Review of "Gödel, Escher, Bach"

"It seems to me that you may begin approaching Zen through any path you know—even if it completely antithetical to Zen. As you approach it, you gradually learn to stray from that path. The more you stray from the path, the closer you get to Zen."

-- Achilles to the Tortoise 

* * *

Where to begin? This is a monstrous book, unlike anything I've read before—the right and proper Compendious Book, I think. I am convinced there is exactly one man in the world who could have written it, because the idea of a 700-page unraveling of the principles behind Gödel's Incompleteness Theorem, that approaches its destination, by turns, from the twisted fancies of Escher's illusionism, from the folds and turns of Baroque music, from the ripples of Zen Buddhist thought, from the manic episodes of an everlasting comic strip in prose, and from the inhospitable acres of formal logic, and all in a book intended for general audiences, is an idea that should not have occurred to any person on this good earth.

And yet there is Douglas Hofstadter.

Half the difficulty of explaining the book comes from even describing the format. Essentially, what we have are alternating chapters of fiction and non-fiction. Two of Hofstadter's characters—the Tortoise and Achilles, from Zeno's paradoxical footrace—go on merry adventures and share witty repartee that in some way will frame all the mathematical ideas Hofstadter wishes to introduce in the upcoming chapter.

To make this all clearer, I'll explain one such pairing in unusual detail. For me, one of the highlights of the book was a chapter called "Little Harmonic Labyrinth," where the Tortoise and Achilles traverse multiple levels of story within a story. The chapter begins ominously as the duo are trapped in the kitchen of the hungry giant Goodfortune (level 1). To pass the time, they begin reading a story, deciding to roleplay as the characters therein (level 2). But this story itself has an internal story, and so on. Keeping track of the "true" level of meaning becomes increasingly difficult as the narration "pushes" and "pops" from level to level, until at the end we are hopelessly disoriented. The chapter ends happily with an amicable parting of the heroes... but at what level? The observant reader (or perhaps the one who has been drawing a diagram?) will realize, to his dismay, that only level 2 of the story was concluded happily, which leaves the real Achilles and Tortoise still trapped in the giant's lair. The discord between the "happy ending" and this anxious realization is more unnerving than I can describe.

All this is a precursor to Hofstadter's formal introduction of the idea of recursivity. And yet even then he does not immediately proceed to the mathematical idea, but first draws parallels from classical music (by some marvel of the mind, we listeners manage to keep organized multiple levels of meaning at once, distinguishing ordinary chord progressions from a key change) and language (we dive in and out of prepositional phrases, appositions, and subclauses, sometimes all nested within one another). All this is preparation for the mathematical concept, and by the time the reader hits A_n = A_n-1 + etc., he is more than ready for it; he understands intuitively the positive need for such an idea. Never will a subject that's been given the Hofstadter treatment seem an airy abstraction or a sterile formula; to say Hofstadter gives mathematical concepts connotations is not enough, because he gives them personalities!

Recursion may have been the particular province of the two chapters I just described, but in many ways, it is the fundamental theme of the book. What unites all the far-flung influences that Hofstadter manages to invite into his book is the idea of "strange loops." Escher's recursive hands, Bach's self-canny fugues... There is an absolutely thrilling discussion of that crown jewel of recursivity, Russell's Paradox, and the searing unnaturalness of any attempt to solve it by prohibiting self-reference (Russell's theory of types). Late in the book, there is an extended discussion of the prospects of artificial intelligence. Hofstadter's threshold, if I had to define it for him, is that a brain (or machine) gets marked apart as "intelligent" once it becomes self-aware. I think this also explains why Hofstadter brings in Zen as an intellectual counterpoint, because enlightenment is often described as a sublimation into non-self-awareness. The Zen monk's eureka moment could be described, "I think not, therefore I am not."

This is not a book for everyone. No one would call it light reading; a paragraph of text usually demands about a paragraph of thought. Often enough this book calls for having a pen and paper next to you, and that's without any note-taking requirement! However, I found the effort well worth it, as this is intellectual stimulation of the first rate, so I would certainly recommend it to anyone who's looking for such a thing and has time on his or her hands.