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jordanlei 's review for:
Gödel, Escher, Bach: an Eternal Golden Braid
by Douglas R. Hofstadter
Gödel, Escher, Bach is a book that captures the intricacies of strange loops and tangled hierarchies in science, mathematics, art, and music. The book explores the role of self-referential processes that arise from what may, at first glance, seem like rigid foundations. Godel's incompleteness theorem is a manifestation of this "strange loop" in mathematics; Godel showed definitively that a sufficiently strong formal system will necessarily contain a statement that is summarized by "this statement is not provable in the formal system". In doing so, Godel created a self-referential statement out of seemingly "rigid" mathematical rules. If such rules can arise from rigid mathematical rules, who is to say that the basic building blocks of physics and biology might not create rules which, at each level seem to be deterministic or logical, but create a self-referential system that is capable of thinking of itself independently of those systems? This "higher-level" self reference is what Hofstadter claims is the key to our understanding of consciousness, and it is a compelling argument which shows how consciousness can arise from seemingly "inert" principles. Even if you don't buy the strong version of Hofstadter's argument, the ties he draws to biology, neuroscience, artificial intelligence, Zen Buddhism, and other topics are are delight in themselves.
Interwoven in the book, between chapters of theory and explanation, are dialogues centered around Achilles and the Tortoise from Zeno's Paradox. Sometimes these dialogues serve to provide crucial context for the next chapter. Other times, these dialogues are themselves a demonstration of the context they wish to explain. The book itself is full of charm, wit, and humor, which makes for a much better reading experience than I anticipated going in. There are times when the book gets a bit slow (I found the section on Bongard Problems in AI longer than it probably needed to be), but overall the pace is both patient enough to guide the reader to the conclusions that need to be reached and fast enough to feel like you're building up to something bigger. What results is, in my opinion, a profound discussion about how consciousness (or, in its simpler forms, self-reference) can arise from seemingly "formal" systems - in mathematics, music, and even our own minds.
Interwoven in the book, between chapters of theory and explanation, are dialogues centered around Achilles and the Tortoise from Zeno's Paradox. Sometimes these dialogues serve to provide crucial context for the next chapter. Other times, these dialogues are themselves a demonstration of the context they wish to explain. The book itself is full of charm, wit, and humor, which makes for a much better reading experience than I anticipated going in. There are times when the book gets a bit slow (I found the section on Bongard Problems in AI longer than it probably needed to be), but overall the pace is both patient enough to guide the reader to the conclusions that need to be reached and fast enough to feel like you're building up to something bigger. What results is, in my opinion, a profound discussion about how consciousness (or, in its simpler forms, self-reference) can arise from seemingly "formal" systems - in mathematics, music, and even our own minds.