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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 is the most challenging book I've ever read, but also one of the best.
The preface gives also very interesting perspectives on how the author developed the book explaining what the book is about and is not.
Hofstadter also from time to time looks at the artwork of M.C. Escher and the music of J.S. Bach.
One of 4 books I felt worth while reading and owning.Published 13 hours ago by Armando A. Hernandez
I like comparative religion texts.... didn't expect to find a Buddist diatribe in this one.
Amazing book. Makes it easy and intuitive to understand some of the greatest discoveries in computing and logic in the last century. Read morePublished 1 month ago by Gonzalo
This book is an enormously satisfying read. While the author states that bookstores struggle to find a genre for his title, I would argue that it is a book a philosophy of... Read morePublished 1 month ago by Matthew Totlis
extremely satisfied with everything, especially Amazon.com's new way of international shippingPublished 1 month ago by Yimin Kui
A brilliant synthesis of recursivity in Science and Art.Published 1 month ago by Marciano Morozowski Filho