A large part of Escher's popularity is due to his depictions of impossible worlds. His prints on this theme are based on his research into perspective. The system making it possible to represent depth on a flat surface, such as a sheet of paper, was developed during the Renaissance, in the fifteenth century.
One important law of perspective dictates that all receding parallel lines are to be represented on the plane as if they passed through a single point, the vanishing point.
One can also construct a representational image using two or three vanishing points, depending on the type of object depicted and the desired effect.
Many of Escher's prints attest to his mastery of the so-called classical laws of perspective. He also explored other ways of representing objects in space, as in Hand with Reflecting Sphere (1935), where he depicted a sphere that reflects the entire space of the room except the area that lies directly behind the globe.
“What is this so-called reality; what is this theory but a beautiful though totally human fantasy? ”• M.C. Escher: His Life and Complete Graphic Work, edited by J. L. Locher
In the lithograph Relativity (1953), Escher uses three vanishing points, all located outside the frame. Two are on the horizon, to the left and right of the frame, slightly below it; the third is at the zenith, above the frame. Each of these vanishing points governs a different gravity, an independent weight. The vanishing point at the zenith, which indicates the axis of gravity, seems to change depending on which way the print is turned.
The work could be turned and correctly interpreted in three different ways, as long as the viewer is in a gravity-free environment.
Escher's contacts with the scientific community, particularly those following his show at the Stedelijk Museum in Amsterdam in September 1954 during the International Congress of Mathematicians, played an important role in his progression towards the depiction of impossible worlds.
In addition to the meeting with the Canadian mathematician H. S. M. Coxeter, this exhibition led to a fruitful exchange of ideas with Roger Penrose, who was attending the conference as a student and was highly impressed by Escher's show. Works such as Relativity (1953) exerted a determining influence on the development of figures that can be drawn but cannot exist in three dimensions.
Roger Penrose sent Escher "Impossible Objects: A Special Type of Visual Illusion," an article he published with his father, L. S. Penrose, in the British Journal of Psychology in February 1958, which paid tribute to Escher's influence.
Escher was impressed by two illustrations that accompanied the discussion of impossible objects: one presented an impossible triangle, the other, a flight of stairs leading downwards and upwards at the same time. Inspired by the Penrose illustrations, he made two lithographs, Waterfall (1961) and Ascending and Descending (1960).
On Ascending and Descending
"[Ascending and Descending] presents a complex of buildings, a kind of cloister with a rectangular inner court… Perhaps they are monks, members of some unknown sect. It may be part of their daily ritual duty to ascend this stairway in a clockwise direction during certain hours. When they are tired, they can change direction and descend for a while. But both motions, though not without an abstruse meaning, are equally useless."• Escher on Escher: Exploring the Infinite
"The water of a fall, which sets in motion a miller's wheel, zigzags gently down through a gutter between two towers till it reaches the point from which it falls down again. The miller can keep it perpetually moving by adding every now and then a bucket of water to check the evaporation."• Escher on Escher: Exploring the Infinite
The field of psychology has also been fascinated by the work of Escher, as human perception is at the centre of the artist’s optical illusions and impossible environments.
Escher was particularly interested in how the eye and brain make sense of a three-dimensional object rendered on a two-dimensional surface.
A great admirer of Escher, Dr. Claude Lamontagne, a professor in the School of Psychology at the University of Ottawa, has interpreted the artist’s work with two animations.
"I try in my prints to testify that we live in a beautiful and orderly world, and not in a formless chaos, as it sometimes seems."• Escher on Escher: Exploring the Infinite