To illustrate the ambiguities in the perception of dimension, Escher exploited the printed page - which always must fool the viewer when it depicts a three-dimensional scene. In "Day and Night", the square gray fields in the foreground gain in definition of shape and contrast; they become an equivalent pattern of distinct black birds and white birds in the upper center and from there develop into three-dimensional creatures flying off into the real world of day and night. The print also illustrate the concept of topological change, in which the figure is deformed without being cut or pierced.Reflection and duality, a situation in which an object and its dual completely define each other, are present as well: black geese fly over a sunlit village, whereas white ones wing over a night view of a mirror image of the same scene.
Relativity
Relativity states that what an observer sees is influenced by context and vantage point. In the woodcut "Relativity", Escher presents three worlds in which three gravitational fields operate perpendicularly to one another. Men are walking crisscross together on the floor and the stairs. Some of them, though belonging to different worlds, come very close together, but can't be aware of each other's existence. For example, in the center a fellow with a coal bag on his back comes up from a cellar. But the floor on which he sets his right foot is a wall for the seated man to his left, while to his right is another man coming downstairs, who lives in yet a third world. Obviously, an image drawn on a two-dimensional surface need not actually be a true reduction of a three-dimensional object.The scene illustrates how pasting local views together to form a global whole can lead to contradictions: it is impossible to see the entire scene in a logical way. In "Relativity", each of the three sections of the woodcut are faithful representations of possible three-dimensional objects but are put together in a manner that, though possible in two dimensions, would be inconsistent in three.
Concave and Convex
"Concave and Convex" illustrates reversible perspectives, or "inversions," as Escher called them. The cluster of cubes on the flag announces the basic visual motif of the composition. In this 1955 lithograph Escher plays with the ambiguity of volumes on the flat picture plane; they switch from solid to hollow, from inward to outward, from roof to ceiling - like the symbol on the flag.How many reversals of perspective can you identify? Hint: Study the stairs carefully!
Waterfall
At first glance, everything appears in order in "Waterfall." The water mill from long ago looks like a great place to explore. But wait - a close second look shows that things are terribly amiss. Some of the columns that support the water trough are placed in impossible positions. Then there's the water: While flowing down the stepped trough, it's actually headed uphill! Note also that the towers are equally high, yet the one on the left is a story higher than the other.The theme of Escher's perpetual waterfall is based upon British mathematician Roger Penrose's "impossible triangle." (See figure below.)
This triangle is a perspective drawing, each part of which is accepted as representing a three-dimensional, rectangular structure. The lines of the drawing are, however, connected in such a manner as to reproduce a physical impossibility.
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