Rating: 
Summary: A Profound Meditation On Human Creativity
Review: Gödel, Escher, Bach: An Eternal Golden Braid debates, beautifully, the question of consciousness and the possibility of artificial intelligence. It is a book that attempts to discover the true meaning of "self."As the book introduces the reader to cognitive science, the author draws heavily from the world of art to illustrate the finer points of mathematics. The works of M.C. Escher and J.S. Bach are discussed as well as other works in the world of art and music. Topics presented range from mathematics and meta-mathematics to programming, recursion, formal systems, multilevel systems, self-reference, self-representation and others. Lest you think Gödel, Escher, Bach: An Eternal Golden Braid, to be a dry and boring book on a dry and boring topic, think again. Before each of the book's twenty chapters, Hofstadter has included a witty dialogue, in which Achilles, the Tortoise, and friends discuss various aspects that will later be examined by Hofstadter in the chapter to follow. In writing these wonderful dialogues, Hofstadter created and entirely new form of art in which concepts are presented on two different levels simultaneously: form and content. The more obvious level of content presents each idea directly through the views of Achilles, Tortoise and company. Their views are sometimes right, often wrong, but always hilariously funny. The true beauty of this book, however, lies in the way Hofstadter interweaves these very ideas into the physical form of the dialogue. The form deals with the same mathematical concepts discussed by the characters, and is more than vaguely reminiscent of the musical pieces of Bach and printed works of Escher that the characters mention directly in their always-witty and sometimes hilarious, discussions. One example is the "Crab Canon," that precedes Chapter Eight. This is a short but highly amusing piece that can be read, like the musical notes in Bach's Crab Canon, in either direction--from start to finish or from finish to start, resulting in the very same text. Although fiendishly difficult to write, the artistic beauty of that dialogue equals Bach's music or Escher's drawing of the same name. As good as all this is (and it really is wonderful), it is only the beginning. Other topics include self-reference and self-representation (really quite different). The examples given can, and often do, lead to hilarious and paradoxical results. In playfully presenting these concepts in a highly amusing manner, Hofstadter slowly and gently introduces the reader to more advanced mathematical ideas, like formal systems, the Church-Turing Thesis, Turing's Halting Problem and Gödel's Incompleteness Theorem. Gödel, Escher, Bach: An Eternal Golden Braid, does discuss some very serious topics and it can, at times, be a daunting book to handle and absorb. But it is always immensely enjoyable to read. The sheer joy of discovering the puns and playful gems hidden in the text are a part of what makes this book so very special. Anecdotes, word plays and Zen koans are additional aspects that help make this book an experience that many readers will come to feel to be a turning point in their lives. Like every other book written by Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid, has an index and a bibliography that must be noted as exceptionally well done. Although filled with English wordplay, this book is in no way tied to the American origin of its author. For years, it was thought that Gödel, Escher, Bach: An Eternal Golden Braid, would be impossible to translate, but so far, it has successfully been translated into French, German, Spanish, Chinese, Swedish, Dutch and Russian. A profound and beautiful meditation on human thought and creativity, this book is indescribably gorgeous and definitely one of a kind.
Rating: 
Summary: Great Book, Too many threads at once.
Review: This book's attempt at explaining this seeming common thread in Mathematical Logic, Music and Art is a noble one. The author tries to explain, in my opinion, too many things at once. Even though the author is never incoherent, the vast task of explaining not only his thesis but also the history behind it, overwhelms the reader time and time again.
As a mathematics student and enthusiast, this book had a very profound impact in the way I think about mathematics. The fact that mathematics (being as complex as it is) cannot be proven by using mathematics is a very, if not the most, important concept this book attempts to uncover.
As far as the historical/biographical aspect of the book, I think it's very well done and very well contextualized.
The book about three of the most important geniuses in areas so diverse and seemingly disconnected, yet in the innermost layer they all are intertwined. Again, great book, great author, spell-bounding conclusions.
I, however, have couple of caveats (to the reader):
1) This book requires some knowledge in mathematical logic,
2) It is not an "easy read," so be prepared to be mentally challenged.
Rating:
Summary: Big Book of Interesting Points
Review: It's difficult for me to decide just exactly how much I like Gödel, Escher Bach. At 740+ pages, it certainly has a lot to say. And since it's not a novel, there are clearly some sections I can say I liked better than others. Yet even after reading the entire book, including authors preface explicitly describing GEB's meaning, I must still say I'm unsure exactly what the book is about.
Hofstadter's thesis is an attempt to explain in a personal way how "animate beings can come out of inanimate matter." This quest begins mainly with an analysis of Gödel's Theorem, which essentially states (please forgive me for any scientific inaccuracies) that it is impossible for any mathematical system to be complete.
Hofstadter works us through this theorem rather slowly and gently, at first looking at simple, crude mathematical systems, and examining their successes and failures to depict our real number system. Interspersed with this examination are fascinating dialogues between fictional characters. These dialogues are at times odd, witty, clever, deep, philosophical, and are the icing of GEB. Hofstadter also from time to time looks at the artwork of M.C. Escher and the music of J.S. Bach. He notes the patterns found in their works and how they loop back on each other, or contain elements of self-reference, important to Hofstadter because it is this act of self-reference which makes Gödel's Theorem possible.
Hofstadter then gradually shifts from looking at mathematical systems and levels of systems to our own thought and our separate levels. He examines cell structure and DNA, and moves outward to artificial intelligence and its relation to our intelligence. This of course raises fascinating questions. What do we think of when we think of the number "two?" We certainly don't have a "10" in binary code sitting somewhere in our heads. Hofstadter attempts to link these two realms of mathematical theory and intelligence theory and believes that intelligence is comprised of hierarchical levels, many independent and unconscious of levels above or below.
Though written in 1979, this book covers ground which we have yet to traverse. Although a computer can now beat the best human chess players, the world is seeking computers with more "intelligence." Where do thoughts come from?
This book is not for those with a light interest in math or numbers. Although you do not have to mathematically derive any of Hofstadter's proofs or understand everything (I didn't), it helps to be familiar with what Hofstadter is trying to say and to have an interest in puzzles, number, and the like. Familiarity with Escher or Bach can help, but is not as requisite as the first.
I am not a computer programmer, nor am I computer myself, so I have no idea whether Hofstadter's observations and assertions are true or false. His book, however, I found very interesting and thought provoking, and quite rewarding. I recommend this book to all those interested in math/computers, and for experts, it is probably required reading.
Rating: 
Summary: Neither Profound nor Impressive
Review: As a computer professional, I have heard the buzz about EGB for years. Many people consider EGB the "AI bible". I thought about buying it a few times, but each time I browsed it in bookstores, it just couldn't hold my interest. I finally borrowed it from the library and read it. Needless to say, I was glad I never bought it. What Hofstadter does is take some math theory, mixed with a huge helping of pseudoscience & cultural tripe, and stretches it into an book that is perhaps 5x longer than it needs to be. The overarching "theme" of the book is that intelligence is the result of a recursive hierarchy in which high-level brain functions (which we know as thought) are meta-level rules built on lower (less meta) level rules which are built on other rules, .... (& so on). IMHO, there is nothing really profound about this concept. Beyond this idea, Hofstadter offers few, if any, meaningful insights on how the mind really works. Perhaps EGB is so revered because there are few really good philosophical books on AI for out there, and some are much worse (like Kuzwell's "The Age of Spiritual Machines"). A more plausible take on how the mind works can be found in Minsky's "Society of the Mind".
Rating:
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.
Rating:
Summary: A readable Mobius strip
Review: If you have never read this book, then I'd like to say that it has a lot of the most greatest knowledge out there. It doesn't just deal with math, art, and music, but also with zen, philosophy, self-ref, self-rep, holism, reductionism, and everything else that is considered pure knowledge of cognitive science and general intelligence. I don't know why some of the people rating it have no idea of what's it about; it's not about Godel's theorem like many think it is, it's about consciousness and how the power of the mind and the "I" comes out of the inanimate matter that creates us. That's not it, the second part of the book talks about computer programming and AI. Can a computer program ever have a sense of self or compose meaningful music? Hofstadter's response to the second one was: "Only if that AI could go through the maze of life on it's own, fighting it's way through it and feeling the cold of a chilly night, the longing for a cherished hand, the inaccessibility of a distant town, the regenaration after a human death, the...and only then can it be considered to do so."
This book really has more than that. I can't say all of the things mentioned in it, not in this tiny little review, but I can say that you should probably read it and hopefully understand it because it truly is a masterpiece.
Rating: 
Summary: Pseudo-science at best
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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