Penrose stairs
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The Penrose stairs or Penrose steps, also dubbed the impossible staircase, is an impossible object created by Lionel Penrose and his son Roger Penrose. It can be seen as a variation on the Penrose triangle. It is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher. This is clearly impossible in three dimensions; the two-dimensional figure achieves this paradox by distorting perspective. Lionel Penrose had first published his concept in the February, 1958 issue of the British Journal of Psychology.
The best known example of Penrose stairs appears in the lithograph Ascending and Descending by M. C. Escher in 1960, where it is incorporated into a monastery where several monks ascend and descend the endless staircase. Escher developed the theme further in his print Waterfall, which appeared in 1961.
The staircase had also been discovered previously by the Swedish artist Oscar Reutersvärd, but neither Penrose nor Escher were aware of his designs.
In terms of sound, the Shepard tone is a similar illusion.
In popular culture
Christopher Nolan incorporates Penrose staircases into his film Inception, since it is explained that normally-impossible structures can be created within lucid dream worlds. It is also used as an example of realization, as one character uses it purposefully to get behind a guard, then forces himself to realize it is an illusion and thus creates a sheer drop in front of him which he then throws the guard off of.