Escher , and composer Johann Sebastian Bach , the book expounds concepts fundamental to mathematics , symmetry , and intelligence. Through illustration and analysis, the book discusses how, through self-reference and formal rules, systems can acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself. One point in the book presents an analogy about how individual neurons in the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants. The tagline "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll " was used by the publisher to describe the book. The main chapters alternate with dialogues between imaginary characters, usually Achilles and the tortoise , first used by Zeno of Elea and later by Lewis Carroll in " What the Tortoise Said to Achilles ".

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