A strange loop is a system that represents itself across levels

Hofstadter defines a strange loop precisely as a "level-crossing feedback loop": a hierarchical system in which movement through different levels of abstraction eventually leads back to the starting point, creating the paradoxical sense of a system referring to itself. His paradigm case is Gödel's incompleteness theorem, which showed that any logical system rich enough to formalize arithmetic can also encode statements about its own logical structure, producing self-referential propositions that generate genuine paradoxes, like a sentence that effectively says "this statement is unprovable."

Hofstadter argues an equivalent structure exists inside a sufficiently complex brain: as the brain builds increasingly abstract internal symbols representing external reality, eventually those symbols become complex enough to represent the brain's own representational activity, closing a loop back on itself. This isn't a physical loop of neurons in any simple circular sense, but an abstract, pattern-level loop occurring at the level of meaning and representation.

Takeaway: self-reference isn't mystical — it's a structural feature that emerges whenever a system becomes complex enough to model itself, in logic or in minds alike.