two records, promising that his records will not break the Crab’s phonograph. The Tortoise’s records are used to prove Fermat’s Last Theorem (aⁿ+bⁿ=cⁿ). Fermat determined that the equation cannot be solved using three positive integers if “n” is greater than two. The records are both by Bach, and the Tortoise shows how the relationship between the prelude and the fugue reveal the self-referential nature of interpretation.

In previous chapters, Hofstadter explores how the human mind engages in multiple levels of meaning. Similarly, Hofstadter shows that computer programs contain diverse levels of description and self-reference. Humans move along these various levels with ease: “We can just shut one out, and pay attention to the other—which is what all of us do” (285). For example, they understand that their bodies are both comprised of molecules and made up of cells. Humans do not find it difficult to hold these two statements of truth in their minds at once.