Hofstadter includes a dialogue alongside each chapter. This term, used in the philosophical sense, describes a written conversation between two figures to explore and illustrate ideas. Aristotle and Plato employed dialogue to uncover concepts about morality, ethics, science, and human nature. Hofstadter features a few main characters in his dialogues, including Achilles, the Tortoise, the Crab, and Zeno. Both the structure of the characters’ narratives and conversations, and the content of their dialogue, reference Hofstadter’s theories about recursion, strange loops, and isomorphisms.

The Fibonacci sequence, named after 13th-century Italian mathematician Leonardo Fibonacci, describes a series of numbers wherein each number is the sum of the two preceding it, such as in the following progression: 0, 1, 1, 2, 3, 5, 8, 13. When plotted, these numbers form a pattern that is manifested throughout nature, including the shell of a snail and the structure of artichoke. Records of Fibonacci numbers have been found in the works of Indian mathematician and poet Pingula as early as 200 B.C.E. Hofstadter uses the Fibonacci sequence to illustrate his concept of recursion. In this sequence, a simple process (adding the two preceding numbers together) creates an unexpected outcome: a repeated pattern in both nature and art.