Gödel, Escher, Bach: An Eternal Golden Braid

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Summary: "THE" Book
Review: I've read GEB in French then in English. It is fascinating in both languages. It must have been one of the most difficult books to translate. But D. Hofstadter took part in the work (he speaks fluent French) and it is as enchanting and captivating to read in French as in English. I second [e-mail]: if you read only one book in your life let GEB be this book.

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Summary: For those who think and have fun with it
Review: This book is full of ideas that walk into your mind and start redecorating it--Picasso-style. Some of the greatest ideas that humankind have ever had are collected and connected in this book. Hofstadter loves a good pun, and this book is filled with them. Recommended for logic fans--those who answere either/or questions with "Yes."

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Summary: Masterpiece
Review: Playing his subject like a virtuoso pianist, Hofstadter weaves his golden braid around unlikely subjects: formal systems, Zen, molecular biology. But even if you know nothing of these, read on: you will learn before you finish, and Achilles and Mr. Tortoise will keep you entertained throughout. In a word, brilliant.

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Summary: Of the thousands of books I have read, this is my favorite.
Review: GEB is a book that changed the way I viewed the world. I believe it is one of the most staggering intellectual accomplishments of our time. It is at times a difficult book, but it rewards the determined reader again and again. GEB is not only an intellectual masterpiece but it is also a spiritual one as Hofstadter's "religion" comes through in its unique way. This is a book to savor and one to which I return constantly.

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Summary: True Art
Review: [e-mail] is absolutely right. As the Hacker's Dictionary puts it, this is the Must Read book for anyserious computer user - though I recommend it to anyone which can appriciate true art

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Summary: A metaphorical fugue on mind and machines
Review: _Godel_Escher_Bach_(GEB) is a monumental book, as demonstrated by enthusiastic reviews it received and its winning of the Pulitzer prize. GEB presents and deals with the topics of formal systems, meta-mathematics, recursion, meaning, thinking, levels of existence and artificial intelligence. I will not even attempt supplying a more detailed description of the contents, as in order to justly represent it the whole book must be included, as this book is crammed and packed with ideas, concepts and views which are all essential to its fabric. As the extremely brief and partial list of topics I mentioned may, or may not, suggest, this subjects the book deals with are fascinating. Any intellectually active person will find it enlightening. Among those who I suspect may be most interested in reading this book, and who have the most tools to appreciate it and profit from it, are programmers. GEB supplies an invaluable insight into the heart of computer programming, grasping concepts a programmer will appreciate as a reach into the very soul of creation. What makes this book really special is, however, the way it is built. The whole book is, metaphorically speaking, one continuous intellectual adventure with views which provoke reader's imagination, oracles who challenge his power of logic and wise old men who teach the mysteries of life. The exploration path the book takes inside knowledge is well defined and well structured, while it keeps the reader free to wander off and explore the land around it whenever he is intrigued by the implications of what he learns. One highly amusing and appealing technique used in GEB is preceding each chapter with a short story (a few pages long) "in the spirit of Lewis Carroll" of Achilles, the tortoise and their merry company, a story which vividly demonstrates key concepts which the actual chapter then goes on to discuss, often based on the metaphors presented in that story. All in all, _Godel_Escer_Bach_ is extremely fascinating, entertaining and enriching. Highly recommended.

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Summary: A book that is about more than Godel, Escher, and Bach
Review: This book is an excellent introduction to several ideas in cognitive science, biology, mathematics, linguistics, computer science, art, and other fields. It cleverly reveals how different fields influence each other in a cross disciplinary fashion and actually "embeds" this structure inside the book. I won't go into more detail, but as soon as you read the book, you will see how this is done. The writing is crisp and engaging, almost as if Lewis Carroll, Noam Chomsky, and your favorite professor in college gave birth to a book. The concepts are revealed through parables, koans, and other forms involving characters named Tortoise, Achilles, and Crab and at one point involve a metagenie.(...)

The only criticisms that I have about the book are
1)Some radically new things have been discovered/done in many of the fields discussed in the book, especially artificial intelligence. The book doesn't talk about some of these developments, and some of the statements in the book are inaccurate or outdated (ex: chess playing computer that can beat human will never be built, replication in biolgy is A LOT more complicated/different than its rather cursory rendering in this book)
2)This book is more helpful as an introduction to spark your interest in various topics than a detailed guide to the many interesting ideas that have arisen in science. After reading about concepts in the book, if they are interesting, it would be helpful to read a more detailed and recent book on the topic.
3)Sometimes, but not usually, the author's desire to be witty or find connections overwelms the actual truth of his statements--at these points the connections made are rather weak.

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Summary: Multi-faceted Thesis
Review: Ancient runic languages scrawled onto South Pacific stones. Gödel's Incompleteness Theorum. Shifted perspectives in artistic pencil pictures. Modern artificial intelligence research. Masterpieces of Baroque harmony.
It's not often that bestselling books manage to link all of the above items in a highly satisfying blend of fact and philosophy, but Gödel, Escher, Bach: An Eternal Golden Braid defies both convention and classification.
The book is such a sprawling, wide-ranging argument that it's difficult to know where to start. Personally, I most enjoyed the chapters on the location of meaning within symbols; Hofstadter's description of the essential elements of a message's structure caught my interest because it seemed applicable in many fields: literature, cryptography, and psychology, to start. I was also quite intrigued by his exploration of the brain's mode of operation: sense impressions stored as complex 'symbols.' Fascinating. The long sections on mathematics and the often goofy dialogue chapters were trying, yes, but persevere; better parts lie in store.
Hofstadter's case is best made when he follow a topic through many disciplines. Though I ultimately disagree with his position on the feasibility of artificial intelligence, he has produced a stimulating read, and I am thankful for it. It is far superior to my other late-night literary conquest of the summer (Harry Potter and the Order of the Phoenix) and I recommend it to anyone with pondering time to spare.
Oh, and as a side note: don't buy Yudkowsky's review. Nothing personal, but this isn't the only thinking man's book out there. It just investigates so many nooks and crannies that almost anyone can find something to further pursue.

Rating:
Summary: Occasionally frustrating, but interesting as a whole
Review: Gödel's incompleteness thoerem is one of the most profound results of abstract mathematics, but unfortunately it is difficult to grasp its full meaning. GEB explains Gödel's thoerem in an interesting way by tying the mathematical result with Escher's paintings and Bach's music. The book can frustrating in some parts, but on the whole it's very interesting and useful to understand the incompleteness theorem.

One interesting thing about GEB is the dialogues. Hofstadter puts fun dialogues between the chapters, usually to introduce the concepts in the next chapter from a different angle. Sometimes this makes the concepts easier to understand, and it can occasionally be confusing to read the dialogue and then wonder what parts of it were real and which were fictional, but mostly they're fun to read and a good break from the mathematics and philosophy.

Gödel, Escher, Bach is worth reading if you're interested in philosophy, logic, artificial intelligence, or mathematics.

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Summary: A wonderful read for all aspiring thinkers
Review: 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.