When systems (think "automated" systems like computer programs, mathematical axioms, formal systems, etc, where conclusions can be drawn/calculated "mechanically" from a few starting points) get large enough, they gain the ability to become self-referential. That is, they become expressive enough to encode statements about themselves. A hallmark of this are "incompleteness theorems" like those of Godel or the Turing halting problem.

The book argues that these "strange loops" (of a system onto itself) are behind the emergence of intelligence and consciousness, because physical matter itself gives rise to human intelligence, albeit being a mechanical system.