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Godel, Escher, Bach: An Eternal Golden Braid

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Douglas Hofstadter uses the art of M.C. Escher, the music of J.S. Bach, and Kurt Goedel's mathematics as the centerpieces for a magnificent inquiry into the nature of the mind. Along the way you will encounter Bertrand Russel, Carroll Lewis, particle physics, molecular biology, Magritte's paintings, and Zen koans. These are all used to probe recursion and the mystery of how we form thoughts. But the list of topics alone is not what makes this book great, it's the playful, joyful sense that characterize's Hofstadter's treatment of this. This sense of wonder is critical, as without it this highly challenging book would be very frustrating. The book's style itself is based on Bach's canons, and the chapters are interspersed with dialogues between the Tortois and the Hare, in the style of Carroll's Alice in Wonderland. The result is an artistic as well as scientific or philisophical masterpiece. I am currently a triple-major in molecular biology, physics, and philosophy, and much of my curriculum has been influenced by the beauty of Hofstadter's book. This will go down as one of the 20th Century's bests books.

Hofstadter has done a superb job of presenting an intriguing melange of disciplines that are seemingly unrelated. The author manages to quickly show that Godel's theorems, Escher's art, and Bach's music have much more in common than most would think. In a lengthy but VERY worthwhile read, he manages to get the reader to analyze many of the assumptions commonly held about the nature of thought and why it is so devilishly difficult to formalize the thought process with rigid rules, among other topics.

That he manages to entertain as well (he writes with a wry sense of humor on what are typically handled as rather dry subjects) and manages to reach the layman is what sets this volume apart as the masterpiece that it is. Although it is accessable to the layman, the book does become progressively more challenging and I strongly recommend completing his suggested exercises before moving on, otherwise you will likely find yourself unable to grasp the point he's trying to make several pages later.

Hofstadter has pulled off a miracle with this book. If you like ideas and like reading about how ideas fit together, then get this book. Definately not a one-sitting book (at least for me) but very interesting and worthwhile. It's like listending to your favorite comedian lecture as a highschool teacher on a subject you can't help but be amazed at. He melds art, music, math, computer science, Zen, and more into a beautiful tapestry of fascination. Highly highly recommended.

The Atlanta Journal Constitution describes Gödel, Escher, Bach (GEB) as "A huge, sprawling literary marvel, a philosophy book, disguised as a book of entertainment, disguised as a book of instruction." That is the best one line description of this book that anybody could give. GEB is without a doubt the most interesting mathematical book that I have ever read, quickly making its place into the Top 5 books I have ever read.
The introduction of the book, "Introduction: A Musico-Logical Offering" begins by quickly discussing the three main participants in the book, Gödel, Escher, and Bach. Gödel was a mathematician who founded Gödel's Incompleteness Theorem, which states, as Hofstadter paraphrases, "All consistent axiomatic formulations of number theory include undecidable propositions." This is what Hofstadter calls the pearl. This is one example of one of the recurring themes in GEB, strange loops.
Strange loops occur when you move up or down in a hierarchical manner and eventually end up exactly where you started. The first example of a strange loop comes from Bach's Endlessly rising canon. This is a musical piece that continues to rise in key, modulating through the entire chromatic scale, ending at the same key with which he began. To emphasize the loop Bach wrote in the margin, "As the modulation rises, so may the King's Glory."
The third loop in the introduction comes from an artist, Escher. Escher is famous for his paintings of paradoxes. A good example is his Waterfall; Hofstadter gives many examples of Escher's work, which truly exemplify the strange loop phenomenon.
One feature of GEB, which I was particularly fond of, is the `little stories' in between each chapter of the book. These stories which star Achilles and the Tortoise of Lewis Carroll fame, are illustrations of the points which Hofstadter brings out in the chapters. They also serve as a guidepost to the careful reader who finds clues buried inside of these sections. Hofstadter introduces these stories by reproducing "What the Tortoise Said to Achilles" by Lewis Carroll. This illustrates Zeno's paradox, another example of a strange loop.
In GEB Hofstadter comments on the trouble author's have with people skipping to the end of the book and reading the ending. He suggests that a solution to this would be to print a series of blank pages at the end, but then the reader would turn through the blank pages and find the last one with text on it. So he says to print gibberish throughout those blank pages, again a human would be smart enough to find the end of the gibberish and read there. He finally suggests that authors need to write many pages more of text than the book requires just fooling the reader into having to read the entire book. Perhaps Hofstadter employs this technique.
GEB is in itself a strange loop. It talks about the interconnectedness of things always getting more and more in depth about the topic at hand. However you are frequently brought back to the same point, similarly to Escher's paintings, Bach's rising canon, and Gödel's Incompleteness theorem. A book, which is filled with puzzles and riddles for the reader to find and answer, GEB, is a magnificently captivating book.

I've always been facinated by the concept of artificial intelligence, and when someone told me how good this book was I went out and bought it, and while I was reading it you could not pry it from my hands it was so interesting. Every chapter you learn at least one thing. It constantly sets you thinking. I was amazed at the connection between goedels theory, escher's art and bach's muxic with it's infinitly repeating themes. And the tortise and hare's in between chapter dialogue really helps you understand the complex concepts.

Read Godel, Escher, Bach: An Eternal Golden Braid. Each time I do, I realize how truly unique it is. A wonderfully composed sonnet about number theory, um, I mean about genetic engineering, no, wait, it's about philosophy. Dear me, I'm confused; I think it's about artificial intelligence. This book weaves together number theory, musical theory, and art in a whirlwind of self-reference. Hofstadter's main theme is whether artificial intelligence is a possibility or not. I'ts most fascinating element is that, while reading this book, one never quite knows if the book is serious or lighthearted, persuasive or informative. Some say that the most enjoyable part of this book comes after each chapter, when the reader is shown the misadventures of Achilles and the Tortoise, creatures who debate the topics of the following chapterin a roundabout way. Books like this contain so many levels of meaning. One true mark of a classic book is that the reader learns something new each time she reads it. Only one book deserves a ten, so a rating of nine is my highest. Kindly enjoy this book, but before you do, I have one last comment; see if you can find the hidden meaning in this review, because it is representative of the hidden meaning in this book.

As pure Art, as magnificent intelligence incarnated as absolute beauty, this is the greatest book ever written by human hands. It is a terrible thing to contemplate that 150,000 people die every day without having read this book. Don't let it happen to you.

This book dramatically illustrates two things: First, that truly fascinating subjects and truly beautiful works of art require fundamental concepts from cognitive science and an implicit understanding of the Universe. Second, that no matter how deep a scientific idea is, it can still be explained to any intelligent reader, without using obscuring clouds of mumbo-jumbo.

Artificial Intelligence, mathematics, cognitive science, computer programming; art, music, language; it doesn't matter whether you know them, or you want to know them, or you just want an unlimited amount of amazing fun - read this book. I could spend the rest of my life reading this book and I would still be noticing wonderful new gems.

Telling people not to read "Gödel, Escher, Bach" is like telling people not to read Harry Potter. This book has become so much of a cultural touchstone that everyone should read it, just to see what the hype is about. In fact, Hofstadter has written a very careful exploration of the nature of consciousness. Now, I don't find the questions that he raises, of self-reference or the consistency of systems of axioms, very interesting, but reading "Gödel, Escher, Bach" reminded me of all the problems that *do* interest me. In that respect, the book's "negative space" had a very deep influence on me, and, since one of the book's themes is negative and positive space, I like to think that my reading is in a spirit that Hofstadter would approve of.

If you're interested in theories of consciousness or Gödel's theorem, this book may appeal to you, especially if you appreciate a playful treatment of these topics and don't mind the author's long-windedness. Now, I was not enthusiastic to begin with, so I don't feel qualified to comment on the flaws in the book's argument. But I will recommend 3 other books on related topics which complement "Gödel, Escher, Bach" nicely, even for more sympathetic readers.



A more accessible, better contextualized, and more enlightening treatment of Gödel's Incompleteness Theorem can be found in "Logicomix" by Doxiadis and Papadimitriou.

Descartes' theory of consciousness assumes, like Hofstadter's, that consciousness is an individual (rather than a social) phenomenon. Descartes' approach is axiomatic without taking into account problems of self-reference. (You might say that Hofstadter tries to update Descartes for the post-Gödel era, which forces Hofstadter to place less faith in deductive reasoning.) You might read the "Discourse on Method" or the "Meditations on First Philosophy". Those books are both much shorter and much wittier than "Gödel, Escher, Bach".

Finally, Ramachandran has interesting things to say on the subject of consciousness and sees self-reference as only one of several defining characteristics of consciousness. He makes some remarks to that effect at the end of "Phantoms in the Brain".

It is quite likely that the hardest question I've ever been asked is, "What's that book about?" This book manages to discuss, coherently, cohesively, and interestingly, everything from molecular biology to quantum physics to computer science to music theory to philosophy to advanced mathematics to Elizabethan literature and beyond. Reading this will definitely change the way you see the world, and if you read one book this entire year, this should probably be it. VERY highly recommended.

As far as the layout and design of the book go, I find this piece to be particularly structured in a way that one studying abstract and modern mathematics might find appealing. It gives specific axioms for use with each topic and in doing so defines more than just what the topic might imply. As the content goes, for those taking an introduction course in abstract algebra, this book may be slightly heavy and unwieldy, however, for those well-learned in some of its background material, this book is enjoyable and pleasurable to read. The author even makes use of antecdotes to enforce his topics. Overall, this book has been one of the most pleasurable assigned readings I have endured.