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Godel Escher Bach An Eternal Golden Braid
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.