Achilles and the Tortoise is a recurring dialogue in Gödel, Escher, Bach which is used as a tool to convey the very logical/mathematical concepts of the book in a style reminiscent ancient Greek philosophy.
The Tortoise can be considered something of a co “protagonist” for the points explained in the book. For each new concept introduced by Douglas Hofstadter before or afterhand, there often a dialogue between Achilles and The Tortoise in a bizarre situation.
A classic example can be seen from the Little Harmonic Labyrinth dialogue, which follows the two characters down a path of “dimension reduction”
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