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

 

 

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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.

Douglas Hofstadter uses the art of M.C. Escher, the music of J.S. Bach, and Kurt Goedel's mathematics as the centerpieces for a magnificent inquiry into the nature of the mind. Along the way you will encounter Bertrand Russel, Carroll Lewis, particle physics, molecular biology, Magritte's paintings, and Zen koans. These are all used to probe recursion and the mystery of how we form thoughts. But the list of topics alone is not what makes this book great, it's the playful, joyful sense that characterize's Hofstadter's treatment of this. This sense of wonder is critical, as without it this highly challenging book would be very frustrating. The book's style itself is based on Bach's canons, and the chapters are interspersed with dialogues between the Tortois and the Hare, in the style of Carroll's Alice in Wonderland. The result is an artistic as well as scientific or philisophical masterpiece. I am currently a triple-major in molecular biology, physics, and philosophy, and much of my curriculum has been influenced by the beauty of Hofstadter's book. This will go down as one of the 20th Century's bests books.

Hofstadter has done a superb job of presenting an intriguing melange of disciplines that are seemingly unrelated. The author manages to quickly show that Godel's theorems, Escher's art, and Bach's music have much more in common than most would think. In a lengthy but VERY worthwhile read, he manages to get the reader to analyze many of the assumptions commonly held about the nature of thought and why it is so devilishly difficult to formalize the thought process with rigid rules, among other topics.

That he manages to entertain as well (he writes with a wry sense of humor on what are typically handled as rather dry subjects) and manages to reach the layman is what sets this volume apart as the masterpiece that it is. Although it is accessable to the layman, the book does become progressively more challenging and I strongly recommend completing his suggested exercises before moving on, otherwise you will likely find yourself unable to grasp the point he's trying to make several pages later.

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5.0 out of 5 stars A Must for every student of cognitive science
I came across this book in 1993. I had to prepare for a seminar on AI as part of my curriculum. My then tutor recommended that I read this book before preparing for my... Read more

Published on Dec 15 1999 by S. Sundaresan

5.0 out of 5 stars Challengingly Fun
Hofstadter has pulled off a miracle with this book. If you like ideas and like reading about how ideas fit together, then get this book. Read more

Published on Aug 19 1999

5.0 out of 5 stars This book, once read, will never be forgotten.
To combine math, music and art together is a daunting enough task but to put it together where you keep on thinking about it (I first read in in the early 70s and I still think... Read more

Published on July 17 1999

5.0 out of 5 stars question?
Question: Where can I buy the model which made by hard paper to represent a picture (in the book) in three-dimentional picture(model). Read more

Published on Mar 17 1999

5.0 out of 5 stars The pinnacle of all human accomplishments.
As pure Art, as magnificent intelligence incarnated as absolute beauty, this is the greatest book ever written by human hands. Read more

Published on Aug 30 1998

5.0 out of 5 stars

The best book I ever read ...

That's just it. This is the best book I've ever read, and that's not a judgement that comes easily believe me. Read more

Published on July 21 1998 by Bernd Wechner

5.0 out of 5 stars An amazing book on AI, number theory, music, and logic
I've always been facinated by the concept of artificial intelligence, and when someone told me how good this book was I went out and bought it, and while I was reading it you... Read more

Published on July 20 1998

5.0 out of 5 stars A delightfully coonfusing book about number theory, I think.
Read Godel, Escher, Bach: An Eternal Golden Braid. Each time I do, I realize how truly unique it is. Read more

Published on July 10 1997

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