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Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas R. Hofstadter
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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. G�del, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.
- Sales Rank: #1648 in Books
- Color: Black
- Brand: Hofstadter, Douglas R.
- Published on: 1999-02-05
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 5.75" w x 1.25" l, 2.20 pounds
- Binding: Paperback
- 824 pages
- Music
- Art
- Mathematics
- Meditation on Human Thought and Creativity
- Artificial Intelligence
Amazon.com Review
Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's G�del, 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 G�del. 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 G�del, 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 G�del'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 G�del, 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 G�del: 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.
From the Inside Flap
Winner of the Pulitzer Prize, this book applies Godel's seminal contribution to modern mathematics to the study of the human mind and the development of artificial intelligence.
About the Author
Douglas R. Hofstadter is College of Arts and Sciences Professor of computer science and cognitive science at Indiana University and author of the Pulitzer-prize winning "Godel, Escher, Bach: An Eternal Golden Braid".
Most helpful customer reviews
462 of 491 people found the following review helpful.
Way out of my comfort zone, but still great.
By frumiousb
I'm here to witness that even people as seriously math-challenged as I am can participate in this wonderful book. It took me a *long* time to read-- I flipped back and forth, beat the pages up, asked my more math-oriented friends for help. I spent forever trying to solve the MU exercise. It was worth it. I still feel like I understood parts of it only in intuitive flashes, but those flashes showed me a room more interesting than most of the well-lit chambers ordinary books provide.
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.
225 of 241 people found the following review helpful.
A Profound Meditation On Human Creativity
By A Customer
G�del, 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 G�del, 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 G�del's Incompleteness Theorem.
G�del, 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, G�del, 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 G�del, 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.
254 of 286 people found the following review helpful.
Escape from predestination
By Curtis L. Wilbur
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.
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