Godel Escher Bach: An Eternal Golden Braid


Godel Escher Bach: An Eternal Golden Braid, by Douglas Hofstadter, is an enlightening discourse discussing the fundamental elements of logic, language, and thinking. Stanford-educated Hofstadter is a professor of cognitive science and has received the 1980 Pulitzer Prize for Godel Escher Bach. Kurt Gödel, the logician; M. C. Escher, the artist; and Johann Sebastian Bach, the composer, come from varying fields but all illustrate common ideas such as what Hofstadter defines as the pinnacle of intelligence, self-reference. Godel's incompleteness theorem defines a statement G which approximately says "This statement cannot be proved within the containing theorem". The statement refers to itself - it is true yet cannot be proved, illustrating a fundamental deficiency of all formal systems. Hofstadter refers to more of these looping self-references in Escher's Drawing Hands and Waterfall as well as Bach's Six-Part Ricercar that contains his own name in four notes. Hofstadter calls these tangled hierarchies that ultimately loop back into themselves "strange loops". While this book was named after those three characters, the names encapsulate only a small portion of the material in the book. Each chapter discusses a different yet related subject matter, and are united by the same two characters at the end of each chapter. These characters, Achilles and the Tortoise, participate in humorous and intricately-written dialogues that tie back in with the concepts from the chapter.

"You don't have to define what it's about, do you? That would ruin it! That's like asking what life is about!" replied my friend Lucas Garron when I started reading the book. I've found out what he means. This book is not a casual read. Chapters in the book contain analysis and elaborations on formal systems, and Hofstadter introduces puzzles to the reader that require more resources than a bed and a desk lamp. I found myself engulfed in his MU formal system puzzle as well as his application of these formal systems in government, DNA replication, and translation of Lewis Carroll's poem The Jabberwock. The puzzles inside are not merely puzzles about the book's material - they often include puzzles on meta-levels requiring the reader to reflect back on him/herself. Hofstadter enlightens the reader through a foray into Zen Buddhism - saying that the only correct answer to contradictory statements such as Godel's incompleteness theorem is to "unask" the question. Hofstadter entices one to explore deeper into meta-levels and meta-meta-levels, until one goes up enough to come back to discovering oneself. Through exploring the fundamental elements of logic, language, and cognition, Hofstadter unlocks what he claims we have "clumped together" as a single unit into a volley of formal systems and self-reference, likening the "beautiful many-voiced fugue of the human mind" to a colony of ants. Readers leaving the book feel that something originally familiar is now infinitely complex.

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