Godel, Escher, Bach: An Eternal Golden Braid

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
Curtis L. Wilbur (San Diego, California USA)
155 out of 182 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.


Brilliant and *still* misunderstood!   June 30, 2003
Michael J Edelman (Huntington Woods, MI USA)
53 out of 61 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.


Down the Rabbit Hole...   May 18, 2007
Tyler C. Powell
20 out of 23 found this review helpful

This is a difficult book.

Difficult to read. Difficult to understand. And, I'm finding, difficult to review. What's it about? Good question. The author, himself, isn't very clear on this point, describing it as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll." I'm not sure I can do better than that. I will tell you this, however: if the book has a "point," it does seem to be that man's consciousness is ultimately mechanical and, therefore, that there is no reason that machines cannot finally be intelligent in the same sense that man is. (And, in fact, be as man in just about every internal way.)

While I take issue with this conclusion, and some of Hofstadter's reasoning along the way, I don't think that my debating his points is the basis on which a prospective reader should decide whether or not to pick up this book. Instead, the prospective reader should know: that this is a lengthy and deep work. It will take a *long* time to read properly, and most readers should not read more than a chapter a day. Many of the sections, and especially the various dialogues that preface the chapters, are quite clever. (These dialogues are usually between Achilles and the Tortoise, of Zeno's paradoxes, and their friends.) Some of the chapters grow incredibly technical. The subject matters vary, wildly and rapidly, and there will be points in reading where you will question your investment.

In the end, you will feel good for having pushed through the hard bits. It will coalesce, more or less, into a whole. Whether you finally agree with Hofstadter's conclusions or not, you'll have learned much and thought about important topics you might otherwise not have.

A good book, certainly not for everyone... but, if you're the "right" audience--someone deeply interested in questions of intelligence, mathematics, computer science and free will, and possessed of a bit of an ironic sense of humor--then this book cannot be recommended highly enough.

Five stars, for the work it represents, and the doors it opens to the reader.


Indescribably brilliant   June 2, 2000
M. H. Bayliss
8 out of 8 found this review helpful

This is one of the most fantastic books ever written. It represents a kind of "unified theory" of math, art and music. In some ways, Hoffstader reminds me of Joyce's Ulysses in terms of the way he uses text to model a different form. In fact, Joyce writes a chapter which is a textual "fugue" just the way hoffstader does. Yes, this is a very dense book with lots of profound thoughts on art, math and music (and philosophy), but I guarantee that you'll find it interesting. Don't read it on a short airplane ride -- read it when you have some time for a deeper read. I read it years ago and look forward to re-reading it again since I have yet to find a book anything like it. Quite an achievement -- this is one to pick for the proverbial desert island.