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 Godel, Escher, BachAn Eternal Golden Braidby Douglas R. Hofstadter Feb 4, 1999
DescriptionDouglas Hofstadter’s book is concerned directly with the nature of “maps” or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel Escher and Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more. Reviews“EGB’s greatest accomplishment is to show that the austere and frigid world of pure mathematics is by no means as remote from the two worlds of art and music as the humanist in the street believes it to be.… Hofstader guides his uninitiated reader through level after level of the mathematical funhouse, not only explaining its layout but also conveying a sense of the wonder and the beauty that do, in fact, reside there.” “I cannot begin to do justice to the wealth of suggestive analyses in Hofstader’s book. In its 700 odd pages, he reviews a wide range of mathematical-type operations: ‘recursion,’ (an entity embedded within a larger version of the same entity, like a story within a story); ‘strange loops’ (systems in which one can start at a point and then work through a number of levels—only to find oneself at the beginning again); systems reflecting upon or referring to themselves, and numerous others. Patiently he explains and explores their manifestations not only in their original, mathematical guise but also in the analogous realms of music, verbal play, and pictures.” “Having taken G(del, Escher, Bach off the shelf, I indulged myself by rereading it for the first time in years. I enjoyed it and appreciated it more than I did sixteen years ago. At that time, I did not sufficiently appreciate the extraordinary patience and clarity and enjoyability of the presentation of the basic structure of G(del’s theorem and its underlying concepts—formal proof, logic and metalogic, and self-reference. All this is presented in a form accessible to the lay reader with no cheating or inaccuracy, and with the omission only of the number-theoretic details of G(del’s proof. Having spent the last thirteen years trying to teach and write, I now marvel at Hofstader’s pedagogical skill at presenting this difficult material.” “A classic dinner-party game I like to play is to ask my guests what science book published, say, during the past 25 years they would take if they were to be stranded indefinitely on a desert island. For me the choice is easy: I would grab a copy of copy of Douglas Hofstader’s G(del, Escher, Bach (GEB) before abandoning ship.… Alternating witty, enlightening dialogues with chapters on such meaty topics as self-reference, recursion, meaning in mathematics, wonderful art of M. C. Escher, minds, thoughts, typesetting, G(delian paradoxes, self-replication, artificial intelligence and heirarchies, GEB is more like a summary statement of most of modern cognitive science than a thematic book, more of a romp over the modern intellectual landscape than a scholarly monograph. Yet it manages to be all these things and more.” Selling TerritoryWorld Excluding UK & Commonwealth |
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