These wide-ranging discussions of art, music, mathematics, philosophy, technology, and language at times suggest the stream-of-consciousness technique of James Joyce. Like Ulysses (1922) and Finnegans Wake (1939), Gödel, Escher, Bach is a maze, but a maze not without a plan. On the dust jacket and again before parts 1 and 2 Hofstadter presents a figure that he carved from a single block of wood. When light shines through this figure in three directions, it casts shadows that form the letters GEB (Gödel, Escher, Bach) or EGB (eternal golden braid). Physically, Gödel, Escher, and Bach are thus joined in a single carving; linguistically, their initials stand for the interlocking strands described in the book’s subtitle. More fundamentally, Hofstadter regards his wooden figure as the representation of a deep truth: “Gödel and Escher and Bach [are] only shadows cast in different directions by some central solid essence.”
For Hofstadter, art, music, mathematics, philosophy, linguistics—indeed, all disciplines—depend on a limited number of basic principles. He thus allies himself with structuralists rather than particularists such as Noam Chomsky, who argue that a task such as language acquisition is so complex that it can have nothing to do with any other field of knowledge. Structuralists such as Jean Piaget claim that only a few logical-mathematical operations underlie all thought. At Carnegie-Mellon University, researchers in artificial intelligence have had some success with a general problem-solver program that instructs a computer to apply basic techniques, such as breaking down problems into smaller parts, to any puzzle—ranging from chess to mathematics. Further support for this structuralist view comes from scientists’ knowledge of certain neurological syndromes. A Viennese neurologist has observed that patients with a particular lesion in the left parietal lobe of the brain have trouble writing, calculating, recognizing their fingers, and distinguishing left from right. All four activities require placing elements of a set (letters, numbers, fingers) in the proper relationship with other members. Thus, it seems that a single skill forms the basis of seemingly disparate tasks.
The unifying principle that links Bach’s music, Escher’s art, and Gödel’s theory is self-reference, which Hofstadter also calls recursion, or Strange Loops; a system that contains a Strange Loop is a Tangled Hierarchy. All these phenomena involve self-reference. Thus, Bach uses the letters of his name to create a theme in the final “Contrapunctus” of The Art of the Fugue. In his Musical Offering, he creates “Canon per Tonos,” an ever-rising canon, which begins in C minor and, after six modulations, concludes in the same key but an octave higher. Escher’s Print Gallery (1956) presents a young man in a gallery looking at a picture in which a woman looks down on a gallery where a...
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Gödel, Escher, Bach provokes thought about thought. In this sense, as in its very structure, the book is recursive. When Hofstadter makes the following comment about Bach’s Musical Offering, he is speaking about his own work as well:One cannot look deeply enough into the Musical Offering. There is always more after one thinks one knows everything. . . . Things are going on on many levels. . . . There are tricks with notes and letters. . . . There is beauty and extreme depth of emotion; even an exultation in the many-leveledness of the work comes through.
Clearly, the Pulitzer Prize committee and hundreds of thousands of readers who bought Gödel, Escher, Bach exulted in its many-leveledness, too, but the book has provoked controversy as well as admiration. Some reviewers complained about its length, its quirky style, and its scope. Other popularizers of scientific ideas— Stephen Jay Gould, Loren Eiseley, Lewis Thomas, Carl Sagan—may reveal less literary inventiveness but do not provoke a paraphrase of Gertrude’s plea to Polonius: “Less matter, with less art.” Hofstadter, certain critics claim, may bemuse rather than amuse his audience.
Some musical theorists have objected that Bach seems dragged into the book because Hofstadter wanted to discuss the composer, not because his music is truly recursive. The “Canon per Tonos” is clever, but it does not rely on paradox in the way that Gödel’s theorem or Escher’s prints do. Researchers in artificial intelligence are also divided on the merits of Hofstadter’s theories; some experts in this field refute his definition of machine...
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