Gödel, Escher, Bach: An Eternal Golden Braid

Gödel, Escher, Bach: An Eternal Golden Braid

Author: Visit Amazon's Douglas R. Hofstadter Page | Language: English | ISBN: 0465026850 | Format: PDF

Gödel, Escher, Bach: An Eternal Golden Braid Description

Amazon.com Review

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.
--This text refers to the






Paperback
edition.

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.
--This text refers to an out of print or unavailable edition of this title.

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• Product Details
• Table of Contents
• Reviews

• Hardcover: 776 pages
• Publisher: Basic Books; First Edition edition (May 31, 1979)
• Language: English
• ISBN-10: 0465026850
• ISBN-13: 978-0465026852
• Product Dimensions: 9.4 x 6.5 x 1.8 inches
• Shipping Weight: 2.7 pounds

Gödel, 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 Gödel, 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.

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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