Ascending and Descending

The lithograph Ascending and Descending by M. C. Escher shows some monks walking up a set of stairs and some monks walking down the stairs. Yet each monk eventually ends up at the same place he started. No matter how much a monk walks, he will not gain or lose any altitude.
Escher got the idea for Ascending and Descending after reading an article by L. S. Penrose. The graphic below shows the original Penrose drawing on the left and a sliced version of it on the right, which shows how the deception was accomplished. It can be seen that the staircase is in a horizontal plane, while the sections lie in a spiral. This is why slice #1 starts at the upper left and ends up in the lower left, instead of staying in the same horizontal plane.
A delightful animation of this "impossible staircase" (by James West of Cambridge, England) appears below:
M.C. Escher work (c) Cordon Art B.V. - Baarn - the Netherlands.
Used by permission. All rights reserved.

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