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Math Trek

Musical Illusions

By
2:39am, June 6, 2007

In M.C. Escher's lithograph "Ascending and Descending," monks are trudging along on a staircase. Some are climbing up and some are walking down, but each monk will end up back at his starting point. The staircase connects to itself, forming a square.

Of course, a real staircase can't lead to its starting point; Escher's image is an optical illusion. He learned about the concept in a 1958 article by mathematician Roger Penrose and his father, psychiatrist and mathematician Lionel Penrose.

A very similar illusion is musical rather then visual. In 1964, Roger N. Shepard of Stanford University created an auditory illusion of a musical scale that seems to ascend forever. Psychologist Diana Deutsch of the University of Califor

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