Escher understood that the geometry of space determines its logic, and likewise the logic of space often determines its geometry. By the 'logic' of space we mean those spatial relations among physical objects which are necessary, and which when violated result in visual paradoxes. A particular type of visual paradox, sometimes called 'impossible drawing', relies on the brain's insistence upon using visual clues to construct a three-dimensional object from a two-dimensional representation. Escher created many works which address this type of anomaly. One of the most intriguing is based on an idea of the mathematician Roger Penrose’s - the impossible triangle. In this lithograph, Waterfall, two Penrose triangles have been combined into one impossible figure. One sees immediately one of the reasons the logic of space must preclude such a construction: the waterfall is a closed system, yet it turns the mill wheel continuously, like a perpetual motion machine, violating the law of conservation of energy.

Text by Richard Bright.

Escher Illustration © 2006 The M.C.Escher Company - Baarn - Holland. All rights reserved. www.mcescher.com