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Godel, Escher, Bach: An Eternal Golden Braid [Paperback]

Douglas R. Hofstadter
4.5 out of 5 stars  See all reviews (194 customer reviews)
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Book Description

Feb. 5 1999
Douglas Hofstadter's book is concerned directly with the nature of "maps" or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel Escher and Bach is a wonderful explorationof fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

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Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.

Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers.

The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. --Richard Dragan

Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.


"Even without the contemporary relevance lent the book by the specter of global warming. The Little Ice Age would be an engrossing historical volume."

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Customer Reviews

Most helpful customer reviews
15 of 15 people found the following review helpful
5.0 out of 5 stars A wonderful read for all aspiring thinkers July 9 2004
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.
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3 of 3 people found the following review helpful
4.0 out of 5 stars overrated, but still very good Feb. 28 2004
By A Customer
No book could live up to this hype and praise, but still very worthwhile. It is best when describing difficult concepts of logic and computer science, weak when dragging in Zen and a tedious detour into molecular biology.
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3 of 3 people found the following review helpful
5.0 out of 5 stars Brilliant and *still* misunderstood! June 30 2003
I've been reading reviews of GEB for years, and the most fascinating thing about them, aprt from the near-uniform enthusiasm of the readers, is that almost none of the enthusiatic readers have any idea of what the book is actually about! The typical reader seesm to think of GEB as a jouyous romp through any number of fascinating bits of logic, math and science without any idea as to what Hofstader's actually doing.
Yes, it's about Goedel, and recursion, and "strange loops", and linguistics Bach and ants and all that- but only trivially. The bulk of the book is taken up with what amounts to a very entertaining tutorial that sets the reader up for the real thesis of the book. What Hofstadter has attempted in GEB is nothing less than a concise, bottom-up theory of mind. You can read it as a theory of AI, or a theory of human intelligence, but either way he's telling you how to construct an intelligent entity.
True, he doesn't really have a theory of *how* a self-aware being should arise from his metaphorical anthill, but then, neither does anyone else. But he does have a very good story as to how intelligence does arise in such conditions.
If you've read this book before without understanding what his aim was, read it again, with that notion in mind. And if you haven't read it, and you're the sort of person who enjoys mathematic and scientific amusements of any sort, well, read it and discover how much fun a speculative theory can be.
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2 of 2 people found the following review helpful
5.0 out of 5 stars My third copy May 25 2002
By A Customer
I have just purchased my third copy of this book. I bought the first copy when it first came out decades ago.
Why, you ask 3 copies -- because I lent my two previous copies out to people who lent them out to people who ...
They never came back.
The book is that good that I'm willing to buy another copy.
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1 of 1 people found the following review helpful
5.0 out of 5 stars literary style demonstrates book's themes Nov. 28 2001
a cursory glance at a random passage of godel, escher, and bach, will likely appear to be jabberwocky, with its unapologetic, evolving vocabulary and sparkles of inside jokes based on such, this is ironic, because the right arm of this book is recursion, which implies that the whole is implied by each part, far from while reading, one most certainly must read godel, escher, and bach in its sequential order, too funny
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1 of 1 people found the following review helpful
5.0 out of 5 stars Ricercar Oct. 4 2001
By llarq
This masterpiece has changed the way I think. I pity those have only read it once, or, even worse, didn't finish it. Only on the second reading can you understand that the entire book is itself a glorious ricercar and an endlessly rising canon. If you don't understand what I mean, read the book. And read it again, and again, and. . . .
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4 of 5 people found the following review helpful
4.0 out of 5 stars hasn't aged well... Oct. 6 2002
By A Customer
When this book first came out, I, along with probably most mathematically and scientifically minded people of my generation, would certainly have considered it one of the best books ever written. Hofstadter has refined the task of writing a book into almost an art form. Drawing on the central theme of "strange loops" (ideas that loop back on themselves in a paradoxical manner, as might be seen in the art of M.C. Escher), Hofstadter successfully draws together ideas from a large variety of different human pursuits. An important idea--shown to be connected to other ideas in artificial intelligence, music, and art--is Godel's incompleteness theorem, which shows that there are limits on our ability to prove concepts that may, nevertheless, be true. This, too, is based on a "strange loop"--these loops seem to crop up everywhere and Hofstadter spends a lot of the book showing how they are pretty much fundamental to human knowledge.
However, after reading the new preface in this 20th anniversary edition, I'm left with the sense that this once great book is now merely good. For one thing, Hofstadter seems to have evolved from a brilliant young man with a lot of great ideas into a somewhat cantakerous middle-aged man. He seems angry at the New York Times, and his readers, for not fully understanding the central message of the book. Yet he also excuses himself from making any attempt to update the book or bring the ideas in line with many of the enormous changes that have happened over the last 20+ years. It seems surprising to me that Hofstadter would constrain his own book to having only one central message--surely he should understand that a book of this complexity will mean many things to many different people, and that indeed is the reason for its popularity.
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Most recent customer reviews
1.0 out of 5 stars Is over rated.
Many people see it as a holy grail and Hofstader has no writing skills. His ideas are mixed in a very wierd way and he try to explain very simple thinghs in a very complicated way. Read more
Published 7 months ago by arjuna solis
5.0 out of 5 stars Super Merci !
I haven't read the boook yet, but the shipping was great and the book is in mint condition :)

Published on March 2 2012 by Thomas
4.0 out of 5 stars Brings back memories.
I bought this because I remember browsing through it when i was a teenager, and found it intriguing, even though I didn't understand most of it at the time, and didn't even come... Read more
Published on Dec 4 2009 by Aeonian
5.0 out of 5 stars A readable Mobius strip
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. Read more
Published on June 24 2004 by Peter Grutsky
1.0 out of 5 stars Pseudo-science at best
I quite agree with the reviewer from East Hartford. Maybe I am not extremely eligible to comment on the portions dealing with Escher and Bach, respectively (I have no appetite for... Read more
Published on June 23 2004
5.0 out of 5 stars A book that is about more than Godel, Escher, and Bach
This book is an excellent introduction to several ideas in cognitive science, biology, mathematics, linguistics, computer science, art, and other fields. Read more
Published on June 17 2004 by underwater girl
5.0 out of 5 stars Pretty good book!
I haven't really heard any hype about the book (a lot of the other reviewers are saying the book doesn't live up to its hype). I'm about 2/3 through, and it's really interesting! Read more
Published on May 24 2004 by Jordan Bell
3.0 out of 5 stars I didn't read this book,
and I'm probably not going to. However, after reading many of these comments, I thought I should point out:
If you want to understand Godel's incompleteness theorem, go pick... Read more
Published on May 24 2004
5.0 out of 5 stars Essential reading
GEB is a great jumping point into issues of the philosophy of the mind, the underpinnings of mathemetical logic and the possibility of artificial intelligence and... Read more
Published on April 8 2004
5.0 out of 5 stars An epic intellectual journey
This book tries to explore several interrelated and complicated questions. These are "what makes a self? Read more
Published on Feb. 24 2004 by Frikle
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