M.C. Escher: Art and Mathematics
Perhaps one of the most appealing characteristics of Escher’s art is that it catches the browser off guard, regardless of who the browser may be or do for a living. Escher plays with the simplest of human expectations, perception, through mixing two and three dimensional objects and through his unique use of perspective. According to The Grolier Multimedia Encyclopedia, perception is the “process and experience of gaining sensory information about the world.” Escher forces us to look at the world in an unexpected way. With a quick glance at one of his impossible building structures, one may be tricked into trusting a first impression, but at a second (and maybe more attentive) look, one can see that through the methods of perspective, M.C. Escher has created fascinating riddles for the eye. By doing this, onlookers of his works are forced to put aside whatever assumptions they may bring to a picture, assumptions of what they expect to see in a picture, and look at the irony that Escher has really presented for us. As a result, M.C. Escher allows us to look at life in a different way, where streams don’t have to flow downwards or stairs conclusively go up and down. Escher claimed that by throwing the eye a curve ball, the eye will find a greater appreciation for the everyday expected :
I try in my prints to testify that we live in a beautiful
and orderly world, not in a chaos without norms, even
though that is how it sometimes appears. My subjects
are also often playful : I cannot refrain from demonstrat-
ing the nonsensicalness of some of what we take to be ir-
refutable certainties. It is, for example, a pleasure to delib-
erately mix together objects of two and three dimensions,
surface and spatial relationships, and to make fun of gravity.
(Schofield, Internet).
Impossible buildings and structures are only one of the styles that M.C. Escher explored in his art. Another fashion that Escher is known for is the tessellation. He was able to achieve remarkable symmetry by dividing the plane into shapes that fit flawlessly to fashion a whole. According to The Mathematical Palette, Escher’s excellence made tessellations popular (220). The art of tessellations is also an example of the importance of math in art. Escher has paired many different objects together in his tessellations : angels and devils, birds and fish, swans, and horseman. According to M.C. Escher : Works of Art, “He likened the task of illustrating a regular design to the laying down of black and white linoleum tiles on a flat surface that could, theoretically, extend to infinity (Afterword).” But Escher did not stop with the mere use of two dimensional tessellations.
Also according to M.C. Escher : Works of Art, “[T]wo-dimensional studies naturally led to Escher’s experimenting with ‘transitions from the plane to space,’ that is, drawing regular motifs that appear to move from a flat plane to three-dimensionality (Afterword).” In his mixing of two and three dimensional objects, Escher made hands come alive and draw themselves (in Drawing Hands), he made men of different shades, who fit together perfectly in tessellation, come apart from the drawing and shake hands (in Encounter), and he made alligator-like creatures lift up from their tessellation, crawl over a book and a cup and then slip back into the tessellation again (in Reptiles). Escher’s two and three dimensional drawings take objects through different levels of reality. When an admirer is gazing at one of Escher’s designs, the admirer, again, adds another level of reality to the artwork. Douglas R. Hofstadter, author of Godel, Escher, Bach: An Eternal Braid, explains that the presence of two levels ” invites the viewer to look upon himself as a part of yet another level; and by taking that step, the viewer cannot help but getting caught up in Escher’s implied chain of levels, in which, for any one level, there is always another level above it of greater ‘reality’, and likewise, there is always a level below, ‘more imaginary’ than it is (15).” This is quite a concept but Hofstadter’s point is well taken, and Escher’s mastery of perspective is to credit for this multifaceted reality.
M.C. Escher’s works are not only enjoyable because of the immense imaginational qualities but also because of their mathematical complexities. Escher said that he “came to the . . . open gate of mathematics. From there, well-trodden paths lead in every direction, and since then I have often spent time there. Sometimes I think I have trodden all the paths . . . and then I suddenly discover a new path and experience fresh delights (Escher, Afterword).” In fact, Escher was not specifically trained in math, but he was intent on discovering naturally the relationship of art and math. He once said that he often felt to have more in common with mathematicians then his artist colleagues. In the introduction to The Graphic Work of M.C. Escher, Escher states, ” By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I made, I ended up in the domain of mathematics.” So it seems that Escher’s education in math was purely by accident or coincidence.
No matter how Escher came about being one of the most ingenious combiners of art and math, his works speak for themselves to be complex mathematical feats. With Escher’s support, mathematician Bruno Ernst examined Escher’s works from a mathematical stand point. Ernst found that the major themes in Escher’s collection of designs, not including division of the plane, could be classified as “the penetration of worlds, the illusion of space, distorted perspectives, the manipulation of solids and spirals, and the rendering of the ‘impossible’ and the ‘infinite’ (Escher, Afterword).” Without, perhaps, even knowing it at first, Escher created designs that are based on and, at the same time, opposed to fundamental math laws. This, along with his keen eye for paradox, irony, and humor could be the reason his works are shown in math classrooms today.
Escher forces us to take a second look at the world around us. In the epigraph by Escher, to his collection M.C. Escher: Works of Art, Escher questions:
Are you really sure that a floor can’t
also be a ceiling? Are you definitely
convinced that you will be on a higher
plane when you walk up a stair case?
Is it a fact as far as you are concerned
that half an egg isn’t also half an empty
shell?
His works are enjoyable on many levels (as they are themselves) and as a significant demonstration of the uses or math in art. Through the presentation of everyday objects, Escher molds our familiar world into a world that challenges our perception and preconceptions and dares us to believe.
Escher, M.C. The Graphic Works of M.C. Escher. [Translated from Dutch by John E. Brigham]. New York : Wings Books, 1960.
Escher, M.C. M.C. Escher: Works of Art. New York : Wings Books, 1994.
Grolier Multimedia Encyclopedia, The. An America Online Reference. Search word “Escher.”
3-30-97.
Hofstadter, Douglas R. Godel, Escher, Bach : An Eternal Golden Braid. New York : Vintage Books, 1979.
Schofield, Paul. The World of Escher: Http://lonestar.texas.net/~escher. 4-7-97.
Staszkow, Ronald and Robert Bradshaw, eds. The Mathematical Palette: Second Edition.
New York : 1995.
