Wednesday, May 6, 2009

Chaos and Godel, Escher, Bach

Chaos: The Making of a Science and Godel, Escher, Back: An Eternal Golden Braid are two additional references for complexity science. I read them in 1987and 1979 respectively when they were published originally.

Chaos is a good overview of the science of chaos and has good explanations of the fundamentals. It is particularly good at describing fractals and their importance, as well as strange attractors.

A twentieth-anniversary edition of the million-copy-plus bestseller has recently been published (2008) “This edition of James Gleick’s groundbreaking bestseller introduces to a whole new readership the story of one of the most significant waves of scientific knowledge in our time. By focusing on the key figures whose genius converged to chart an innovative direction for science, Gleick makes the story of chaos theory not only fascinating but also accessible, and opens our eyes to a surprising new view of the universe.”

Godel, Escher, Bach subtitled “A metaphorical fugue on minds and machines in the spirit of Lewis Carroll” won the Pulitzer Prize and is a book that influenced my thinking. While the book subject is much broader than chaos, complexity and emergence, it does introduce the topic. The chapter entitled “Ant Fugue” discusses the workings of an ant colony and how behavior emerges from the collective that exceeds the intelligence of any individual ant.

Amazon’s review of the 1999 edition states: “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.

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.”

Chaos: Making a New Science
James Gleick, Penguin Books, 1988, 352 p

Godel, Escher, Bach: An Eternal Golden Braid
Douglas Hofstadter, Basic Books, 1979, 777 p

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