Hofstadter's great achievement in Goedel, 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 Goedel'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 Goedel, 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 Goedel: 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.

Product Description

Reading Godel, Escher, Bach is like joining a club. People who see you reading it will open spontaneous conversations and often gift you with unexpected insights. (I had a fascinating conversation with a total stranger about Godel's theorem.)

Wish I could give more than five stars.


Escape from predestination   December 14, 1999
 155 out of 174 found this review helpful

It seems highly appropriate that Douglas Hofstatder should re-release his epic work now. His central theme plays so eloquently in this place and time: Every system folds in on itself, be it physics, mathematics, or any form of language. All these systems are inherently self-referential, and as such, take on a life of their own. A life their creators could never imagine. Many reviewers have focused on the explicit messages of the book, their likes or dislikes, but the great beauty of this work lies within the realm of what it does not say. It is, no doubt, the most difficult book I have ever read, and I have to admit it took me several false starts to finally get through the thing. It is so incredibly deep - one cannot simply wade through it like a sci-fi novel. But if you take your time, spend, say about a year on it - work through the TNT exercises, discover the hidden messages the author has left, read the bibliography - and at some point it will strike you; the incredible richness of the message. The book, you, the world, all of it IS open. The pages of this universe are blank, unwritten. Dr. Hofstadter has woven a message of eternal optimism, one that transcends even the infinite depth to the tapestry of topics spread before us: The great freedom that we, nature's most remarkable matrix, are part of a future without destiny. Even if we were created, any purpose impressed upon us is lost in a cacophany of unexpected relationships. Deterministic, yet infinitely complex and unpredictable. We can never understand anything completely, and thus every life can experience the magic of observing that which cannot be explained. This is a book of wonders, and you will never regret the time you spent on it.


What's the big deal?   March 21, 2002
 87 out of 128 found this review helpful

I'm afraid I must also be one of the naysayers of this work. I found it to be greatly overrated and highly pedantic. I think it gives many people an incorrect idea about what Godel's theorem really means. The major points of this book could have been summed up in under 100 pages, yet it drones on for 700+ pages.

In making such a long tome about Godel's theorem, Hofstadter in a sense, set up a huge set of axioms to describe Godel's theorem, which is the very thing Godel showed you cannot do! You've got to love the irony, that this monstrous description of Godel's Theorem is necessarily incomplete because of Godel's Theorem at work. Talk about your "strange loops".

Many topics are included that really don't belong, for instance molecular biology and virus assembly. I did my Ph.D. dissertation on viral assembly and I can tell you there is nothing "Godelian" about it. Its a matter of protein-protein interactions and thermodynamics. Another example is Zen buddhism. I am tired of everyone including something about Zen anytime they want their work to have a mystical or undefinable feel. Any Zen master will tell you Zen is nothing special outside of daily life, and that trying to make it extraordinary is to miss the point. Further, I found the dialogues between Mr. Tortoise, Achilles and Mr. Crab to be a bit juvenile.

The preface to the 20th anniversary edition sounded more like an excuse not to update the book (the gist of the preface is: "Its perfect now, why ruin perfection?" although it takes Hofstadter 23 pages to say so). Many of the ideas in the book are way out of date (by about 20 years, go figure).

I found nothing earth-shattering, life-changing or deeply meaningful about this book. I suspect many people read it because they want to be members of the "I am smart because I read GEB club".


A Profound Meditation On Human Creativity   October 2, 2000
 60 out of 62 found this review helpful

Goedel, 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 Goedel, 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 Goedel's Incompleteness Theorem.

Goedel, 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, Goedel, 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 Goedel, 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.


Brilliant and *still* misunderstood!   June 30, 2003
 54 out of 62 found this review helpful

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.