“What happens if the chain of levels is not linear, but forms a loop? What is real, then, and what is fantasy?”

In the Introduction, Hofstadter outlines what he considers to be the focal point of his work—the concept of strange loops. These self-referential phenomena occur across a hierarchical spiral, ending where they began. This idea, forming the foundation of Self-Reference and Strange Loops, is explored across genres and disciplines.

“It is an inherent property of intelligence that it can jump out of the task which it is performing, and survey what is done; it is always looking for, and often finding, patterns.”

Hofstadter asserts that human intelligence distinguishes itself from machine learning by its ability to work outside of formal systems. Finding these patterns requires both Connection and Openness Through Interdisciplinary Approach. By drawing on multiple disciplines, humans can see how the patterns in some structures overlap with other structures through isomorphisms, a mathematical term Hofstadter applies to other fields to illustrate how human cognition functions.

“Perhaps by then I’ll have thought of the right answer to YOUR puzzle, using your figure-ground hint, relating it to MY puzzle.”

In this allegorical dialogue, Achilles and the Tortoise exchange riddles that each is seeking an answer to. Their conversation leads to the revelation that the solution to one may lead to a solution to the other. Hofstadter uses this narrative to exemplify the theme of Self-Reference and Strange Loops. The hint for each riddle is self-referential, occurring across multiple tiers and returning in an infinite spiral.