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Godels Incompleteness Theorem
The primary metaphor in “Contracrostipunctus” by Douglas R. Hofstadter is the phonograph. It has been sold to Crab as a Perfect phonograph, i.e. a phonograph that is capable of reproducing any and all sounds. However, Tortoise goes to great lengths to invent music that is defined by the fact that it is capable of destroying phonographs. A phonograph capable of playing all sounds will be capable of playing this music, and in doing so will destroy itself.