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Gödel, Escher, Bach: An Eternal Golden Braid Paperback – February 5, 1999
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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.
About the Author
Douglas R. Hofstadter is College of Arts and Sciences Professor of Cognitive Science and Computer Science at Indiana University, Bloomington, where he also directs the Center for Research on Concepts and Cognition.
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This book is about the meaning of meaning, the interpretation of interpreting, thinking about thinking, and being about being. Due to the nature of this book, I think it safe to say that there will be as many takes on it as there are people who read it. I tip my hat to Hofstadter, whose masterpiece is truly in a category of its own, reaching out into the world unlike any book I've encountered (yet).
Do not let the size or density of this book prevent you from going through it! The return, though hard to define, is much greater than the investment it demands.
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Mathematics about mathematics. Thinking about thinking. Mathematics about thinking. Meta-everything.
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done with this book.
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.
Does the book succeed in its goal? The task of reducing mind to math, of connecting the nature of consciousness to an idea in formal systems, is such a lofty goal, that even if true, the author could never rigorously prove this thesis, only approach it from every conceivable direction. This matters less than you might think, because the value of GEB is less about its conclusion and more about the journey getting there, much like The Emperor's New Mind. Whether it convinces you or not, it will give you a lot to think about by trying.
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.
This is one of those books you read, and then remember forever.
Using Godel the mathematician, Escher the patternist painter/artist and Bach the composer, Douglas Hofstadter, in this timeless book unites mathematics, art and music through thought illustrations (then problem/questions) and informative Platonic-inspired dialogues (including the composite character Aunt Hillary, the massed intelligence of an ant colony.
It's a must read. Supposedly, it was written for high school age nerdish boys, but I greatly enjoyed it in my mid-20's and fondly remember it in my late 60's.
A truly timely book, with my highest recommendation.
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